212

Click here to load reader

Introductory Physics Problems David J. Jeffery Department of

  • Upload
    lykhanh

  • View
    233

  • Download
    6

Embed Size (px)

Citation preview

Page 1: Introductory Physics Problems David J. Jeffery Department of

������������ �������� ���������� ����������! �"$# �

%'&)(+*-,/.�0�.2143�1)576

%8149�&:5<;<=!1)>2;�?A@CB$D26FEG*IHJELK M�1)&ANO;<D/BPD26FEG*IHJE

QR,S&TDS?VUW;7&X;71ZY>�*[(A1)5\EG*[;]6

BC?+H^&X;71_N-N[?S`�Q�,a&ADa?

b

b b b b

b b

b

b b

BC?T57;79�1_>2;7&:cT5<&A= B$daefN-*IEGD�*->achgiER1)N-@kjl9fdaefN-*-EGDa1_,�m

nXoAoFp .W&A>+da&:5<6 p

Page 2: Introductory Physics Problems David J. Jeffery Department of

������������ ��������

�������������� ��!�"�$#&%�'(#*)$+, �)-%����/.�021�34)6587:9;9�<>=@?BAC?�DFEHGJI�KMLND(DFOQP8DFGRI�A�S@I�EHS2E�?UT�LVAF?�K�W=YX[Z\G�D]W]E�I�Z�D/G�^Q_H`(^(?�=@I�?�ab>`HKcLND(DFO4=2?�A*d*AF=YS@A�L�SYK>=2X�K�S2K�I$Z\G�D/XH=@I�P8DFG\efZ\D6=YXV?:Z\G�E�I�Z�D/G\?�L(^gG�Kih/E�K�?UZjZ�DMZ�`�KRA�EHZ�`HD/G�a�7kZ�=@?�P8G�K�KBI�D/EHGJ?UK�l�AFG�KA�XVWQI�A�XmLVKMP8G\K�K�SY^nE�?UKiWQAFX�WmW]=@?:Z\G�=2LHE]Z\K�WpoHL�E]ZcXHD�ZcEV?UKiWCP8D/GcI�DFe&e&K�GJI�=@A�Sp_�EHG�_ND/?�K�?�a

b>`HKQ_HG\DFLHS2K�e�?6AFG�KCq/G�D/EH_NK�WrL(^�Z\DF_H=@I�?s=YXtIJ`�A�_]Z\K�GJ?�u&?�K�Kv�D/X/Z\K�X[Z\?sLVK�SYD"l-a�b>`�KQIJ`�AF_]Z�K�GsDFGJW]K�G�=2XHqP8DFS2S2D"lc?nG\DFEHq/`HS2^wZ�`HKxZ�GJAFW]=YZ�=2DFXVA�S-IJ`�A�_HZ�K�G�yiZ\DF_H=@I�D/G\WHK�G\=YXHqt=YXz=YX[Z\G�D]W]E�I�Z�D/G�^{_H`(^]?�=2I�?nLND(DFO]?�a}|HDFGmKiAFIJ`IJ`�AF_]Z�K�G�Z�`HK�G�K~A�G\K�Z:l�D-I�S2A/?�?�K�?�DFPV_HG\DFLHS2K�e�?�u�=2X&DFGJW]K�G�D�PpA�_�_VKiA�GJA�X�I�K�=2X�A-IJ`�A�_]Z\K�G�Z\`HK�^sAFG�K/u�5U�i<�esE�S�Z\=Y_HS2K�TIJ`HD/=2I�KC_HG\DFLHS2K�e�?sAFX�W�5��F<MP8E�SYSYTkAFX�?�l�K�Gs_HG\DFLHS2K�e�?�a��cS2e&D/?UZgAFSYS;Z�`HK_HG\DFLHS2K�e�?6`VA*dFKCI�D/e&_HSYK�Z�K?UEHq/qFKi?:Z\K�WA�XV?Ul�K�GJ?�a�b>`HKMA�X�?�l�K�G\?;e�A*^gLNKRZ�`HK�qFG\K�A�Z�K�?UZ;LNK�XHK��HZ~D�P�7:9�9�a[b>`HKMh[EHK�?UZ�=2DFXV?�AFX�WCA�XV?Ul�K�GJ?;I�A�XCLNKR_ND/?UZ�KiWDFXQZ�`�K-l�K�L=2Xm_NW]P�P8D/G�e�A"Zia

b>`HKg_HG\DFLHS2K�e�?R`�A*dFKsLVK�K�Xr?UEHq/qFKi?:Z\K�WmL(^�e�A�X(^�?UD/EHG\I�K�?�oVL�E]Z�`VA*dFK4AFSYS�LNK�K�Xxl~G�=YZUZ\K�XxL[^�e&K/a-��=2dFK�XZ�`VA"Z-Z�`�K�=2W]KiAF?RP8DFG-_�G�D/LHSYK�e�?-A�G\K4Z\`HK�I�D/ege&D/X�I�DF=2XxDFP�Z\`HK�G�KiA�S2emo�7B_HG\K�P8K�GMZ�D�I�AFSYSje4^�d/K�GJ?U=2DFX�?RD�P�Z�`�K_HG\DFLHS2K�e�?>G\K�WHA/I$Z\=YD/X�?�a

��ZcZ\`HK6K�X�WD�P�Z�`HKsLVD(DFOA�G\K�Z�`HG\K�KsAF_H_NK�X�W]=@I�Ki?�a�b>`HK-��GJ?UZc=2?cAFXmK�h[E�A"Z\=YD/X�?U`HK�K�ZR?�EH=YZ\AFLHSYKMZ\DCqF=2dFK�Z\D?UZ�E�W]K�X[Z\?�AF?BA�Z�K�?UZ�AF=2W�AFX�W�A�G\K�d(=2K�l�?�`HK�K�Z�aBb>`HKsXHK��(ZR=@?�A&Z\AFLHSYK4D�Pj=2X/Z\K�q/G\AFS2?�acb>`HK6S@AF?UZRD/XHK6=@?BAC?�K�Z�D�PA�XV?Ul�K�G�Z\AFLHS2K�?�P8DFG~e4EHSYZ�=2_HSYK4IJ`HDF=@I�KMh[EHK�?UZ�=2DFX�?�a

7:9�9�=@?�XHD"l�?�E]�CI�=2K�X[Z�S2^CI�D/eg_�SYK�Z�KRZ�D&LVK-A4G�KiAF?�DFX�AFLHS2KcG�Ki?UD/EHGJI�KcP8D/G>LVDFZ�`Q?�K�e&Ki?:Z\K�GJ?�DFP�=2X/Z\G�D]W]EVI$Z�D/G�^_H`(^]?U=@I�?�u�I�S@AF?\?U=@I�AFS6e&K�IJ`�AFXH=@I�?�o6��EH=@W�_H`(^]?�=2I�?�o4l�A*d/K�egDFZ�=2DFX�osZ�`HK�G�e&D]W]^(X�AFeg=@I�?�o4AFX�W�K�SYKiI$Z�G\=@I�=YZ:^�AFX�We�A�q/XHK�Z\=2?�emoND/_]Z�=@I�?�o�?�_VKiI�=@A�S�G�K�S2A�Z�=2d(=�Z:^/o�AFX�W�h[E�AFX[Z�EHe�e&K�IJ`�AFXH=@I�?�a6b>`HKgI�D"dFK�G\AFqFKMP8DFGM?�DFe&K6Z\DF_H=@I�?&58K/a qVaYoqFK�DFe&K�Z\G�=@I�AFS�D/_]Z�=@I�?J<~=@?R?UZ�=2S2S�e�AFG�q/=YX�AFS�a�b>`HK�G\Ks_�G�D/L�A�LHS2^mA�G\K6XHD�Z-h[EH=YZ�KsK�XHDFE�qF`�_HG\DFL�SYK�e&?�A"Z�_HG\K�?�K�X[ZBP8D/GK�d/K�G\^rZ�D/_H=2IFo�L�E]ZCZ�`�K�A�E]Z\`HDFG&l~=2SYScLNK�EH_�WHA"Z\=YX�q�A�X�WwAFW�W]=YX�qxZ\D�Z�`HK�e�AF?�I�=YGJI�E�e&?UZ\AFX�I�Ki?�A�S2SYD"l-a{�R?UK�G=2X�?:Z\G�EVI$Z�D/G\?>I�A�X�oHDFP�I�DFEHGJ?UK/oHAFWHWA�XVWQe&D]W]=YP8^QA/?�Z�`HK�^CSY=@?UZ�a

�;dFK�G\^[Z�`H=2XHqQ=2?Ml~G\=�Z�Z�K�Xx=2Xx_�S2AF=YXrb �]� =2Xxe4^�D"l~X�=@W]=2D/?�^[XVI�GJA"Z�=@Ig?:Z:^(S2KFa4b>`�K&h[EHKi?:Z\=YD/X�?MA�G\KgAFSYS�`�A*d/KI�D]W]Ki?sAFX�WrOFK�^[l�DFGJWH?�P8D/GsK�A/?U^�?UK�SYKiI$Z\=YD/X�K�S2K�I$Z\G�D/XH=@I�A�S2S2^�DFGsL[^�`�AFX�Wpa���P8D/GUZ\G\AFX�_HG�D/qFGJA�e�P8D/G4?�K�S2K�I�Z�=2XHqZ�`�K-_HG�D/LHS2K�e�?~A�X�WQDFEHZ�_HE]Z�Z�=2XHq&Z�`�K�e�=2X�h[EH=Y�/oHAF?\?U=2qFX�egK�X[Z�oHA�XVWCZ\K�?UZ~P8DFG\e&A�Z\?>=@?~A�S@?UD�A*d"A�=2S@A�LHS2KFa� cDFZ�KMZ�`�Kh[EH=2�Fo�K�Z\I�a�I�G�KiA"Z\=YD/X�_HG\D]I�K�WHEHG�Kg=@?-AQL�=�ZsI�SYD/XHO(^FopLHE]Z6=YZ-l�D/G�O]?�a4�R?UK�G-=YX�?UZ�G\E�I�Z�DFGJ?MI�D/EHS2W�K�A/?U=2SY^xI�DFXV?:Z\G�E�I�ZZ�`�K�=2GcD"l~XQ_�G�D/qFGJA�e�?�P8D/G~_HG\DFLHS2K�e�?�K�S2K�I�Z�=2DFX�a

7Rl�D/EHS2WxS2=YO/K4Z\DZ�`�AFXHO�Z�`�KC¡BK�_�A�G�Z�e&K�X[Z-D�P~9�`(^]?�=2I�?R¢}£cK�AFS�Z\`�9�`(^]?U=@I�?�D�P�7:WHA�`�D�¤(Z\A"Z\K��cXH=2dFK�G\?�=�Z:^P8DFG~=YZ\?B?UEH_�_VD/GUZ>P8DFG>Z\`H=@?~l�D/G�O�ajb>`�AFXHO]?~A�S@?UD4Z�D&Z\`HK6?:Z\E�W]K�X/ZJ?>l~`HD�`HK�SY_NK�WQ��=2qF`[ZUT�Z�Ki?:Z>Z\`HK-_HG\DFLHS2K�e�?�a

¥ ?T>2;71_>2;<E

¦4§�¨H©�ªi«/¬"­��®RE�AFX[Z�=YZ�=2K�?�oH�cXH=YZ\?�oNv�DFX(d/K�GJ?U=2DFX�?�o]¯�K�A/?UE�G�K�egK�X[Z~¤(=2qFX�=��VI�A�X[Zc|�=Yq/EHG�Ki?�oHAFX�Wm�cX�I�K�G�Z\AF=YX[Z�=2K�?�±°RXHK�Tk¡R=2egK�X�?�=YD/X�A�S�²M=2XHK�e�A�Z�=@I�?³ ¤]I�A�S@A�GJ?>A�X�W´jK�I�Z�D/G\?µ±b>l�D�T;AFX�WQb>`�G�K�K�T!¡B=2e&K�X�?�=YD/X�A�Sp²M=2XHK�e�A�Z�=@I�?¶  BK�l>Z�D/X�· ?c¸�A*lc?>A�XVWQ¡R^(X�A�e&=@I�?~7¹  BK�l>Z�D/X�· ?c¸�A*lc?>A�XVWQ¡R^(X�A�e&=@I�?~7�7º�²M=2XHK�Z\=2I-�;XHK�G\qF^CAFX�WQ»xD/G�O¼ 9�DFZ�K�X[Z\=2AFS��;XHK�G\qF^CAFX�W�v�DFX�?�K�G\d"A"Z\=YD/XnD�Pj��X�K�G\qF^½ ¤(^]?UZ�K�e&?cD�P�9jAFGUZ\=2I�SYKi?>A�X�W¯�DFe&K�X/Z\EHe�i¾±v�D/SYS2=2?�=2DFX�?�/�x¿~DFZ\A�Z�=2DFX7�*��¿~DFZ\A�Z�=2DFX7U7� ³ ��h/E�=YS2=YL�G�=2EHe�AFX�Wm��S@AF?UZ�=@I�=YZ:^

Page 3: Introductory Physics Problems David J. Jeffery Department of

��µ±��GJA*d(=�Z:^� ¶ |�S2EH=2W�?� ¹ °�?\I�=2SYS@A"Z\=YD/X�?>A�X�W�¤(=2e&_HS2K6£BA�G\e&DFXH=@IM¯�D�Z\=YD/X�"ºr»rA*dFKi?�7$uN��K�XHK�G\AFSp»�A*d/K�?>A�X�W»rA*dFKi?�D/X�A&¤(Z�G\=YXHq� ¼ »rA*dFKi?�7�7$uV¤(D/EHX�W»�A*d/K�?� ½ b>`HK�G�e&D]W]^(X�AFeg=@I�?>7$uHb�K�e&_NK�GJA"Z\EHG�K/oH£cKiA"Z�oV|�=2GJ?:ZB¸�A*l�F¾�b>`HK�G�e&D]W]^(X�AFeg=@I�?>7�7$u�¯�=@I�G\D/?\I�D/_H=2IR´B=2K�l�H�xb>`HK�G�e&D]W]^(X�AFeg=@I�?>7�7U7$uV¤]K�I�D/X�W¸�A*lzAFX�W��X[Z�G\DF_(^�/���;SYKiI$Z�G\=@I-v�`VA�G\qFK� ³ �;SYKiI$Z�G\=@I�|�=2K�S@WH?��µ±�MAFE�?�?�·H¸�A*l� ¶ �;SYKiI$Z�G\=@I�9�DFZ�K�X/Z\=2AFS� ¹ v�AF_�AFI�=�Z\DFGJ?�AFX�W�v�A�_�A/I�=YZ\A�XVI�K�[º�v�EHG\G\K�X[ZcA�X�W¿~K�?�=@?:ZJA�X�I�K� ¼ v�=2G\I�EH=YZ\?� ½ ¯�AFqFXHK�Z�=@IM|�=2K�S@WH?Rv�AFE�?�=YXHq�|�DFGJI�K�?³ ¾±v�EHG\G\K�X[Z\?Bv�AFE�?U=2XHq&¯�A�q/XHK�Z\=2IM|�=2K�S@WH?³ �x|VA�GJAFWHA*^�· ?�¸�A*l�D�P�7!X�W]EVI$Z�=2DFX�AFX�Wn7!XVW]E�I$Z\DFGJ?³ ��¸�v�AFX�WQ¸�¿cv�v�=2G\I�EH=�ZJ?�oV�cSYZ�K�G\X�A�Z�=2XHqnv�EHG�G\K�X[ZioHA�X�Wb�GJA�XV?:P8D/G�e&K�GJ?³/³ ¯�A��]l�K�SYS�· ?~��h[E�A"Z\=YD/X�?�o]�;SYKiI$Z�G\DFe�AFqFXHK�Z�=@IB»rA*dFKi?�o]A�XVWm¤]_VKiI�=@A�S�¿~K�S2A�Z�=2d[=YZ:^³ µt�;SYKiI$Z�G\DFe�AFqFXHK�Z�=@IR¿cA/W]=@A"Z�=2DFX³[¶ ��K�DFe&K�Z\G�=@I�AFS�°R_]Z�=@I�?³/¹ 7!X[Z�K�GUP8K�G�K�X�I�K³ º�¡R=���GJAFI$Z\=YD/X³/¼ ¤(_NK�I�=2AFS�¿~K�S2A�Z�=2d[=YZ:^³/½ 9;`HD�Z\DFX�?~AFX�WQ¯�A"ZUZ\K�G~»rA*dFKi?µ[¾�¯�D/G�K-�BLVD/E]ZB¯�A"Z�Z�K�G~»�A*d/K�?µV�x�BSYS��BLVD/E]ZB��Z�D/e�?µ(�tv�D/X�W]E�I�Z�=2DFXD�Pj��S2K�I$Z\G�=@I�=YZ:^C=2X�¤(DFS2=2W�?µ ³  BE�I�S2K�AFGc9�`(^]?U=@I�?�C©�©;«������F«(­�x7!X[Z�G\D]W]E�I�Z�DFG\^C9�`(^]?�=2I�?~�;h[E�A"Z\=YD/X¤(`�K�K�Z��b�A�LHS2KMD�P�7!X[Z�K�q/G\AFS2?³ ¯�E�S�Z\=Y_HS2K�TUv�`HD/=2I�K69�G\DFLHS2K�e �BX�?Ul�K�Gcb�A�L�SYKi?

�L1)@ 145\1)>�H^1_E

�BGUP8O/K�X�o��ga�� ½ º�¾Ho ���"�8'H1�3�����+, ��"0���1��8'H�i�*)������R%�'(#*)$+, �+@)$�,)65, BK�l���DFG\O�u��RI�A/W]K�e&=@I�9;G�Ki?�?J<�5,�BGJ<��K�G\X�?UZ�K�=YX�o��VaYo�|�=2?�`(L�A�XHK/oN9�a�¯�a2oN¢ �MA/?U=2DFG\D"l~=@I��FoN¤�a��F¾F¾/¾Ho����i�F1��$��%�'(#*)$+, �)45,�B_H_VK�GM¤HAFWHW]S2K4¿c=Yd/K�Gio cK�l��/K�GJ?UK�^�u�9;G�K�X/Z\=2I�K-£BA�S2S <M5��>|��-<

v�AFG\W]l�K�S2S�oH¡sa�� ½F½ µ�o���'H1��4�"�$�!�"�! 6+@)$�k���$#Q�"�#�V1J \']�N��0Y�%$F#C5, BK�l���DFG\O�uj»�a »�aN cD/GUZ\DFX�¢�v�D/e&_�A�X(^H<5�v�A[<

v�S@A�G\O�o#�Va&��aYom�c=YZ�O/K�X�om�6aCvRa2o¢ v�DFX�XHDFGioQ¿-a&¡4aQ� ½/¶ º]o%�']#*)J+, ���0'���N�(����� '�1�3)�"��+, ��"0*�+�/.�0Y1�)5,��W]=YX(LHE�G�q/`�u;°RSY=2dFK�GcA�X�W!��D"^(W¸pZJWpa <Q5kv��Bv><

|�G�K�X�IJ`�oH�6aV9�a�� ½ º(�Fo,�s1.-j�!�"��+����/��1J \'+�"�V+, $)65, BK�l���DFG\O�u�»�a�»�a� cD/GUZ\DFXm¢ v�DFe&_�AFX(^Fo]7!X�IFa <5,|�GJ<��G\=��&Z\`�?�oj¡4a��Va;� ½F½/¶ o��������������� ���+,�"�t�k�10>�+�"�V���]32��1J J'3����+, �)n5,�c_�_VK�Gg¤]A/WHW]S2Kn¿~=2dFK�Gio� cK�l4�/K�GJ?UK�^�u9�G\K�X[Z�=@I�K-£RA�S2S@<�5���G$<

£RA�S2SY=@WHA*^Fo�¡4a2o�¿~K�?�XH=@IJO�o�¿6aYo�¢ »�AFSYO/K�Gio��Va���¾/¾F¾�o65��]�N�7�"3�1��V�8��0 )&�9�-%;'(#*)$+, $)�:<;>=F�!1��N�F1J� ¹ Z\`x��W]=�Z\=YD/X5, BK�l���DFG\ONu�»{=2SYK�^H<M5,£B¿�»�<

£BK�IJ`[Z�o-�ca2o-¢@?�ABAUAFIFo��sa6� ½ º*µ�o#C�DN��+, $)r5,¯�K�XHSYD�9jAFG�O�o-v�A�S2=�P8D/G�XH=@AHu{�RWHW]=@?UD/X]T�»�K�?�S2K�^�9;EHLHS2=2?�`H=2XHqv�DFe&_�AFX[^H<�5,£�?p<

Page 4: Introductory Physics Problems David J. Jeffery Department of

�[AFIJO]?�DFX�o]¡4a+��ap� ½ º ¶ o���0 �*)J)$+, ��"0�;�0Y1J ������i�"#"���"3g+, $)c�*Z\`m��W]=YZ�=2DFXr5, cK�l ��D/G�O�u�»{=2SYK�^]<M5�/A[<²MGJA�E�?�OFD/_]P:o]²&a3��aYo�¢ ��K�=@?UK�G�oH�saV��¾/¾ ³ ��'�1M%;'(#*)$+, ��"0�����+��"1��J)�165, cK�l ��D/G�O�uj¯�Ii��G\A*l>T!£c=2SYS <�5,² �~<¸�A*lcW]K�X�oj¡4aj|�a�� ½ º ¶ o��R���$�V�����i�"�� ���+,�"�±�k� �V1���)������>�"02 ��]0 �()'�"�N�R1�0 ����+��i+ ��#�5,¸�DFX�W]D/X�unv�`�A�_�e&AFXA�X�W£BAFSYS <M5,¸�A/<

�/K ��K�G\^Fo�¡sa��VaN��¾/¾H�/o����"�8'H1�3�����+, ���0 � �F.�0Y1�)s5,9�D/GUZ�v�D/SYLNDFG\XHKFo�v�A�XVAFWHA�u�9�DFG�Z�_NK�X[Z\G\AFq/A�e}9�EHLHS2=@?U`H=2XHq(<5,¯��jbc<

¯�K�G�e&=2X�oc 6a�¡sa�� ½/¹F¼ o��BD+�F J1 �"������+ 3�1x+ � �BD�1J �+���0�R1�0 ����+��i+ ��#�5, cK�l ��DFG\ONu�¯�I���GJA*l>T!£c=2SYS ��D(DFOv�DFe&_�AFX[^H<�5,¯�Ki<

¤(`�=Y_He�AFX�oB��a*bMa2o"»{=YS@?UD/X�oB�Vai¡4aYo�¢{b�D]WHWpo��sai»�a��F¾F¾F¾��R�6�������������� ���+,�"���!�c%�']#*)J+, ���0��� �+,1��� J1�5��D/?UZ�DFX�u£cD/EHqF`[Z�D/X¯�=���=2X�v�D/e&_�A�X(^H<�5�¤(»�bc<

»�DFSYP,?UD/X�o"¿-a2o*¢{9jA/?�A/IJ`HDB��o.�Vai¯�aF� ½/½ ¾�o"%�']#*)$+, $)���; =/�!1����F1J� -j+ �8' ���i�F1��$�g%�']#*)J+, �);5���S2K�X(d(=2K�lr7!SYS2=2XHDF=@?�u¤]I�DFZUZio�|HD/G�Ki?Ue�A�X�y"¸�=YZUZ\SYK/o,��G\D"l~Xm£c=2qF`HK�Gc�;W]E�I�A"Z\=YD/XV<�58»�9�<

Page 5: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � 1)&AEGda5<1_=!1)>W;J`SY>a*[;<E ` ¥ ? >W(A1)5\EG*-?T>�E `�UF*[cT>�*��fHJ&A>2;���*[cTda5\1)E `&T>a,hY8>�H^1)57;7&T*->2;<*-1)E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾���h[e4EHS�ZB¾/¾F¾���¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u��\I�S2K�A�G\S2^��s=YXm_H`(^]?�=2I�?� ª�¬"¨ �V«������V¬ ��­��  cD�ZBA&?�K�G\=YD/E�?>h[EHK�?UZ�=2DFX�a

�Fa>7!Xm_H`(^]?U=@I�?�AUAFG�q/DFXnZ�`HK-l�DFGJW��\I�S2K�A�G\S2^��4e&K�AFX�?�uA[<nI�SYKiA�G\SY^/aLN<nE�X�I�S2K�AFG�S2^FaIi<QA�P Z�K�G~µ�_�A�q/K�?�D�PjA�S2qFK�LHG\A�aWV<nl~G\DFX�qFS2^FaK*<QAFSYSpDFP�Z\`HK6A�LND"dFK/a

¾F¾���h[e4EHS�ZB¾/¾F¾[��¾C�&���MK�A/?U^�e&K�egD/G�^�uje4E�?:Z~LNKFu���XHD�Z~XHKiI�Ki?�?\A�G\=YS2^C?�D��� ª�¬"¨ �V«������V¬ ��­��  cD�ZBA&?�K�G\=YD/E�?>h[EHK�?UZ�=2DFX�a

�]a>7!Xm_H`(^]?U=@I�?�AUAFG�q/DFXnZ�`HK-_H`�G\A/?UK��Ue4E�?UZ>LNK��ge&K�AFX�?�uA[<C=@?�aLN< A:EV?:ZBA/I�I�K�_]Zc=YZ~Z�`�A�Z�aIi<nX�D�ZcXHKiI�K�?\?\A�G\=YS2^C?UDVaWV<QI�A�X�· ZcLNKFaK*<QAFSYSpDFP�Z\`HK6A�LND"dFK/a

¾F¾���h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�P8EHX�WHAFe&K�X[Z\AFS�h[E�A�X[Z�=YZ�=2K�?³ a~b>`HG\K�K-h[E�AFX/Z\=�Z\=YKi?>E�?�E�A�S2SY^nZ\AFOFK�XmAF?�P8EHXVWHA�e&K�X[ZJA�S�AFG�K/u

A[<�S2K�XHqFZ�`�o]A�G\K�A�oFd/DFS2EHe&KFo LV<je�AF?\?�o/l�K�=2qF`[Z�o/`HK�P Zio I�<�SYK�XHq�Z\`�o/e�A/?�?�oFZ\=Ye&K/o WV<jZ\=Ye&KFoWHEHG\A�Z�=2DFX�oHAFqFK/o Ki<�S2K�XHqFZ�`�o]e�A/?�?�oHW]K�XV?U=YZ:^Fa

¾F¾���h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�O(=YS2DFq/G\AFe�Z�D�qFGJA�e�?µ�a~� O(=2SYD/qFGJA�e =@?�u

A[<6�i¾F¾/¾CqFGJA�e�?�a LV<4�����i¾����4qFGJA�e�?�a I�< ³ � ��µV� ¹ q/G\AFe�?�a W�<M�nqFGJA�e�?�a Ki<R¾q/G\AFe�?�a

¾F¾���h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�¤(7�_HG�K��H�Q?�^(esLNDFS@?¶ a~b>`HKs¤]7;EHXH=YZB_HG\K����Q?U^(e4LVD/S2?~¯mT;AFX�WegT;?:ZJA�X�WQP8DFGiu

A[<Ce&K�q/Am5 P,A/I$Z�D/G~D�P���¾"!i<>A�X�WQe&=YS2S2=;5 P,A/I$Z�D/G~D�P>��¾ � !�<�aLN<ne&K�q/Am5 P,A/I$Z�D/G~D�P���¾ ! <>A�X�WQe&=YS2S2=;5 P,A/I$Z�D/G~D�P>��¾ ����<�aIi<nO(=2SYD�58P,AFI$Z\DFG~DFP��i¾"!�<>AFX�Wne&=2SYS2=�58P,AFI�Z�DFG~DFP��i¾ ��� <$aWV<nO(=2SYD�58P,AFI$Z\DFG~DFP��i¾"!�<>AFX�Wne&=2SYS2=�58P,AFI�Z�DFG~DFP��i¾ � !�<$aK*<ne&K�G�q/K�G-5 P,A/I$Z�D/G~D�P>��¾�#�<>A�X�We&K�S2L�Am5 P,A/I$Z\DFG~D�P>��¾ � !�<�a

¾F¾���h[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/X[d/K�GJ?U=2DFXCP,AFI$Z\DFG%$REHXH=YZ:^�P,AFI�Z�D/G¹ a~� EHX�=�ZJ?cI�D/X[d/K�GJ?U=2DFXCP,AFI$Z\DFG~=@?c?�DFe&K�Z\=Ye&K�?~I�A�S2SYKiWQA�u

Page 6: Introductory Physics Problems David J. Jeffery Department of

� v�`�AF_]Z�a>��®REVA�X[Z�=YZ�=2K�?�oH�cXH=YZ\?�o�v�D/X(dFK�GJ?�=YD/X�?�o(¯�KiAF?�EHG�K�e&K�X[Z�o�¤(=2qFX�=��VI�A�X[Zc|�=Yq/EHG�Ki?�oHAFX�W�cX�I�K�G�Z\A�=2X[Z�=2K�?

A[<�P,A/I$Z\DFG~D�P�EHXH=YZ:^FaLN<CP,A/I$Z\DFG~D�Pj�]aIi<CP,A/I$Z\DFG~D�P�AgP8K�l-aWV<CP,A/I$Z\DFG~D�P���¾�aK*<CP,A/I$Z\DFG~D�P�P,AFI�Z�a

¾F¾���h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/X[d/K�GJ?U=2DFXnD�PjA�X=YX�IJ`º(aB°RXHKM=2X�IJ`m=2?~AF_H_HG\D*�]=Ye�A"Z\K�S2^�u

A[<���ema LV<���O(ema I�<R��I�ema W�<~� � ¶ µ�I�ema Ki<��pP Zia

¾F¾���h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/X[d/K�GJ?U=2DFXneg=2S2KMZ�D�O(e¼ aM�Me&=YS2K-=@?cA�_H_�G�D*�]=2e&A�Z�K�SY^�u

A[<���eaLN<���O[emaIi<�� � ¹ ¾ ½ O(emaWV<� � ¶ µ;I�emaK*<���P Z�a

¾F¾���h[e4EHS�ZB¾/¾[º�¾F¾4�4µ�µ&e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u���¾geny"?�Z�D�e&_H`½ a~��`(EHe�A�X�5,A4dFK�G\^�?U_NK�KiW]^C`(EHe�A�XN<;I�A�XnG\EHX���¾je���?$a�»{`�A"Z~=@?;Z\`H=@?~?U_NK�KiWn=2Xne&=2SYKi?>_VK�G�`�DFEHG-58e&_H`N<��

������ � ��DFECW]D6X�D�Z;XHK�K�WgZ\D6W]DsA�X(^4K��]_HS2=2I�=�Z�I�A�S@I�EHS@A"Z\=YD/X�5,A�SYZ�`�DFEHq/`4Z\`�A"Z�l~=YS2S�l�DFG\O6Z\D[D(<$o.A:E�?:Z�Z�`H=2XHOAFLVD/E]ZcK�d/K�G\^(W�A*^gG\K�AFSY=YZ:^Fa;v�AFXQ^/DFEDFE]Z\G�EHXmA�I�AFG�#��Ki?Jy"XHD(y"e�A*^[LNK��

A[<���¾/¾je&_H`�a LV<���e&_H`�a I�<��F� � �jO[e���?$a W�<~�/� � ³ º�e&_H`�a K*<~�F� � ³ º�eg=2S2K�?�a

¾F¾���h[e4EHS�ZB¾/¾ ¼ ¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u;?�K�I�DFX�W�?�=2X�A&WHA*^��¾Ha~���]A/I$Z\SY^Q`HD"lze�AFX[^?UKiI�D/X�WH?cAFG�KMZ\`HK�G\K6=2X�ACWHA*^���£cD"l�e&AFX(^Q?�K�I�D/X�WH?cAFG�KMZ\`HK�G\K6=2X�ACWHA*^nZ�D�DFGJW]K�G

DFP�e�A�qFX�=�Z\E�W]K�� ������ � °RGJW]K�G;D�P�e&AFqFXH=YZ�EVW]KRe&KiA�X�?�G�D/EHX�W]KiW�DB�mZ\DsZ\`HKRX�K�A�G\K�?UZ�_ND"l�K�G�D�P���¾�u�K/a qVaYo�Ha �4G\DFEHX�W�?>DB��Z�D��i¾�� $ �MAFX�W ½F½ ��G\DFEHX�W�?>DB��Z\D�i¾ � aA[< ¼/¹ µ[¾F¾�?�A�X�Wx��¾���?�aLN<���µFµ[¾�?�AFX�W���¾ � ?�aIi<���µFµ[¾�?�AFX�W���¾��p?�aWV< ¼/¹ µ[¾F¾�?�A�X�Wx��¾��p?�aK*<�� ����¾��p?�a

¾F¾���h[e4EHS�ZB¾/¾ ½ ¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u�`(EHXVW]G�KiWne&=2SYS2=2DFXmLH=2SYS2=YD/X�F�Fa>»�G�=YZ�K6Ag`(EHX�WHG�KiWne&=2SYS2=YD/XmLH=YS2S2=YD/Xe&=2SYKi?~=2X?\I�=2K�X[Z�=Y�VIMXHDFZ\A�Z�=2DFX�a

A[<���¾���eg=�a LV<��i¾"!�e&=�a I�<��i¾"#�e&=ka W�<���¾�����e&=�a Ki<��i¾ � #�eg=�a¾F¾���h[e4EHS�ZB¾���¾/¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u;I�DFX(dFK�GUZ>`(EHX�W]G\K�WQe&=YS2S2=YD/XL�=YS2SY=2DFXe&=YS2K�?~Z�D�O(ema�i�]aBv�D/X[d/K�G�Z>Ag`(EHX�WHG�KiWQe&=2SYS2=2DFXmLH=2SYS2=YD/XQe&=2SYKi?~=2X/Z\D&O[=2S2DFe&K�Z\K�GJ?�a

A[<�� � ¹ ����¾���O(eaLN<�� � ¹ ����¾�!�O(eaIi<�� � ¹ ����¾�#�O(eaWV<�� � ¹ ����¾�����O(emaWV<�� � ¹ ����¾ � #�O(ema

¾F¾���h[e4EHS�ZB¾��F�i¾F¾C�&� ³ K�A/?U^�e�A�Z�`�u�K��]_VK�G�=2e&K�X[Z\AFSYS2^�e&K�AF?�EHG\=YX�q��ja� ³ a~b�D�W]K�Z\K�G\eg=2XHK���K��]_NK�G\=Ye&K�X[ZJA�S2SY^�u

A[<nI�DFX(dFK�GUZ>e&=YS2K�?c_VK�G~`HDFEHG~=2X[Z�D�e&K�Z\K�GJ?>_VK�Gc?UKiI�D/X�Wpa

Page 7: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~� ®RE�A�X[Z\=�Z\=YKi?�o��BXH=YZ\?�oNv�DFX(dFK�G\?�=2DFX�?�o[¯�K�AF?�EHG\K�e&K�X[Zio�¤(=Yq/XH=Y�VI�AFX/Zc|�=2qFEHG\K�?�oHA�X�W�cXVI�K�G�Z\AF=YX[Z\=YKi? ³

LN<ne&KiAF?�EHG�K�Z\`HK-G\A�Z�=2D4DFP�Z\`HK6I�=2GJI�S2KMAFG�KiA6Z\D�I�=2G\I�SYK-I�=2GJI�EHegP8K�G\K�XVI�KFaIi<ne&KiAF?�EHG�K�Z\`HK-G\A�Z�=2D4DFP�I�=YGJI�S2K-I�=2G\I�EHegP8K�G\K�X�I�K�Z�D�I�=2G\I�SYK-W]=@A�e&K�Z�K�GWV<ne&KiAF?�EHG�K�Z\`HK-G\A�Z�=2D4DFP�Z\`HK6I�=2GJI�S2K�q/=YG�Z�`QZ�D�I�=YGJI�S2KM`HK�P ZiaK*<ne&KiAF?�EHG�K�Z\`HK6AFI�I�K�S2K�GJA"Z\=YD/XCXHKiA�G>Z�`�K6�;A�G�Z�`�· ?~?�EHG�P,AFI�KMW]EHKMZ\D�qFGJA*d(=�Z:^/a

¾F¾���h[e4EHS�ZB¾��i�F¾F¾C�6���4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�P8GJAFI$Z\=YD/X�A�S�K�G�G\DFG��µ�a ��D/E�`VA*dFKgZ�GJA*dFK�SYKiWxAmW]=@?:ZJA�X�I�K���¾�� ��O(emaCb>`HK&P8GJAFI�Z�=2DFX�AFSjEHX�I�K�GUZJA�=2X[Z:^t5,|���<MDFG-G\K�S@A"Z\=Yd/KgK�G�G\DFGM=2X

^/DFEHG�Z�GJA*dFK�S�W]=@?:ZJA�X�I�K�=@?�uA[<��/aLN<Q¾�aY�/aIi<Q¾�a ¶ aWV<�HaK*<��i¾Ha

¾F¾���h[e4EHS�ZB¾�� ³ ¾F¾C� ³ �4K�A/?U^�e�A�Z�`�u;?�=2q�a ��q�ajAFW�W]=�Z\=YD/X� ¶ a~�RWHWK��]_VK�G�=2e&K�X[Z\AFSpd"A�S2EHK�? ³ a �[º6AFX�W ½ a ½ oHA�XVWnq/=Yd/KRZ\`HK6A�XV?Ul�K�G�Z�DCI�DFG\G�KiI$Z~?U=2qFX�=��VI�A�X[Z>��qFE�G�Ki?�a

A[<�� ³ a2�*º]aLN<�� ³ a �]aIi<�� ³ a2�FaWV<�� ³ aK*<���µ�a

¾F¾���h[e4EHS�ZB¾���µ[¾F¾C� ³�³ K�A/?U^�e�A�Z�`�u;?�=2q�a ��q�a�esE�S�Z\=Y_HS2=@I�A"Z\=YD/X� ¹ a~¯�E�S�Z\=Y_HS2^nK��]_VK�G�=2e&K�X[Z\AFSpd*AFSYE�K�? ³ a �[º6AFX�W ½ a ½ oHA�X�Wq/=Yd/KBZ\`HK6A�X�?�l�K�G�Z�DCI�DFG\G�KiI$Z~?U=2qFXH=Y�VI�A�X[Z>��qFEHG\K�?�a

A[< ³ ¾HaLN< ³ µ�aIi< ³ �]aWV< ³ �]a ³K*< ³ �]a µ

¾F¾���h[e4EHS�ZB¾�� ¶ ¾F¾4�4µ��MK�A/?U^�e�A�Z�`�u;?�=2q�a ��q�ajA�XVWnK�G�G\DFG�*º(a ��D/E-`�A*dFK A:E�?UZ�e&K�A/?UE�G�KiWRA~S2K�X�q�Z�`M=2X6I�K�X/Z\=Ye&K�Z�K�GJ?�AFX�W�K�?UZ�=2e�A"Z�KiWM=�ZJ?�EHXVI�K�G�Z\AF=YX[Z:^~Z\D�� � �?U=2qFXH=Y�VI�A�X[Z

��q/EHG\KB58l~`H=@IJ`6=@?�EV?UE�AFSYS2^MA�S2S�Z�`VA"Z�I�A�X6LNK�WHDFXHK*<$a���D/E6l~G\=�Z\KjZ�`�A�Z�WHA�Z�EHe�W]D"l~X-=2X-Z\`HK�?�=Ye&_HS2K�?UZ�o"_�G�D/_VK�GK��(_NK�G\=2egK�X[ZcG�K�_VD/GUZ\=YXHq&?UZ:^[S2KM^FD/EQO(XHD"l-ajb>`�A�ZBWHA"Z\EHe�=@?�uA[<�5,µ � �*º���¾ � ¾ ¼ < ����¾ � I�emaLN<x5,µ � ����¾ � ¾ ¼ < ����¾ � I�emaIi<x5,µ � �*º���¾ � ¾ ¼ �/< �x�i¾ � I�emaWV<nµ � �"º��x�i¾ � I�e���¾ � ¾ ¼ ������¾ � I�e�aK*<nµ � �"ºFº�����¾ � I�e���¾ � ¾ ¼ ����¾ � I�e�a

¾F¾���h[e4EHS�ZB¾�� ¹ ¾F¾C� ³ �MK�A/?U^�e�A�Z�`�u;?�=2q�a ��q�ajA�XVWQ?�SYD/_VK� ¼ a ��D/E�A�G\KmWHK�Z�K�G�e&=2XH=2XHq�A�?US2DF_NKmP8G\DFe Z:l�D�_NDF=2X/ZJ?�DFX{ArLNK�?UZUT��HZnS2=YX�KFu�=2X 5�� �H<gP8D/G�e�A"ZC_NDF=2X[Z���=2?

5 ¶�� ¶ ¾��µ[� � �*<jA�X�WQ_NDF=2X/ZB�s=2?-5U��¾ � ¹ ¹ � � ³ <$a�»{`�A"Z~=@?�Z�`HK-?�SYD/_VKRZ�D�I�D/G�G\K�I�Z�?�=Yq/XH=Y�VI�AFX/Z���q/EHG�Ki? � ������ �¤(=2qFX�=��VI�A�X[Z>��qFE�G�Ki?~I�A�XmA�S2l>A*^(?�LNK-SYD[?:Z~=2X�?UEHLHZ�GJAFI$Z\=YD/X�?�aA[<CµVa ¾�aLN< ³ a ½/¹ aIi< ³ a ½/¹ �/aWV<nµVaK*< ³ a ½ a

Page 8: Introductory Physics Problems David J. Jeffery Department of

µ v�`�AF_]Z�a>��®REVA�X[Z�=YZ�=2K�?�oH�cXH=YZ\?�o�v�D/X(dFK�GJ?�=YD/X�?�o(¯�KiAF?�EHG�K�e&K�X[Z�o�¤(=2qFX�=��VI�A�X[Zc|�=Yq/EHG�Ki?�oHAFX�W�cX�I�K�G�Z\A�=2X[Z�=2K�?

¾F¾���h[e4EHS�ZB¾�� ¹ ¾F¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�u�P8GJAFI�Z�=2DFX�AFSNE�X�I�K�GUZJA�=2X/Z:^QA�X�W?U_NK�KiW� ½ a ��D/E6`�A*dFK�A:E�?:ZjI�AFS2I�EHS@A"Z�KiW-ABW]=@?UZ\A�XVI�K�� ¶�� º�e�P8G\DFe�AR?U_NK�KiW-D�P ³ � º �s¾ � ¶ ew? � ��A�X�W6A~Z�=2egK�D�PV� � º �s¾ � ��?�a

�R?U=2XHq6Z\`HKM¯�DFX[Z�K�e�A*^FDFG�P8G\A/I$Z�=2DFXVA�S�E�X�I�K�GUZJA�=2X/Z:^ge&K�Z\`HD]WpoHI�AFS2I�EHS2A�Z�K~Z\`HK�EHX�I�K�GUZJA�=2X[Z:^4DFP�Z�`HK�W]=@?:ZJA�X�I�KAFX�W�l~G\=�Z\KCZ\`HKWH=2?UZ\AFX�I�KA�X�W�=�ZJ?4E�X�I�K�GUZJA�=2X/Z:^�Z\DxI�D/G�G\K�I�Z4?�=Yq/XH=��NI�A�X[Z4��qFEHG\K�?�a ������ � v�A�S@I�EHS@A"Z\K�WEHXVI�K�G�Z\AF=YX[Z\=YKi?�I�A�XW]=���K�Gc?�S2=Yq/`/Z\SY^QW]K�_NK�X�WH=YXHq&D/Xnl~`HK�G�K�^FD/EnG\DFEHX�WQDB��=2XnZ\`HK-I�AFS2I�EHS2A�Z�=2DFX�aj�BSYS2D"l�P8D/GZ\`�A"ZiaA[<Q� ¶�� º�� ³ � ¶ emaLN<� ¶�� º��{� � ¾jemaIi<� ¶�� º��{��emaWV< ³ ¾ � ³ eaK*<� ¹ � ³ ea

¾F¾���h[e4EHS�ZB¾��*º�¾F¾4� ³�³ e&D]W]K�GJA"Z\K�e�A�Z�`�u�|���P8G\=2I�Z�=2DFXmI�D(K��CI�=2K�X[Z��¾Ha ��D/En`�A*d/K�A:E�?UZ~I�A�S@I�E�S2A�Z�K�WQA4I�D(K��CI�=2K�X[Z>D�P�P8G\=2I�Z�=2DFXD�P�¾ � �"º ¶ P8G\DFe A4e�AF?\?�D�P;�/��¾ �r�F¾jO(q4AFX�WnAsZ�=2e&K

DFP�� � º �n¾ � ³ ?�a��B?�=YXHq�Z\`HKc¯�DFX[Z\K�e�A*^FD/G�P8GJAFI�Z�=2DFX�AFS]EHX�I�K�GUZJA�=2X[Z:^-egK�Z�`HD]Wpo[I�AFS2I�EHS2A�Z�K�Z�`�K~EHX�I�K�GUZJA�=2X[Z:^-D�PZ\`HKcI�D(K��CI�=YK�X/Z�AFX�Wsl~G\=YZ�K�Z�`HK~I�D[K��CI�=2K�X[Z�A�X�W4=�ZJ?jEHX�I�K�G�Z\AF=YX[Z:^MZ�D-I�DFG\G�KiI$Zj?U=2qFXH=Y�VI�A�X[Z��VqFEHG\K�?�a ������ �v�AFS2I�EHS2A�Z�KiW4E�X�I�K�GUZJA�=2X/Z\=YKi?�I�AFX�W]=���K�G�?US2=Yq/`[Z�S2^4W]K�_VK�X�W]=2XHq6DFX&l~`HK�G�K~^/DFEgG�D/EHX�WgDB�Q=YX&Z\`HKBI�AFS2I�EHS@A"Z�=2DFX�a�BSYS2D"l�P8D/G>Z�`�A�Z�aA[<n¾ � �"º ¶ ��¾ � ¾ ³ aLN<Q¾ � �"º ¶ ��¾ � ¾/�]aIi<Q¾ � � ¼ ��¾ � ¾ ³ aWV<Q¾ � � ¼ ��¾ � ¾��FaK*<Q¾ � ����¾ � ¾ ³ a

¾F¾���h[e4EHS�ZB¾�� ¼ ¾F¾4� ³ µ&e&D]W]K�GJA"Z\K�e�A�Z�`�u�|�� e&DFe&K�X[Z\EHe�]�Fa ��D/E�`�A*dFK A:E�?UZ�I�A�S@I�EHS@A"Z\K�W4Z�`HKRe�A�qFX�=�Z\E�W]K~D�P�A-S2=2XHK�AFG�e&DFe&K�X[Z�E�efZ\D6LVK ¹ � ¾H��O(qje ��? � �>P8G\DFe A-e�AF?\?

DFP ³ � ¾ ��¾ � ³ O(q�A�X�W�?�_VK�K�WrDFPc� � ¾/¾ �{¾ � ¾ ³ e±? � ��a��R?U=2XHq�Z\`HKn¯�D/X/Z\K�e�A*^FD/GMP8G\A/I$Z\=YD/X�A�S�E�X�I�K�GUZJA�=2X/Z:^e&K�Z\`HD]Wpo�I�A�S@I�EHS@A"Z\KsZ\`HK�EHX�I�K�G�Z\AF=YX[Z:^�D�P�Z�`HK&e�A�q/XH=YZ�E�W]K&DFP�S2=YXHKiA�GMe&DFe&K�X[Z\EHe AFX�W�l~G\=YZ�K&=�Z6AFX�W�=YZ\?EHXVI�K�G�Z\AF=YX[Z:^�Z�DxI�DFG\G�KiI$Zs?�=Yq/XH=Y�VI�AFX/Z-�VqFEHG\K�?�a������� � v�AFS2I�EHS2A�Z�KiWrEHX�I�K�GUZJA�=2X[Z�=2K�?6I�A�X�W]= �NK�Gg?�S2=Yq/`/Z\SY^W]K�_VK�X�W]=2XHq�DFXl~`HK�G�KM^FD/EQG\DFE�X�WnD ��=2XQZ\`HK6I�AFS2I�EHS@A"Z�=2DFX�a��BSYS2D"l�P8D/G>Z�`�A�Z�aA[<n¾ � �"º ¶ ��¾ � ¾ ³ aLN<Q¾ � �"º ¶ ��¾ � ¾/�]aIi<Q¾ � � ¼ ��¾ � ¾ ³ aWV< ¹ � ¾ ��¾ � ¹ aK*<Q¾ � ����¾ � ¾ ³ a

¾F¾���h[e4EHS�ZB¾�� ½ ¾F¾4� ¶ �4e&D]W]K�GJA"Z\K�e�A�Z�`�u�|�� _HS2D�Z�Z�=2XHq�F�]a ��D/E±`VA*dFK�A�?UK�G�=2K�?&DFPMW�A"Z\A{5�A�S2Scl~=YZ�`{EHX�I�K�G�Z\AF=YX[Z:^�¾�a �/<$u��/a ¾�o ³ a µVo ¶ a ¹ o~º]aY�/o ¼ a º]o�AFX�W���¾Ha2�Fa ��D/E

AFG�KgZ�D�_�SYDFZ-Z�`HKC?\h[E�A�G\K&G�D(D�Z-DFP�Z\`HK�?�K�X(EHesLNK�GJ?�aQ£cD"l WHD�^FDFE�DFLHZ\A�=2X�Z�`HKCAF_H_HG\DF_HG\=@A"Z�Km5,AFL�?�DFS2E]Z�K*<EHXVI�K�G�Z\AF=YX[Z:^sP8DFGjZ\`HKB?\h/EVA�G\K~G�D(D�ZJ?�E�?�=YXHq6Z�`HKB¯�DFX[Z�K�e&A*^/DFG�P8GJAFI$Z\=YD/X�A�S�EHX�I�K�GUZJA�=2X[Z:^6e&K�Z�`�D(WnA�X�Wgl~`�A�Z=@?~=YZ~Z�`�A�Z>E�X�I�K�GUZJA�=2X/Z:^��A[<nb�A�O/K>Z�`HKBP8G\A/I$Z\=YD/X�A�S]EHXVI�K�G�Z\AF=YX[Z:^gD�P�A�Z:^(_H=@I�A�SNWHA"Z\EHemo[A/?�?�=2qFX4Z�`H=@?�P8GJAFI�Z�=2DFX�AFSHEHX�I�K�G�Z\AF=YX[Z:^6Z\D-Z�`�KW�A"Z�E�e· ?M?�h[E�AFG�K4G�D(DFZ�oN��X�W�Z�`HK&?\h/EVA�G\KsG\D[DFZ�· ?RAFL�?�DFS2E]Z�KgEHX�I�K�G�Z\A�=2X[Z:^mE�?U=2XHq=�ZJ?�XHK�l~S2^�AF?\?U=2qFX�K�WP8GJAFI�Z�=2DFX�AFScEHX�I�K�G�Z\AF=YX[Z:^Fo>A�XVWtEV?UK�Z\`H=@?nA�LV?UD/SYE]Z\K�EHX�I�K�G�Z\A�=2X[Z:^�P8DFGQA�S2SB?�h[E�AFG�K�G\D(D�Z\K�WwWHA"ZJAHa��G\K�A/?UD/X�A�L�SYKM?�h[E�AFG�K�G\D[DFZcA�L�?�DFS2E]Z�KMEHXVI�K�G�Z\AF=YX[Z:^�=@?~µ�a

LN<Qb�A�O/K>Z�`HKBP8G\A/I$Z\=YD/X�A�S]EHXVI�K�G�Z\AF=YX[Z:^gD�P�A�Z:^(_H=@I�A�SNWHA"Z\EHemo[A/?�?�=2qFX4Z�`H=@?�P8GJAFI�Z�=2DFX�AFSHEHX�I�K�G�Z\AF=YX[Z:^6Z\D-Z�`�KW�A"Z�E�e· ?M?�h[E�AFG�K4G�D(DFZ�oN��X�W�Z�`HK&?\h/EVA�G\KsG\D[DFZ�· ?RAFL�?�DFS2E]Z�KgEHX�I�K�G�Z\A�=2X[Z:^mE�?U=2XHq=�ZJ?�XHK�l~S2^�AF?\?U=2qFX�K�WP8GJAFI�Z�=2DFX�AFScEHX�I�K�G�Z\AF=YX[Z:^Fo>A�XVWtEV?UK�Z\`H=@?nA�LV?UD/SYE]Z\K�EHX�I�K�G�Z\A�=2X[Z:^�P8DFGQA�S2SB?�h[E�AFG�K�G\D(D�Z\K�WwWHA"ZJAHa��G\K�A/?UD/X�A�L�SYKM?�h[E�AFG�K�G\D[DFZcA�L�?�DFS2E]Z�KMEHXVI�K�G�Z\AF=YX[Z:^�=@?c¾ � �Fa

Ii<Qb>`�K6A�L�?�DFS2E]Z�KMEHXVI�K�G�Z\AF=YX[Z:^�=@?>Z�`�K6?�h[E�AFG�K�G�D(DFZ>DFP�¾ � �Hu�=�a KFa2oH¾ � µ ¶ aWV<Qb>`�K6A�L�?�DFS2E]Z�KMEHXVI�K�G�Z\AF=YX[Z:^�=@?>Z�`�K6?�h[E�AFG�K�G�D(DFZ>DFP�¾ � �Hu�=�a KFa2oH¾ � µ�a

Page 9: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~� ®RE�A�X[Z\=�Z\=YKi?�o��BXH=YZ\?�oNv�DFX(dFK�G\?�=2DFX�?�o[¯�K�AF?�EHG\K�e&K�X[Zio�¤(=Yq/XH=Y�VI�AFX/Zc|�=2qFEHG\K�?�oHA�X�W�cXVI�K�G�Z\AF=YX[Z\=YKi? ¶

K*<Qb>`�K6A�L�?�DFS2E]Z�KMEHXVI�K�G�Z\AF=YX[Z:^�=@?>Z�`�K6?�h[E�AFG�K�G�D(DFZ>DFP�¾ � �Hu�=�a KFa2o ³ a

¾F¾���h[e4EHS�ZB¾[��¾/¾F¾C� ¶ �4K�A/?U^&Z\`H=2XHO(=YXHqVu�_HS2D�Z�Z�=2XHq�A4_ND"l�K�G~S2=YXHKiA�G\SY^� ³ a ��D/E`VA*dFKRZ\A�O/K�XmA&?UK�ZcD�P�W�A"Z\A&_VA�=2G\?M5 � ��[<�a�b>`HK�G\KM=2?~AgZ\`HK�D/G�K�Z�=@I�AFSVP8D/G�e4EHS@A4G\K�S@A"Z\=YX�q � A�X�W��Vu

� � $�� � ���� l~`HK�G�K�gA�XVW � AFG�K~I�DFX�?UZ\AFX/ZJ?�a���DFE&l>A�X[ZjZ�D6Z�K�?UZ�Z\`H=2?�P8DFG\esEHS@AME�?�=YX�q-^FDFE�G�WHA"ZJA-A�X�W&S2=YX�K�A�G;qFGJA�_H`H=@I�AFSAFX�A�S2^]?U=@?�a� cD"l � A�X�W���AFG�K � � �_HG\K�W]=@I$Z\K�W-Z\DMLVK>S2=YXHKiA�G\SY^MG\K�S@A"Z\K�W6L(^MZ\`HK�D/G�^/a�¤(DM^FD/E6_HS2D�Z�P8EHX�I�Z�=2DFX�?DFP�Z\`HK � AFX�W���WHA"ZJAsZ\`�A"ZBAFG�K�_HG\K�W]=@I$Z\K�WQZ�D&LNK-SY=2XHKiA�G\SY^CG\K�S@A"Z\K�WpaA[<nb>`�KsP8EHXVI$Z�=2DFXV?-A�G\K � �&A�X�W�� � a67kP;^FD/E�D/L]Z\AF=YX�ACS2=YXHK&l~=YZ�`H=2X�EHX�I�K�GUZJA�=2X[Z:^FoNZ�`HKgZ\`HK�D/G�^m=@? � � ¦ � �� ����� ��xa

LN<Qb>`�K�P8EHX�I�Z�=2DFX�?rAFG�K � � A�XVW����Fa�7kPQ^FDFE�D/L]Z\AF=YX A�S2=YXHK±l~=YZ�`H=2XfEHXVI�K�G�Z\AF=YX[Z:^/o6Z�`�K�Z\`HK�D/G�^�=2?¦ � �� ����� ��xa

Ii<Qb>`�KsP8EHXVI$Z�=2DFXV?-A�G\K � �&A�X�W�� � a67kP;^FD/E�D/L]Z\AF=YX�ACS2=YXHK&l~=YZ�`H=2X�EHX�I�K�GUZJA�=2X[Z:^FoNZ�`HKgZ\`HK�D/G�^m=@? � � ¦ � �� ����� ��xa

WV<Qb>`�K�P8EHX�I�Z�=2DFX�?rAFG�K � � A�XVW�� � a�7kPQ^FDFE�D/L]Z\AF=YX A�S2=YXHK±l~=YZ�`H=2XfEHXVI�K�G�Z\AF=YX[Z:^/o6Z�`�K�Z\`HK�D/G�^�=2?¦ � �� ����� ��xa

K*<Qb>`�K~P8EHX�I�Z�=2DFX�?�AFG�Kc?�=2X�5 � <jAFX�W�� � a�7kPp^/DFEgDFL]ZJA�=2X&AMS2=2XHKcl~=YZ�`H=2X�EHX�I�K�G�Z\A�=2X[Z:^Fo"Z\`HK~Z\`HK�D/G�^4=2? � � ¦ � �� ����� ��

¾F¾���h[e4EHS�ZB¾[�]�i¾F¾C� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu�_HS2D�Z�Z�=2XHqgZ\A�X�5�N<~SY=2XHK�AFG�S2^�"µ�ac��=2dFK�X ��� $���ZJA�X�5 �N< ��� o�=@W]K�X[Z�=YP8^QZ�`HK6X�K�l d"A�G\=2AFLHSYKi? ��������A�X�W ��� ����Z\`�A"ZBG\K�WHE�I�K-Z\`HK6Kih/EVA"Z�=2DFXZ\D

Z\`HK-K�h[E�A�Z�=2DFXD�PjA4S2=2XHKFo��!� ��� $"� ��� ��� ��� aA[< �QA�X�WmI�D[?�5 �N<$aLN< ���-AFX�WQI�D/?�5�N<�aIi< � �-AFX�WCZJA�X�5 �N<�aWV< �QA�X�WQZ\AFX�5��<$aK*< �QA�X�W ��a

¾F¾���h[e4EHS�ZB¾[�F�F¾F¾4� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuj_HS2D�ZUZ\=YX�q&A�?\h[E�A�G\K�G�D(D�Z~S2=YX�K�A�G\S2^� ¶ ac��=2dFK�X � $����$# � � �!% �&� 58l~`�K�G\K'�No(%�o�A�X�W � A�G\KQI�DFX�?UZ\AFX/ZJ?\<�oj=2WHK�X[Z�=YP8^rZ�`HKXHK�l d*AFG�=@A�L�SYKi? �������

AFX�W �)������oVAFX�WZ�`�KsXHK�l I�DFX�?UZ\AFX[Z\?* � A�X�W�* � Z�`�A�ZBG�KiW]E�I�K-Z�`HKsK�h[E�A"Z\=YD/XmZ�D&Z\`HKsKih/EVA"Z�=2DFXmDFPjACSY=2XHKFo������� $"* � �)����� � * � aA[< �!� ��� $ ��o���� ��� $&+ ��o)* � $z� �$# ����%�oHA�X�W�* � $ � aLN< � � ��� $ � � o�� ����� $&+ ��o�* � $����$# ���!%po�AFX�W'* � $ � � aIi< �!� ��� $ ��o���� ��� $�� � ��o)* � $�� � # � �!%po�AFX�W�* � $ � aWV< � � ��� $ ��o�� � ��� $�� �!+ ��o)* � $z� �$# ���!%�oHAFX�W�* � $ � aK*< �!� ��� $ ��o���� ��� $&+ ��o)* � $z� �joHAFX�W�* � $ � a

¾F¾���h[e4EHS�ZB¾[� ³ ¾F¾4� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuj_HS2D�ZUZ\=YX�q&AFXm=YX(dFK�G\?�K�l~=�Z\`m?�=2XHqFEHS@A�G\=YZ:^� ¹ ac��=2dFK�X � $����]5 �(, � <�5,l~`HK�G\K-�6A�X�W � AFG�K>I�D/X�?:ZJA�X[Z\?J<$o"=@W]K�X/Z\=�P8^6Z�`HK>XHK�l�d"A�G\=2AFLHS2K�?���� ����A�X�W �)������oFAFX�W

Z\`HK�XHK�l�I�DFXV?:ZJA�X[Z\?.* � A�X�W/* � Z�`�A�Z�G\K�W]E�I�KjZ�`�K�K�h[E�A�Z�=2DFXMZ�DcZ�`HK�Kih[E�A"Z\=YD/X-D�PHA>SY=2XHK/o �!� ��� $0* � �)����� � * � aA[< �!� ��� $ ��o���� ��� $�� �]5 �1, � <$o2* � $��No�A�XVW'* � $�¾HaLN< � � ��� $ � � o�� ����� $&+ ��o�* � $"�NoHAFX�W�* � $ � aIi< � � ��� $ ��o�� � ��� $�� �]5 � ��� <$o2* � $��No�A�XVW'* � $�¾HaWV< � � ��� $ ��o�� � ��� $ �1, � o)* � $ � �3�NoHA�XVW4* � ${¾HaK*< �!� ��� $ ��o���� ��� $ � �� o)* � $ � �3�NoHA�XVW4* � ${¾Ha

¾F¾���h[e4EHS�ZB¾[�"µ[¾F¾4� ¶&³ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuj_HS2D�ZUZ\=YX�qg_ND"l�K�G-�*y ³ S2=2XHK�AFG�S2^

Page 10: Introductory Physics Problems David J. Jeffery Department of

¹ v�`�AF_]Z�a>��®REVA�X[Z�=YZ�=2K�?�oH�cXH=YZ\?�o�v�D/X(dFK�GJ?�=YD/X�?�o(¯�KiAF?�EHG�K�e&K�X[Z�o�¤(=2qFX�=��VI�A�X[Zc|�=Yq/EHG�Ki?�oHAFX�W�cX�I�K�G�Z\A�=2X[Z�=2K�?

�/º(ac��=2dFK�X � $�� � ��� � 58l~`HK�G�K �4=@?�A6I�D/X�?:ZJA�X[ZJ<�o/=@W]K�X/Z\=�P8^gZ\`HKBXHK�l{d"A�G\=2AFLHSYKi? � ����� A�XVW � ����� o(A�X�W&Z\`HKBX�K�lI�DFX�?UZ\AFX/ZJ? * � A�X�W�* � Z\`�A"ZcG\K�WHE�I�K�Z�`�K-K�h[E�A"Z\=YD/XnZ\DgZ�`HK-Kih/EVA"Z�=2DFXD�PjAgSY=2XHK/o�� � ��� $�* � � � ��� � * � aA[< �!� ��� $ ��o���� ��� $ ��o)* � $0�No�A�XVW'* � ${¾HaLN< �!� ��� $ � � o��)����� $ � ��� � o�* � $"�No�AFX�W4* � $"�NaIi< �!� ��� $ ��o���� ��� $ � ��� � o)* � $��NoHA�X�W�* � $�¾HaWV< �!� ��� $ ��o���� ��� $&+ ��o)* � $ � ���No(AFX�W�* � ${¾�aK*< �!� ��� $ � � o��)����� $ � ��o)* � $ � ���No(AFX�W�* � $�¾Ha

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾���h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�A/I�G\K�T�P8D[DFZ>I�DFX(dFK�G\?�=2DFX�Fa~�BegK�G�=@I�AFX�`(^]W]G\AFEHS2=2I-K�XHqF=2XHK�K�GJ?cD�P Z\K�XxE�?UKgAFI�G�K�T�P8K�K�ZcZ\DQe&K�A/?UE�G�K6d/DFS2EHe&K6D�P�l�A�Z�K�GiaR�BX�AFI�G�K�T�P8D(DFZB=2?Z\`HKRAFegD/EHX[Z;D�Ppl>A"Z\K�GjZ\`�A"Z�l~=YS2SVI�D"dFK�G�AM�VA"Z�AFI�G\K~D�PpS@A�X�W�Z�DC�~P8D(DFZ�a�¤]A*^ ³ � ¾�=YX�DFP�GJA�=2XgP8K�S2SVD/XCA-_HS@A�=2XDFP ³ ¾jO(e ��a�£cD"l�e�AFX[^QAFI�G\K�T�P8K�K�Z�DFP�l>A"Z\K�G�P8K�S2S ��5, BD�Z\K��M?\h[E�A�G\K�eg=2S2K-K�h[E�A�S@? ¹ µ[¾4A/I�G\K�?�a <

¾F¾���h/P8EHS2S�¾/¾/��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�|�K�G\eg=pD/XmSYKiI$Z�E�G�Ki?~A�X�WQe&=2I�G�DFTkI�K�X[Z�EHG\=2K�?� ª�¬"¨ �V«������V¬ ��­�� |HK�G\e&=�o�eg=@I�G\D�T!I�K�X[Z�EHG\^Fo(e&=2I�G�D]I�K�X[Z�EHG\^

�]a~�RI�I�D/G\WH=YXHqmZ\D�£B¿�»wT ½ o��;XHG\=2I�D�|HK�G\e&=;D/X�I�K�XHDFZ�KiW�Z�`�A�Z4A�?UZ\A�XVWHA�GJW ¶ ¾me&=YX(E]Z\KCEHXH=2dFK�G\?�=YZ:^�S2K�I$Z\EHG\Kl>AF?-X�K�A�G\S2^xAme&=2I�G�DFTkI�K�X[Z�E�G�^/a � � � � � �FEHS2=@A�X�^FKiA�Gio�l~`H=@IJ`�=@?-K��HAFI�Z�S2^ ³/¹/¶ a � ¶ WHA*^]?�o�=@?6K��HAFI$Z\SY^³ � � ¶F¶ º ¹ ����¾��4?�K�I�DFX�W�?�ag�BI$Z\E�A�S2S2^Fo�AmI�D/X(dFK�X�=YK�X/Z�e&XHK�e&DFX�=2Ig=@?�Z�`�A�Z-AQ^FKiA�GM=@? ������¾��p?�Z�Dl~=�Z\`H=2X¾ � ¶�� u�Z�`�=2?~=@?�A:E�?UZRA&I�D/=YX�I�=2WHK�X�I�KFa~5,¯�D/G�KMK��]A/I$Z\SY^nA��/EHS2=2AFX^/K�AFG�=@?M� � ¾F¾Fµ ¶ ¾ ½F¹ � �x�i¾��p?�a <A[<n£BD"l�S2DFXHq&=@?cAge&=2I�G�DFTkI�K�X[Z�EHG\^�=2XQe&=2X[EHZ�K�?BAFI$Z\E�A�S2S2^ �LN<n»{`VA"Zc=@?�Z�`HK-_NK�GJI�K�X/ZJA�q/KMWH=���K�G\K�X�I�KMLVK�Z:l�K�K�XmSYKiI$Z\EHG�K-AFX�Weg=@I�G\D�T!I�K�X[Z�EHG\^Fa

¾F¾���h/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujS2=Yq/`[Z�Z\G\A*d/K�SNZ�=2e&KMZ�Dn¤(E�X³ a~b>`HK~e&KiA�X�¤(EHX]T!�;AFGUZ\`4W]=@?:ZJA�X�I�KFoV� � µ ½F¹ �g��¾�� � I�emo/=2?jAMI�D/X(dFK�X�=YK�X/Z�?UZ\AFX�WHA�GJW6E�XH=�Z�=2X�AF?UZ�G\DFXHD/es^/a;5,�BSYSA/?:Z\G�D/XHDFe4^n=@?Mv>�-¤�oNXHDFZM¯�²6¤L(^Z�`�K4L(^Fa <�b>`H=@?REHXH=YZ�=@?RI�A�S2SYKiWZ�`HK&AF?UZ�G\DFX�DFe&=2I�A�S�E�XH=�ZiaM��=2dFK�X�Z�`�K?�_VK�K�WD�P�SY=2qF`[Zc=@? ³ � ¾F¾ ����¾�e���?�oHl~`VA"Z~=2?~Z�`HK-S2=Yq/`[Z�Z\G\A*d/K�SNZ�=2e&KMP8G�D/e Z\`HKs¤(EHXm=2XQe&=2X[EHZ�K�?�

¾F¾���h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj_HE�S2?\A�G~_NK�G\=YD]WH?>=2X�A&WHA*^µ�a~9;EHS2?\A�G�9�¤]¿ � ½/³ º � �]��`�AF?jG\D�ZJA"Z\=YD/Xg_NK�G\=2D(Wm�/a ¶/¶ º ¼ ¾ ¹ µFµ ¼F¼ ºF�/º ¶ 5 ³ <]e&?�o�l~`�K�G\K~Z�`HKBLHG\A/IJOFK�Z�K�W4X(EHesLNK�G=@?>Z�`�K-EHX�I�K�GUZJA�=2X[Z:^�=YXZ�`�K-S2A/?:ZcW]=2qF=YZ�aA[<n£BD"l�e�A�X(^�Z\=Ye&Ki?cW]D(K�?�Z\`HK-_HEHS@?�AFG~G�DFZ\A�Z�KM=YXr� � ¾gWHA*^]?>OFK�K�_H=2XHqgZ�GJAFIJO�DFP�?�=Yq/XH=Y�VI�AFX/Z���q/EHG�Ki? �LN<Q£BD"l�e�A�X(^mZ�=2e&K�?MW]D(K�?BZ�`HKg_HEHS@?\A�G�G�DFZ\A"Z\Ks=2X�=2X�K��]A/I$Z\SY^r�&WHA*^�58=�a K/aYoj� � ¾/¾F¾F¾ � � � WHA*^]?\<cOFK�K�_H=2XHq

Z\G\A/IJO�D�Pj?U=2qFX�=��VI�A�X[Z>��qFE�G�Ki?�=2X�?�D�P,AFGcAF?>^FD/EHG~I�AFS2I�EHS2A�Z�D/G>AFSYS2D"lc?�

¾F¾���h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujS2K�A�_m?�K�I�D/X�WH?¶ a~b>`HKRe&K�A�XC?�DFS@A�G�WHA*^4=@?�O[X�D"l~X&Z�D6=2X�I�G\K�A/?UKR?UKiI�EHS@A�G\SY^4L(^gAFLVD/E]ZR� � µ����¾ ��� ?UKiI�DFXVWH?�_NK�G>I�K�X/Z\EHG\^gW]E�Ke�A�=2XHS2^mZ�DQZ�`HK4Z�=@WHAFS�=2X[Z�K�G\A/I$Z�=2DFXxD�PjZ\`HK�¯�D(DFXxAFX�W�¤(E�X�agv�EHG\G�K�X[Z�S2^FoNZ�`HK&e&K�AFX�?�DFS@A�GMWHA*^m=2?MA�LNDFEHZ¼/¹ o µ/¾F¾�a ¾/¾/�g?�K�I�D/X�WH?BSYD/XHq�a ������ � ��DFZ�`�_�AFGUZJ?s5�A/<RA�X�W�5,LV<RA�G\Ksh[EHK�?UZ�=2DFX�?RD�P�`�D"l�S2DFX�qQA"ZMACq/=Yd/K�XGJA"Z\KMWHD[Ki?~AgqF=2dFK�XmA�e&D/EHX[Z�ZJA�O/KRZ\DCAFI�I�EHe4EHS2A�Z�K/aA[<n�BLVD/E]Zs`HD"l D�P Z\K�X�W]D(K�?-AmS2K�AF_�?�K�I�DFX�WxXHK�KiWxZ�D�LNK�=YX[Z�G\D]W]E�I�K�W�=YX�?UZ\AFX�WHA�GJW�Z\=Ye&KC=2XrDFGJW]K�G�Z\DO/K�K�_?UZ\AFX�WHA�GJWA�X�W?UD/S2AFG�Z�=2egK6?�^(X�IJ`HG\DFXH=2��KiW �

LN<n7kP>Z\`HKCI�EHG\G\K�X[Z6G\A�Z�K&D�P>=2X�I�G\K�A/?UK&=2XrZ�`HKCWHA*^�I�D/X/Z\=YX(EHKi?�o�A�LNDFE]Z6`�D"lfS2DFXHq�=2Xr^FK�AFG\?Ml~=2S2S�=�ZsZ\A�O/KLNK�P8D/G�K�A-S2K�A�_C?�K�I�DFX�WC=2?;XHK�KiW]K�WCW�A�=2SY^�u�=�a KFa2o(`HD"lwSYD/XHq6EHX[Z�=2SVZ�`HKRegKiA�Xn?�DFS@A�G�WHA*^4=@?�A�LNDFE]Z ¼/¹ µ[¾H�?�K�I�DFX�W�? �

Page 11: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~� ®RE�A�X[Z\=�Z\=YKi?�o��BXH=YZ\?�oNv�DFX(dFK�G\?�=2DFX�?�o[¯�K�AF?�EHG\K�e&K�X[Zio�¤(=Yq/XH=Y�VI�AFX/Zc|�=2qFEHG\K�?�oHA�X�W�cXVI�K�G�Z\AF=YX[Z\=YKi? º

¾F¾���h/P8EHS2S�¾/¾ ¹ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�?U=2e&_HSYK-K�G�G\DFG>_HG\DF_VA�q/A�Z�=2DFX¹ ac¤]A*^�^FD/E-`�A*dFK�Z:l�DcK��(_NK�G\=2egK�X[Z\A�S/d"A�S2EHK�?���A�XVW��Co"A�XVWMZ�`HKi?UK�W]=���K�G�P8G\DFezZ�`HK;Z�G\EHK;d"A�S2EHKi?�L(^MEHXHO(XHD"l~XW]K�d(=2A�Z�=2DFX�?�����A�XVW���� G\K�?�_VKiI$Z\=Yd/K�S2^Fa�°BP�I�DFE�G\?�KFo/^FDFECWHDFX�· Z�O(XHD"lwl~`�A�Z;Z�`�KRW]K�d[=@A"Z\=YD/X�?;AFG�K/oFLHEHZ�^/DFEKi?:Z\=Ye�A"Z\K�Z�`HK�=YG>e�A"�]=2esEHe�AFL�?�DFS2E]Z�K�d"A�S2EHK�?�Z�D&LNK/��A�X�W � u�=�a KFa2o� ������ �CA�XVW � ������� � =@W]KiA�S2SY^/a�b>`�K�CAFX�W � h[E�AFX[Z�=YZ�=2K�?~A�G\K�^FDFE�G�Ki?:Z\=Ye�A�Z�K�WEHXVI�K�G�Z\AF=YX[Z\=YKi?�D/G~SYKi?�?~I�DFG\G�KiI$Z\SY^�5,LHE]ZcdFK�G�^CI�DFe&e&DFXHS2^H<�^FDFE�GK�G�G\DFGJ?�a;»xK6A/?�?�EHe&K ������� ���A�X�W � ����� ����u�Z�`�=2?B=2?~DFP Z�K�XmZ�`HKsI�AF?�K-K�?�_VKiI�=@A�S2SY^Q=YX�I�D(DFOFKiW(TkEH_Q=2X[Z�G\D_H`(^]?�=2I�?>S2AFL�?�a�»�K-l~=YS2S�XHD"lz_HG\D"dFKM?UD/egK-?�=Ye&_HS2K-K�G\G\DFG�_HG�D/_�A�q[A"Z\=YD/XCP8DFG\esE�S2AFKFaA[<Q¤]`HD"l�Z\`�A"ZjZ\`HKcEHXVI�K�G�Z\AF=YX[Z:^6=2X�� ��� =@?$� ��� a ������ � �BW�WVy"?�EHL]Z\G\A/I$ZjZ�`�K~Z�G\EHK658L�E]Z;EHXHO(XHD"l~XN<d"AFSYEHKi?���GJ?:Zia

LN<¤]`HD"l�Z\`�A"ZjZ\`HK� �� � ��� �K�G�G\DFG�=2X���� =@?$����� �� �4� ��� ����Z�D��i?:ZjDFGJW]K�Gj=YX�?�e&AFSYS�� ���{A�X�W � ���h[E�AFX[Z�=YZ�=2K�?�a�b>`�KBG\K�S@A"Z�=2dFK~K�G�G\DFGJ?�A/WHW&DFXCe4EHSYZ�=2_HSY=@I�A�Z�=2DFX�u�Z�`�=2?�=@?;A6q/K�XHK�G\AFS�A�XVW�dFK�G�^4E�?UK�P8EHSNG�EHS2KFa������ � b�Dx�i?:Z�DFGJW]K�GRe&K�A�XV?BZ\`�A"ZM^FD/E�I�AFX�XHK�qFS2K�I$Z�`H=2qF`HK�GRD/G\W]K�GBZ\K�G\e�?BS2=YO/KQ5 � ���R< � o�5 � ���g< � oAFX�W�� � � �H5�� �4<"! �-AF?�LNK�=2XHq�XHK�qFS2=Yq/=YLHS2^n?�e�A�S2S�a

Ii<n»{`VA"Zc=@?�Z�`HK&��?UZ~DFGJW]K�G�P8D/G�e4EHS2AsP8DFG>K�G�G\DFG�=YX$#�5%�R<$o�l~`HK�G\K&#�5 �N<�=@?~A�X(^CW]= �NK�G�K�X[Z�=@A�LHS2K�P8EHX�I$Z\=YD/X ������� � �j�]_�A�XVW�#�5%� � ����<�=YX�A&b�A*^[S2DFGi· ?�?�K�G\=2K�?>A�LNDFE]Z���AFX�WnZ�G\EHX�I�A�Z�KMZ\D�i?:Z~D/G\W]K�G�a

WV<n»{`VA"ZB=@?>Z�`�K���?UZcDFGJW]K�G>P8D/G�e4EHS2A4P8D/G>Z�`HK6G\K�S@A"Z\=Yd/KMK�G\G�D/G�=2Xr� ��� � ������ � �B?�KMZ�`HKsG�Ki?UEHSYZcD�P�Z�`�K_VA�G�Z-5�I�<>AFX�?Ul�K�Gia

K*<n»{`VA"Z�=@?jZ\`HKs�i?:Z�DFGJW]K�GjP8D/G�e4EHS@A�P8DFG�Z\`HKBG\K�S@A"Z\=Yd/K~K�G\G�D/G�=2X'� ��� � ������ � v�DFesL�=YXHKcZ�`HKc_VA�G�ZR58LV<AFX�Wr5,W�<>AFX�?�l�K�G\?�a

¾F¾���h/P8EHS2S�¾/¾[º"¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujK��]AFe&_HSYKMK�G�G\DFG>_HG\DF_�AFq/A�Z�=2DFXº(a~�BX�?Ul�K�G�Z\`HK�P8DFS2SYD"l~=2XHqBK�G�G\DFG�_HG\DF_�AFq/A"Z\=YD/Xsh[EHK�?UZ�=2DFXV?�E�?�=2XHq�Z�`HK���?UZ�D/G\WHK�G�K�G\G�D/G�_HG\DF_VA�q/A�Z�=2DFXMP8D/G�e4EHS2AFKAFX�Wnl~=YZ�`�DFE]Z~E�?�=YX�q&AgI�AFS2I�EHS@A"Z�D/G�a>5 ��D/E�A�G\KR=2XA4S@A�Leg=@?�K�K�X?\I�(K�XHKMA�X�WW]D/X�· Z~l>A�X[Z�Z�D&LVDFZ�`HK�G~l~=�Z\`A�S2D�Z4D�P~P8E�?\?U=2XHqVa <�¿~K�Z\A�=2X�D/XHSY^r?�=Yq/XH=��NI�A�X[Z-��q/EHG\K�?�a�¿~K�e&K�e4LVK�GsK�G�G\DFGJ?-A�G\K�Z:^(_H=@I�A�S2S2^xD/XHSY^±��T!W]=2qF=YZA/I�I�E�G\A�Z�K�DFXHS2^FaA[<C»{`VA"Zc=@?�Z�`HK6?�EHe�DFP�� � º���¾ � ³ A�X�Wm¾ � ¼ � ��¾ � ��AFX�W=�ZJ?~K�G\G\DFG �LN<n»{`VA"Z�=@?;Z�`HKR_HG�D]W]EVI$Z;DFP�� � º ��¾ � ³ A�X�Wn¾ � ¼ ����¾ � ��58Z�D4I�DFG\G�KiI$Z;?�=Yq/XH=Y�VI�AFX/Z;��qFEHG\K�?J<jAFX�WgZ�`HKRK�G\G�D/G

=2XZ�`HK-_�G�D]W]E�I�Z�������� � �;?UZ�=2e&A�Z�K�Z�`�K-G�K�S2A�Z�=2dFKMK�G\G�D/G\?�I�G\E�W]K�SY^/aIi<n»{`VA"Z~=2?M� � º �r¾ � ³ W]=Yd(=@W]K�WQL(^C¾ � ¼ � �r¾ � �g58Z�D�I�D/G�G\K�I�Z�?�=Yq/XH=Y�VI�AFX/Z���q/EHG�Ki?\<�A�XVW�Z�`�K�K�G�G\DFG�=2XnZ\`H=2?d"AFSYEHK �������� � ��?:Z\=Ye�A"Z\K�Z�`HK-G\K�S@A"Z\=Yd/K�K�G�G\DFGJ?�I�G\E�W]K�S2^Fa

WV< ��D/E�A�G\KRe4EHS�Z\=Y_�SY^(=2XHq&Z�D/qFK�Z\`HK�Gc?�=Y�nd"A�S2EHK�?>KiAFIJ`l~=�Z\`�� � K�G\G�D/G�a�»{`�A�Z>=@?>Z\`HK-_VK�G\I�K�X[Z\AFqFK�K�G\G�D/G=2XZ�`HK-_�G�D]W]E�I�Z�

¾F¾���h/P8EHS2S�¾/¾ ½ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�b�A*^[S2DFGi· ?�?�K�G\=2K�?¼ ac¤(D/e&Kc`�A*dFKc?�K�K�X�b�A*^(S2DFGi· ?j?�K�G\=YKi?�o[?UD/e&Kc`�A*dFK>XHDFZ�a�»�KBl�DFX�· Z�_HG\D"dFK~=YZ*)[l�K/· S2SBA:E�?UZ�l~G\=YZ�K~=YZ�W]D"l~X�a��cX(^?�E]�CI�=2K�X[Z�S2^nW]= ��K�G\K�X[Z�=@A�LHS2K�P8EHX�I�Z�=2DFXm=YXQZ�`�K�X�K�=2qF`(LVD/G�`�D[D]WnD�P�Ag_NDF=2X[Z�� � I�AFXQLNK-A�_H_HG\D*�]=Ye�A�Z�K�WnL(^CAb�A*^(SYD/G�· ?B?�K�G\=YKi?cK��(_VA�X�?�=YD/X�A�LNDFEHZ�� � P8D/G�AQ?UE]�CI�=YK�X/Z\SY^�?�e�A�S2S�X�K�=2qF`(LVD/G�`�D[D]WpaMb>`HKgqFK�XHK�GJA�S�P8DFG\esEHS@A=@?

#�5�N< $,+-./ �5�1, � � <

.0�1 #�2

.435� � <�

l~`HK�G�K�# 2.435� � <;=2?�Z�`�K 0 Z\`QW]K�G�=2d"A"Z\=Yd/KBD�P5#K�d"A�S2E�A"Z\K�WQA"Z�� � a�b>`�KBZ\K�G\e&?�=2XCZ\`HK�?�K�G\=2K�?�A�G\KBS@A�LNK�S2K�WCL(^Z\`HK�=2G>_VD"l�K�G�D�P�5 ��, � � <$u~5��, � � < � =@?���K�G\D�Z\`nDFGJW]K�G�o�5� , � � < �B=@?R�i?:Z>DFGJW]K�G�o�5��, � � <���=@?>��X�WCD/G\WHK�GioAFX�Wr?UD�D/X�ab>`�Knb�A*^(S2DFGi· ?M?�K�G\=YKi?-=@?6I�D/X[d/K�G\qFK�X/ZC5,=�a KFa2o�WHD[Ki?UX�· ZsK��]_HSYD]W]K&Z\D�=2X]��XH=YZ:^H<�P8DFGs?�E]�CI�=2K�X[Z\SY^

?�e�A�S2S�5 �(, � � <$a�b>`HK~?Ue�AFSYS2K�G>5� , � � <�=@?�Z�`HK�SYKi?�?�=2e&_VD/GUZJA�X[Z�Z�`HK>`H=2qF`HK�G�DFGJW]K�G�Z�K�G�e�?�a�7!Xg_H`(^(?�=@I�?>5,AFX�WDFZ�`HK�G���K�S@WH?�XHD-W]D/EHL]ZJ<�oFD/XHK>=2?�DFP Z�K�X&=2X[Z�K�G\K�?UZ�KiW6=2XgZ�`HK~LNK�`�A*d(=2DFG�XHKiA�Gj?UD/e&K�=2e&_VD/GUZJA�X[Zj_VD/=YX[Z � � oFAFX�W?�DgZ�G\EHX�I�A�Z�Ki?�Z�`HK6b�A*^(SYD/G�· ?�?�K�G\=2K�?�Z�Dg��XVWAFX�?U=2e&_HSYK-AF_H_HG\D*�(=2e�A"Z\KRK��(_�G�Ki?�?�=YD/XCP8D/G>Z�`HK-XHK�=Yq/`(LVD/G�`HD(D]W

Page 12: Introductory Physics Problems David J. Jeffery Department of

¼ v�`�AF_]Z�a>��®REVA�X[Z�=YZ�=2K�?�oH�cXH=YZ\?�o�v�D/X(dFK�GJ?�=YD/X�?�o(¯�KiAF?�EHG�K�e&K�X[Z�o�¤(=2qFX�=��VI�A�X[Zc|�=Yq/EHG�Ki?�oHAFX�W�cX�I�K�G�Z\A�=2X[Z�=2K�?

DFP � � a�|HD/G~K��HA�e&_HS2K

#�5�N< $���� ���#�5� � <� ��K�G�DFZ�`DFGJW]K�G~AF_H_HG\D*�(=2e�A"Z\=YD/X )#�5� � < � 5�1, � � < #���5� � <� ��?UZcDFGJW]K�G>AF_H_HG\D*�]=Ye�A"Z\=YD/X )#�5� � < � 5�1, � � < # � 5� � < � 5��, � � < �

� # � � 5 � � <� �"XVWQD/G\WHK�G~A�_H_�G�D*�]=2e&A�Z�=2DFX�a

b>`HKs��K�G\D�Z\`�DFGJW]K�G~K��]_�A�X�?�=2DFX�oNA�_H_HG\D*�]=Ye�A�Z�K�?�Z\`HK6P8E�X�I$Z\=YD/X�AF?cAnI�DFXV?:ZJA�X[Z*)�Z�`HKQ��?UZcDFGJW]K�GcK��]_�A�X�?�=2DFXAF_H_HG\D*�(=2e�A"Z\K�?NZ�`�K�P8EHX�I�Z�=2DFX6L(^MA>SY=2XHK;Z�`�A�Z�=2?�Z\AFXHqFK�X/Z�Z�D~Z\`HK�P8EHXVI$Z�=2DFX4A"Z � � )"Z\`HK��"XVWMDFGJW]K�G�K��]_�A�X�?�=2DFXAF_H_HG\D*�(=2e�A"Z\K�?�Z�`HKMP8E�X�I$Z\=YD/XL(^nA&h[E�A/W]G\A�Z�=@IRZ�`�A�Zc=2?�ZJA�XHq/K�X[Z>Z�D&Z�`�KMP8EHX�I$Z\=YD/X � � aA[<n¡RGJA*l AmqFK�XHK�GJA�S�P8E�X�I$Z\=YD/X�DFX�Z�`HKQv�AFGUZ\K�?�=2AFXx_�S2AFXHKCA�X�WrA�ZsAmqFK�X�K�GJA�Sj_NDF=2X/Z � � ?\IJ`HK�e�A"Z\=2I�A�S2SY^?�`HD"lz`HD"l�Z\`HK-��K�G�DFZ�`�op�i?:ZioHA�X�Wm�"X�WD/G\W]K�G~A�_H_HG\D*�]=Ye�A�Z�=2DFX�?�Z�DgZ\`HKMP8EHX�I�Z�=2DFXmLVK�`�A*dFK/aLN<Qb�A*^(SYD/G>K��]_�A�XVW

#�5��< $ �� � �

Z\Dn�"X�WQDFGJW]K�G>AFLVD/E]Z�� � ${¾Hac5�£cK�G�K �1, � � =@? A:E�?UZ���oHDFP�I�DFEHGJ?�KFa <Ii<Qb�A*^(SYD/G>K��]_�A�XVW #�5��< $ + � � �Z\Dn�"X�WQDFGJW]K�G>AFLVD/E]Z�� $�¾Ha

WV<Qb�A*^(SYD/G>K��]_�A�XVW#�5��< $ �

+ � � �Z\Dn�"X�WQDFGJW]K�G>AFLVD/E]Z�� $�¾Ha

K*<Qb�A*^(SYD/G>K��]_�A�XVW #�5�N< ${?�=YX�5 �N<Z\D ³ GJW�DFGJW]K�GMAFLVD/E]Z�� $ ¾�ag BD�Z\K4Z\`�A"Z �re4E�?:Z-LNK�=YX�GJAFW]=@A�X�?RP8D/GMZ�`HK�b�A*^[S2DFGi· ?BK��(_VA�X�?�=YD/X�Z\Dl�DFG\O4P8DFG�Z�`HKRZ�G\=Yq/DFXHD/e&K�Z�G\=@I>P8EHX�I�Z�=2DFX�?�a�b>`H=@?;=@?�LVKiI�A�EV?UKBZ�`HKMW]K�G\=2d*A�Z�=2dFKi?�D�P�Z�`HKi?UKBP8EHX�I$Z\=YD/X�?>A�G\KWHK�G\=Yd/K�WQE�?U=2XHq&GJAFW]=@A�X�?�a

P\<mb�A*^(SYD/G>K��]_�A�XVW #�5�N< $�I�D/?�5 �N<Z\Dn�"X�WQDFGJW]K�G>AFLVD/E]Z�� $�¾Ha

Page 13: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � >S1 j %8*I=!1)>�EG*[? >a&AN��Z*I>a1)=!&X;<*IHJE

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾[�sh[e4EHS�ZB¾/¾H�i¾F¾ ³ � ³ K�A/?U^�e�A�Z�`�ujZ\G\A*d/K�SNZ�=2e&KMP8G�D/e�W]=@?:ZJA�X�I�K*y�?U_NK�KiWpuj²MXHD*�]d[=2S2SYK�Fa ��D/E�`�A*dFK�A:EV?:Z4Z�GJA*dFK�S2K�WxZ\`HKnL�A/IJOxG\D/A/WH?MP8G\DFe ²MXHD*�]d(=YS2SYKCZ�D� RAF?�`[d(=2SYS2KFa'��D/EHG&A*dFK�GJA�q/Kg?�_NK�K�W�l�A/?¹ ¾-e&_H`�o]LHE]Z>^FD/E�D]I�I�A/?U=2DFXVA�S2SY^g`H=YZ>AFXC=YXV?:ZJA�X[Z\AFXHK�D/E�?;?�_VK�K�W�DFP;� ³ ¾-e&_H`�a~5�v�D/EHS@WCLNKB^FD/E�· G�Kc`VA�EHS2=YX�ql~`H=YZ�K4SY=2qF`[Z\XH=YX�q�a <!��DFEHG�D]W]DFe&K�Z�K�GBZ�GJA*dFK�S�W]=@?:ZJA�X�I�Ks=@?�� ¶ ¾&e&=YS2K�?�aR£BD"l�SYD/XHqC`�A*d/K6^FD/E�LVK�K�X�D/X�Z�`�KG\D/A/W �

A[<��*y"µ4`HD/EHGJ?�a LV<��i¾g`HDFEHGJ?�a I�<�µ�a2�*ºs`HD/EHG\?�a W�< ¹ `HD/EHG\?�a Ki<>AFLVD/E]ZB�g`HDFE�G\?�a

¾F¾[�sh[e4EHS�ZB¾/¾/�F¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u;A*d/K�GJA�q/KB?U_NK�KiWD"dFK�G�Z:l�D&_H`�AF?�K�?�]a ��D/E�e&D"d/K ³ e&K�Z�K�GJ?6W]E�KCl�Ki?:ZsAFX�WxZ�`HK�X�o�l~=�Z\`HDFE]ZgAWH=2?\I�D/X/Z\=YX(EHD/E�?6IJ`�AFXHqFK&=2X�W]=YG\K�I�Z�=2DFX�o�qFDmD/X/Z\DAQI�=2G\I�EHS2AFGB_�A�Z�`�5�I�=2G\I�SYK � � � �����±��e&K�Z\K�GJ?\<cLVK�X�W]=2XHqQZ�DCZ\`HKgSYK�P Z�EHX[Z\=YS�^FD/E�A�G\K6`HKiAFW]KiW�W]EHK4K�AF?UZ�ab>`H=@?M`�A/?BZJA�O/K�X�^/DFE��i¾Q?�K�I�DFX�W�?�a6»{`VA"Z-=2?�^/DFEHG-A*dFK�G\AFqFKs?�_NK�K�WxA�_H_�G�D*�]=2e&A�Z�K�SY^�� ������ � ¡RGJA*l AW]=@A�q/G\AFemaA[<nAFLVD/E]Z ³ e��"?�aLN<QAFLVD/E]Z6� � ¶F¶ e ��?JaIi<QAFLVD/E]ZB¾ � ³ e��"?�aWV<QAFLVD/E]Z6� ¶ � ¶ e ��?JaK*<QAFLVD/E]ZB¾ � ½ e��"?�a

¾F¾[�sh[e4EHS�ZB¾/¾/�H��¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujS2=Yq/`[Z�XH=2XHq�A�X�WnZ�`(EHXVW]K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ¾�T ¶

³ a~b>`HK�?�_VK�K�W�D�P>?UD/EHX�Wx=YX�AF=YGC5�A"Z���A"Z�e _HG\K�?\?UEHG\K&A�X�Wr��¾���v><�=@? ³ µ ³ e ��?$a���SY=2qF`[Z\XH=YX�qQ�NAF?�`xD]I�I�EHGJ?� � ¶ O(e�A*l>A*^Fa�£cD"lzSYD/XHq&EHX[Z�=2S�^FD/En`HKiA�G>Z\`[E�X�W]K�G �

A[<~�F� ¼ � º�?�o LV<>¾ � ¾F¾FµFµ;?�o I�<�µ � µ;?�o W�< ¶ � ¶ ?�o Ki<�� � ¶ ?�a

¾F¾[�sh[e4EHS�ZB¾/¾/�/��¾C�&���MK�A/?U^�e&K�egD/G�^�u�P8G\K�K�P,A�S2S�?U_NK�KiWAFX�WAFI�IFa� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¶�¼ T�µ

µ�a~�R?;A�X&D/L,A:K�I�ZjP,A�S2S2?�P8G\K�K�SY^4EHX�W]K�G;q/G\A*d(=YZ:^6A�X�W&XHK�qFS2K�I�Z�=2XHq-A�=2G�G�Ki?U=@?UZ\A�XVI�KFoF=�ZJ?;?�_VK�K�W AFX�W=YZ\?cA/I�I�K�S2K�GJA"Z�=2DFXQ=2? a

A[<6=2X�I�G�KiAF?�K�?*);I�D/X�?:ZJA�X[Z�a LN<4WHK�I�G\K�A/?UKi? );=YX�I�G�KiAF?�K�?�a I�<s=YXVI�G\K�AF?�K�?*)�=2X�I�G\K�A/?UKi?�a WV<WHK�I�G\K�A/?UKi? )]W]KiI�G\K�A/?UKi?�a Ki<�=@?cI�DFX�?UZ\AFX/Z )HI�D/X�?:ZJA�X[Z�a

¾F¾[�sh[e4EHS�ZB¾/¾ ³ ¾F¾ ³ �s�4K�A/?U^�e�A�Z�`�ujZ\G\A*d/K�SNZ�=2e&KFoH`(EHe�AFXnZ\K�G\eg=2X�AFS�?U_NK�KiW¶ a~b>`HK�Z\K�G\eg=2X�AFSNd/K�S2D]I�=YZ:^�D�P�A4`(EHe�A�X=YXmA�=2G>=2?>AFLVD/E]Z-�i��¾se&_H`�a���Z>Z�`H=@?~?�_VK�K�WQ`HD"l�S2DFXHq&W]D(K�?>=YZ>Z\A�O/KZ\D&P,A�S2S��se&=2SYKi?�a

A[<~�4eg=2X(E]Z�Ki?�a LV<��Meg=2X(E]Z�K/a Ii<B�-`�DFEHGia W�<~�4`HDFE�G\?�a K*<��-?UKiI�DFXVWpa

¾F¾[�sh[e4EHS�ZB¾/¾�µ[¾F¾C�6� ³ K�A/?U^CWHK�W]E�I�Z�=2DFX�u;`[E�e&AFXnZ\K�G\e&=YX�AFSpdFK�SYD]I�=YZ:^¹ a>»{`�A�Z4=@?4AF_H_HG\D*�]=Ye�A"Z\K�S2^�Z\`HKCZ\K�G\eg=2X�AFS;dFK�SYD]I�=�Z:^�D�PBA�`(EHe�AFX�=YXtA�=2G� ������ � ��D/E�W]DFX�· Zg`�A*dFK&Z\DO(XHD"l�Z�`HK6AFX�?Ul�K�G )(^FD/EI�A�XmW]K�W]EVI�K-=YZ�a

Page 14: Introductory Physics Problems David J. Jeffery Department of

��¾ v�`�AF_]Z�a;� °RXHK�T!¡R=Ye&K�XV?U=2DFX�AFS�²M=YX�K�e�A"Z\=2I�?

A[<���¾jO(e��*`�G�a LV<���O(e��*`�G�a I�<~�F¾F¾jO(e��*`�G�a W�<>¾ � ��O(e��*`�G�a Ki< ³ ����¾ � O(e ��?�a

¾F¾[�sh[e4EHS�ZB¾/¾ ¶ ¾F¾C�6��Me&D]W]K�GJA"Z\K�e&K�egD/G�^�ujW]K���XH=YZ�=2DFXmD�P�O[=2XHK�e&A�Z�=@I�?º(a~²M=2XHK�e�A�Z�=@I�?>=@?�u

A[<�Z\`HK6W]Ki?�I�G�=2_]Z�=2DFXD�P�e&D�Z\=YD/X�aLN<CZ\`HKMZ�KiIJ`HXH=@h[EHK�?>DFP�Z\`HK6I�=2XHK�e�A�aIi<QWH^[XVA�e&=2I�?>L(^QA�X�D�Z�`�K�G>X�A�e&K/aWV<CZ\`HK&?:Z\E�W]^mD�PjZ\`HKgI�A�E�?�K�?BD�P�e&D�Z\=YD/X�=2X�Z�K�G�e�?RD�P�_H`(^]?�=2I�A�S�h[E�AFX[Z�=YZ�=2K�?�oNe&D[?:Z�_HG�D/e&=YXHK�X[Z�S2^QP8D/G\I�K

AFX�We�AF?\?�aK*<CZ\`HK-GJA"Z�KMDFP�IJ`�AFXHqFK�D�P�AFI�I�K�S2K�GJA"Z\=YD/Xnl~=YZ�`Z�=2e&KFa

¾F¾[�sh[e4EHS�ZB¾/¾ ¹ ¾F¾4� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�AFI�I�K�S2K�GJA"Z\=YD/XnD/_H_VD[?U=YZ�KMd/K�S2D(I�=�Z:^¼ ac¤]A*^n^FDFEmA�G\K�egD"d(=2XHq&=YXZ\`HK-_VD[?U=YZ�=2dFK ��TkW]=2G\K�I$Z\=YD/X�o]LHE]Zc^/DFEHGc?�_NK�K�W=@?~W]K�I�G�KiAF?�=YX�q�a

A[<)��D/EHGcAFI�I�K�SYK�G\A�Z�=2DFXn_NDF=2X[Z\?~=2XZ�`HK © �N­ �8ª ���V« ��TkWH=YG\K�I�Z�=2DFX�aLN< ��D/EHGcAFI�I�K�SYK�G\A�Z�=2DFXn_NDF=2X[Z\?~=2XZ�`HK ��«��V¨]ª ���N« �HT!W]=2G�KiI$Z\=YD/X�aIi< ��D/E�A�G\KRXHDFZBAFI�I�K�S2K�GJA"Z\=YX�qgA�Z~AFSYS�oH^/DFEQAFG�K-W]KiI�K�SYK�G\A�Z�=2XHq�aWV< ��D/EHGcAFI�I�K�SYK�G\A�Z�=2DFXn_NDF=2X[Z\? ©�«/¬*©;«����������,¨]¬ Z�DgZ�`HK���TkA��]=2?�aK*< ��D/EHG�AFI�I�K�S2K�GJA"Z\=YD/X�_VD/=YX[ZJ?4=2X�Z\`HK © �N­ �,ª ���N« ��TkWH=YG\K�I�Z�=2DFX�a��RI�I�K�SYK�G\A�Z�=2DFX�AFSYl>A*^]?6_NDF=2X[Z\?g=YXtZ�`�K?\A�e&K-W]=2G�KiI$Z\=YD/XA/?>dFK�S2D]I�=YZ:^Fa

¾F¾[�sh[e4EHS�ZB¾/¾[º�¾F¾4� ¶�¶ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�AFI�I�K�S2K�GJA"Z\=YD/XQAFX�Wn=2X�?UZ\AFX/ZJA�XHK�DFE�?~A/I�IFa½ a~��ZRZ�=2egK4��K�G�D�^/DFE�A�G\K6e&D"d(=YX�qCA"Z4�i¾je��"?>=2X�Z�`�Ks_ND/?�=�Z\=Yd/K �[TkW]=2G\K�I$Z\=YD/X�ac��Z4�i¾�?�oH^FD/E�A�G\K6e&D"d[=2XHqCA�Z� ¶ e��"?�=YX�Z\`HK�_VD[?U=YZ�=2dFK �[T!W]=2G�KiI$Z�=2DFX�ag»{`VA"Z6=@?-^FD/EHG6A*dFK�G\AFqFK4A/I�I�K�S2K�GJA"Z�=2DFXxD"dFK�GRZ\`HK���¾;? ��»{`�A�Z6=2?^/DFEHG>=2X�?:ZJA�X[Z\AFXHK�D/E�?~AFI�I�K�SYK�G\A�Z�=2DFXQA�Z>Z�`HK ¶ ?>_NDF=2X[Z�A[<nb>`�KCA*dFK�GJA�q/K4A/I�I�K�SYK�G\A�Z�=2DFXrA�X�WxZ\`HK ¶ ?-=2X�?UZ\A�X[ZJA�XHK�DFE�?-A/I�I�K�SYK�G\A�Z�=2DFX�A�G\KgLND�Z\`�¾ � ¶ e��"? �s=2XrZ�`�K© �V­ �8ª ���V« �/T!W]=2G�KiI$Z\=YD/X�a

LN<Qb>`�KCA*dFK�GJA�q/K4A/I�I�K�SYK�G\A�Z�=2DFXrA�X�WxZ\`HK ¶ ?-=2X�?UZ\A�X[ZJA�XHK�DFE�?-A/I�I�K�SYK�G\A�Z�=2DFX�A�G\KgLND�Z\`�¾ � ¶ e��"? �s=2XrZ�`�K��«��V¨Hª ���N« �[T!W]=YG\K�I�Z�=2DFX�a

Ii<Qb>`�K�A*dFK�GJA�q/KnAFI�I�K�SYK�G\A�Z�=2DFX�=@?�¾ � ¶ e��"? �Q=YX±Z�`�K ��«��N¨]ª ���V« �[T!W]=2G�KiI$Z�=2DFX�a±b>`HK�G�Km=@?&XHD�ZCK�XHDFE�qF`=2X]P8D/G�e�A"Z\=YD/XnZ\D�W]K�Z\K�G\eg=2XHKMZ\`HK ¶ ?>=2X�?:ZJA�X[Z\AFXHK�D/E�?>AFI�I�K�S2K�GJA"Z\=YD/X�a

WV<Qb>`�KA*d/K�GJA�qFKCA/I�I�K�S2K�GJA"Z�=2DFX�AFX�WrZ\`HK ¶ ?6=2X�?UZ\A�X[ZJA�XHK�DFE�?gAFI�I�K�S2K�GJA"Z\=YD/X�?sAFG�KQLVDFZ�` ¶ e��"? �C=2X�Z�`�K��«��V¨Hª ���N« �[T!W]=YG\K�I�Z�=2DFX�a

K*<Qb>`�K�A*dFK�G\AFqFK�AFI�I�K�S2K�GJA"Z\=YD/Xt=@?n¾ � ¶ e ��? �m=2XwZ�`�K © �N­ �,ª ���V« �[T!W]=2G�KiI$Z�=2DFX�a�b>`HK�G�K�=2?nXHD�ZnK�XHDFE�qF`=2X]P8D/G�e�A"Z\=YD/XnZ\D�W]K�Z\K�G\eg=2XHKMZ\`HKMZ�`HK ¶ ?>=YX�?UZ\AFX[Z\A�X�K�DFEV?�A/I�I�K�S2K�GJA"Z�=2DFX�a

¾F¾[�sh[e4EHS�ZB¾/¾ ¼ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�?�EHG�P,AFI�K�qFGJA*d(=�Z:^�_NDF=2X[Z\?~W]D"l~X��¾Ha~b>`HKMAFI�I�K�SYK�G\A�Z�=2DFXnW]E�KBZ\D4q/G\A*d(=YZ:^4XHKiA�G�Z�`�K���A�G�Z�`�· ?�?�EHG�P,AFI�Kg5,l~`HD/?�KRAFL�?UD/SYEHZ�K�e&AFqFXH=YZ�EVW]KR=@?>W]K�X�D�Z�KiW

L(^H<$uA[<C_NDF=2X[Z\?~KiAF?UZ�aLN<n_NDF=2X[Z\?cWHD"l~XnZ\D"l�AFG\WCZ�`HK6��A�G�Z�`�· ?>I�K�X[Z\K�G~e&DFG\KMDFG~S2K�?\?�aIi<n_NDF=2X[Z\?c?UZ�GJA�=2qF`[Z>EH_me&DFG\K�D/G>SYKi?�?�aWV<n`VAF?>XHD�W]=2G�KiI$Z\=YD/XmA�ZcA�S2S�aK*<n_NDF=2X[Z\?>Z\D"l�AFG\WCZ�`HK6¯�D[D/X�a

¾F¾[�sh[e4EHS�ZB¾/¾ ½ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�P8G\K�K�P,A�S2S�=2X�W]K�_VK�X�W]K�X[ZcDFP�e�AF?\?�uj�MAFSY=2S2K�D�F�Fa>7kZM=2?�G\K�_NDFG�Z�KiWmZ�`�A�Z-�MAFSY=2S2K�Dx5�I�=2G\I�A�� ¶�½ ¾[<~W]G\DF_H_NK�W�L�A�S2S@?BDFP�W]= �NK�G�K�X/ZMe�AF?\?RA�ZRZ\`HK&?�AFegKsZ�=2e&KsP8G\DFe

Z\`HKMZ�D/_DFP�Z\`HK6¸�KiA�XH=2XHq�b�D"l�K�G>DFP�9�=@?\A4=2XmDFGJW]K�G�Z\DCW]K�e&DFXV?:Z\G\A�Z�KRZ�`�A�Z�uA[<�Z\`HK-`HKiA*d[=2K�G>L�AFSYS�`H=�Z~Z\`HK-qFG\DFE�X�W���GJ?UZcL[^QA4S@A�G\qFK�e�A�G\qF=2X�aLN<CZ\`HK-S2=Yq/`/Z\K�G~L�AFSYSp`�=�Z~Z\`HK-qFG\DFEHXVWC��GJ?UZ>L(^A4S@A�G\qFK�e�A�G\qF=2X�aIi<nLND�Z\`mL�A�S2S2?>`�=�Z~Z\`HK-qFG\DFEHXVWQA�Z>e&D/G�KMDFG~S2K�?\?�Z�`�K6?�AFegK�Z\=Ye&KFa

Page 15: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� °RXHK�T!¡B=2e&K�X�?�=2DFX�AFS�²M=YXHK�e�A"Z�=@I�? �/�

WV<CZ\`HK-L�AFSYS@?>l�D/EHS@WnS2K�d(=YZ\A"Z\KMZ�D"l>A�GJW�Z\`HK6¯�D(DFX�aK*<CZ\`HK6¸�KiA�XH=2XHq�b�D"l�K�G�l>AF?�S2K�AFXH=YX�q�a

¾F¾[�sh[e4EHS�ZB¾/¾ ½ ��¾C� ³ �4K�A/?U^�e�A�Z�`�u�LVA�S2S�Z�`HG\D"l~XWHD"l~X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ¾�T\�"º

�i�]a~��L�A�S2SF=@?�Z\`HG\D"l~XMWHD"l~X[l>A�GJWMA"Z;�*��e��"?�a�»{`�A�Z�=@?�=YZ\? ���� � � � ¾�?�S@A"Z\K�G�AF?\?UEHe&=2XHq~XHDBAF=YG�G�Ki?U=@?UZ\A�XVI�K��A[<~��¾je���?$a LV< ³ ��e��"?$a Ii<~�F��e���?$a W�< ,B�je ��?$a K*<��i��e��"?�a

¾F¾[�sh[e4EHS�ZB¾���¾/¾F¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�ujO(=2XHK�e�A"Z\=2I�Kih/EVA"Z�=2DFXV?�ujA�G\G\D"l{��=2qF`[Z� ³ a~�zZ\AFSYS�AFG\IJ`�K�G;l~=YZ�`m`HK�G>SYD/XHqFLND"l�?U`�D[DFZ\?>A�XmA�G\G\D"lw?UZ�GJA�=2qF`[Z�EH_A�Z-��¾F¾�e ��?$ajb>`HK-A�G\G�D"lwG\=2?�K�?�o]?US2D"lc?�o

`HD/S2W�?gP8DFG�A�X±=YXV?:ZJA�X[Z�o�A�X�W�Z�`HK�XwWHK�?\I�K�XVWH?g_H=2IJO(=2XHqrEH_w?U_NK�KiWpa±b>`�Km?�_NK�K�WtD�PRZ�`HK�AFG�G\D"l l~`HK�X±=YZG\K�A/IJ`HK�?�Z�`�K-SYK�dFK�S�P8G\DFe�l~`H=2IJ`m=YZcl�A/?>?U`HDFZc=2?�o]XHK�qFS2K�I$Z\=YX�q&AF=YG~G\K�?�=@?:ZJA�X�I�KFuA[< ½ a ¼ e ��? ��aLN< ½ a ¼ e ��?$aIi<�F¾F¾je���?$aWV< ¶ ¾je��"?$aK*<��i¾F¾je���?$a

¾F¾[�sh[e4EHS�ZB¾��F�i¾F¾C� ³ �MK�A/?U^�e�A�Z�`�u�O(=2XHK�e�A�Z�=@IRKih[E�A"Z\=YD/X�?�u�P8G\K�K�P,A�S2S��µ�a~��`(EHe�A�XQP,A�S2S2?>D ��?UD/e&KR`H=2qF`m?\I�A ��DFS@W]=2XHq�a��cLNDFEHZc`HD"l{P,A�GcWHD[Ki?�`HK*y�?U`HK�P,AFSYS�=2X ³ ?�K�I�D/X�WH?�a~5, cK�qFS2K�I�Z

AF=YG~G\K�?�=2?UZ\AFX�I�K/a <A[<Cµ/µ�emaLN< ¼/¼ emaIi<�/��emaWV< ½ a ¼ eaK*<nµVa ½ ea

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾[�sh/P8EHS2S�¾/¾F¾H�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujKiAF?�^CI�A�G~e&DFZ�=2DFX�Fa~��I�A�Gc?UZ\A�G�Z\?�P8G\DFe}G�Ki?:Z~l~=YZ�`�AFI�I�K�S2K�GJA"Z\=YD/X���e���? �"a

A[<C»{`VA"Zc=@?>=�ZJ?c?U_NK�KiWmA"P Z�K�G-��¾�?�aLN<n»{`VA"Zc=@?>=�ZJ?cW]=@?:ZJA�X�I�KMZ�GJA*dFK�S2K�WQA"P Z\K�G-��¾;?�aIi<n»{`VA"Zc=@?>=�ZJ?c?U_NK�KiWl~`HK�Xm=YZc`�AF?�Z\G\A*d/K�S2K�W��i¾F¾jema

¾F¾[�sh/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�Z:l�D�TkDFL,A:KiI$Z~I�A�G~_VAF?\?U=2XHqg_HG�D/LHS2K�e�]a~��Z4Z�=2egKQ��K�G�DVo�Z\`HK�G\KC=@?sA�I�A�G4?UZ�D/_H_NK�W�A"Z&A�S2=Yq/`/ZgA�X�W�AmZ\G�EVIJOxe&D"d(=YX�q�A"Z4A�I�DFXV?:ZJA�X[ZsdFK�SYD]I�=�Z:^xD�P³ ¾je��"?j=@?;��¾/¾jefLNK�`�=YX�W�Z�`HK�I�A�Gia��BS2?�DsA�Z�Z�=2e&KB��K�G�DVo"Z�`�KRI�AFG;?UZ\A�G�Z\?;AFI�I�K�S2K�GJA"Z\=YXHqMP8D/G�l>A�GJWgA"ZB��e���? � aA[<n¡RGJA*l±_�SYDFZ;D�P�_ND/?�=�Z\=YD/X �Qd/K�GJ?UEV?�Z�=2e&K � ?U`�D"l~=YXHq6Z�`HKBZ�GJA A:K�I�Z�D/G�^gI�EHG\dFKi?jD�P�LND�Z\`CdFK�`H=2I�SYKi?�a�»{`�A�ZAFG�K�Z\`HKMZ�`HG\K�K-h[E�AFSY=YZ\A�Z�=2dFK�S2^nW]= ��K�G\K�X[Z~l�A*^]?�Z�`�KMZ�`HK6I�EHG�d/K�?>I�AFXQ=2X[Z�K�G\?�K�I�Z�

LN<Q��Z-l~`�A�ZRZ\=Ye&K&DFGRZ�=2e&K�?-W]DnZ�`HK�I�A�GMA�X�W�Z�G\E�IJO�_�AF?\?�w7:?�=�Z-_ND/?\?U=2LHS2KsP8D/GRZ\`HK�G\K4Z�DLVK&DFX�SY^mDFX�K_VAF?\?>l~=�Z\`QZ\`HK-qF=2dFK�XI�DFX�WH=�Z\=YD/X�? �

¾F¾[�sh/P8EHS2S�¾/¾H�F�i¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�¯�K�G\I�T8�[A�qgO(=YXHK�e�A"Z�=@I�K�h[X�aj_HG\DFL�SYK�e� ª�¬"¨ �V«������V¬ ��­�� ¯�K�GJI�KiW]K�?~AFX�W#�[A�q/E�A�G

Page 16: Introductory Physics Problems David J. Jeffery Department of

�i� v�`�AF_]Z�a;� °RXHK�T!¡R=Ye&K�XV?U=2DFX�AFS�²M=YX�K�e�A"Z\=2I�?

³ a~��ZRZ�=2egKg��K�G�DCZ�`HK�G�K4=2?�AnI�A�G45�A �[A�q/E�A�G$<>?:Z\DF_H_NK�WxA"ZMA�G�KiW�S2=Yq/`/ZMA�X�W�¯�K�GJI�KiW]K�?45 Z�`VA"ZM`�AF?�A:E�?UZRG\EHXZ\`HK&G�KiW�<R=2?Me&D"d(=YX�qA�Z ¶ ¾je��"?MA�XVW�=@?6��¾je AF`HK�A/W�DFP;Z�`�K��[A�qVa4�BS2?�D�A"ZMZ�=2e&Kg��K�G\DnZ\`HK&SY=2qF`[ZMZ�E�G�X�?q/G�K�K�XnAFX�W�Z\`HK �[A�qQ5,W]G\=Yd/K�XQL[^�AFXQA"ZJA*d(=2?UZ�=@IBI�A"Z�K�qFD/G�=@I�AFSH=Ye&_NK�GJA"Z\=Yd/Ki<�?:ZJA�G�Z\?�AFI�I�K�S2K�GJA"Z\=YXHq6P8DFG\l�AFG\W�A�Z¹ � ¾je���? �"aA[<C»{`VA"Zc=@? ¶ ¾je��"?�=2Xmeg=2S2K�?~_NK�G~`HD/EHG �� cDFZ�K�Z�`HK�G�K6AFG�Kg� ¹ ¾ ½ e&K�Z�K�G\?�Z\D&Z�`HK-e&=2SYK/aLN<��=2dFK�X�Z�`�K4I�D/X�W]=YZ�=2DFX�?�o�esE�?UZBZ\`HK&�[A�qn_�AF?\?~Z\`HKg¯�K�GJI�K�WHK�?��»{`(^���5,7kP;^FD/EHGRAFX�?Ul�K�GR=2?BXHD�o�^/DFE

I�A�Xm?UO(=2_Z�`HK-G\K�?UZ~D�P�Z\`HK6h[EHK�?UZ�=2DFX�a <Ii<mv�AFS2I�EHS@A"Z�K�Z\`HKMZ�=2e&KMZ�D&Z�`�K-_�AF?\? �WV<mv�AFS2I�EHS@A"Z�K�Z\`HK6W]=@?:ZJA�X�I�KRP8G\DFe�Z�`HK-S2=2qF`[Z>Z�D&Z�`�K�_VAF?\? �K*<Q£BD"l�P,A/?:Zc=@?�Z�`HK �[A�q&q/DF=2XHqgA�Z>Z�`HK-_�A/?�?>=2Xme&K�Z�K�G\?>_NK�GR?UKiI�DFXVW � ����e&=YS2K�?>_NK�Gc`�DFEHG �

¾F¾[�sh/P8EHS2S�¾/¾H� ½ ¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujG�K�S2A�Z�=2dFK�O[=2XHK�e&A�Z�=@IMK�h[E�A�Z�=2DFX�?µ�a~b>`HK~µ-?UZ\AFX�WHA�GJW4O[=2XHK�e&A�Z�=@I>K�h[E�A�Z�=2DFX�?�D�PpI�D/X�?UZ\A�X[Z�AFI�I�K�SYK�G\A�Z�=2DFXn��TkWH=Ye&K�XV?U=2DFX�AFS]e&D�Z�=2DFXgl�K�G\K>WHK�G\=Yd/K�WA/?�?�EHe&=YX�qne&D�Z\=YD/X�l~=YZ�`�G\K�?�_NK�I$ZRZ�Dm?UD/e&K6�H�]K�W�G�K�P8K�G\K�X�I�K6P8GJA�e&KFa ��E]ZMl~`�A"ZM=YP;^FD/E�`�AFWx?�A*^�ACZ:l�DFTD/L,A:K�I�Z�_HG\DFL�SYK�e Z�`�A�Z�^/DFE4l~=2?�`HK�W6Z�DMG\K�W]E�I�K;Z\D�ARDFX�K�TkDFL,A:KiI$Z�_HG�D/LHS2K�e�L(^6IJ`�A�X�qF=2XHqBG\K�P8K�G�K�X�I�K�P8G\AFe&K�?�u=�a K/aYoVIJ`�A�XHq/=YX�qsZ\D&Z�`HKMP8GJA�e&KMD�P�Z�`HK-D/XHKMD�P�Z�`HK-D/L,A:K�I�Z\?>DFG~=2XmD�Z\`HK�G~l�DFGJWH?�Z�D�A&G\K�S@A"Z�=2dFKRP8GJA�e&KFaA[<Q¤]`HD"l�Z�`�A�Z�Z�`�K���GJ?:Z�Z:l�DcO(=2XHK�e�A�Z�=@IjK�h[E�A�Z�=2DFX�?�A�_H_HS2^RZ�DcG\K�S@A"Z\=Yd/KjegDFZ�=2DFX�a�¿~K�I�A�S2S�Z\`HK�?�K;Kih/EVA"Z�=2DFXV?AFG�K/u

� $ � � ��� � � ��� � � � A�X�W � $ � � � � � �

LN<¤]`HD"l�Z\`�A"Z~Z\`HK6DFZ�`HK�G>Z:l�D�O(=2XHK�e�A"Z\=2IMKih[E�A"Z\=YD/X�?~A�_H_�SY^nZ�D�G\K�S@A"Z�=2dFKMe&D�Z\=YD/X�a ������ � b>`H=2?c=2?�X�· Zd/K�G\^C`�AFG\Wn=�Pj^FD/EnO(XHD"l�Z�`HKMZ\G�=@IJO�a

¾F¾[�sh/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�I�D/SYS2=@W]=YX�q4Z\G\AF=YXV?¶ a~b�G\AF=YXr��=@?-e&D"d[=2XHqmK�A/?:Z6A�Z ¹ ¾je��"?MAFX�WxZ�GJA�=2X �f=2?Me&D"d(=YX�ql�K�?UZsA"Z ¶ ¾je��"?�DFX�AmI�D/SYS2=2?�=2DFXrI�DFE�G\?�Kl~=YZ�`nZ�GJA�=2Xn�6a(��Z>An��¾/¾F¾Me&K�Z\K�GJ?�AF_�A�G�Z�Z�`�KBZ:l�D6Z\G\AF=YX�K�XHqF=2XHK�K�G\?;XHD�Z\=2I�KRKiAFIJ`�DFZ�`HK�G�AFX�WC?�S2AFe D/X�Z�`�KLHGJA�O/K�?�aA[<C»{`VA"Z�esEV?:Z�Z�`�K~G�K�S2A�Z�=2dFK>AFI�I�K�S2K�GJA"Z\=YD/XsLNK65,AF?\?�EHe&=YXHqM=YZj=2?�I�DFX�?UZ\AFX[ZJ<�P8DFG�Z\`HK�Z�GJA�=2X�?�Z�D A:E�?UZjZ�D/E�IJ`A�Z6G�K�S2A�Z�=2dFK�d/K�S2D(I�=�Z:^���K�G\D�58=�a KFa2o�Z\D�`�A*dFKCAm=2XHXHD]I�E�DFE�?-e�AFG�q/=YX�AFS�I�D/SYS2=2?�=2DFXV< � 7:?-d/K�S2D]I�=YZ:^�D�P>Z�`�KZ\G\AF=YXV?>G�K�S2A�Z�=2dFKRZ�D&Z�`�K-qFG\DFEHX�WnXHK�I�K�?\?�AFG�=2S2^���K�G\D&l~`HK�XZ\`HK�^I�DFS2S2=2W]K �

LN<n»{`VA"Zc=@?�Z�`HK-G\K�S@A"Z\=Yd/KMA/I�I�K�S2K�GJA"Z�=2DFXQ=YX �· ?-5,=�a KFa2oH=2XmEHXH=YZ\?~DFP�Z�`�K-qFGJA*d[=YZ\A�Z�=2DFX�AFSNA/I�I�K�S2K�GJA"Z�=2DFXN<��Ii<Q¡RDrZ�`�K_VAF?\?UK�XHqFK�G\?gDFXtZ�`�KmZ�GJA�=2X�?gK��]_VK�G�=2K�XVI�K�A /T�P8DFGJI�Km?UK�ZCL(^�Z�`HK�A/I�I�K�S2K�GJA"Z�=2DFX�=YX �· ?&^/DFED/L]Z\AF=YX�K�WQ=YXZ�`�K-_�A�G�Z658LV<~AFX�?�l�K�G�

WV<Q�BX�WL(^CZ�`�K-l�A*^�l~`�A�Z~=2? ¹ ¾je��"?�=2XO(=2SYD/e&K�Z�K�G\?�_NK�Gc`�DFEHG �7:?>Z�`�=2?>P,A/?:Z>P8D/GcAsZ\G\AF=YX �

¾F¾[�sh/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujGJA�=2X�W]G\DF_�?>?\A�X�?~AF=YG>G\K�?�=2?UZ\AFX�I�K¹ ac¤]A*^Z\`�A"ZMG\AF=YXVW]G�D/_�?~P,AFSYS>� ¼ ¾F¾�e�Z\DnZ\`HK4q/G�D/EHX�Wpa&5,A[<B�R?�?�EHe&=2XHqnZ\`HK�G\Kg=2?RXHDmA�=2GRG\K�?�=2?UZ\AFX�I�Ksl~`�A"ZM=2?Z\DFE�IJ`]T!W]D"l~XCd/K�S2D]I�=YZ:^ ��5,LV<�»xD/EHS2Wn=�Z>LNK�?\A"P8KBZ�Dgl�AFSYO&=2XCZ�`�KRGJA�=2XCl~=YZ�`HD/E]Z>AF=YG�G\K�?�=2?UZ\AFX�I�K �mv�D/e&_�A�G\KZ\`HK6W]G\DF_m?U_NK�KiWnZ\D&LHEHS2SYK�ZB?U_NK�KiW �'��D/EQl~=2SYS���X�Wm?UD/e&K�EV?UK�P8EHS�=2X]P8DFG\e�A"Z�=2DFXmA�LNDFEHZcLHEHS2SYK�ZB?U_NK�KiWH?~A"Z

`[Z�Z�_�u yFy"`[^(_NK�G�Z�K��[Z\LVD(D/ONa I�D/enyiP,AFI�Z\?$y(a°BPjI�D/EHG\?�KFo[Z\`H=2?c=2?>XHD�`�K�S2_D/XA4Z\K�?UZ�a

¾F¾[�sh/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u;¤(EH_NK�G�T!A�G\e&A/W]=2SYS2D4D/X¯�D[D/Xº(ac¤(E�_VK�GUT!A�G\e�AFW]=2SYS2D�=@?mDFXzZ�`�Kr¯�D[D/Xzl~`�K�G\K $ � � ¹ e��"? �xW]D"l~X(l>A�GJW�A�XVW�Z\`HK�G\Kx=@?mG\K�A�S2S2^{XHD{A�=2GG\K�?�=2?UZ\AFX�I�K/aA[<n£BKc��^]?�EH_�P8G\DFe Z�`�KR?�EHGUP,A/I�KB?UZ\AFGUZ\=YX�q-P8G�D/e G\K�?UZ�l~=YZ�`QA�XnA/I�I�K�SYK�G\A�Z�=2DFX&D�P ¶ e ��? �~P8DFG��F¾�?�a�b>`HK�X`�=2?c?�EH_NK�G\_VD"l�K�G~?UZ\AFSYS@?�aj£BD"l�`H=2qF`m=@?>`HK6A�X�WQl~`�A�Zc=2?>`H=@?~d/K�S2D(I�=�Z:^��

Page 17: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� °RXHK�T!¡B=2e&K�X�?�=2DFX�AFS�²M=YXHK�e�A"Z�=@I�? � ³

LN<Q�cP Z�K�GB?:ZJA�S2SY=2XHq&`H=@?~AFI�I�K�S2K�GJA"Z\=YD/Xn=@?~W]EHK�Z�D�q/G\A*d(=YZ:^Fa�£cD"l�`�=Yq/`mWHD[Ki?>`HKMG�=@?�K�LNK�P8D/G�KMLNK�q/=YXHX�=YXHqgZ\DP,AFSYS �

Ii<Q�;dFK�X/Z\E�A�S2S2^¤(EH_NK�G�T!A�G\e&A/W]=2SYS2D�esE�?UZBP,AFSYS�L�AFIJOQZ�DCZ�`HK4SYEHXVA�GB?�EHG�P,AFI�K/a~»{`�A"Z�=2?B`H=@?BI�GJAF?�`�?�_VK�K�W �5�|HD/GUZ\EHX�A"Z\K�S2^FoH`�=2?>=2X(d[E�SYXHK�G\AFLH=2SY=YZ:^C=@?~?:Z\=YS2S�DF_NK�GJA"Z\=Yd/KFa <

¾F¾[�sh/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujS2=YXHKiA�GcA/I�I�K�SYK�G\A�Z�=2DFXQl~=�Z\`QZ\=Ye&K¼ a~b>`HKcWHK�G\=Yd"A"Z\=Yd/K>D�PNA&��TkWH=Ye&K�XV?U=2DFX�AFS]AFI�I�K�S2K�GJA"Z\=YD/X�o � $�� � ��� � =@?�AMI�DFXV?:ZJA�X[Z�a�|HG\DFe AFX[Z�=@W]=���K�G\K�X[Z\=2A�Z�=2DFX5,=�a KFa2o =YX[Z�K�qFGJA"Z\=YD/XV<$o�l~G�=YZ�K�W]D"l~X�Z�`�K K��]_HG�Ki?�?�=2DFX�? P8DFG A/I�I�K�SYK�G\A�Z�=2DFX�ozdFK�SYD]I�=YZ:^Fo A�XVW _ND/?�=�Z\=YD/XG\K�e&K�e4LVK�G�=2XHqgZ�`VA"ZBA&I�D/X�?:ZJA�X[Z~D�P�=YX[Z�K�qFGJA"Z\=YD/XQA�G\=@?UKi?~A"Z~K�d/K�G\^�=YX[Z�K�qFGJA"Z\=YD/X�a

¾F¾[�sh/P8EHS2S�¾/¾ ¹ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�W]G�=2_H_H=2XHq�?�`HD"l�K�G½ a>7kZi· ?BLVK�K�X�D/XHK6D�P�Z\`HD/?�KsWHA*^]?cAFX�WmXHD"l ^FD/E`VA*dFK<A:E�?UZRS@A�=2X�W]D"l~XZ�Dn?�S2K�K�_��{AFX�WmK�d/K�G\^/Z\`H=2XHq�=2?RW]K�A/Wh[EH=2K�Z��wK��]I�K�_]ZnZ�`HK�G�K/· ?CArG\K�q/EHS@A�GCW]G\=Y_HTkW]G\=2_tP8G\DFe�^FD/EHGC?U`�D"l�K�G�XHDF����S2KFaz BD�Z\`H=YX�q�I�A�X{?UZ�D/_{=�Ziu�=YZS2D(DFe�?;=2X�Z\`HK�?�=2SYK�X�I�KRSY=2OFK�9�D[K/· ?;_VK�X�W]EHS2EHema ��DFEnZ�D[?�?�o/^/DFE&Z\EHG�X�o[^/DFEnAFG�KBqFDF=2XHq6=2X�?\A�XHK��±�VX�A�S2SY^&^/DFEI�DFe&K6Z\DQ_H`(^]?�=2I�?�a�7kZ�=@?M��e P8G�D/e}Z\`HKgXHDF����S2K6Z�DQZ�`�Ks��D(D/G�u~^/DFE�_HG\E�W]K�X/Z\SY^�e&KiAF?�EHG�KiWZ�`H=@?MW]=@?:ZJA�X�I�KD/X�I�K&A�X[Z�=@I�=2_�A�Z�=2XHqAmWHAFG�O�X�=Yq/`/ZMD�P�Z�`HK�?�DFEHS�a ��D/E�I�DFEHX[Z6� ¹ W]G\=Y_�?�=2Xt� ³ _�EHS2?�K&LVKiA"ZJ?�uRZ�`H=@?�P8K�A�Z-D�PZ\G�K�egK�X�W]D/E�?-W]DFE�LHSYK�I�DFX�I�K�X[Z�GJA"Z\=YD/X�DFXHS2^�q/D[Ki?RZ�D�?U`�D"l `HD"l�P,AFG-^FDFE�A�G\KsP8G\DFe Z�`HK ��WHK�A"Z\`xDFP�KiAFIJ`WHA*^CWH^[=2XHqVa ���cX�WQ^FD/EQA/?UO�^/DFEHGJ?UK�S�P�l~`�A"Z>=2?�Z\`HKMe&D/?UZ~AFX�WCS2K�A/?:Z~X(EHe4LVK�G�DFP�W]G\DF_V?�=2XQZ�`HK-A�=2G~A"Z>Z�`�K?\A�e&K�Z�=2e&K��

Page 18: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� UFH^&TN[&:5 E &A>�,��$1)H ;7?T5\E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾ ³ h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�W]K���XH=YZ�=2DFXmD�P�AFI�I�K�S2K�GJA"Z\=YD/X�Fa~�RI�I�K�SYK�G\A�Z�=2DFX=2?�u

A[<n?�_NK�K�W�aLN<nd/K�S2D]I�=YZ:^FaIi<CZ\`HK-GJA"Z�KMDFP�IJ`�AFXHqFK�D�P�dFK�SYD]I�=YZ:^Cl~=YZ�`Z�=2e&KFa�7kZc=@?~A � ¦&� � � ��aWV<CZ\`HK-GJA"Z�KMDFP�IJ`�AFXHqFK�D�P�dFK�SYD]I�=YZ:^Cl~=YZ�`Z�=2e&KFa�7kZc=@?~A � ¦ � ��aK*<CZ\`HK-GJA"Z�KMDFP�IJ`�AFXHqFK�D�P�W]=@?U_HS@AFI�K�e&K�X[Zcl~=YZ�`Z�=2e&KFaj7kZc=@?cA � ¦ � ��a

¾F¾ ³ h[e4EHS�ZB¾/¾/�F¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujEHX�=�P8D/G�e�I�=YGJI�E�S2AFG�e&DFZ�=2DFX�]a ��D/EnA�G\KcqFD/=YX�q6=YXA6I�=2GJI�S2KRA"Z>A6I�D/X�?UZ\A�X[Z>?U_NK�KiW�58=�a K/aYo]AsEHXH=YP8DFG\e�?�_NK�K�WV<$a�7:?;^/DFEHG�� �� � ¦ ����}K�dFK�GIJ`�AFXHqF=2XHq��A[<n BD�o]Z\`HK6?�_VK�K�WQ=2?cI�DFX�?UZ\AFX[Z�aLN< ��Ki?�o�=�Zc=@?~I�D/X�?:ZJA�X[Z�S2^nIJ`�AFXHqF=2XHq&?U=2X�I�KMZ�`HK-e&D�Z\=YD/XQ=@?~=2XA ­�ª�¬"¨3� �V§�ª�����« aIi< ��Ki?�o�=YZ6=2?6I�DFX�?UZ\AFX[Z�S2^xIJ`�AFXHqF=2XHqm?U=2X�I�K&Z\`HKCe&D�Z\=YD/Xr=2?-=2X�A �,¬ �,« A�X�WrW]=2G�KiI$Z\=YD/X�=@?6I�DFX�?UZ\AFX/Z\SY^IJ`VA�XHq/=YXHqVa

WV<Q BD�o]Z\`HK-dFK�SYD]I�=�Z:^�=@?cI�D/X�?UZ\A�X[ZiaK*< ��Ki?�o�DFX « �N«[¬ � �Vª�§�«/¬ �,«���ª LNK�XVWpa

¾F¾ ³ h[e4EHS�ZB¾/¾/� ¹ ¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujK�SYK�d*A�Z�D/G>WH=2?�_HS@AFI�K�e&K�X[Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ¾�T ½

³ a~��e�A�Xl�AFSYO]?�µ/¾je�Z\D�A�XnK�SYK�d"A"Z�D/G~A�X�WCZ�`HK�XG\=@?UKi?>º�¾jema�»{`VA"ZcA�_H_�G�D*�]=2e&A�Z�K�SY^&=@?>`H=2?>W]=@?�_HS2A/I�K�egK�X[ZP8G\DFe Z\`HK6?UZ\A�G�Z�=2XHq&_NDF=2X/Z �

A[< ¼ ema LV<��F�i¾jema I�< ³ ¾jema W�< ¹/¶ ¾F¾jema Ki< ¼ ¾jema

¾F¾ ³ h[e4EHS�ZB¾/¾/�[º"¾C� ³ �4K�A/?U^�e�A�Z�`�u�q/G�D/EHX�WQ?U_NK�KiW� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¶ º*T!� ³

µ�a~�BX&AF=YG\_HS@A�XHK�`�A/?jA�X&A�=2G\?�_VK�K�W4D�P�� ¶ ¾jO(e �"`HG�A�X�W4=2?��V^[=2XHq-=2XgA�l~=2X�WgD�P�º"¾jO(e��*`�G�a�b>`�K�q/G�D/EHX�Wg?U_NK�KiWDFP�Z\`HK6A�=2G�_�S2AFXHKRe4E�?UZcLVK6?�DFe&K�l~`�K�G\KR=2XZ�`HK-GJA�XHq/KFu

A[<~� ¶ ¾� ³ ��¾jO(e��*`�G\a LV<M� ¼ ¾� ³ �F¾jO(e �"`HG\a Ii<�� ¼ ¾�]� ¶ ¾jO(e��*`HG\a W�<~�"µ[¾�]� ¹ ¾jO(e��*`�G\aK*<cº"¾�]� ¶ ¾jO(e��*`HGJa

¾F¾ ³ h[e4EHS�ZB¾/¾ ³ ¾F¾C� ³�³ K�A/?U^�e�A�Z�`�u;WH=2?�_HS@AFI�K�e&K�X[Z\?>=2XQ´jK�q/A/?¶ a ��D/E�A�G\K6=2X�¸�A/?c´jK�q[AF?RA"ZBZ\`HKs=2X[Z�K�G\?�K�I�Z�=2DFX�D�PjZ\`HKg¤(Z�G\=Y_�AFX�W�b�G�D/_H=@I�A�XVA�58l~`HK�G�KsZ�`HKg¯��M¯���GJA�X�W�o BK�l ��D/G�O�oH BK�l ��D/G�O�o]�j�HI�A�S2=YLHE�G�o]A�XVWQb�G�D/_H=@I�A�XVA4AFG�K*<$a���DFEqFD&A�LNDFE]Z�� � � �,« � �V¬iªi§ DFXQZ�`HK-KiAF?UZ?�=2WHKgDFP;Z\`HKC¤[Z�G\=Y_xZ�DQZ�`�KC£BA�G\S2K�^[Tk¡�A*d(=2W�?UD/Xxv�A"P8KFo�I�G\D/?\?cZ\`HKC¤[Z�G\=Y_xZ�DZ\`HK&l�Ki?:Z6?�=2W]K/o�A�XVW�qFDmA�LNDFEHZ§�¨ ���j¨ � ����«4­ � ��ªi§ Z�D�Z�`HKc¯�DFX[Z�KBv�A�G\S2D�AFX�W6Z\`HK�G\K>SYD[?UK�� �N­�ª DFPV^FD/EHG�D�P��(��¾/¾R?UZ\AFOFK>A"ZjZ\`HK>G�D/EHSYK�ZUZ\KZJA�LHS2KFaA[<)��D/EHGjZ\D�Z\AFS(Z�GJA*dFK�SHW]=2?UZ\AFX�I�K~=@?�AFLVD/E]Z�������� ���,«(­ oiZ�D�ZJA�S�WH=2?�_HS@AFI�K�e&K�X[Z;A�LNDFE]Z���� � �,« � �V¬*ª�§ o/AFX�W^/DFE`�A*dFK�� �V¬"« Z�`�AFX�� ¶ ¾4SYK�P Z�a

Page 19: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ³ ¤HI�A�S@A�GJ?>A�X�W´jKiI$Z�D/G\? � ¶

LN< ��D/EHG�Z�DFZ\A�SNZ\G\A*d/K�S�W]=2?UZ\AFX�I�KM=@?>A�LNDFE]Z�������� ���,«(­ o�Z\D�Z\AFSpW]=2?�_HS@AFI�K�e&K�X[Z~A�LNDFE]Z�� � � � ���,«(­ � �V¬iªi§ oAFX�W^FD/En`�A*d/K�� ��¬"« Z�`VA�X � ¶ ¾sS2K�P Zia

Ii< ��D/EHG�Z�DFZ\A�SNZ\G\A*d/K�S�W]=2?UZ\AFX�I�KM=@?>A�LNDFE]Z�������� ���,«(­ o�Z\D�Z\AFSpW]=2?�_HS@AFI�K�e&K�X[Z~A�LNDFE]Z�� � � � ���,«(­ � �V¬iªi§ oAFX�W^FD/En`�A*d/K ��«(­�­ Z�`VA�X � ¶ ¾sS2K�P Zia

WV< ��D/EHG�Z�DFZ\A�SNZ\G\A*d/K�S�W]=2?UZ\AFX�I�KM=@?>A�LNDFE]Z�������� ���,«(­ o�Z\D�Z\AFSpW]=2?�_HS@AFI�K�e&K�X[Z~A�LNDFE]Z�� � � � ���,«(­ � �V¬iªi§ oAFX�W^FD/En`�A*d/K�� ��¬"« Z�`VA�X � ¶ ¾sS2K�P Zia

K*< ��D/EHG�Z�DFZ\A�SNZ\G\A*d/K�S�W]=2?UZ\AFX�I�KM=@?>A�LNDFE]Z�������� ���,«(­ o�Z\D�Z\AFSpW]=2?�_HS@AFI�K�e&K�X[Z~A�LNDFE]Z�� � � � ���,«(­ � �V¬iªi§ oAFX�W^FD/En`�A*d/K�`VA*d[X�· Z~qFDFZ�� ��­��k¨]¬"« S2K�P Z�a

¾F¾ ³ h[e4EHS�ZB¾/¾�µ[¾F¾C� ³ �4K�A/?U^�e�A�Z�`�u;WH=2?�_HS@AFI�K�e&K�X[Z\?>=2XQ´jK�q/A/?>_�A�G�Z~7U7¹ a ��D/ECA�G\K�=2XC¸�A/?j´jK�q[AF?�l~`HK�G�K>Z\`HKB?UZ�G\K�K�Z\?�AFG�KcAFSYe&D/?UZ;A�S2SHS@A�=@WgDFE]Z;=2XCAMG\K�I$ZJA�XHq/EHS@A�G�qFG\=2W�a��R?�?�EHe&K~Z�`�Kq/G�=@W=2?~K��HAFI$Z\SY^A�S2=Yq/XHK�WQl~=YZ�`mZ�`�KsI�AFG\W]=2X�AFS�W]=YG\K�I�Z�=2DFX�?�a ��D/E�W]G�=2dFK6�ge&=2SYKi?~XHDFG�Z�`mD/XQZ\`HK4¤[Z\G�=2_�o�Z�EHG\XG\=Yq/`[Z>D/X|�S@A�e&=2XHqFD&A"Z~Z\`HK6£BAFG�S2K�^[T!¡RA*d(=@WH?UD/Xv�A"P8K/oHW]G\=Yd/K�KiAF?UZ ³ e&=2SYKi?�Z�D�¯�AFG�^(S@A�X�Wpo(Z\EHG\X?�DFE]Z\`QD/X¯�AFG�^(S@A�X�WgA�XVWgWHG�=2dFK-�~e&=2SYK>Z\D6b�G\DF_H=@I�AFX�AHo/A�X�WpoF��X�AFSYS2^FoFZ�EHG\X&G�=2qF`[Z�DFX�b�G�D/_H=@I�A�XVA�AFX�W&W]G\=Yd/K ³ e&=2SYKi?�a»{`HK�G�KCAFG�K�^/DFE � £cD"l e�A�X(^�e&=2SYKi?6`�A*d/KgZ�GJA*dFK�S2K�W � »{`�A�Zs=@?-^FD/EHGMZ�DFZ\A�S�W]=@?U_HS@AFI�K�e&K�X[Z � ������ �¡RG\A*l�A&W]=2AFqFGJA�emaA[<°RXQZ�`�Ks¤[Z�G\=Y_�5�A"Z~Z�`�K6¯��M¯ ��G\AFX�WCP8D/G~l~`�A"Zc=YZ�· ?~l�DFG�Z�`V<�o ½ eg=2S2K�?�o�A�X�W ��� � �,« aLN<m°RXQZ�`�Ks¤[Z�G\=Y_�5�A"Z~Z�`�K6¯��M¯ ��G\AFX�WCP8D/G~l~`�A"Zc=YZ�· ?~l�DFG�Z�`V<�o ½ eg=2S2K�?�o�A�X�W ��� � �,«!� �V¬*ª�§ aIi<m°RXQZ�`�Ks¤[Z�G\=Y_�5�A"Z~Z�`�K6¯��M¯ ��G\AFX�WCP8D/G~l~`�A"Zc=YZ�· ?~l�DFG�Z�`V<�op�Meg=2S2KFo�AFX�W�� � ���,«(­&� �V¬*ª�§ aWV<m°RXQZ�`�Ks¤[Z�G\=Y_�5�A"Z~Z�`�K6¯��M¯ ��G\AFX�WCP8D/G~l~`�A"Zc=YZ�· ?~l�DFG�Z�`V<�op�Meg=2S2KFo�AFX�W�� � ���,«(­ aK*<m°RXQZ�`�Ks¤[Z�G\=Y_�5�A"Z~Z�`�K6£BA�GJW¿~D]IJOv�A"P8K*<$o ½ e&=YS2K�?�o�AFX�W�� � ���,«(­ a

¾F¾ ³ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�A/WHW]=2XHq&dFK�I�Z�D/G\?º(a ��D/EmI�A�XmAFWHWQdFKiI$Z\DFGJ?�u

A[<Cq/K�D/egK�Z�G\=2I�A�S2SY^�D/G~SY=2OFK-?\I�AFS2AFG\?�aLN<nq/K�D/egK�Z�G\=2I�A�S2SY^�D/G~L(^nI�D/eg_NDFX�K�X[Z\?�aIi<nS2=2OFK-?�I�A�S@A�GJ?�DFG~L(^nI�D/e&_VD/XHK�X[Z\?�aWV<nS2=2OFK-?�I�A�S@A�GJ?�DFG~L(^nW]=2d(=2?�=YD/X�aK*<nS2=2OFK-?�I�A�S@A�GJ?�DFG~L(^C=2X/Z\K�q/G\A�Z�=2DFX�a

¾F¾ ³ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujd/K�I$Z\DFG~I�D/e&_VD/XHK�X[Z~EHXH=@h[EHK�XHKi?�?¼ a~b>`HK6I�DFe&_NDFXHK�X/ZJ?>D�P�esEHSYZ�=YTkWH=Ye&K�XV?U=2DFX�AFS�_H`(^]?U=@I�AFS�dFK�I�Z�D/G\?�u

A[<nAFG�KMEHX�=2h[EHK/aLN<QI�A�XLVK6IJ`�D/?�K�XDFXHS2^�Z:l�Dgl>A*^]?�u�Z�`�KMZ:l�D&l>A*^(?�l~=2SYS�SYKiAFWnZ�DCW]= �NK�G�K�X[Zc_H`(^(?�=@I�A�S�LNK�`�A*d(=2DFGiaIi<QI�A�XLVK6IJ`�D/?�K�X=YXm=2X]��XH=YZ�K�SY^Qe&AFX(^Cl�A*^]?�u�KiAFIJ`l�A*^nSYKiAFWH?�Z\D&A&W]= ��K�G\K�X[Zc_H`(^]?U=@I�AFSpLVK�`�A*d(=YD/G�aWV<QI�A�XgLVKcIJ`�D/?�K�Xs=2X&=YXH��XH=YZ�K�S2^se�AFX[^-l>A*^]?�a�£cD"l�K�d/K�Gio�Z\`HK~_H`(^]?U=@I�?�DFP�Z\`HK~dFKiI$Z�D/G�G�K�e&AF=YXV?�Z\`HKc?\A�e&K

AFX�Wx=YX�A�X(^�_�G�D/LHSYK�e�Z�`�K&IJ`�DF=@I�K&D�P>I�DFe&_NDFXHK�X[Z\?�58=�a KFa2o�Z\`HK�IJ`HDF=@I�K&D�P>AmI�D(DFGJW]=2X�A"Z\K&?�^]?:Z\K�eC<R=2?AFG�L�=�Z\G\AFG�^/a���E]ZB?�DFe&K-IJ`HDF=@I�Ki?�e&AFOFK�Z�`�K-_HG�D/LHS2K�e�AgS2D�ZcK�A/?U=2K�Gia

K*<QI�A�XHX�D�Z~LVK6WHK�Z�K�G�e&=2XHK�WmA�Z~AFSYS�=YXm_HG\=YXVI�=2_HSYK/a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾ ³ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujdFKiI$Z\DFG>=2WHK�X[Z�=YZ:^�Fa>7kP�Z�`HK-?�EHe D�P�Z:l�DgdFKiI$Z�D/G\?�=@?�_NK�G\_NK�X�W]=@I�E�S2AFG�Z\DgZ�`HK�=YG~W]= �NK�G�K�X�I�K/o]_HG\D"dFKcZ\`�A"Z�Z�`�K�d/K�I�Z�DFGJ?�`�A*dFK�K�h[E�AFSe�A�q/XH=YZ�E�W]K/a ������ � �B?�KMZ�`�K6?�I�A�S@A�G>_HG\D(WHE�I$Z~D�Pj?�EHe�A�XVWWH=���K�G\K�X�I�KFa

¾F¾ ³ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujS@A*l�D�PjI�D[?U=2XHKi?

Page 20: Introductory Physics Problems David J. Jeffery Department of

� ¹ v�`�AF_]Z�a ³ ¤]I�AFS2AFG\?>AFX�Wn´jKiI$Z\DFGJ?

�]ac��=2dFK�XQd/K�I$Z\DFGJ?���CA�XVW �� A�XVWCZ\`�A"Z~Z\`HK6A�XHq/SYKMLNK�Z:l�K�K�XnZ\`HK�e =2?�������&_HG�D"d/KcZ\`HK-S2A*lzD�PjI�D[?U=2XHK�?�u

$ # � � ��� � ,r�!� � I�D/?�� l~`HK�G�K =@?~Z\`HK6e�A�q/XH=YZ�E�W]K4D�P��� � �� AFX�W � $ �4,�� ���� a ������ � �R?UK6Z�`HKg?�I�A�S@A�G~_HG\D]W]E�I$ZRD�P�� l~=�Z\`=YZ\?�K�SYP:a

¾F¾ ³ h/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujd/K�I$Z\DFG~G\D�ZJA"Z�=2DFXVA�SNZ�GJA�X�?UP8DFG\e�A"Z\=YD/X�?³ ac¤]A*^4^FD/Eg`VA*dFKcA-d/K�I$Z\DFG�?�_VKiI�=Y��K�WCL[^5�� �H<j=2X�G�K�S2A�Z�=2dFK>Z\Dgv�A�G�Z�Ki?U=@A�X �HT �gA��]K�?�a� BD"lwI�G�KiA"Z\K~XHK�l � ��T � �A��(Ki?ML(^�G�DFZ\A�Z�=2XHqZ�`HK�D/S2WrA"�]Ki?ML[^��mI�DFEHX[Z\K�GJI�S2D(IJO(l~=@?UK/a�b>`HK&dFK�I�Z�D/G-`�AF?�X�· Z6egD"d/K�WpuM=YZ6=2?s?:Z\=YS2SjZ�`�K?\A�e&KMe�A�qFX�=�Z\E�W]K6A�XVWn_H`(^]?�=2I�A�S�W]=2G�KiI$Z\=YD/X�a ��EHZcG�K�S2A�Z�=2dFKRZ�D&Z�`�K-XHK�l A"�]K�?�=YZc=2?B?U_NK�I�=���KiWL[^x5� � � �@<$aA[<C»{`VA"Z�AFG�K6Z�`HKsZ�GJA�X�?UP8DFG\e�A"Z�=2DFXmG\K�S@A"Z\=YD/X�? � � $�#�5� � ��/<BA�X�W � � $ p5�� � ��/<�a ������ � ¡BGJA*l Aq/D(D(WQW]=@A�qFGJA�emo(W]GJA*l�?UD/e&KR_NK�G\_VK�X�W]=@I�EHS@A�GJ?�o[S2D(DFO&P8D/G>?�=2eg=2S@A�G�Z�G\=2AFXHqFS2K�?�o]A�X�WnE�?UK�Z\G�=2qFD/XHDFe&K�Z\G�^/a

LN<¤]`HD"l�A�S2qFK�L�G\AF=2I�A�S2SY^nZ�`�A�ZBZ�`�Kse�A�q/XH=�Z\E�W]K6DFPjZ�`HK4dFKiI$Z�D/Gc=@?cZ\`HK4?\A�e&K6=2X�Z�`�KsG\D�Z\A�Z�KiW�?U^]?UZ�K�e�A/?=2XmZ�`�K6��GJ?:ZB?�^]?:Z\K�emu�=�a KFa2oHZ\`HK6e�A�q/XH=�Z\E�W]K6=@?cG\D�ZJA"Z\=YD/X=2X(d"A�G\=2AFX/Zia�¡R=@A�qFGJA�e&e�A"Z\=2I�A�S2SY^/o]D�P�I�D/EHGJ?UK/o=YZ�· ?�I�S2K�A�G;Z�`HK�e�A�q/XH=�Z\E�W]KR=2?;=YX(d"A�G\=2AFX[Z�u�^FDFE�EV?UKiW&Z�`�A�Z�I�DFX�W]=YZ�=2DFXn=YX��VX�W]=2XHq6Z\`HKBZ\G\AFX�?UP8DFG\e&A�Z�=2DFXG\K�S@A"Z\=YD/X�?�u>Z�`H=@?�_�A�G�ZR=@?�K�?\?UK�X/Z\=2AFSYS2^mAnI�D/X�?�=2?UZ�K�X�I�^�IJ`HKiIJONa ������ � b�A�OFK6Z�`HK�?\I�A�S@A�GB_HG�D]W]EVI$ZMD�P5 � � � �@<�l~=�Z\`m=�ZJ?UK�S�PjA�X�WE�?�K�Z�`HKMZ\G\AFX�?UP8DFG\e&A�Z�=2DFXQG�K�S2A�Z�=2DFX�?�a

Page 21: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � � ?:j$&A>�,�� Da5<1)1 j %*-=!1_>�EG*[?T>a&AN �Z*->a1_=!&X;<*-H E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾Fµgh[e4EHS�ZB¾/¾H�i¾F¾C� ¶ µ&K�A/?U^&Z\`H=2XHO�u�=YXVW]K�_NK�X�WHK�X[ZcDFG�Z�`HD/qFD/X�A�S�e&D�Z\=YD/X�Fa>7kZi· ?A�e�A�G\dFK�SYD/E�?gZ�`H=2XHqVa 7kP-Z�`HK �HT!W]=2G�KiI$Z�=2DFX�AFX�W �[TkWH=YG\K�I�Z�=2DFX±P8DFGJI�Ki?nA�G\K�=2X�W]K�_NK�XVW]K�X[Z�oBZ�`HK�X{Z�`�K��TkW]=2G\K�I$Z\=YD/XAFX�W �[TkW]=2G\K�I$Z\=YD/Xne&D�Z\=YD/X�?~A�G\KFuA[<CLND�Z\`m_VD[?U=YZ�=2dFK/aLN<nD/_H_ND/?�=�Z\KFaIi<nLND�Z\`mXHK�q[A"Z�=2dFK/aWV<n=2X�W]K�_VK�X�W]K�X/ZiaK*<QWHK�_NK�X�W]K�X[Z�a

¾F¾Fµgh[e4EHS�ZB¾/¾/�F¾F¾4� ¶�¶ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVujEHXH=YP8DFG\e e&D�Z\=YD/X=@?>G\K�S@A"Z�=2dFK�]a ��D/EQA�G\KB=2XmA-P8K�A�Z�EHG\K�S2K�?\?�X�A�G\G\D"l±G\D(DFe�_HS@A*^(=YXHqgI�A�Z\IJ`nl~=YZ�`A6P8G\=2K�X�Wpa�£BD"l�I�AFXn^FD/E�Z�K�SYSp=YP�Z\`HKMG�D(DFe=@?B=2X�ACL�EH=YS@W]=2XHqCD/GB=@?RAC?�K�AFSYKiW�I�D/eg_VA�G�Z�e&K�X[ZBD/X�?UEH_NK�G�T!?Ue&D(D�Z\`HSY^QG�E�XHXH=2XHq�oNXHDFXHTkA/I�I�K�SYK�G\A�Z�=2XHq&Z�GJA�=2X5,DFG�_HS2AFXHKi< � ������ � ¿~K�d(=2K�l�^/DFEHG�l~`HDFS2KsS2=YP8K4K��(_NK�G\=2K�X�I�K )�Z�G\^�A�X�K��]_VK�G�=2e&K�X[Z�58LHE]ZMXHDFZ�l~`H=2S2K4^/DFEAFG�K-W]G\=Yd(=2XHq[<�aA[<C»{`�K�Xg^FDFEsZ�`HG\D"lrZ�`�K�LVA�S2S � � � ��� Z�`�K�S2DFX�q�A��(=@?�D�P�Z\`HK>G�D(D/eo*=YZjl�D/EHS2Ws`�A*dFK>W]= �NK�G�K�X[Z�?�_VK�K�WH?

5,G�K�S2A�Z�=2dFK�Z�DgZ\`HK-G�D(D/e�<�=2XZ�`HKMZ:l�D&_VD[?�?�=YL�SYK-W]=2G�KiI$Z\=YD/X�?>=�P�^FD/EQl�K�G\KMDFXmA4Z�GJA�=2X�aLN<n»{`�K�Xg^FDFEsZ�`HD"l�Z�`HK>L�AFSYS ���� �� ��� � ¦ ��� � � Z�D�Z�`HK>S2DFXHqMA"�]=@?�D�P�Z\`HK>G�D(D/e�=�Zjl�DFEHS@WsI�EHG�d/K

D �xA&?:Z\G\AF=Yq/`[Z�S2=YX�KC58G\K�S@A"Z�=2dFK�Z\D4Z\`HK-G\D[D/eC<;=YP�^FDFEl�K�G\K�D/XA4Z\G\AF=YX�aIi<m°RXmAgZ�GJA�=2XQZ�`HKMZ\`HG�D"l~XL�AFSYSpl�DFEHS@WQ��=2qF��AFq4l~=2S@W]SY^Q=YX��=2qF`[ZiaWV<m°RXmAgZ�GJA�=2XQZ�`HKMZ\`HG�D"l~XL�AFSYSpl�DFEHS@WW]D�SYD(D/_�?>=YXQ��=2qF`[Z�aK*<Qb>`�K�G\K�=@?~XHD&l>A*^&Z�D&Z\K�S2S�AF?>S2DFXHq�A/?�Z�`HK�Z�GJA�=2Xm=2?>d/K�G\^n?�egD(DFZ�`�a

¾F¾Fµgh[e4EHS�ZB¾/¾ ³ ¾F¾C� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuj_HG\DBA:K�I�Z�=2SYKM_�AFG\AFLVD/SY=@I�A�GJI³ a>»{`H=@IJ`wLVKi?:ZnWHK�?\I�G\=YLNK�?&Z\`HK�_�A�Z�`wD�P-A�L�A�S2S~Z�`�G�D"l~X±DFXwS2K�dFK�S~qFG\DFEHXVWtA�Z�AFX{A�XHq/SYK ³ ¾��mA�LND"dFKZ�`�K`HD/G�=2��D/X[Z\A�SpA/?~?UK�K�XQP8G�D/e}A&?U=@W]KMd(=YK�l-aA[<nb>l�D4?UZ�GJA�=2qF`[Z�SY=2XHK�?�Z\`�A"Z>e&K�K�Z~A�Z>AFXQAF_VK���u�D/XHKcP8D/G�Z\`HKMG�=@?�=YXHq4_H`�A/?UK )[D/XHKRZ�`HKMW]K�I�SY=2XH=2XHq&_H`�A/?UK/ab>`�K-G�=@?U=2XHqg_H`�A/?UK-S2=YX�K�=@? �� � ¦ Z\`HKMSYK�XHq�Z\`mD�P�Z�`HK6W]KiI�S2=YX�=YXHq&_H`VAF?�K�S2=2XHKFa

LN<Q�}?Ue&D(D�Z\`�I�EHG\dFK&Z\`�A"ZgG�=@?UKi?6A�XVW�P,A�S2S2?sl~=�Z\`�W]=2?UZ\AFX�I�K/a��B?6P,A�GsA/?-Z�`�KCK�^/KnI�AFXxZ\K�S2S�o�Z\`HKnI�EHG�d/KI�DFEHS@WQLVK-_�AFG\AFLVD/SY=@I�a

Ii<Qb>l�D4?UZ�GJA�=2qF`[Z�SY=2XHK�?�Z\`�A"Z>e&K�K�Z~A�Z>AFXQAF_VK���u�D/XHKcP8D/G�Z\`HKMG�=@?�=YXHq4_H`�A/?UK )[D/XHKRZ�`HKMW]K�I�SY=2XH=2XHq&_H`�A/?UK/ab>`�K-G�=@?U=2XHqg_H`�A/?UK-S2=YX�K�=@? � � �� �Z�`HK-S2K�XHqFZ�`mD�P�Z�`HK6WHK�I�S2=2XH=YX�q�_H`�AF?�KMSY=2XHK/a

WV<Q� ?�e&D(D�Z�`rI�E�G�d/K4Z\`�A"Z6G\=@?UKi?-A�X�W�P,A�S2S2?Ml~=YZ�`�WH=2?UZ\AFX�I�K/o�LHE]Zs?�E�WHW]K�XHS2^�LHG\K�AFO(?�D �tA�X�W�W]Ki?�I�K�X�WH?d/K�G�Z�=@I�AFSYS2^Fa

K*<Q� ?�egD(DFZ�`zI�EHG\dFK�Z\`�A"ZmG�=@?�K�?A�X�WwP,AFSYS@?l~=�Z\`zW]=@?UZ\A�XVI�KrA�X�WwZ\`HK�XzG�=@?�K�?A�X�W�P,A�S2S2?A�q[A�=2X�l~=�Z\`WH=2?UZ\AFX�I�K/a�� ��A/I$Z\G�=@A�XI�A�e&K�S�I�EHG\dFK/a

¾F¾Fµgh[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujq/G\A*d(=YZ:^g=@?cAFSYl>A*^]?�W]D"l~X(l>A�GJWCD/X��A�G�Z�`µ�a~��L�AFSYS�=@?;Z\D/?\?UKiW�=2X/Z\DsZ\`HK-A�=2G�AFX�W�P,AFSYS@?�Z�D4Z�`HK�qFG\DFE�X�Wn?�DFe&KRWH=2?UZ\AFX�I�KMA*l�A*^/a�v�D/X�?U=@W]K�G�=YZ\?�e&D�Z\=YD/Xn=2XZ\`HK-dFK�GUZ\=2I�A�SpW]=2G�KiI$Z�=2DFXmD/XHSY^QA�X�WQXHK�q/SYKiI$ZBAF=YG>G\K�?�=2?UZ\AFX�I�K/aA[<nb>`�K-L�A�S2Sp`�AF?~A&I�DFX�?UZ\AFX/ZcA/I�I�K�SYK�G\A�Z�=2DFXW]D"l~X(l�AFG\Wpa

Page 22: Introductory Physics Problems David J. Jeffery Department of

� ¼ v�`�AF_]Z�ajµ b>l�DFT�A�X�Wmb>`HG\K�K�Tk¡R=Ye&K�X�?U=2DFXVA�Sp²M=YX�K�e�A"Z\=2I�?

LN<Qb>`�KgLVA�S2S���G\?UZ6AFI�I�K�S2K�GJA"Z\K�? ��©��4¨]¬ � DFX�=�ZJ?MG�=@?�=YXHq_�A�Z�`rA�X�W�Z�`HK�X�AFI�I�K�S2K�GJA"Z\K�? � ���)� �s¨]¬ � D/X=YZ\?~P,A�S2SY=2XHq&_�A"Z\`�a

Ii<Qb>`�KgLVA�S2S���G\?UZ6AFI�I�K�S2K�GJA"Z\K�? � ���)� �s¨H¬ � DFX�=�ZJ?MG�=@?U=2XHq_�A"Z\`�AFX�W�Z�`HK�XrA/I�I�K�S2K�GJA"Z�Ki? ��©��s¨]¬ � D/X=YZ\?~P,A�S2SY=2XHq&_�A"Z\`�a

WV<Qb>`�K-L�A�S2S�W]D(K�?>XHDFZBAFI�I�K�S2K�GJA"Z\K�A�ZBA�S2S�aK*<Qb>`�K-L�A�S2Sp=2?BA�S2l�A*^]?�AFI�I�K�S2K�GJA"Z\=YXHqg=2XQZ\`HK-EH_(l>A�GJWnW]=2G�KiI$Z\=YD/X�a

¾F¾Fµgh[e4EHS�ZB¾/¾ ¶ ¾F¾4� ³ �Me&D]W]K�GJA"Z\K�e�A�Z�`�ujq/G�D/EHX�Wn?�_NK�K�WQP8G\DFe�9;^[Z�`�a�Z\`HK�D/G�K�e¶ a~�B=YG�dFK�S2D]I�=YZ:^s=@?�µ[¾Meg=8y*`�G�W]EHKBXHDFG�Z�`�a�»{=2X�W�dFK�SYD]I�=�Z:^4=2? ³ ¾Me&= y"`HG�WHEHKcl�K�?UZ�a�»{`�A"Z�=2?�Z�`HKce�AFqFXH=YZ�E�WHKDFP�q/G�D/EHX�WCd/K�S2D]I�=YZ:^�58=�a K/aYoHZ�`HK-q/G�D/EHX�W?U_NK�KiW�<��

A[< ¶ ¾je&= �*`HG�o LV<�, ¶ ¾je&= �"`HG�o Ii<�µ/¾je&= �*`HG�o W�< ³ ¾�eg= �*`�G�o K*<~� ¶ ¾/¾je&= �"`HG$a

¾F¾Fµgh[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu;I�K�X[Z�G\=Y_NK�ZJA�S�AFI�I�K�SYK�G\A�Z�=2DFX¹ a~|�G�D/e W]=Ye&K�X�?U=2DFXVA�S~A�X�AFSY^]?�=2?58=�a KFa2o;L(^�IJ`HK�IJO(=2XHq�P8D/GgI�DFG\G�KiI$ZgEHXH=YZ\?J<sD/XHK=2W]K�X[Z�=Y��K�?gZ\`HKnP8D/G�e4EHS@A�P8D/GI�K�X[Z�G\=Y_NK�ZJA�S�A/I�I�K�SYK�G\A�Z�=2DFXnZ�D�LNKFuA[<���� � � $ � � aLN<'� � � ��$ � � �/aIi<'��� � � $ � ��� aWV<'��� � � $ � aK*<'� � � ��$ � �Fa

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾Fµgh/P8EHS2S�¾/¾H��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�uj_HG�D A:K�I�Z�=2SYKMe&D�Z\=YD/X=2XmqFK�XHK�GJA�S�Fa>7!X�AFX�?Ul�K�G\=2XHqgZ�`H=@?B_�G�D/LHSYK�emoH^FD/E�DFL]ZJA�=2XmAFSYS�Z�`HKsG�KiA�S2SY^QE�?UK�P8EHS�K��]_HG�Ki?�?�=2DFX�?�P8D/GB_HG\DBA:KiI$Z�=2S2K-egDFZ�=2DFX�=2XZ\`HK6A�L�?�K�XVI�KMD�PjA�=2G~G�Ki?U=@?UZ\A�XVI�KFa�°BZ\=YD[?UKMq/K�XHK�G\AFSY=YZ:^�=2?cK�?\IJ`HK�l�K�Wpa�¸�K�Z���AFX�W �CLVK6Z�`HK-`HD/G�=2��D/X[Z\A�SpAFX�Wd/K�G�Z�=@I�A�S�I�D(DFGJW]=2X�A"Z\K�?�ax�R?�?�EHe&KCZ\`HKn_HG\DBA:KiI$Z\=YS2Kn=@?sS@A�E�X�IJ`HK�W�P8G�D/e � $�¾xA"Z � $�¾�A"Z&A�X�AFXHqFS2K�Z\DZ\`HK&`HDFG\=Y��DFX[Z\AFS�DFP ��� � , � ������ ����!�a6b>`�K4D/XHSY^�A/I�I�K�S2K�GJA"Z�=2DFX�=2? , �uB=�a K/aYo�q/G\A*d(=YZ:^Q=2XxZ�`HK&XHK�q/A"Z\=Yd/K �W]=2G\K�I$Z\=YD/X�ajb>`HK-S@A�EHX�IJ`m?�_VK�K�W=2? � �A[<C»{`VA"ZBA�G\K�Z�`HK���AFX�W �nK��]_HG\K�?\?�=YD/X�?�A/?~A4P8EHX�I$Z\=YD/X�D�P�Z�=2egK/aLN<¤]=YX�I�K �mA�XVW � A�G\KcS2=YX�K�A�G\S2^gG\K�S@A"Z\K�W�l�KBD/XHS2^gX�K�K�WCZ�Ds��X�WCK��]_HG�Ki?�?�=2DFX�?�P8DFG�K�=YZ�`HK�G�D/XHKFu�Z�`�KRDFZ�`HK�G

LNK�=2XHq6D/L]Z\AF=YX�K�W&A�S2l�A*^]?�L(^4A-?�=Ye&_HS2Kce4EHS�Z\=Y_�SY=@I�A�Z�=2DFX�a�°BP Z�K�X�=YX�K�SYK�egK�X[Z\A�G\^6_HG\DBA:KiI$Z\=YS2K~_HG\DFLHS2K�e�?�oD/XHKc=@?;X�D�Z�?�D6=2X/Z\K�G\K�?UZ�KiW&=YX � aj�R?UKBZ�`HKRK��]_HG\K�?\?U=2DFX�?�P8G\DFe Z\`HKBA�XV?Ul�K�G;Z�D6_�AFGUZ�5,A/<jZ�D6D/L]Z\AF=YX ��A/?P8E�X�I$Z\=YD/XQDFP �AFX�WCX�D�Z � a�|�=2X�WCZ�`HK �d*AFSYE�KBZ\`�A"Z~qF=2dFKi? ������sA�XVWCqF=2dFKBZ�`HK�K��]_HG\K�?\?�=YD/X�P8DFG�������[a

Ii<¤]DFS2dFK�P8DFG ��A/?~AsP8E�X�I$Z\=YD/XDFP ��a�b>`H=@?>=@?>Z�`HK-q/K�XHK�G\AFS�G\AFXHqFKRP8DFG\esEHS@AHaWV<Q�BXn=2e&_VD/GUZJA�X[Z�?�_VKiI�=@A�S�I�A/?UK~P8D/G;Z\`HK�G\AFXHqFK~P8D/G�e4EHS@A-D]I�I�E�G\?�l~`HK�X � $ � � aj|�=YXVW�Z�`�=2?�K��]_HG\K�?\?U=2DFX�a|�=2X�WQZ�`HK��gZ\`�A"Zcq/=Yd/K�? � ���� AFX�WqF=2dFKRZ�`HK�� ���� K��]_HG\K�?\?U=2DFX�aK*<Q|�=2X�A�S2S2^FoHl~`�A�Z~=2?>Z\`HK-K��]_HG\K�?\?�=YD/XCP8DFG ��=YP � ${¾Ha

¾F¾Fµgh/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_HG\DBA:KiI$Z�=2S2K�e&DFZ�=2DFX=YXmdFD/SYS2K�^(L�AFSYS�]a~b>`HK�l�DFe&K�X�· ?�dFDFS2S2K�^(L�A�S2SVI�DFEHG�Z�`VAF?�AsXHK�Z�`�K�=2qF`[Z�DFP�� � �"µ�e�A�XVWCK��(Z\K�X�WH? ½ � ¾je DFXQK�=YZ�`HK�G�?�=@W]KRDFP�Z�`�KXHK�Z�ax°RX�A�A:E�eg_t?UK�G�d/KCAm_HS2A*^/K�Gs?�_H=2OFKi?C587MZ\`H=YX�O�Z\`�A"Zi· ?sZ�`HKnl�D/G\W�<RZ\`HKnLVA�S2S�A"Z ³ � ¾F¾je A�LND"dFK&Z�`�KI�DFEHG�Z~=YX�A&W]=2G�KiI$Z\=YD/X_NK�G\_NK�X�W]=@I�E�S2AFG~Z�DgZ�`�K6XHK�Zia;b>`HK-=2XH=YZ�=@A�S�d/K�S2D]I�=YZ:^C=2? � � ����� � �� � �{A�X�WQZ�`�KXHK�Zc=2? ¼ � ¾je A*l�A*^&P8G\DFe Z�`HK6?�K�G\dFK�G�aA[<n|�=2G\?UZ�op?�DFS2dFK6=2X ���'�� ��� �rP8D/GR=2XH=YZ�=@A�S�dFK�SYD]I�=YZ:^ � � A/?RACP8EHX�I$Z\=YD/X�D�P � � � � ��XVA�S�`HDFG\=Y��DFX[Z\AFS_ND/?�=YZ�=2DFX ��58e&KiAF?�EHG�KiW�P8G�D/e S2AFEHX�IJ`�_ND/?�=YZ�=2DFXV<�o � � 5,S2AFEHX�IJ`t`HK�=2qF`[ZJ<�o ��5 ��XVA�S�`HK�=2qF`[ZJ<�o;A�XVW Na

Page 23: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�ajµ}b>l�D�T;AFX�Wb>`HG�K�K�T!¡B=2e&K�X�?�=2DFX�AFS�²M=YXHK�e�A"Z�=@I�? � ½

¤]OFK�ZJIJ`�A&qFGJA�_H`D�P � � AF?~AgP8E�X�I$Z\=YD/X�D�P �CP8DFGRI�DFXV?:ZJA�X[Z ��u;=2X�W]=@I�A�Z�K-D/Xm?�OFK�Z\IJ`Z�`�K � � P8DFG�� $�¾=2Xn?�^(esLNDFS@?�AFX�WgZ�`HK�S2D(I�A"Z\=YD/X�D�PpZ�`�K �Ue�A��(=2esE�e �6D�P � � a�b>`�K�Xn?�OFK�Z\IJ` � � AF?;A6P8EHX�I�Z�=2DFXCDFP �nP8D/GI�DFX�?UZ\AFX[Z���aLN<n»{`VA"Zc=@?�Z�`HK-e&=2XH=Ye4EHe�?U_NK�KiWQX�K�K�WHK�WnP8DFG>Z�`�K-L�A�S2SpZ�D�I�SYKiA�G>Z�`�K-XHK�Z �Ii<n»{`VA"Z�=@?jZ\`HKBe�A��(=2esE�e ?�_VK�K�WCAFSYS2D"l�K�Wg=�PpZ\`HKBLVA�S2S�=@?jZ�D4?:ZJA*^4=2XnI�D/EHG�Z��B?\?UE�egKRXHD6D/XHK~Z�D/E�IJ`HKi?Z\`HK-L�AFSYS�a

¾F¾Fµgh/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujEHXH=YP8DFG\e}I�=YGJI�E�S2AFG�e&DFZ�=2DFXmA�X�Wmbc��´³ aBv�D/X�?U=@W]K�GcAgbc��´ 5�b�GJA�=2X (A&��GJA�XVW]KM´B=YZ�K�?\?�Ki<$a

A[<Q¤HA*^�=�Zc`�A/?>Ag?�_NK�K�WQD�Pj�]� ¹ O(e �"`HG>A�X�WQ=2?�e&D"d(=YX�qg=2XmA4I�=YGJI�S2KFaj»{`�A�Z~=2?�Z\`HKMeg=2XH=2esEHe}G\A/W]=2E�?�D�PZ\`HK-I�=2G\I�SYKR=�P�Z�`HKMI�K�X[Z�G\=Y_NK�ZJA�SpAFI�I�K�S2K�GJA"Z\=YD/X�=2?�Z\D4LNKMOFK�_HZ�S2K�?\?�Z\`�A�Xm¾ � ¾ ¶ �Q�j�]_HS@A�=2Xnl~`(^&=YZ>e4E�?UZLNKMZ�`�K-eg=2XH=2esEHe}G\A/W]=2E�?�a ������ � ¤]IJ`HK�e�A�Z�=@I�A�S2S2^�_HSYDFZBI�K�X/Z\G�=2_NK�Z\AFS�AFI�I�K�S2K�GJA"Z\=YD/Xnd/K�GJ?UE�? a

LN<n7kP4Z�`HKrGJAFW]=2E�?=@?x� � ¾/¾jO(emoBl~`�A�Zm=@?QZ�`HKre�A"�]=2esEHe ?U_NK�KiWf58=2X eny"?mA�X�W�O(eCy"`HG$<CLNK�P8D/G�K�Z�`�KA/I�I�K�S2K�GJA"Z�=2DFXQK��HI�K�K�WH?~¾ � ¾ ¶ ��m�j�]_HS@A�=2XQl~`(^C=YZc=@?>Z�`HK-e�A��(=2esE�e�?U_NK�KiWpa ������ � ¤HIJ`HK�e�A"Z\=2I�A�S2SY^_�SYDFZBI�K�X[Z\G�=2_VK�Z\AFS�AFI�I�K�S2K�GJA"Z\=YD/XndFK�G\?�E�? � a� � � � £cK�G\K�l�K�E�?�K $ ½ � ¼ e���? ��A/?CA�EHXH=YZQDFP6AFI�I�K�S2K�GJA"Z\=YD/X�az�BX�AFI�I�K�S2K�GJA"Z\K�WtP8GJA�e&K�=2?K��HAFI$Z\SY^�S2=2OFKMLVK�=YX�qgq/G\A*d(=YZ\A�Z�=2DFX�AFSH��K�S2Wm?�DsP,AFG>Age&K�IJ`VA�XH=@I�AFSNK��]_VK�G�=2e&K�X[Z\?�=2X/Z\K�G\X�A�SNZ\D4Z\`HKMP8GJA�e&KAFG�K�I�DFX�I�K�G\XHK�WpaQb>`H=2?s=2?sAFI$Z\E�A�S2S2^�Am_HG\D�P8DFE�X�W�DFL�?�K�G\d"A"Z�=2DFXxZ�`VA"Zs?UZ\A�G�Z�KiWr��=2X�?:Z\K�=2XrDFXr`H=@?-l�A*^Z\D�`H=@?-qFK�XHK�GJA�S�Z\`HK�D/G�^�DFP~G�K�S2A�Z�=2d[=YZ:^FaCb>`�K�_�?UK�E�W]DFT�q/G\A*d(=YZ\A"Z\=YD/X�A�S�P8DFGJI�K�_NDF=2X[Z\?-D/_H_ND/?�=�Z\K&Z�DmZ�`�KA/I�I�K�S2K�GJA"Z�=2DFXmA�XVWm`�AF?Be&AFqFXH=YZ�EVW]K����Va~b>`H=@?c_V?UK�E�W]DCD/Gc=YX�K�G�Z�=@A�S�P8D/G\I�K-=2?R?UD/e&K�Z�=2e&K�?RI�A�S2S2K�WZ�`�KqFT�P8D/G\I�K�AFX�W6=@?j?U_NK�I�=��VK�WsA/?�AcP8D/G\I�K�_NK�G�EHXH=YZ�e�AF?\?�=2XgEHXH=YZ\?�D�P Na�b>`(E�?�I�=2G\I�SY=2XHq�l~=�Z\`gA/I�I�K�SYK�G\A�Z�=2DFX¾ � ¾ ¶ m=2?�A:E�?UZ-SY=2OFKgLNK�=2XHqm=YXxqFGJA*d[=YZ\A�Z�=2DFX�AFS���K�S2WxD�P�¾ � ¾ ¶ ml~`HK�G�K4Z�`HK&q/G\A*d(=YZ\A"Z\=YD/X�A�S�P8DFGJI�Kg_VD/=YX[Z\?GJAFWH=2AFSYS2^�DFE]Z:l>A�GJWpa

¾F¾Fµgh/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�?�l~=Ye&e&=YX�qC��XHq/SY=@?U`IJ`�A�X�XHK�Sµ�a ��D/E{`�A*dFK�W]KiI�=@W]K�W{Z�D�?�l~=Ye�Z�`�Kx��X�qFS2=2?�`{IJ`�A�XHX�K�ScP8G\DFe ��G\=2?UTk BK��mZ\D�|HD/SYO/K�?UZ�DFX�KFuxA�W]=2?UZ\AFX�I�K�D�PAFLVD/E]Z~µ/¾jO(e G\DFEHq/`HSY^&Z\DgZ�`HK-XHD/GUZ\`]Tkl�Ki?:Zia ������ � ¤]egKiA�G~^/DFEHG�LVD]W]^A�S2SpD"dFK�G�l~=YZ�`P,A"ZJ?�Z�D&_HG\K�d/K�X[Z`(^(_VDFZ�`HK�G�e&=@AHaA[<C7kP�^FD/E?�l~=2e}A"Z~µ�O(e��*`�G�`�D"l�S2DFXHq&l~=2SYS�=YZ~Z\AFOFKM^FD/E �LN<Q�R?B=YZcZ\EHG�XV?cDFEHZR^FD/EmS2AFX�W�A"Z� cK�l�¿~D/e&XHK�^mA�LNDFE]Z-��¾jO(e ?UD/E]Z�`]Tkl�K�?UZcD�P;|HD/SYO/K�?UZ�D/XHKFa>»{`�A�ZB=2?

Z\`HK6A*dFK�G\AFqFK�IJ`�A�XHX�K�S�I�E�G�G\K�X[ZcW]EHG\=YX�qg^/DFEHG~?�l~=Ye �Ii<Q�B_H_HG\D*�]=Ye�A"Z\K�S2^nl~`�A�ZR`�A/?cLNK�K�X�^FDFE�GRA*dFK�G\AFqFK�dFK�SYD]I�=YZ:^mW]EHG\=YXHqCZ�`HKs?�l~=2e G\K�S@A"Z\=Yd/KMZ�D�Z\`HK6���(KiW��A�G�Z�`�az�B?\?UEHe&K�Z\`�A"Z|HDFS2OFKi?:Z\DFXHKm=@?�K��HA/I$Z�S2^�X�DFG�Z�`]Tkl�Ki?:Z�DFP6��G\=@?:T! cK��mAFX�Ww cK�l�¿cDFe&XHK�^t=2?K��HAFI$Z\SY^Q?UD/E]Z�`]Tkl�K�?UZ>DFP�|�DFS2OFK�?UZ�D/XHKFa ������ � ´jK�SYD]I�=�Z:^QG�Kih/E�=YG\K�?>A&W]=2G�KiI$Z�=2DFX�?�_VKiI�=Y�VI�A�Z�=2DFXQZ�D(D�a

¾F¾Fµgh/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u��Be&AF��D/XmI�G�D[?�?�=2XHqs7¶ a~¡RK�K�_=2XmZ�`�K6�ce�A���DFXH=@A�X&A:EHXHq/SYK-^/DFEl~=2?�`Z�DCI�G\D/?\?~AgG�=2dFK�G~SY=2d(=2Wl~=YZ�`m_H=2G\AFXH`�A&A�XVWI�G�D]I�D(WH=YS2K�?�a�¸�K�Z�tLVKQZ�`HKI�D(DFGJW]=2X�A"Z\K � ��� ��� Z\`HKnG\=Yd/K�GsAFX�W ��Z�`�KQI�D(D/G\W]=2X�A�Z�K ���� �� ��� � ¦ ��� � � Z\D�Z�`�KG\=Yd/K�Gia�b>`�K6G�=2dFK�G~l~=2W]Z�`�=@? � ���� $ ��¾jema���DFE�A�G\K-qFD/=YX�q&Z�D�_�A/WHW]S2KsAFI�G�D[?�?-5,DFX�A�X�E�X�?:ZJA�LHS2K6G\D�Z�Z�=2XHqS2DFq��wE�?�=2XHq4^/DFEHG~LVA�G\KR`�AFX�WH?J<>A�X�WQ^FD/EHG~_�A/WHW]S2=YXHq�?�_VK�K�W=@? � � ������� � $�¾ � ¶ ¾�e ��?$aA[<n£BD"l�SYD/XHq�W]D(Ki?C=YZQZJA�OFK�^FDFEwZ\DtI�G�D[?�?CA/?�?�EHe&=2XHq�Z�`VA"ZQ^/DFEf5,l~=2?�K�S2^H<CAF=Ye ?:Z\G\AF=Yq/`[Zn=YX�Z�`HK �[TWH=YG\K�I�Z�=2DFX �

LN<Q�R?�?�EHe&=2XHqnZ\`HKgG�=2dFK�GB��D"lc?�A"Z-A?:Z\K�AFWH^d/K�S2D]I�=YZ:^ ��� $f¾ � �F¾je��"?B`HD"l P,A�G-W]D"l~X�?UZ�G\K�AFe 5,=�a KFa2o�=2XZ\`HK���W]=2G�KiI$Z\=YD/XV<�`�A*dFK�^FD/EQq/DFXHKMl~`H=2S2KMI�G�D[?�?�=2XHq �

Ii<n»{`VA"Z~=2?>^/DFEHG�XHK�ZcdFK�S2D]I�=YZ:^&G�K�S2A�Z�=2dFKRZ�DgZ�`HK-?�`HDFG\KMW]EHG\=YXHq4Z�`�KMI�G�D[?�?�=2XHq � ������ � ¿~K�e&K�esLNK�G�Z\D?�_NK�I�=YP8^QWH=YG\K�I�Z�=2DFX�a

Page 24: Introductory Physics Problems David J. Jeffery Department of

��¾ v�`�AF_]Z�ajµ b>l�DFT�A�X�Wmb>`HG\K�K�Tk¡R=Ye&K�X�?U=2DFXVA�Sp²M=YX�K�e�A"Z\=2I�?

WV<Q BD"l�S2K�Z�· ?�e�A�OFKRZ�`�K�X�D�ZUT�Z�D(DFT�S2=YO/K�S2^gA/?�?�EHe&_]Z\=YD/XCZ�`VA"Z>Z�`HKMG\=Yd/K�G�dFK�S2D]I�=YZ:^�=YXQZ�`�K ��TkW]=2G\K�I$Z\=YD/Xn=@?>AS2=2XHK�AFG>P8EHX�I$Z\=YD/XmD�P �No(Z\`HK6W]=@?:ZJA�X�I�KM=YXZ�`�K��/T!W]=2G�KiI$Z\=YD/X�aj¸�K�Z

��� 5 �H< $ ��� ���� �� ����

l~`�K�G\K � ${¾gA"Z�Z�`HK-?UZ\A�G�Z�=2XHq&?U`�DFG\KRA�XVW � � ���� $�¾ � ¼ e��"?�aj��=2dFK�XCZ\`�A"Z~K�d/K�G\^[Z�`H=2XHq�o[K��HI�K�_]Z>Z�`�KG\=2dFK�G>d/K�S2D(I�=�Z:^/o(=2?�Z\`HK-?�AFegK-A/?�=2XZ�`HKMKiA�G\SY=2K�G�_�A�G�Z\?>DFP�Z\`HK-h/E�K�?UZ�=2DFX�o]`HD"l�P,A�GcW]D"l~X�?UZ�G\K�AFe 58=�a K/aYo=2XZ�`HK���WH=YG\K�I�Z�=2DFXV<�W]D�^/DFEegD"d/K��

¾F¾Fµgh/P8EHS2S�¾/¾ ¹ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u��ce�A���DFX�I�G\D/?\?U=2XHq47U7¹ a~¡RK�K�_�=YXgZ�`�KB�ce�A���DFXH=@A�X A:EHX�qFS2K~^FDFE&l~=@?U`gZ\DsI�G\D/?\?jAMG�=2dFK�G�SY=2d(=2W&l~=YZ�`�_H=2GJA�XH`�AMAFX�W�I�G\D]I�D]W]=2SYKi?�a�¸�K�Z �LNK�Z�`HKMI�D(DFGJW]=2X�A"Z\KRAFSYD/XHq6Z\`HKMG�=2dFK�G�AFX�W �&Z\`HK�I�D(DFGJW]=YXVA"Z�KR_VK�G�_NK�XVW]=2I�EHS@A�G�Z�D4Z�`HKMG\=Yd/K�Gia�b>`�K �[TkDFG\=Yq/=YX=@?cA"ZBZ�`HK-G\=Yd/K�GcI�K�X[Z�K�G�a�b>`HK6l>A"Z�K�G~dFK�SYD]I�=YZ:^CDFP�Z\`HK6G\=Yd/K�G-58l~`�=2IJ`�=@?~=2XmZ�`HK6_ND/?�=YZ�=2dFK��HT!W]=2G�KiI$Z\=YD/XV<�=2?BA_�AFG\AFLVD/SY=@IBP8EHX�I$Z\=YD/X�D�P�Z�`HK6W]=@?UZ\A�XVI�K�P8G�D/e Z\`HK6I�K�X/Z\K�G~DFP�Z�`�K-G�=2dFK�G�u

��� 5�H< $ � � � � � � ,�� ��� ���

l~`HK�G�K $ � ¶ e�=@?M`�A�SYP;Z\`HK&G�=2dFK�GRl~=@W(Z\`�AFX�W � � � � $ ��e��"?�=@?RZ�`HK�I�K�X[Z�K�GMl>A"Z\K�G-?U_NK�KiWpa ��D/E�`�A*d/Ke&D�Z\DFG�T�LND/A�Z�l~=�Z\`CA ¶ e��"?;?U_NK�KiWpa�¤]A*^s^/DFE�_NDF=2X/Z;Z�`HKcLND/A�Z�W]=2G�KiI$Z\SY^g=YXCZ�`HK��[T!W]=2G�KiI$Z�=2DFX�AFX�W�I�G\D/?\?�Z�`�KG\=Yd/K�GiaA[<n£BD"l�S2DFXHq�W]D(Ki?>=�Z~ZJA�OFKM^/DFEQZ�DCI�G\D/?\?�a ������ � b>`�=2?~=@?>K�A/?U^/aLN<Q£BD"l�P,AFGcW]D"l~X�?UZ�G\K�A�e 5,=�a KFa2oH=2XnZ\`HK-_ND/?�=�Z\=Yd/K���TkWH=YG\K�I�Z�=2DFXV<�`�A*d/K�^/DFEnZ�GJA*dFK�S2K�W � ������ � ��DFEmA�G\K

q/DF=2XHq4Z�D�`�A*d/KBZ\DCW]D�A�X=YX[Z�K�qFGJA"Z\=YD/X�a

Page 25: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� ��1 ��;7?T>�� E���& ��E�&A>�, %'6F>a&A= *-HJE�Q

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾ ¶ h[e4EHS�ZB¾/¾H�i¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�Z\`HK-X(EHesLNK�G~DFP� cK�l>Z�D/X�· ?cS2A*lc?�Fa~ BK�l>Z�D/X�DFX�I�KgZ�`HD/EHqF`[ZsA�LNDFEHZs`�A*d(=YX�qm?�=Y�xS@A*lc?MD�P~e&D�Z�=2DFX{5,DFGs?�DZ�`HKC=2X�?UZ�G\E�I$Z\DFGs?�K�K�e�?�Z�D�G\K�I�A�S2S@<�oLHEHZcK�dFK�X[Z�E�AFSYS2^n?�K�ZUZ\SYKiWDFX�u

A[<�DFXHK/a LV<�Z:l�D�a I�<�Z\`HG\K�KFa W�<�P8DFEHGia K*<�Z\`HG\K�K6A�XVWn`�AFS�P:a

¾F¾ ¶ h[e4EHS�ZB¾/¾/�F¾F¾C� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu�l~`�A�Z�P8D/G\I�K�?~W]D�]a~|�DFGJI�K�?~I�A�XmI�AFE�?UK-A/I�I�K�SYK�G\A�Z�=2DFX�?�a�b>`HK�=2G~D�Z\`HK�G~=2e&_VD/GUZJA�X[Z~e&AFXH=YP8K�?UZ\A"Z\=YD/XQ=@?>Z\`�A"Z~Z\`HK�^I�A�XmI�AFE�?�KFu

A[<Cd/K�S2D]I�=YZ:^�58l~=YZ�`HD/E]ZBI�AFE�?�=YXHq�A/I�I�K�SYK�G\A�Z�=2DFXV<�aLN<ne�A/?�?�aIi<nLND]W]=2K�?>Z\D&WH=2?UZ�D/GUZiuj=�a KFa2o]��K���oHI�DFe&_HG\K�?\?�oH?UZ�G\K�ZJIJ`�o]K�ZJI�aWV<nLND]W]=2K�?>Z\DgS2=2dFKK*<nLND]W]=2K�?>Z\DgG\EHS2KFa

¾F¾ ¶ h[e4EHS�ZB¾/¾ ³ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu;AFI�I�K�SYK�G\A�Z�=2DFXnAFX�WQZ�`H=2G\WS@A*l� ª�¬"¨ �V«������V¬ ��­�� A�S@?UD&_H`(^]?�I�=�² ��T ¶F½ TJ� ¶

³ a>7kPj cK�l>Z�DFX�· ? ³ G\WnS2A*lz=2?~Z�G\EHKFo]l~`(^CZ\`HK�X�W]D(Ki?~A�X(^[Z�`H=2XHq�AFI�I�K�S2K�GJA"Z\K�A�ZcA�S2S �A[<nb>`�K-K�h[E�A�S�AFX�WQDF_H_ND/?�=�Z\KMP8DFGJI�Ki? � � � � `�A*dFK�Z\DgLNK-DFXZ\`HK6?�AFe&K�LND]W]^FaLN<Qb>`�K-K�h[E�A�S�AFX�WQDF_H_ND/?�=�Z\KMP8DFGJI�Ki? � �}`�A*d/KBZ\D�LVK-D/XnZ\`HK6?�AFe&K�LND]W]^FaIi<Q BD�Z\`H=YX�q4e&D"dFKi?;A�Z>AFSYS�AF?�9jA�G\e&K�XH=@W]K�?�A�G\qFEHKiW�=2XCZ�`�K ¶ Z�`nI�K�X[Z�EHG\^ �cvRa[¯�D�Z�=2DFXQ=2?�LHE]Zc?�K�K�eg=2XHqVa�BX(^[l>A*^�9jA�G\e&K�XH=@W]Ki?�?�K�K�e�?MZ�Dm`�A*d/KgLNK�K�X�AQ_�G�K�ZUZ:^x?�e�A�G�Z-qFEH^�?�=2X�I�K&`HK/· ?6I�G�KiW]=YZ�K�Wxl~=YZ�`rZ�`�K?�_H`HK�G�=@I�AFS��;AFGUZ\`CZ�`�K�DFG\^nAFX�WQZ�`HK6W]=@?\I�D"dFK�G�^gZ\`�A"Z~Z\`HK6¯�D(DFXm?U`�=YXHKi?>L(^nG\K���KiI$Z�KiWnS2=2qF`[Z�a

WV<Q�RI�I�K�S2K�GJA"Z�=2DFX`�A/?>XHD�Z\`H=YX�q&WHDgl~=YZ�`mP8D/G\I�K�?�aK*<Q|�DFGJI�Ki?>`�A*dFK�XHD�Z\`H=2XHq�W]D�l~=�Z\`�AFI�I�K�S2K�GJA"Z\=YD/X�a

¾F¾ ¶ h[e4EHS�ZB¾/¾�µ[¾F¾C� ³�³ K�A/?U^�e�A�Z�`�u�_NK�GJ?�DFX�· ?�l�K�=Yq/`/Zµ�a>7kP�^FD/EQ`�A*d/K�Age�AF?\?>D�P ¹ ¾�O[q&A�XVW $ ½ � ¼ e��"? �"oH^/DFEl�K�=Yq/`AFLVD/E]Z�u

A[<���¾� sa LV< ¹ ¾� 6a Ii< ¹ ¾F¾; 6a W�< ¶ ¾F¾� sa Ki<~�F¾� 6a

¾F¾ ¶ h[e4EHS�ZB¾/¾ ¶ ¾F¾4� ¶ �4K�A/?U^�e�A�Z�`�u�LND]W]^nAFX�WmI�DFX[ZJAFI$Z>P8D/G\I�K�?¶ a~b>`HK�P8D/G\I�KRDFP�qFGJA*d(=�Z:^&G\K�A/IJ`HK�?�DFE]ZcA/I�G\D/?\?;?�_�AFI�K�AFX�Wn_�EHSYS@?>DFXK�A/IJ`nLH=YZ~D�P�^FDFE�G�LND]W]^C=2X�W]K�_NK�XVW]K�X[Z�S2^DFPRK�d/K�G\^�D�Z\`HK�G&LH=YZ�a±»xK�I�A�S2ScA�P8D/G\I�KS2=2OFKQZ�`H=@?�A �1� � � � ¦ 4a�»{`(^�WHDFX�· ZC^FD/EtAFI�I�K�SYK�G\A�Z�KW]D"l~X(l>A�GJWpo(K��HI�K�_]Z~l~`HK�XmD ��Z�`HK-q/G�D/EHX�WpaA[<nb>`�K �4� � � ��� �1� ¦ �G�KiAFIJ`HKi?jDFEHZ�AFI�G�D[?�?j?�_�AFI�KBA�XVW&_HE�?�`HK�?;EH_(l�AFG\W&D/X�K�AFIJ`&LH=YZ�DFPp^FDFE�GLND]W]^n=2X�W]K�_VK�X�W]K�X/Z\SY^QD�P�K�d/K�G\^�D�Z�`�K�G~LH=YZ�a;b>`�K�q/G�D/EHX�WnP8DFGJI�KM=@?~A�S@?UD�A �1� � � � ¦ 4a

LN<Qb>`�KsqFG\DFE�X�WmK��]K�G�Z\?�A&P8D/G\I�KsDFXmZ\`HK&?UD/SYKi?cD�P�^/DFEHGBP8K�K�ZMAFX�WmZ�`�K4?�DFS2K�?cDFP�^FD/EHGcP8K�K�ZMDFXmZ�`�K4XHK��(ZS@A*^FK�G~D�P�^FD/EHG~LVD]W]^A�X�WQZ\`HK6XHK��[ZcS@A*^FK�G~D�P�^FD/EHG~LVD]W]^DFXQZ�`�K6XHK��(ZBS@A*^FK�G>D�P�^FDFE�G~LVD]W]^mA�X�Wm?�DD/XnEHX[Z\=YS�Z\`HK�Z�DF_QD�P�^FDFE�G�`HKiAFWpaj��AFIJ`CS@A*^FK�G�_HEV?U`HKi?�EH_Ql~=YZ�`DFX�SY^�K�XHDFEHq/`CP8D/G\I�KBZ\D4L�AFS2AFX�I�KRZ�`�Kq/G\A*d(=YZ:^&P8DFGJI�K-D/XQZ\`HK6e�AF?\?~A�LND"dFK/a;b>`HK-q/G�D/EHX�WQP8DFGJI�K-A�XVWnZ\`HK-P8D/G\I�K�?>K��]K�GUZ\K�WL(^CZ�`�K6S2A*^/K�GJ?�D�PD/EHG�LVD]W]=2K�?�A�G\K ¦ � �� �C¦ �1� ¦ ��aN� ¦ � �� ��¦ � � ¦ AFI$ZJ?BD"d/K�G�ACdFK�G�^m?�`HDFG�Z

Page 26: Introductory Physics Problems David J. Jeffery Department of

�F� v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?~¸�A*lc?~A�X�W¡B^(X�AFe&=2I�?~7

GJA�X�qFKFu�?UDm?�`HDFG�ZRZ\`�A"Z6=YP;Z\`HK�W]=@?:ZJA�X�I�KgLNK�Z:l�K�K�X�Z\`HKgZ:l�DDFL3A:K�I$ZJ?�K��]K�G�Z�=2XHqK�h[E�A�S�AFX�W�D/_H_ND/?�=�Z\KI�DFX[Z\A/I$Z>P8DFGJI�Ki?>DFXK�A/IJ`QDFZ�`HK�G~=2?>e&DFG\K�Z�`�AFXmeg=@I�G\D/?\I�D/_H=@IcZ\`HK�G\KM=2?~X�D&I�DFX[Z\A/I$Z>P8DFGJI�K-A�Z~AFSYS�a

Ii<¤]=YX�I�K-^FD/EAFG�KMA�S2l�A*^]?�DB��Z�`HK-q/G�D/EHX�Wpo[Z�`�K6h/E�K�?UZ�=2DFX`�AF?>XHDCAFX�?�l�K�G�aWV<¤]=YX�I�K ^FDFE}A�G\K�AFSYl>A*^]?�DB��Z\`HK qFG\DFEHXVWpoZ�`HK�h[EHK�?UZ�=2DFX}=2?±`(^(_VDFZ�`HK�Z�=@I�AFSmAFX�W�Z�`HK A�X�?�l�K�Gio

?�_NK�I�E�S2A�Z�=2dFKFaK*<n7!XDFG\LH=YZ�o(^FD/EQW]D/X�· Z~A/I�I�K�S2K�GJA"Z�K�W]D"l~X(l�AFG\W�AFX�WC^/DFEA�G\K�I�K�G�Z\A�=2XHS2^�DB�mZ�`�K�q/G�D/EHX�Wpa�¤(DgLNK�=2XHq4D/XZ\`HK-qFG\DFE�X�Wne�A*^C`VA*dFK�XHD�Z\`H=YX�q4Z\DCW]D&l~=�Z\`ml~`[^Q^FD/EQW]D/X�· ZBA/I�I�K�S2K�GJA"Z�KMW]D"l~X(l>A�GJWpa

¾F¾ ¶ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u� BK�l>Z�D/X�· ?c�"X�WS@A*l¹ a~ BK�l>Z�D/X�· ?B�"X�WQS@A*l�=@?�u

A[< � $ �� � ��� ��NaLN<��� $ � �� � ��� aIi< �� � ��� $ � ��NaWV<Q|�DFG~K�dFK�G\^&P8DFGJI�K�Z\`HK�G\K-=2?~AFXQKih[E�A�S�AFX�WQDF_H_ND/?�=�Z\K�P8DFGJI�KFaK*<Q|�DFG~K�dFK�G\^CAFI�I�K�SYK�G\A�Z�=2DFXCZ\`HK�G\K-=@?~A�XK�h[E�A�S�A�X�WQDF_H_ND/?�=YZ�K-AFI�I�K�S2K�GJA"Z\=YD/X�a

¾F¾ ¶ h[e4EHS�ZB¾/¾ ¹ ��¾4�4µ ³ e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=YXHK�GUZ\=2AFSpP8GJA�e&K�?º(a~ BK�l>Z�D/X�· ?~S2A*lc?�`HD/S2Wl~=YZ�`mG\K�?�_VKiI$Z>Z�DVu

A[<�G�DFZ\A�Z�=2XHqgP8G\AFegKi?�a LV<>A/I�I�K�SYK�G\A�Z�KiWCP8GJA�e&K�?�a I�<�=2XHK�G�Z�=@A�SpP8GJA�e&Ki?�a W�<>XHD/X]T�=2XHK�GUZ\=2AFSP8GJA�e&Ki?�a K*<�_H=2I�Z�EHG\KMP8GJA�e&K�?�a

¾F¾ ¶ h[e4EHS�ZB¾/¾[º�¾F¾C� ¶ �MK�A/?U^�e&K�egD/G�^�u� BK�l>Z�D/X�· ?c�"X�WS@A*l�e�A�X[Z�GJA¼ a~|�G�D/e�`HK�G\KsD/X�=2X�Z�`�=2?MI�D/EHGJ?UK/o�AQOFK�^Z�`H=2XHqQZ�DG�K�egK�esLNK�G&5 Z\DQG\K�I�=�Z\KsZ\DQ^/DFEHGJ?UK�S�PJ<cl~`HK�X�P,A/I�K�W�l~=�Z\`AFX[^CP8DFGJI�KM_HG\DFLHS2K�e =@?�Z�`VA"ZB cK�l>Z�D/X�· ?R�"X�WQS2A*l 5 �� � ��� $ � ��(<�=2?�uA[< � � � � ��� � � � ���xa/�cXVW4=YZj=2?jA�� ¦ �1� Kih[E�A"Z\=YD/X�oFA�XVW4?�DR=@?jA�S2l>A*^(? � � � ����I�DFe&_NDFXHK�X[ZL(^&I�D/eg_NDFX�K�X[Z�a��cX�W �� � ��� =@?jZ\`HK � ¦ � � ?�EHe D�P�A�S2S]P8D/G\I�K�?�A/I$Z�=2XHq-D/X&Z�`HKcLND]W]^gD�Ppe�AF?\? �xa7kZM=@?RX�D�Z-A�X(^Q_VA�G�Z�=@I�EHS@A�GRP8DFGJI�K/aR7kP>A�S2S�Z\`HKsP8D/G\I�K�?�?UE�e�Z�Dn��K�G\Dnd/K�I$Z\DFG\=2AFSYS2^Fo �� � ��� $ � �� $f¾HaM7kP^/DFEmA�G\KMqF=2dFK�XQZ�`�K6AFI�I�K�S2K�GJA"Z\=YD/X�o[Z�`HK�X^/DFEmI�AFXQDFP Z�K�XmE�?�K �� � ��� $ � ���Z�D�?�DFS2dFK�P8DFGcAFXmEHXHO(XHD"l~XP8D/G\I�KFa

LN< � � � � ��� � � � � ��ap�cXVW�=�ZR=2?RA � ¦&� � � � K�h[E�A"Z\=YD/X�a~�cX�W �� ����� =@?~Z\`HK � ¦&� � � � ?�EHe D�PAFSYS�P8DFGJI�K�?sAFI$Z\=YX�q�DFX�Z�`HKnLVD]W]^xD�P~e�AF?\? �xaQ7kZs=@?-XHD�ZgA�X(^�_�AFGUZ\=2I�EHS2AFGMP8DFGJI�K/an7kPcA�S2SjZ�`�K�P8DFGJI�Ki??�EHe Z�D���K�G\D�o �� � ��� $ � �� $ ¾Ha�7kPc^/DFE�AFG�K�q/=Yd/K�XrZ�`�KQAFI�I�K�SYK�G\A�Z�=2DFX�o�Z�`HK�X�^FD/E�I�A�X�DFP Z�K�X�E�?�K�� � ��� $ � ���Z\D�?UD/SYd/KRP8D/GcA�XEHXHO(XHD"l~XQP8DFGJI�K/a

Ii< � � � � � � � ��� l~`HK�XzZ�`HK�G�K�=@?�A � � ��� � �� � X�K�Z�P8DFGJI�K/a ��KiI�AFE�?UK�Z\`HK��"X�WzS@A*l =@?�A� ¦ �1� Kih/EVA"Z�=2DFX�oj=�Z&=2?gd"A�S2=@W�58l~`HK�X�=YZg=@?gd"A�S2=2W�<sI�D/eg_NDFX�K�X[ZgL(^�I�D/e&_VD/XHK�X[Z�ar�cXVW �� � ���=@?>Z\`HK&� ¦ � ��?�EHe D�PjA�S2S�P8DFGJI�Ki?~AFI�Z�=2XHq&DFXQZ�`HK-LND]W]^nDFP�e�AF?\? �xaj7kZc=@?>XHDFZBA�X(^�_�A�G�Z�=@I�E�S2AFGP8D/G\I�KFa~7kP�^/DFE�A�G\K-qF=2dFK�XmZ�`HKgAFI�I�K�S2K�GJA"Z\=YD/X�o]Z\`HK�X�^/DFE�I�A�X�D�P Z\K�X�E�?�K �� � ��� $ � ��QZ�DQ?UD/SYd/KMP8DFGRAFXE�XHO(XHD"l~XnP8D/G\I�KFa

WV< � � � � ��� ��� � � � ���xaWV< � � �� � � � ����a

¾F¾ ¶ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujW]^(X�A�e&=@I�?~W]K���XHKiW½ a~¡R^(X�A�e&=@I�?>=@?>Z�`�A�ZcLHGJA�X�IJ`D�P�_H`(^(?�=@I�?�Z�`VA"Z�u

A[<CK��]_HS2AF=YXV?>egDFZ�=2DFXmA�X�WmA/I�I�K�SYK�G\A�Z�=2DFXQ=YXZ�K�G�e�?>DFP�Z�`�K-O[=2XHK�e&A�Z�=@IMK�h[E�A�Z�=2DFX�?�aLN<nK��]_HS2AF=YXV?>egDFZ�=2DFXmA�X�WmA/I�I�K�SYK�G\A�Z�=2DFXQ=YXZ�K�G�e�?>DFP�K�G\G\DFG~A�X�AFSY^]?�=2?�aIi<CZ\G�KiA"ZJ?~W]^(X�A�e&D/?�aWV<CZ\G�KiA"ZJ?>K�S2K�I$Z\G�=@I�=YZ:^nAFX�Wne�AFqFXHK�Z�=@?Ue}DFG>K�S2K�I�Z�G\DFe�A�q/XHK�Z\=2?�emaK*<nK��]_HS2AF=YXV?>egDFZ�=2DFXmA�X�WmA/I�I�K�SYK�G\A�Z�=2DFXQ=YXZ�K�G�e�?>DFP�P8DFGJI�Ki?~A�X�We�AF?\?�K�?�a

¾F¾ ¶ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujW]K��VXH=�Z\=YD/X�W]^(X�A�e&=@I�?�A:K�D/_�A�GJW]^

Page 27: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?c¸�A*lc?>A�X�Wm¡R^[XVA�e&=2I�?>7 � ³

��¾Ha �\¸�K�Zi· ?�_HS@A*^��]1J� D+�"����#"a;|HD/G �(��¾/¾Ho/Z�`HK6AFX�?�l�K�G�=@?�u�b>`�K�L�G\AFX�IJ`nDFP�_H`(^]?U=@I�?�Z\`�A"Z~K��]_HS@A�=2X�?>e&D�Z\=YD/XQAFX�WA/I�I�K�SYK�G\A�Z�=2DFXQ=YXZ�K�G�e�?>DFP�P8D/G\I�K�?>A�X�We�AF?\?�K�?�a �A[<C»{`VA"Zc=@?>O[=2XHK�e&A�Z�=@I�?�o��cS2K�� �LN<n»{`VA"Zc=@?~W]^(X�A�e&=@I�?�o��cS2K�� �Ii<n»{`VA"Zc=@?~?:ZJA"Z�=@I�?�o��BSYK����WV<n»{`VA"Zc=@?>K�I�D/XHDFe&=@I�?�oH�cS2K�� �K*<n»{`VA"Zc=@?~I�=2XHK�e�A"Z\=2I�?�oV�cS2K�� �

¾F¾ ¶ h[e4EHS�ZB¾/¾ ½ ��¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�e�AF?\?~A�X�WQl�K�=Yq/`[Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³

�F�Fa �\¸�K�Zi· ?R_HS@A*^��]1J� D+�"�\�"# 1 |HD/G��]��¾F¾�oHZ\`HK4AFX�?Ul�K�GR=2?�u>Z�`�K�^�A�G\KFoNG�Ki?U_NK�I�Z�=2dFK�SY^/o�Z\`HK4G\K�?�=@?:ZJA�X�I�K6D�P;AnLVD]W]^Z\DCAFI�I�K�S2K�GJA"Z\=YD/XnA�X�WQZ\`HKMP8DFGJI�KMD�P�qFGJA*d(=�Z:^�D/XAgLND(WH^Fa �»{`�AFGcA�G\K A�X�W o��cS2K�� �

A[<>AFI�I�K�S2K�GJA"Z\=YD/X )(XHDFG\e�A�SNP8DFGJI�K LN<>e�AF?\? )]XHD/G�e�AFSVP8D/G\I�K I�<�P8D/G\I�K )Hl�K�=2qF`[Z W�<�e�AF?\?*)l�K�=2qF`[Z K*<�qFGJA*d[=YZ:^ )(egD/e&K�X[Z�EHe

¾F¾ ¶ h[e4EHS�ZB¾���¾/¾F¾4�Q���Me&D]W]K�GJA"Z\K�e&K�egD/G�^�u�XHD/G�e�A�SNP8D/G\I�K�i�]a~b>`HK-X�DFG\e&AFSNP8DFGJI�KM=2?�u

A[<nA�G�K�_HEHS@?U=2dFKCI�DFX[Z\A/I$Z6P8D/G\I�KnK��(K�GUZ\K�WrL(^rA�?�EHGUP,A/I�K�Z\`�A"Zg_VD/=YX[ZJ?s_NK�G\_VK�X�W]=@I�EHS@A�G\S2^xD/E]Z:l�AFG\WxP8G\DFeZ\`�A"Z?UEHG�P,AFI�KFa�7!X{_HG\=YX�I�=Y_�SYK�=YZI�A�XwLVKxI�A�S@I�E�S2A�Z�K�WtP8G\DFe�Z�`HKxI�DFe&_HG\K�?\?�=YD/X�A�ScW]=@?�_HS2A/I�K�egK�X[ZCD�PZ\`HKQ?�EHG�P,AFI�K�P8G�D/e K�h[EH=2SY=2LHG\=YEHemojLHEHZ4=2X�K�S2K�e&K�X[ZJA�G\^x_HG\DFL�SYK�e&?sDFXHKQE�?�E�A�S2SY^rI�AFS2I�EHS@A"Z�Ki?6=YZsP8G\DFe BK�l>Z\DFX�· ?B�"XVWnD/G ³ GJWnS@A*l�AF?\?�EHe&=YXHqgZ\`HK6?UE�GUP,A/I�K�Z�D&LNK6I�DFe&_HS2K�Z\K�S2^nG\=Yq/=2W�a

LN< �� � ��� =YX �� � ��� $ � ��VaIi<CZ\`HKMZ�K�X�?�=YD/XnP8D/G\I�K�=2X�AgG�D/_VK/aWV<CZ\`HKMZ�K�X�?�=YD/XnP8D/G\I�K�=2X�AgG�D/_VK�Z�`VA"ZBA�S2S2D"lc?>^FDFEnZ�D�_HEV?U`mDFXmAgG�D/_VK/aK*<QAFXnD/G\W]=2X�AFG�^/o/G\EHX]TkD�P T�Z�`HK�T�e&=2SYSNP8D/G\I�KFo]Ag_VKiW]K�?UZ�G\=2AFXCP8D/G\I�KFo]A6P8D/G\I�KRl~=YZ�`�DFE]Z~_HG\K�Z\K�X�?�=YD/X�?�DFG~A�=2G\?�o(AWHD"l~XHG�=2qF`[Z�P8DFGJI�K/oHA4G\K�q/EHS@A�G�T�q/EH^gP8DFGJI�KFo A:EV?:ZRAg_HS@A�=2Xm?�AFS�Z�T�DFP T�Z\`HK�TkK�AFGUZ\`CP8DFGJI�K/a

¾F¾ ¶ h[e4EHS�ZB¾���¾[��¾C�&���Me&D]Wpa�Z�`H=2XHO(=2XHq�ujG\K�A/I$Z�=2DFXnP8DFGJI�Ki?>D�PjA4LND(DFO� ³ a~� LND[D/O�?�=�ZJ?-A"Z-G�Ki?:ZMDFXrAnZ\A�L�SYK/agb>`HK&G\K�A/I$Z�=2DFX�P8DFGJI�K4Z�`�A�ZMP8DFS2SYD"lc?RP8G\DFe  BK�l>Z�D/X�· ? ³ GJW�S@A*l�Z�DZ�`�K

q/G\A*d(=YZ\A"Z\=YD/X�A�SVP8DFGJI�KMDFP�Z\`HK6�;AFGUZ\`nDFXZ\`HKMLVD(DFOQ=2?�Z\`HKFuA[<Cq/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�K�DFP�Z\`HK-LND[D/OCDFXQZ�`�K6�;A�G�Z�`�aLN<nX�DFG\e&AFS�58=�a K/aYo�_VK�G�_NK�X�WH=2I�EHS2AFG~EH_(l�AFG\WV<�P8D/G\I�KMD�P�Z\`HKMZ\AFLHS2K-DFXQZ�`HK-LND(DFO�aIi<CZJA�LHS2KMP8G\=2I�Z�=2DFXQP8DFGJI�KMDFXQZ�`HK-LND(DFO�aWV<nLND(DFO�P8G\=@I$Z�=2DFXP8D/G\I�K�D/XnZ\`HKMZ\AFLHS2KFaK*<nLND(DFOCX�DFG\e&AFS�P8DFGJI�KMDFXQZ�`�KMZ\A�L�SYK/a

¾F¾ ¶ h[e4EHS�ZB¾��F�i¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�ujZ\K�X�?�=2DFX=YX�AgG�D/_VK��µ�a~�&� � � � � � � ��e�AF?\?�DFP���¾jO(q6=@?�?UE�?�_NK�X�W]KiW�P8G\DFe�A6G\DF_NKFa�»{`�A"Z�=2?;Z�`�KcZ�K�X�?�=YD/X�P8DFGJI�K~Z\`�A"Z�Z�`�K

G\DF_NKMK��]K�G�Z\?>D/XnZ\`HK-e�AF?\? �A[<n�BLVD/E]Z6��¾/¾�  W]D"l~X(l�AFG\W�aLN<Q�BLVD/E]ZR��¾/¾�  W]D"l~X(l�AFG\W�aIi<Q�BLVD/E]ZR��¾/¾� �EH_(l�AFG\W�aWV<Q�BLVD/E]Z6��¾/¾� �EH_(l�AFG\W�aK*<Q�BLVD/E]ZR��¾/¾� �`HDFG\=2��DFX[ZJA�S2SY^/a

¾F¾ ¶ h[e4EHS�ZB¾��i�F¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujXHD&e&D�Z\=YD/XQ=2e&_HS2=YKi?~XHK�Z~P8D/G\I�KM��K�G\D� ¶ a~� � � � � � � � �te�AF?\?�D�PR�i¾jO(qm=2?M?�E�?U_NK�XVW]K�WxP8G\DFe AG�D/_VK/as»{`�A�Z6=2?�Z\`HK � �P8DFGJI�KgDFXxZ�`�K

e�AF?\?�

Page 28: Introductory Physics Problems David J. Jeffery Department of

�"µ v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?~¸�A*lc?~A�X�W¡B^(X�AFe&=2I�?~7

A[<n�BLVD/E]Z6��¾/¾�  W]D"l~X(l�AFG\W�aLN<Q¾; 6aIi<Q�BLVD/E]ZR��¾/¾� �EH_(l�AFG\W�aWV<Q�BLVD/E]Z6��¾/¾� �EH_(l�AFG\W�aK*<Q�BLVD/E]ZR��¾/¾� �`HDFG\=2��DFX[ZJA�S2SY^/a

¾F¾ ¶ h[e4EHS�ZB¾��i�/��¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�u�?UZ�D/_H_H=2XHq�A4L�=YO/K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ¾�T!�H�

� ¹ a~�zLH=@I�^]I�S2K�TkG�=@W]K�G�?�^(?UZ�K�e `�AF?�A6e�A/?�?�D�P ¼ ¾jO(q�a�b>`HKBL�=YO/KF· ?�=2XH=YZ�=@A�S�dFK�SYD]I�=�Z:^ ¹ e��"?;XHDFG�Z�`�a�»{`VA"Z>=2?�Z�`�KI�DFX�?UZ\AFX/Z>P8D/G\I�K�X�K�K�WHK�WQZ�D�?UZ�DF_QZ�`�K-LH=YO/K-=YXµ;?�

A[< ¼ ¾�  ?�DFE]Z\`�a LV< ¼ ¾�  XHDFG�Z�`H=�a I�< ¼ ¾�  K�A/?:Zia W�<&��¾/¾�  ?UD/E]Z�`�a Ki<4�i�F¾� ?�DFEHZ�`�a

¾F¾ ¶ h[e4EHS�ZB¾��i��µ/¾4� ¶ µ&e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�W]=2d[=2XHq&l�DFe�A�X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ¾�T!�[º

�*º(a>»{`�A�Z�=2?�Z\`HKcA�_�_HG�D*�]=2e�A"Z�K�e�AF?\?�D�PpA ¶ ¾F¾; �l�DFe�A�X �n»{`VA"Z�=@?�qFGJA*d[=YZ\A�Z�=2DFX�AFSFP8D/G\I�K�Z�`�A�Z;�;A�G�Z�`gK��]K�GUZJ?D/X�`HK�Gia��~P Z\K�G&?U`HK A:EHe&_�?6P8G\DFe A�W]=2d(=YX�q�LVD[A�GJWpo�l~`�A"Zg=2?s`HK�GgAFI�I�K�S2K�GJA"Z\=YD/X�=2XrZ�`�KQA�LV?UK�X�I�KCDFPcA�=2GG\K�?�=2?UZ\AFX�I�K �A[<n�BLVD/E]Z ¶ ¾jO(q�o ¶ ¾F¾� so�AFX�W ½ � ¼ e��"? �&W]D"l~X(l�AFG\W�DFX�I�KC?U`HKC?UZ\AFGUZJ?Me&D"d[=2XHq�W]D"l~X(l>A�GJWpopLHE]Zs��K�G\DLNK�P8D/G�K�Z\`�A"Zia

LN<Q�BLVD/E]Z ¶ ¾jO(qVo ¶ ¾� so�AFX�W ½ � ¼ e ��? �QW]D"l~X(l�AFG\WrD/X�I�Km?�`HK�?:ZJA�G�Z\?4egD"d(=2XHqrW]D"l~X(l�AFG\Wpo�LHEHZ&��K�G\DLNK�P8D/G�K�Z\`�A"Zia

Ii<Q�BLVD/E]Z ¶ ¾�O[qVo ¶ ¾� soHA�X�W ½ � ¼ e��"? ��W]D"l~X(l�AFG\WCA�ZBA�S2S�Z�=2e&K�?�aWV<Q�BLVD/E]Z ¶ ¾�O[qVo ¶ ¾F¾; 6oHA�XVW ½ � ¼ e���? ��W]D"l~X(l�AFG\WQA"ZcA�S2SpZ\=Ye&K�?�aK*<Q BDFXHK-DFP�Z\`HK�?�K6h[EHK�?UZ�=2DFX�?~I�A�XLVK6AFX�?�l�K�G�KiWCl~=YZ�`Z�`HK-q/=Yd/K�X=YXHP8DFG\e&A�Z�=2DFX�a

¾F¾ ¶ h[e4EHS�ZB¾�� ³ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�SYK�d*A�Z�D/G>A/I�I�K�S2K�GJA"Z�=2DFX� ¼ a~�BXK�SYK�d"A"Z�D/G A:E�?UZB?:ZJA�G�Z\?>e&D"d(=YXHqgEH_(l>A�GJWpa

A[<)��D/EP8K�K�S�?US2=Yq/`[Z�S2^C`HK�A*d(^&P8D/GcA4e&D/egK�X[Z�aLN< ��D/EP8K�K�S�?US2=Yq/`[Z�S2^CSY=2qF`[Z>P8DFGcAge&DFe&K�X/ZiaIi< ��D/EP8K�K�S�?US2=Yq/`[Z�S2^CSY=2qF`[ZcA�XVWI�A�G\K�P8G\K�KRP8DFGcAge&DFe&K�X[ZiaWV< ��D/EP8K�K�S�Z�D�ZJA�S2SY^QI�A�G\K�P8G\K�KMA�XVWnK�Z�`HK�G�KiA�S�aK*< ��D/E�I�DFe&K�Z�D&EHXVW]K�GJ?:ZJA�X�WQZ\`�A"Z~Z\`HK�G\K-A�G\K�X�D4P8D/G\I�K�?�=2XQP8D*�]`HD/SYKi?�a

¾F¾ ¶ h[e4EHS�ZB¾�� ³ ��¾4� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVujK�S2K�d"A"Z\DFG~AFI�I�K�SYK�G\A�Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ��T ³ �

� ½ a~��l�DFe�A�Xxl~`HD`�AF?-Ae�AF?\?�D�P ¶ ¾jO(qQ=@?M=2X�AFXxK�SYK�d*A�Z�D/GRZ\`�A"Z-=@?-AFI�I�K�S2K�GJA"Z\=YX�qW]D"l~X(l>A�GJW�A"Zs��e���? �"a»{`�A�Zc=2?�Z\`HKMP8DFGJI�K�Z\`HKM��D(DFG~K��(K�GUZJ?>DFX`HK�G �m»{`�A�Zc=2?�Z\`HKMP8DFGJI�K-?�`HKMK��]K�G�Z\?>D/XZ�`HKM��D(D/G�

A[< ³F½ ¾�  EH_(l>A�GJW ) ³/½ ¾� �W]D"l~X(l>A�GJWpa LV< ³/½ ¾� �WHD"l~X[l>A�GJW ) ³/½ ¾�  E�_[l>A�GJWpa Ii<>µ ½ ¾� WHD"l~X[l>A�GJW )Nµ ½ ¾�  EH_(l�AFG\W�a W�<cµ ½ ¾� �EH_(l>A�GJW )�µ ½ ¾; �W]D"l~X(l�AFG\Wpa Ki<6��¾F¾; �EH_(l�AFG\W )�i¾F¾� �W]D"l~X(l>A�GJWpa

¾F¾ ¶ h[e4EHS�ZB¾���µ[¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujXHK�ZcK��(Z�K�G�XVA�SNP8DFGJI�Ki?~A�X�WI�K�X/Z\K�G~DFP�e�AF?\?��¾Ha>7kP�^/DFE�O(XHD"l XHD�Z\`H=2XHqQAFLVD/E]ZBZ\`HKs=2X[Z�K�G\X�AFS�P8DFGJI�Ki?cDFP;A�LVD]W]^�AFX�W�DFX�SY^O(XHD"l�Z�`HKgXHK�Z�K��(Z�K�G�XVA�S�P8D/G\I�K

Z\`�A"Z-AFI�Z\?RDFX�Z\`HKgLVD]W]^�AFX�W�XHDFZRl~`HK�G�KgDFX�Z�`HKgLVD]W]^mZ\`HK&_�A�G�Z�=@I�E�S2AFGBK��(Z\K�G\X�A�S�P8DFGJI�Ki?RA/I$Z�oNZ\`HK�X�opL(^=YZ\?�K�SYP:o� cK�l>Z�D/X�· ?R�"X�WQS2A*l�P8DFGcAgXHD/X]T�_NDF=2X[Zce�AF?\?�D/XHS2^QA�S2S2D"lc?�^/DFEQZ�D&_HG\K�W]=@I$ZiuA[<�Z\`HK�� �� � ¦ ���� DFP�Z�`�K-LVD]W]^/aLN<CZ\`HK�� �� � ¦ �� � DFPpZ�`HK-I�K�X[Z�K�G�DFP�e&A/?�?�D�P�Z�`HK�LVD]W]^/a ��DFEnI�A�XQO[X�D"l{XHD�Z\`H=YX�q4A�LNDFEHZ�=2X[Z�K�G\X�AFS

e&DFZ�=2DFX�?>DFP�Z\`HK-LVD]W]^QDFG>=YZ\?~G\D�ZJA"Z�=2DFXVA�S�LVK�`�A*d(=YD/G�aIi<CZ\`HK �C¦&¦ �� �� � � � � D�P�Z�`HK�Z�D/_m_VD/=YX[ZcD�P�Z�`HK-LND]W]^Fa

Page 29: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?c¸�A*lc?>A�X�Wm¡R^[XVA�e&=2I�?>7 � ¶

WV<CZ\`HK �C¦&¦ �� �� � � � � D�P�Z�`HKMLND�ZUZ\DFe}_VD/=YX[ZcD�P�Z�`�K-LVD]W]^/aK*<CZ\`HK �C¦&¦ � � � � � � D�P�Z�`�KsI�K�X/Z\K�G~DFP�e�A/?�?>DFP�Z\`HK-LND(WH^Fa���DFE�I�AFXO(XHD"l�XHDFZ�`H=2XHqCA�LNDFEHZ=2X[Z�K�G�X�AFSpe&D�Z�=2DFXV?>D�P�Z�`HK-LND]W]^nD/G�=YZ\?cG�DFZ\A"Z\=YD/X�A�S�LNK�`�A*d(=2DFGia

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾ ¶ h/P8EHS2S�¾/¾F¾H�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�P8G\=2I�Z�=2DFXHS2K�?\?>=2X�I�S2=YX�K�Fa~b>`HK�G�KM=@?cA���O(q4L�SYD]IJOCD/XmA4P8G\=2I�Z�=2DFXHS2K�?\?>=2X�I�S2=YX�KMZ�`�A�Z>=@?cA�Z ³ ¾ � P8G\DFe�Z�`HK-`HD/G�=2��D/X[Z\A�S�a

A[<C»{`VA"Z�=@?�Z�`HKBXHDFG\e�A�S(P8DFGJI�K>D/X4Z\`HK~LHS2D]IJO � ������ � � ¡RG\A*lwARP8G�K�K~LVD]W]^gW]=@A�qFGJA�e A�X�WgG\K�e&K�e4LVK�GZ\`HK6I�S@AF?\?>e�A�X[Z�GJAHu � �� � ��� $ � ��C=@?~A�S2l>A*^(?�Z\G�EHK-AFX�W=�Zi· ?>Z\G�E�KMI�DFe&_NDFXHK�X/ZcL(^nI�DFe&_NDFXHK�X/Zia �

LN<n»{`VA"Zc=@?�Z�`HK-XHK�Z~P8DFGJI�K-W]D"l~XQZ�`HK6?�S2DF_NK��Ii<n»{`VA"Zc=@?�Z�`HK6A/I�I�K�SYK�G\A�Z�=2DFXW]D"l~XnZ\`HK6?�SYD/_VK �WV<¤(Z\A�G�Z�=2XHqgP8G\DFe G\K�?UZc`HD"l�P,AFGcW]D(K�?�Z\`HK-LHS2D(IJOQ?US2=2WHK�=2Xr��¾�?�

¾F¾ ¶ h/P8EHS2S�¾/¾F¾/�F¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu>��D/L?�l~=2XHqF=2XHq&DFXmAgG�D/_VK� ª�¬"¨ �V«������V¬ ��­�� �BWHAF_]Z�KiWnP8G\DFe�%�'(#*)$+, �)'���i� ��# :���¾F¾[�]o]¯�A*^/o ¶F¶ o]X�D�a ¶ o ¶ �

�]a ��D/E�`�A*dFK>Z\=YKiW&^FDFE�GjqFD(D]W&DFS@W4_VA�S ��D/LgD/XCAMG�D/_VK>P8G\DFe Z�`�KBI�K�=YS2=YX�q �{LHE]Z;XHDFZ�A�G\DFE�X�W4Z�`HKcX�K�IJO �{AFX�W`�A*d/KR?�K�Z~`H=2e�?�l~=YXHq/=YX�q�aj�B?\?UE�egKRZ�`�K�G\K�=@?�XHK�q/SY=2qF=2LHS2K�AF=YG>G\K�?�=2?UZ\AFX�I�K/o(XHK�q/SY=2qF=2LHS2KBP8G\=2I�Z�=2DFXA"Z>Z�`HKM_H=2dFDFZ_NDF=2X[Z�o�AFX�WCZ\`�A"Z~Z\`HK-G\DF_NKM?UZ\A*^]?~?UZ�GJA�=2qF`[Z�aA[<n¡RGJA*lzAg?�IJ`HK�e�A"Z�=@IMW]=@A�qFGJA�e =2S2SYE�?UZ�GJA"Z\=YX�q���D/L�· ?�e&D�Z\=YD/X�a�¯�AFG�O�D/XnZ\`HK-SYD"l�K�?UZ>_VD/=YX[ZB9wA�X�WnZ�`�K`�=Yq/`HK�?UZc_VD/=YX[ZR® �{l�K�SYSpD/XHKMD�P�Z�`HK-`H=2qF`�K�?UZ>_NDF=2X[Z\?�a

LN<n7!XVW]=2I�A"Z\K�Z\`HK~dFK�SYD]I�=�Z:^6AFX�W4A/I�I�K�S2K�GJA"Z�=2DFX4dFKiI$Z�D/G\?�A�Z�_NDF=2X[Z\?j9rA�XVW&®4a"7kPpA�dFK�I�Z�D/G�=@?���K�G�DVo"=YXVW]=2I�A"Z\KZ\`�A"ZBAFX�WQK��]_HS@A�=2Xl~`(^C=YZc=@?>��K�G\D�a

Ii<n»{`VA"Z�`VA�_H_NK�X�?;=�PpZ\`HKBG\DF_NKcLHG\K�AFO]?�?UEVWHW]K�X�SY^�A"Z�_VD/=YX[Z�9 �BA�Z�_NDF=2X[Z>® ���j�]_HS@A�=2X&Z�`HKB?�EHL�?�K�h[EHK�X[Ze&DFZ�=2DFXmh/EVA�S2=�ZJA"Z�=2dFK�SY^/a

¾F¾ ¶ h/P8EHS2S�¾/¾ ³ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujLHSYD]IJOnAFX�W ³ GJWCS@A*l³ a ��D/E4`�A*d/K�L�SYD]IJO<A:E�?UZ;?U=YZUZ\=YX�q�D/Xs`HD/G�=2��D/X[Z\A�S/�VA�Z�q/G�D/EHX�Wpa B�%�#� �Fb>`�=2?�=@?jAR_�G�D/LHSYK�e P8DFG�G\EHe&=YX�A�Z�=2DFX �D/G~_VK�G�`�AF_�?>G\EHe&=YX�AFX[Z\?�aA[<n¡RGJA*l�A6P8G\K�K�LND(WH^nW]=@A�qFGJA�e�P8D/G�Z�`HKMLHS2D]IJONa�7!X�WH=2I�A"Z�KMA�S2S�Z�`�KRP8D/G\I�K�?�AFI�Z�=2XHq4D/XnZ\`HKMLHS2D(IJO�a�»{`�A�Z=@?>Z\`HK6I�AFE�?UK�D�P�Z�`�K�?�KMP8DFGJI�K�?>AFX�WmA�G\KBZ\`HK�^I�DFX[ZJAFI$Z~D/G~LVD]W]^�P8D/G\I�K�?�

LN<Q BD"l�L(^&Z�`�K ³ GJWCS@A*l�l~`�A�Z�P8D/G\I�K�?>W]D(K�?�Z\`HK-LHS2D(IJO�K��]K�G�Z~AFX�WQDFXl~`�A"ZcA�XVWCl~`HK�G�KMK��HA/I$Z�S2^CW]D(K�?=YZcK��]K�GUZ>Z�`�K�e �

¾F¾ ¶ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�P8EH����^QWH=2I�K6A"ZcA�XHq/SYKµ�a ��D/EwAFG�K=2XwA�I�A�G�AFI�I�K�SYK�G\A�Z�=2XHq�A�Z���¾je���? �*a�� P8EH����^t_�A�=2G�D�P-W]=@I�Km=2?C`�A�XHq/=YX�qr?�DFe&K�A�X�qFS2KnP8G\DFeZ\`HKQd/K�G�Z�=@I�AFS�a��B?\?�EHe&=YXHqxZ�`�KW]=@I�KmA�G\KQAx_NDF=2X/Z&e�AF?\?�ojl~`VA"Z&=2?4Z�`�=2?&A�X�qFS2K�� ������ � ¡RG\A*l A�P8G�K�KLND]W]^WH=2AFqFGJA�ema�¿cK�e&K�e4LVK�GcZ�`�Kse�A�X[Z�GJAHu � �� � ��� $ � ��n=@?BAFSYl>A*^]?�Z�G\EHKsAFX�Wm=�Zi· ?cZ�G\EHKsI�DFe&_VD/XHK�X[ZBL(^I�DFe&_VD/XHK�X[Zia �

¾F¾ ¶ h/P8EHS2S�¾/¾/��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�?UO(=2=YXHq�W]D"l~X�`H=YS2S�=2X[Z�D�Ag`HK�A/WQl~=2X�W¶ a ��D/ECA�G\KB?UO(=2=YX�qsW]D"l~X�A ³ ¾��~=2X�I�S2=2XHKFajb>`HKB?�S2DF_NKB=@?;I�D/e&_HSYK�Z�K�SY^4P8G�=@I$Z\=YD/XHS2K�?\?�a���`HD/G�=2��D/X[Z\A�S�l~=YX�W �w=�a K/aYoAMl~=2X�W&K��HA/I$Z�S2^s_NK�G\_NK�X�W]=@I�E�S2AFGjZ�DMZ\`HKBW]=2G�KiI$Z\=YD/XgDFPpqFGJA*d[=YZ:^Fo�AMl~=2X�W&_�AFG\AFSYS2K�S(Z\D-Z�`�KB?UE�GUP,A/I�K>D�PpG\K�?UZ�=2XHq��E�=2WxA"Z�Z�`H=@?BS2D]I�A�Z�=2DFX�opA��NA"Z�oN�VA�Z�l~=2X�W �{=@?RL�SYD"l~=2XHqC=2X�^/DFEHGBP,AFI�KgK��]K�GUZJ?RA���¾F¾;  P8DFGJI�K4`HDFG\=Y��DFX[Z\AFSP8D/G\I�K�D/XQ^/DFE�a���D/EHG~e�AF?\?>=2?-�i¾F¾jO(qVaA[<C»{`VA"Zc=@?>^FDFE�GcAFI�I�K�S2K�GJA"Z\=YD/X � ������ � ¡BGJA*l�Z\`�A"Z~P8G\K�KMLND]W]^QW]=@A�q/G\AFema

Page 30: Introductory Physics Problems David J. Jeffery Department of

� ¹ v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?~¸�A*lc?~A�X�W¡B^(X�AFe&=2I�?~7

LN<Q£BD"l�P,AFGcW]D�^FD/ECZ�GJA*dFK�S�A�S2DFXHq4Z�`�K6?US2DF_NKM=YXr��¾;?�A/?�?�EHe&=2XHq&^FDFEm?UZ\A�G�Z>P8G�D/e G\K�?UZ�Ii<Q BD"l�Z\`HK~`�AFG\W4_�A�G�Z�a��B?\?�EHe&K>Z�`�A�ZjZ�`HK~l~=2X�WgP8DFGJI�K>=@?jXHDFZjI�DFX�?UZ\AFX[Z�oFL�E]Z�=YXVI�G\K�AF?�K�?jA�Z�A-I�DFXV?:ZJA�X[ZGJA"Z\K�P8G�D/e ��¾/¾� �Z�Dn��¾/¾� �=YXZ\`HK���¾�?�DFP�Z\G\A*d/K�S�a�£BD"l�P,AFGcW]D�^FD/EnZ\G\A*d/K�SpA�S2DFX�q4Z\`HK6?�SYD/_VK-XHD"l ������� � ��DFEml~=YS2S�`�A*d/KBZ\DCW]D�A�X=YX[Z\K�qFGJA"Z\=YD/X�a

¾F¾ ¶ h/P8EHS2S�¾/¾ ³ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�Z�K�XV?U=2DFXm=2XmA&WHAFXHqFS2=2XHq&G�D/_VK¹ a~� G\DF_NKM=2?~WHAFXHqFS2=2XHqgP8G�D/e Z�`HK6I�K�=2SY=2XHqVaj7kZ\?~e�AF?\?>_NK�G~EHXH=YZcS2K�XHqFZ�`m=2?cqF=2dFK�XQL(^

� 5�H< $ � � � � � � � � � � �

l~`HK�G�K ��=@?Me&K�A/?UEHG\K�W�EH_(l�AFG\W�P8G�D/e�Z�`HKCW�A�XHq/SY=2XHqK�X�W�D�P�Z�`HK&G\DF_NKgZ\A�O/K�X�AF? � $ ¾Hag»{`�A"Z6=@?�Z�`�KK��(_�G�Ki?�?�=YD/XCP8D/G>Z�`HKMZ\K�X�?�=YD/X�A"ZcA�X(^C_NDF=2X[Z��nA�S2DFXHq4Z�`�K-G�D/_VK/a

¾F¾ ¶ h/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�W]D/EHLHS2K-=YX�I�SY=2XHKMl~=YZ�`mZ:l�D4LHS2D]IJO]?º(a ��D/EQ`�A*d/K�AsP8G\=2I�Z�=2DFXHS2K�?\?�Z�G\=2AFXHqFEHS@A�G�LHS2D]IJOCl~`H=@IJ`nqF=2dFKi?�^FDFEnZ:l�Dg=2X�I�S2=YX�K�W?US2DF_NK�?�a�¤(SYD/_VK&�M=@?�A�Z � � Z\DZ\`HK4`�DFG\=Y��DFX[Z\AFS�A�X�W�?US2DF_NKg�nA"Z�� � a ��D/E�`�A*d/KsA�P8G\=2I�Z�=2DFXHS2K�?\?c_�EHSYS2K�^�A�ZBZ\`HKgAF_VK���A�X�W�AFX�=@W]K�AFS�G\DF_NKI�DFXHXHKiI$Z\=YXHq4Z:l�D4LHS2D]IJO]?�o[DFXHK�DFXK�A/IJ`n?�SYD/_VK/a�b>`�K�G\DF_NK�=2?�_�AFG\AFSYS2K�SVZ�DgK�A/IJ`Q?�SYD/_VK/a�b>`�KM?�S2DF_NK4��LHS2D(IJO`�A/?~e�AF?\? � � A�X�WQZ\`HKs?�SYD/_VKs�Ho�e�AF?\? � � a�»{`VA"ZB=@?~Z\`HK-K��]_HG\K�?\?U=2DFX�5�?�AFX�?cAgZ�K�X�?�=YD/XQP8D/G\I�K-d"A�G\=2AFLHSYK*<P8D/G>Z�`HK6A/I�I�K�SYK�G\A�Z�=2DFXW]D"l~X?�S2DF_NK-�4P8D/G~e�AF?\? � � a ������ � ¡BGJA*l�Z:l�D4P8G�K�K-LVD]W]^W]=2AFqFGJA�e�?�a

¾F¾ ¶ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�ujegD/XHOFK�^CDFXmA&_HEHS2S2K�^¼ a~�BXn=@W]K�AFSVG\DF_NKs58=�a KFa2o]e&A/?�?�S2K�?\?�o/LHE]Z>=�Z>`�AF?�P8G�=@I$Z\=YD/XQ?�D-Z�`�KRe&DFX�OFK�^&I�AFXCqFG\=2_C=�Z$<�`VA�XHq[?�D"dFK�G�=@W]K�AFS�Z\G�K�KLNDFEHq/`�58=�a K/aYoNP8G\=2I�Z�=2DFXHS2K�?\?J<$acb>`HK6_VA�G�Z\?cD/X�LVDFZ�`�?�=@W]K�?B`�A�XHqndFK�G�Z�=@I�AFSYS2^Fa~�fLHSYD]IJOD�P~��¾�O[qC?�=YZ\?RDFXmZ�`�Kq/G�D/EHX�WC=@?�Z�=2K�WQZ\DgD/XHK�K�X�WD�P�Z�`HKMG\DF_NKFaj�cXm=@W]K�AFSpe&DFXHO/K�^�D�P�e�AF?\? ¶ O(q4I�S2=2esL�?>EH_Z\`HKMG�D/_VKMDFXQZ�`�KD/_H_VD[?U=YZ�K-?�=2WHK-D�P�Z\`HK-LNDFEHq/`QP8G\DFe Z�`HK-LHS2D]IJO�aA[<n¡RGJA*l P8G\K�KmLVD]W]^±W]=@A�qFGJA�e�?4P8DFG�LND�Z\`wegD/XHOFK�^�A�XVW�LHS2D]IJO�a�¿~K�e&K�e4LVK�G&Z�`HK�D/XHS2^�P8DFGJI�Ki?gZ�`�A�ZAF_H_NK�A�GcAFG�KRZ�`�D/?�KMZ�`�A�Z~A/I$Z�� ��Z�`�K-DFL,A:KiI$ZcA"Z~Z\`HK-DFG\=Yq/=YXQD�P�Z�`HK6WH=2AFqFGJA�ema

LN<n7kPjZ\`HKse&D/XHOFK�^A/I�I�K�SYK�G\A�Z�Ki?cAF?�?U`�KsI�S2=Ye4L�?�oV`HD"l�S@A�G\qFK-e4E�?UZ�AFI�I�K�SYK�G\A�Z�=2DFXmLVK4=YX�DFGJW]K�GBZ�`�A�ZBZ�`�KX�DFG\e&AFS�P8DFGJI�KMDFXLHS2D]IJOCqFD(K�?�Z\D&��K�G\D�o]L�E]Z~Z�`HK-L�SYD]IJOn?UZ\A*^]?�e&D�Z�=2DFX�SYKi?�?�

Ii<¤HA*^6Z�`VA"ZjZ�`�Kce&DFXHO/K�^-Z\`HK�XC?UZ\AFGUZJ?�AFI�I�K�S2K�GJA"Z\=YX�q�W]D"l~XgZ\`HKcG\DF_NKcA"Z ³ e��"? � a�»{`�A�Z�=2?�Z�`HK>Z\K�X�?�=YD/X=2XZ�`HK-G\DF_NK��»{`VA"Zc=@?>Z�`HK-X�DFG\e&AFSNP8DFGJI�KMDFXZ�`�K-LHSYD]IJO��

¾F¾ ¶ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\D(IJO/K�Z>_VD]WmW]Ki?�I�K�X[ZcDFX�v�A�S2SY=@?UZ�D� ª�¬"¨ �V«������V¬ ��­�� ¡RA*d(=@W#��D"l~e�A�XmA�X�Wm��¾/¾H�/u�� ¤(_VAFI�K4°�WH^(?\?�K�^

½ a~�R?�Z\`H=2?�=@?R5,DFG�l�A/?;l~=YZ�`H=2XCS2=Yd(=2XHqse&K�egD/G�^H<���¾F¾��Fo/SYK�Z�· ?�?\A*^4^/DFEnAFG�KR¡RA*d(=@W ��D"l~e&AFXCA�X�WC^FDFE�· d/K A:E�?:ZAFG�G\=Yd/K�WmA"Z��FE�_H=�Z\K�Gia ��K�P8D/G�K6q/DF=2XHqCD ��Z�DQ=YX(d/K�?UZ�=2q/A"Z\K-Z�`VA"ZRe&D/XHDFS2=�Z\`�5,AFX�W�qFDnLVK�^FDFXVW�`(EHe�A�XHO(=2X�W�<$o^/DFEmW]K�I�=2W]K-D/XAgS2=�Z�Z�S2K-K��HI�E�G\?�=YD/XnZ\Dnv�A�S2SY=@?:Z\D�o]D/XHKMD�P �FEH_�=�Z\K�Gi· ?>µ&e�A A:D/G~egD(D/X�?�aA[<n�R?6^/DFEHG-S@A�X�WH=YXHq�_VD]W�W]Ki?�I�K�X�WH?sI�S2D/?�K&Z�D�Z\`HKv�A�S2S2=2?UZ�D�?�EHG�P,AFI�K/o�^/DFEHG6G\D]IJOFK�Z�Z\`HG\E�?:Z4=2? ³ � ¹ ¾� AFX�W^FD/EHG~W]K�?\I�K�X/Zc?�_VK�K�W=@? ¦ � � � � ��CaH»{`�A"Zc=@?>Z\`HK-qFGJA*d(=�ZJA"Z�=2DFXVA�SVP8DFGJI�KMDFX^FD/EHG>_VD]W �

LN<¤HA*^�^/DFE�G\K�W]EVI�KCZ\`HG\E�?:ZgZ�Dr�F�F¾F¾�  AFX�Wr��XVW�Z�`VA"ZgZ�`HK_VD]W�`�AF?gA�W]D"l~X(l>A�GJWrAFI�I�K�S2K�GJA"Z\=YD/X�D�P¾ � ³/½ e��"? � aj»{`�A"Zc=@?>Z\`HK-e�AF?\?�DFP�^/DFEHG>_ND]WQ=2X�I�SYE�WH=YXHq�^/DFEHGJ?�K�SYP �

Ii<n»{`VA"Z�· ?�Z�`�K�P8G\K�K�T�P,AFSYS]A/I�I�K�SYK�G\A�Z�=2DFXsWHEHK;Z\DMqFGJA*d[=YZ:^�XHK�AFG�Z\`HKBv�A�S2SY=@?UZ�DM?UEHG�P,AFI�KR5,=�a KFa2o ��jo�Z�`HK~A�XVA�S2DFqZ\D �P8DFG~q/G\A*d(=YZ:^gX�K�A�Gc��A�G�Z�`�· ?~?�EHGUP,A/I�K*<��

WV<¤HA*^4^/DFE&`�A*dFKcA6e&A/?�?�D�P�º"¾�O[qVa�»{`�A�Z�· ?�^/DFEHG�l�K�=2qF`[Z�D/XQv�A�S2SY=@?:Z\DsA�XVW&l~`�A"Z;=@?jZ\`HKBGJA"Z\=YD-DFPp^FDFE�Gv�AFSYS2=@?:Z\Dgl�K�=2qF`[Z>Z�D&^/DFEHGc��A�G�Z�`nl�K�=2qF`[Z �

K*<Q BD"l�Z\`HK�`�AFG\Wt_�AFGUZiaz�~P Z\K�Gn��XH=@?U`H=2XHq�^/DFEHG�K��]I�EHGJ?U=2DFX±DFX±Z�`�K�=2I�^t?�EHG�P,AFI�K/o>^FDFE±S@A�EHX�IJ`{AFX�Wq/D�=2X/Z\D�EHXH=YP8DFG\e I�=2G\I�EHS@A�G�e&DFZ�=2DFX�o6S2D"l>TUv�A�S2SY=@?:Z\D{DFG\LH=YZ�a b>`HKtqFGJA*d(=�ZJA"Z�=2DFXVA�S6AFI�I�K�SYK�G\A�Z�=2DFX =2?AF_H_HG\D*�]=Ye�A"Z\K�S2^�Z�`�K�?�AFe&K�AF?&Z\`HK�?�EHG�P,AFI�K�q/G\A*d(=YZ\A�Z�=2DFX�AFScAFI�I�K�S2K�GJA"Z\=YD/X±AFX�W±Z�`HK�G\A/W]=YEV?�D�PMZ�`�KD/G�L�=�Z>=2?�A�_�_HG�D*�]=2e�A"Z�K�SY^ A:E�?UZBv�A�S2SY=@?:Z\D�· ?;GJAFWH=YE�?�D�P��"µ/¾/¾jO(emajv�AFS2I�EHS2A�Z�KBZ�`HK�DFG\LH=YZ\A�S�?�_VK�K�Wpa�b>`HK�X

Page 31: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ¶  cK�l>Z�DFX�· ?c¸�A*lc?>A�X�Wm¡R^[XVA�e&=2I�?>7 �[º

�VX�W±Z�`HK�DFG\LH=�ZJA�Sc_NK�G\=2D(W�5,=�a KFa2o>Z�`�K�Z�=2e&K�Z�D�D/G�L�=�ZCD/X�I�K*<&=YX�?�K�I�DFX�W�?CA�X�W±=2X{`HDFE�G\?�a ������ �¿cK�e&K�e4LVK�GBI�K�X/Z\G�=2_NK�Z\AFS�AFI�I�K�S2K�GJA"Z\=YD/XQAFX�W �� � ��� $ � ��Va

¾F¾ ¶ h/P8EHS2S�¾/¾[º"¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\DF_NK-A�X�WLHS2D]IJOn?U^]?UZ�K�e��¾Ha ��D/En`�A*d/KBA6LHS2D]IJO�D�P�e�AF?\? ���4DFXnA6P8G�=@I$Z\=YD/XHSYKi?�?�o(`HDFG\=2��DFX[ZJA�SV?�EHG�P,AFI�KFa���DFEQAFG�KB_HEHS2SY=2XHqg=�Z~A�S2DFXHq4l~=�Z\`

A�EHXH=YP8DFG\e4T!W]K�X�?U=YZ:^rG�D/_VKD�Pce�A/?�? ���$a��R?U=@W]KnP8G�D/e =�ZJ?4e�A/?�?gA�X�W�l�K�=Yq/`/Z4Z�`HKG\DF_NKn=@?4=@W]KiA�S�arb>`�KZ:l�D�K�XVWH?6DFP~Z�`HKCG\DF_NKnAFG�KnA�Z6Z�`�KQ?\A�e&KC`HK�=Yq/`/Z4l~`H=2IJ`�=@?4l�K�SYS�A�LND"dFK&Z�`�KnqFG\DFE�X�Wpa�b>`HKQ?�^]?:Z\K�e =2?K�X/Z\=YG\K�S2^�Z:l�D�T!W]=2e&K�X�?�=YD/X�A�S�a � � � � b>`H=@?-=2?sA�XrK�X[Z�=2G\K�S2^x?�^[e4LVD/SY=@I�AFS�A�X�WxZ\`H=YX�O[=2XHq�h[EHKi?:Z\=YD/X�E�X/Z\=YS_�AFGUZ�5 P\<�a��cS@?UD-Z\`H=@?�h[EHKi?:Z\=YD/XCI�DFE�S2W�LNKBAsesEHSYZ�=YT�_VA�qFK�G�oF_VD[?�?�=YL�SY^gl~=�Z\`nA6`VA�X�W(T!W]GJA*l~X�W]=2AFqFGJA�e L[^4Z�`�K=2X�?UZ�G\E�I$Z\DFG~=2XmA4Z\K�?UZceg=@?�K�K�X�?�I�(K�XHK/aA[<n¯�E�?:Z~Z\`HK-G\DF_NKM?\A�q&A"ZcS2K�A/?:ZcAgLH=YZ��»{`[^QDFG>l~`(^CXHDFZ�LN<Q�R?�?�EHe&=2XHqgAFX(^g?\A�q4=2?�XHK�q/SY=2qF=2LHS2KcP8D/G�Z\`HK�G�Ki?:Z�D�PpZ�`�=2?>h[EHK�?UZ�=2DFXA�X�W�Z�`HK�`HDFG\=2��DFX[ZJA�S�_�EHSYS2=2XHqsP8D/G\I�K

^/DFEQK��]K�G�Z~DFXQZ�`HKMG\DF_NK�`VAF?�e�A�qFX�=�Z\E�W]K ���$o�l~`�A"Z~=@?�Z�`HK-AFI�I�K�SYK�G\A�Z�=2DFXCDFP�Z�`�K-LHSYD]IJOCAFX�Wnl~`VA"Z~=2?Z\`�A"ZcDFP�Z\`HK-G\DF_NK��mb>`HK�G�K6AFG�K�XHD�D�Z\`HK�G~K��(Z�K�G\X�AFSp`HDFG\=Y��DFX[Z\AFSNP8DFGJI�K�?�ajb>`HK-_HEHS2S2=YXHq�=@?~?UZ�K�A/W]^nAFX�WD/XHqFD/=YX�q�u�=�a KFa2o]Z�`�K�G\K6A�G\KRXHD�=2XH=YZ�=@A�S�?UZ\AFGUZ�T�EH_K ��K�I�Z\?�a�¿~K�e&K�esLNK�G~Z\Dgq/=Yd/K�Z�`HK6W]=2G\K�I$Z\=YD/X�a

Ii<n»{`VA"Z4=@?sZ�`HKQP8DFGJI�K ����Z\`HKnG\DF_NKnK��(K�GUZJ?6D/XrZ�`HKLHS2D(IJOrAF?gAmP8EHXVI$Z�=2DFXtD�P � �xA�XVW�Z�`HKG�K�SYK�d"A�X[Ze�A/?�?�K�?>D/XHSY^��

WV<n»{`VA"ZM=2?RZ�`�KsZ\K�X�?�=YD/X�P8D/G\I�K4A"Z�Z�`�K4e&=@W]_VD/=YX[ZMD�P�Z\`HK&G�D/_VK ��� T ��� �nA/?RAnP8EHX�I�Z�=2DFX�DFP � �QA�XVW�Z�`�KG\K�S2K�d"AFX/Z~e�AF?\?�K�?�DFXHS2^��

K*<n»{`VA"ZB=@?>Z�`�K-Z�K�X�?U=2DFXP8D/G\I�K6A"ZcZ\`HK-e&=2W]_NDF=2X[ZBD�P�Z\`HK6LHS2D]IJO � � T ��� � AF?BAgP8EHX�I$Z\=YD/X�D�P � � AFX�WZ�`�KG\K�S2K�d"AFX/Z~e�AF?\?�K�?�DFXHS2^��

P\<���=2dFK�X�Z�`HK�e�AF?\?�K�? � � $ ¶ � ¾jO(qwA�X�W � � $ ¾ � ��O(qVo�AFX�WzZ�`HK�A/I�I�K�S2K�GJA"Z�=2DFXzD�PgZ�`HK�?�^]?:Z\K�e� $�� � ¾�e ��? �*o�l~`�A"Zc=@? � � �

q(<C»{`VA"Zc=@?�Z�`HK-LHS2D]IJO�· ?~?�_VK�K�WmA"Z6�i¾je�P8G\DFe Z\`HK6?UZ\A�G�Z�=2XHqg_VD/=YX[Zc=YP�=YZB?UZ\A�G�Z\?�P8G\DFe�G�Ki?:Z �

Page 32: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� ��1 ��;7?T>�� E���& ��E�&A>�, %'6F>a&A= *-HJE�Q7Q

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾ ¹ h[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u���d/K-?U_NK�I�=2AFS�P8DFGJI�K�?�Fa~|�=2dFK-?U_NK�I�=2AFSpP8DFGJI�Ki?>A�G\KFu

A[<Cq/G\A*d(=YZ\A�Z�=2DFX�AFSpP8DFGJI�K/oVXHD/G�e�AFS�P8DFGJI�K/oNZ�K�XV?U=2DFX�oVP8G\=2I�Z�=2DFX�P8D/G\I�KFopA�X�W�Z�`HK4SY=2XHK�AFGBP8D/G\I�Kn5 Z\`HK&£cD(DFO/KF· ?S@A*l�P8D/G\I�Ki<�a

LN<nq/G\A*d(=YZ\A�Z�=2DFX�AFSFP8D/G\I�KFo�XHD/G�e�AFS(P8DFGJI�KFo�Z�K�XV?U=2DFX�o�P8G�=@I$Z\=YD/X4P8D/G\I�KFoFAFX�W4SYK�P Z�P8DFGJI�K-5 Z\`HKRv�A�_HZ\A�=2X&£cD(DFO/KF· ?S@A*l�P8D/G\I�Ki<�a

Ii<nq/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�KFo]XHD/G�e�A�S�P8D/G\I�KFo(Z\K�X�?�=YD/X�o(P8G\=2I�Z�=2DFXP8DFGJI�K/oHA�X�WQG�=2qF`[Z>P8DFGJI�K/aWV<nq/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�KFo]XHD/G�e�A�S�P8D/G\I�KFo(Z\K�X�?�=YD/X�o(P8G\=2I�Z�=2DFXP8DFGJI�K/oHA�X�WA�=2G>P8DFGJI�K/aK*<nq/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�KFo]XHD/G�e�A�S�P8D/G\I�KFo(Z\K�X�?�=YD/X�o(P8G\=2I�Z�=2DFXP8DFGJI�K/oHA�X�W ª�§�« �V¬ F« a

¾F¾ ¹ h[e4EHS�ZB¾/¾/�F¾F¾C�6���4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�O(=YX�K�Z�=@I�P8G\=2I�Z�=2DFXQP8DFGJI�K�]a~b>`HK�e�A�q/XH=�Z\E�W]K�D�PpZ\`HKRO(=2XHK�Z\=2IBP8G\=2I�Z�=2DFXCP8D/G\I�KBLNK�Z:l�K�K�XQA6LND]W]^CA�XVWnAs?�EHG�P,AFI�KBK�h[E�AFS2?�AgI�D(K��CI�=2K�X[Z�D�PP8G\=2I�Z�=2DFXZ�=2e&K�?�uA[<�Z\`HK6A�G\K�A4D�P�e�AFI�G�D[?�I�DF_H=@IBI�DFX[Z\A/I$Z~LVK�Z:l�K�K�XZ�`�K-LVD]W]^A�X�WnZ�`HK6?�EHG�P,AFI�KFaLN<CZ\`HK-e�A�q/XH=�Z\E�W]K-DFP�Z�`�K-XHDFG\e�A�S�P8DFGJI�K-A/I$Z�=2XHq&DFXQZ�`�K-LVD]W]^/aIi<CZ\`HK-e�AF?\?>D�P�Z�`HK-LND]W]^FaWV<CZ\`HK6W]K�X�?U=YZ:^CDFP�Z\`HK-LVD]W]^/aK*<CZ\`HK6W]K�X�?U=YZ:^CDFP�Z\`HK6A�=2Gc?UE�G�G\DFEHXVW]=YX�qsZ\`HK-LVD]W]^/a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ³ ¾F¾C�6� ¶ e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�P8G\=2I�Z�=2DFXmI�D(K��CI�=2K�X[ZJ?c?U=2��Ki?³ a>»{`H=@IJ`m=2?>S@A�G\qFK�G�u�Z�`�K6I�D(K��CI�=2K�X[ZcDFP�?UZ\A"Z\=2IMD/G~O(=YXHK�Z�=@IRP8G�=@I$Z\=YD/X �

A[<nb>`�K�^QAFG�KMA�S2l>A*^(?�Kih/EVA�S�aLN<Q BK�=YZ�`HK�G�ajb>`HKBS2AFG�q/K�G;W]K�_VK�X�WH?;DFX&Z�`�KBe�A"Z\K�G\=2AFS2?j=2X(dFD/SYd/K�WgA�X�W&=YZ\?�A�LNDFE]Z�A ¶ ¾�T ¶ ¾�?�_HS2=�Z�DFX�l~`H=@IJ`

=@?~S@A�G\qFK�G�aIi<Qb>`�K-O[=2XHK�Z�=@I-I�D(K��CI�=2K�X[Z~=@?~A�S2l�A*^]?�S2AFG�q/K�GiaWV<Qb>`�K-O[=2XHK�Z�=@I-I�D(K��CI�=2K�X[Z~=@?>E�?UEVA�S2SY^QS2AFG�q/K�GiaK*<Qb>`�K6?:ZJA"Z�=@IMI�D(K��CI�=YK�X/Zc=@?~A�S2e&D/?UZcA�S2l�A*^]?M5,AFSYl>A*^]? �*<-S@A�G\qFK�G�a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ³ ��¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�P8G\=2I�Z�=2DFXQZ�D�`HKiA"Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=pG\K�S@A"Z\K�WnZ�DC² ��T ½ µ�T ½ L�E]ZcXHD�Z~G\K�AFSYS2^�Z�`VA"Z

µ�a~b>`HKMP8G\=@I$Z�=2DFXLNK�Z:l�K�K�X�?�SY=@W]=2XHq�?UE�GUP,A/I�K�?�Z\K�X�W�?�Z�DCIJ`�AFXHqFK�e�AFI�G\D/?\I�D/_H=@IBO(=2XHK�Z\=2IMK�XHK�G\qF^�=2X[Z�D�uA[<&_ND�Z�K�X[Z�=@A�SBK�XHK�G\qF^/a LN<�G\K�?UZCe&A/?�?CK�XHK�G�q/^Fa I�<gZ\`HK�G\e�A�ScD/GC`HKiA"ZnK�XHK�G\qF^/a WV<e�AFqFXHK�Z�=@IRK�XHK�G\qF^/a Ki<�XHDFZ�`H=2XHqVa

¾F¾ ¹ h[e4EHS�ZB¾/¾�µ[¾F¾4�Q�-µ&e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�Z�`�K-SY=2XHK�AFG>P8DFGJI�KMS@A*l� ª�¬"¨ �V«������V¬ ��­�� ?U_HG\=2XHqgP8DFGJI�KMS2A*l-oH£BD(DFOFK/· ?�S@A*l

¶ a~b>`HK6?�_HG\=YX�qsP8D/G\I�K�=@?�uA[<nA ¦ � � � � �� SY=2OFK�Z\`HK6�;AFGUZ\`�· ?~?�EHG�P,AFI�K�q/G\A*d(=YZ:^Fa

Page 33: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ¹  BK�l>Z\DFX�· ?~¸�A*lc?~AFX�WQ¡R^(X�A�e&=@I�?~7�7 � ½

LN<n_�G�D/_VD/GUZ\=YD/X�A�S�Z�DmZ\`HK ��� � � � D�P�Z�`HKC?�_HG\=YXHq�?UZ�G\K�ZJIJ`�P8G\DFe =�ZJ?-K�h[EH=2SY=2LHG\=YE�e S2K�XHqFZ�`�a�7kZi· ?6AFXK��HA�e&_HS2K�DFP�A&h[E�A/W]G\A�Z�=@IRP8DFGJI�KFa

Ii<n_�G�D/_VD/GUZ\=YD/X�A�S*Z\D~Z�`HK ¦ � �DFP[Z\`HK;?�_HG\=YXHqc?UZ�G\K�ZJIJ`MP8G�D/e�=YZ\?�K�h[EH=2SY=2LHG\=YEHe S2K�XHqFZ�`�a�7kZ�· ?�AFX-K��HA�e&_HS2KDFP�A&I�EHLH=@I�P8DFGJI�KFa

WV< �/� � � � � � � � � �tZ�DgZ�`�K6?U_HG\=2XHqg?UZ�G\K�ZJIJ`nP8G\DFe =YZ\?cK�h[EH=2SY=2LHG\=YEHe�SYK�XHq�Z\`�aj7kZ�· ?~A�XQK��HA�e&_HS2KMD�PAgS2=YX�K�A�G>P8D/G\I�KFa

K*<n=@?cAFSYl>A*^]? � � ��a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�W]GJA�q4P8DFGJI�K-A/?~I�DFX[ZJAFI$Z>P8D/G\I�K¹ a~b>`HK6WHG\AFqsP8D/G\I�K�=@?~A�XmK��]AFe&_HSYKMDFP:u

A[<nAgS2=YX�K�A�G>P8D/G\I�KM=YX�A�S2S�I�A/?UKi?�aLN<QAgq/G\A*d(=YZ\A"Z\=YD/X�A�SVP8DFGJI�K/aIi<QA4Z\K�X�?�=YD/XP8DFGJI�KFaWV<QA&I�DFX[Z\A/I$Z>P8DFGJI�K/aK*<QAFXAFXH=2e&AFSpP8DFGJI�K/a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ µ&K�A/?U^&Z\`H=2XHO(=YXHqVu�L�AFS2AFX�I�KiW�P8DFGJI�Ki?>DFXmA�I�D �NK�KMI�EH_º(a ��D/E&AFG�K�_HE�?�`H=2XHq6AMI�D �NK�KcI�EH_�AFI�G�D[?�?�ARZ\AFLHSYK65 A:E�?UZ�A�XgDFGJW]=2X�A�G\^MZ\AFLHSYK/oFXHDFZ�A�X&=Ye�AFqF=2X�A�G\^MP8G�=@I$Z\=YD/XHS2K�?\?ZJA�LHS2Ki<RA"ZMA ¦ � � � � �� d/K�S2D(I�=�Z:^/a�b>`�Kse�A�q/XH=�Z\E�W]Ki?BDFP�Z�`HKg_HE�?�`�P8D/G\I�K4A�XVWmP8G�=@I$Z\=YD/X�A�S�P8DFGJI�KgA�G\K� � � �]A�X�W�� ���*��oHG\K�?�_VKiI$Z�=2dFK�SY^/aA[<nb>`�K'� ���*�[=2? �4� � � �}Z�`VA�X � � � �]AFX�WnZ�`H=@?~=@?>l~`[^nZ�`HK6I�EH_mW]D(K�?~XHDFZcAFI�I�K�S2K�GJA"Z\KFaLN<Qb>`�K � ���*�F=2? � � ��Z\`�A�X � � � ��o[L�E]Z�XHK�dFK�GUZ\`HK�S2K�?\?jZ\`HKBP8G\=@I$Z�=2DFXVA�SHP8D/G\I�KB_HG\K�d/K�X[Z\?;A�X(^�AFI�I�K�S2K�GJA"Z\=YD/X�aIi<Qb>`�K�G\K�=@?~XHDgP8G\=2I�Z�=2DFX�AFS�P8DFGJI�KMl~`HK�X^/DFEQ_HE�?�`QZ\`HK6I�E�_mA�ZBA&I�DFXV?:ZJA�X[Z~dFK�S2D]I�=YZ:^FaWV<Qb>`�K'� ���*�[esE�?UZ �� � � ��� � � �]=YXmDFGJW]K�G�P8D/G>Z�`HK�G�KMZ\D&LVK-XHDCA/I�I�K�S2K�GJA"Z�=2DFX�aK*<Qb>`�K'� � � �[esE�?UZcLNK �� � ¦ � � � �(=2XmDFGJW]K�G�P8D/G>Z�`HK�G�K�Z�D�LNK-XHD�AFI�I�K�SYK�G\A�Z�=2DFX�a

¾F¾ ¹ h[e4EHS�ZB¾/¾[º�¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujEHX�=�P8D/G�e�I�=YGJI�E�S2AFG�e&DFZ�=2DFX¼ a~�BXH=�P8D/G�e I�=2G\I�EHS@A�G>e&D�Z�=2DFX=@?�u

A[<Ce&DFZ�=2DFX=YX�A&I�=2G\I�SYK-A�ZBAgI�DFX�?UZ\AFX[Z>d/K�S2D]I�=YZ:^FaLN<ne&DFZ�=2DFX=YX�A�XmD"d"A�SpA�ZBAgI�DFX�?UZ\AFX[Z>d/K�S2D]I�=YZ:^FaIi<ne&DFZ�=2DFX=YX�A�XmD"d"A�SpA�ZBAgI�DFX�?UZ\AFX[Z~?�_NK�K�W�aWV<ne&DFZ�=2DFX=YX�A�X�I�=YGJI�S2K-A"ZcA&I�DFXV?:ZJA�X[Zc?U_NK�KiWpaK*<ne&DFZ�=2DFX=YX�A�X�I�=YGJI�S2K-A"ZcAgXHDFX�I�DFX�?UZ\AFX[Z~?�_NK�K�W�a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�I�K�X[Z�G\=Y_NK�ZJA�S�A/I�I�K�SYK�G\A�Z�=2DFX½ a>7!XmEHXH=YP8DFG\e�I�=YGJI�EHS@A�G~e&DFZ�=2DFX�o(Z\`HK6AFI�I�K�S2K�GJA"Z\=YD/Xn`�A/?�u

A[<nA&I�DFX�?UZ\AFX/Z~e�A�q/XH=YZ�E�W]K6AFX�WA�S2l�A*^]?�_VD/=YX[ZJ? � � �� � ��� P8G�D/e Z�`HK6I�K�X[Z�K�G~D�P�egDFZ�=2DFX�aLN<QAI�D/X�?UZ\A�X[ZMe�A�qFX�=�Z\E�W]K�A�X�WxA�S2l�A*^]?R_VD/=YX[ZJ? � � � ��� Z�`�K&I�=YGJI�E�S2AFGR_�A�Z�`w58=�a K/aYo�Z\A�X�qFK�X[Z�Z�DZ�`�K

I�=YGJI�E�S2AFG�_VA"Z�`N<$aIi<QA&I�DFX�?UZ\AFX/Z~e�A�q/XH=YZ�E�W]K6AFX�WA�S2l�A*^]?�_VD/=YX[ZJ? ��� � � ����Z\DgZ�`HK6I�K�X[Z�K�G~D�P�egDFZ�=2DFX�aWV<QAg��K�G\Dgd"AFSYEHK/aK*<QAgXHD/X�I�D/X�?UZ\A�X[Z~e�A�q/XH=�Z\E�W]K/o]LHE]ZRA&I�D/X�?UZ\A�X[ZcW]=2G�KiI$Z\=YD/X�a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ½ ¾F¾ ³ ���MK�A/?U^�e�A�Z�`�u;I�K�X[Z�G\=2_VK�Z\A�S�A/I�I�K�S2K�GJA"Z�=2DFX��¾Ha~b>`HKMP8D/G�e4EHS@A6P8D/G>Z�`HK-e�A�q/XH=YZ�E�W]K-DFP�I�K�X[Z�G\=Y_NK�ZJA�S�A/I�I�K�S2K�GJA"Z�=2DFXQ=2?�u

� � � � � � � � ��� � � $ � �

l~`HK�G�K � =@?&Z�`HK�?U_NK�KiWwD�P-A�EHXH=YP8DFG\e I�=2G\I�EHS2AFG�e&D�Z�=2DFX�AFX�W =2?CZ�`HK�GJAFWH=YE�?CD�PMZ�`HK�egDFZ�=2DFX�a ¤]A*^� $ ��¾�e ��?>A�X�W $ ¶ emo]l~`�A�Zc=2? ��� � � � � � � ��� ��� �

Page 34: Introductory Physics Problems David J. Jeffery Department of

³ ¾ v�`�AF_]Z�a ¹  cK�l>Z�DFX�· ?~¸�A*lc?~A�X�W¡B^(X�AFe&=2I�?~7U7

A[<Q�F¾je��"? �"aLN<��i¾je��"? �"aIi< ¶ e ��? ��aWV<��i¾F¾je���? �*aK*<�� ¶ e��"? �"a

¾F¾ ¹ h[e4EHS�ZB¾/¾ ½ ��¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�I�K�X[Z�G\=Y_NK�ZJA�S�P8D/G\I�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¶ º*T\� ³

�F�Fa~|�DFGcA4LVD]W]^nZ�D&e&D"dFK�=YXmA&I�=2G\I�SYKMA"ZcAgEHXH=YP8DFG\e�?�_VK�K�WQ=YX�A�X=2XHK�G�Z�=@A�SNP8GJA�e&KM=�Zc=@?>XHK�I�K�?\?�AFG�^gZ\D&?�EH_H_�SY^A(y"A�X P8D/G\I�KFu

A[<>I�K�X/Z\G�=YP8EHq[A�S LV<�=2XHK�G�Z�=@A�S I�<�q/G\A*d(=YZ\A"Z\=YD/X�A�S W�<�Z\K�X�?�=2DFX Ki<>I�K�X[Z�G\=Y_NK�ZJA�S

¾F¾ ¹ h[e4EHS�ZB¾/¾ ½ ��¾4� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�I�=2G\I�EHS@A�G>e&D�Z�=2DFX=2XX�DFX]Tk=YX�K�G�Z�=@A�S� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¶�½ T!�H�so]LHE]ZR7$· d/KMI�DFG\G�KiI$Z\K�WC=YZ

�i�]a>7!Xwl~`�A�Zn?U=YZ�E�A�Z�=2DFX�o>=YPMAFX(^Fo>I�A�X{ArLND]W]^�e&D"dFKm=2X{A�I�=2G\I�EHS2AFG&_�A"Z\`�A"ZnI�D/X�?UZ\A�X[ZC?�_VK�K�W±l~=�Z\`HDFEHZnAI�K�X[Z�G\=Y_NK�ZJA�S�P8D/G\I�KFa

A[<gXHDFX�KFo LV<&=2X{I�K�GUZJA�=2Xw?�_NK�I�=@A�SBXHDFX]Tk=2XHK�G�Z�=@A�S~P8GJA�e&Ki? I�<&=2X{A�S2ScXHD/X]T�=2XHK�GUZ\=2AFS~P8G\AFe&K�?�oWV<�=YX�A�S2Sp=2XHK�G�Z�=@A�SpP8GJA�e&Ki?�o K*<�A�S2l�A*^]?�a

¾F¾ ¹ h[e4EHS�ZB¾���¾/¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�K�X/Z\G�=2_NK�Z\AFSpP8DFGJI�K� ³ a~b>`HK6I�K�X[Z�G\=2_VK�Z\A�S�P8D/G\I�KM=2?�u

A[<nA�e4^(?UZ�K�G�=2DFEV?�P8DFGJI�K�Z�`�A�Z � � �� � � �l~`HK�X�K�dFK�GjA�X&DFL,A:KiI$ZjqFD(Ki?�=YX[Z�DMEHX�=�P8D/G�e I�=2G\I�EHS2AFG�egDFZ�=2DFX�aLN<QAge4^(?UZ�K�G�=2DFEV?�P8DFGJI�KRZ�`�A�Z~Z�G\^(?�Z\D&Z�`HG\D"l�^/DFE � z_HS2A*^(q/G�D/EHX�WCe&K�G�G\^[T�q/D�TkG�D/EHX�WH?�aIi<n=2XmP,AFI�Z �� � ��� D�P �� ����� $ � ��Cl~`�K�XmZ�`�=2?BK�h[E�A"Z\=YD/Xm=2?c?�_NK�I�=@A�S2=2��K�WQZ\D�Z�`HK4I�AF?�KMD�PjEHXH=YP8DFG\e}I�=YGJI�E�S2AFGe&DFZ�=2DFX�a&7kZ-=2?�� � �Ane4^(?UZ�K�G�=2DFEV?BP8D/G\I�KgZ�`�A�Z-AF_H_NK�A�GJ?�l~`HK�X�K�dFK�G-^FD/E�`�A*d/K4EHX�=�P8D/G�e I�=YGJI�E�S2AFGe&DFZ�=2DFX�a�9jAFGUZ\=2I�EHS2AFG>_H`(^(?�=@I�A�S�P8D/G\I�K�?M58K/a qVaYo�qFGJA*d[=YZ:^Fo[Z\K�X�?�=YD/XP8DFGJI�KFoHAFX�WQXHDFG\e�A�S�P8DFGJI�K*<�esE�?UZBAFI�Z5�?UD/e&K�Z�=2e&K�?~=2X�I�D/esLH=2X�A�Z�=2DFXV<�Z\D�qF=2dFK-A�I�K�X/Z\G�=2_NK�Z\AFSpP8DFGJI�K-l~`�=2IJ`Z�`�K�X�I�AFE�?�K�?>EHXH=YP8DFG\e}I�=YGJI�E�S2AFGe&DFZ�=2DFX�a

WV<n=2XmP,AFI�Z �� � ��� D�P �� ����� $ � ��Cl~`�K�XmZ�`�=2?BK�h[E�A"Z\=YD/Xm=2?c?�_NK�I�=@A�S2=2��K�WQZ\D�Z�`HK4I�AF?�KMD�PjEHXH=YP8DFG\e}I�=YGJI�E�S2AFGe&DFZ�=2DFX�a6b>`HK4P8DFGJI�K4=�ZJ?UK�S�P�=2? � � � � � �{ACLND(WH^�P8DFGJI�K4K�e�A�X�A�Z�=2XHqCP8G\DFe�Z\`HK&I�K�X[Z\K�G�D�P;e&D�Z\=YD/XZ\`�A"Zc_�EHSYS@?~D/XnZ\`HK6I�=2G\I�SY=2XHq&DFL3A:K�I$ZcA�Z�DFe�L[^A"Z\DFema

K*<QAge4^(?UZ�K�G�=2DFEV?�P8DFGJI�KRZ�`�A�Z � � � � � �� � � �rl~`HK�XHK�d/K�G~A�XmD/L,A:K�I�Z>q/D(K�?>=2X/Z\D�I�=2G\I�EHS2AFG>egDFZ�=2DFX�a

¾F¾ ¹ h[e4EHS�ZB¾��F�i¾F¾4� ³ �4e&D]W]K�GJA"Z\K�e�A�Z�`�u�I�K�X[Z�G\=Y_NK�ZJA�S�P8D/G\I�K�^/D�Tk^FDg?:Z\G�=2XHq� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ��T ³[¶

��µ�a~�f^FD�Tk^FD�DFP;��¾F¾�qCA�X�W�?UZ�G\=2XHqCS2K�XHqFZ�` ¼ ¾�I�e}=2?�?Ul~=2G\SYKiW�A�G\DFEHX�WmL(^`HDFS@W]=2XHqCZ\`HKsK�X�W�DFPjZ�`HKg?:Z\G�=2XHqC=2XZ\`HKCA�L�?�K�XVI�KgD�P�q/G\A*d(=YZ:^�A�X�W�A�=2GMG�Ki?U=@?:ZJA�X�I�KFagb>`HKC?:Z\G�=2XHql~=YS2SjLHG\K�AFO�=�P�Z�K�X�?U=2DFXxP8DFGJI�KgK��HI�K�K�W�?&��¾� sa�BLVD/E]Zc`HD"l�P,A/?:ZBI�A�XQZ�`HK-^/D�Tk^FD4LVK6?�l~EHXHq�l~=YZ�`HD/E]ZcLHG\K�AFO[=2XHq4Z�`HK6?UZ�G\=2XHq �

A[< ³ � ��e��"?$a LV< ¹ � ³ e��"?$a I�< ¼ ¾�e ��?�a WV<~��¾F¾�e ��?Ja Ki<��i¾je��"?�a

¾F¾ ¹ h[e4EHS�ZB¾��i�F¾F¾ ³�¶ ��Z�D/EHqF`QZ�`�=YXHO(=2XHq�ujS2=YP Z�=2XHq&P8G�D/e}Ag`(EHe&_� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹ ��T ³/½

� ¶ a~b>`HK�G�Ks=2?R`(EHe&_�DFXmZ\`HKsG\D/A/Wml~=�Z\`�ACI�^(S2=YXVW]G�=@I�AFS�?�`�A�_NKFaRb>`HKsGJAFW]=2E�?~DFPjZ�`HK4`(EHe&_�=2?4��µ � º�ea~7!X�AFX=@W]K�AFSY=2��KiWr_H=@I$Z�E�G�K/o�AFLVD"d/KCA�LNDFE]Z4l~`�A"Zg`HDFG\=Y��DFX[Z\AFS�?U_NK�KiW�esEV?:Z4A�I�A�G4A"ZsZ\`HK�Z\DF_�DFP�Z\`HKn`(EHe&_�S2=�P ZP8G\DFe Z\`HK-`(EHe&_ �

A[<��i��e���?$a LV<���µ � º�e��"?$a Ii<���µ/µ�e��"?$a WV<���¾je��"?�a Ki<��i¾ � µ�e��"?$a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

Page 35: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ¹  BK�l>Z\DFX�· ?~¸�A*lc?~AFX�WQ¡R^(X�A�e&=@I�?~7�7 ³ �

¾F¾ ¹ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_H=2q&DFX�?US2=@W]KFujl~=YZ�`�A�XVWQ?\A�X�?�P8G\=@I$Z�=2DFX�Fa~��P8G\K�K�Tk?�_H=2G�=YZ�KiWn_H=2q�58S2K�Zi· ?cI�A�S2Sp`H=2e�»rA�S@W]DC9�K�_H_NK�G$<�SYD"d/K�?>?�SY=@W]=2XHq�W]D"l~XIJ`(E]Z\K�?�a

A[<Q¤HA*^�Z�`HK�G�K�=@?�A�P8G\=2I�Z�=2DFXHS2K�?\?�IJ`(E]Z�K�A�XVWt»rA�S@W]D�AFI�I�K�SYK�G\A�Z�K�?&W]D"l~XwA"Z ¶ � ¾�e ��? ��a{»{`�A"ZC=@?&Z�`�K=2X�I�SY=2X�A"Z\=YD/X�A�XHq/SYK�D�P�Z�`HK6IJ`(E]Z\K��������� � ¿~K�e&K�e4LVK�G>Z�`�A�Z~P8G�K�K-LVD]W]^W]=@A�qFGJA�ema

LN<Q BD"l±Z�`HKcK�d(=YSVe&AFqF=@I�=@A�X&D�Pp_H`(^]?�=2I�?�Z�EHG\X�?;DFX&O(=YXHK�Z�=@I~P8G\=2I�Z�=2DFX�A�XVW&»�AFS2W]DsDFXHS2^4A/I�I�K�SYK�G\A�Z�Ki?�W]D"l~XA�Z ³ � ¾je���? ��� »{`�A"Zg=2?sZ�`HKI�D(K��CI�=YK�X/Z4D�PcO(=YX�K�Z�=@I&P8G\=2I�Z�=2DFX � ������ � �B_NW�A"Z�KQZ�`VA"Z6P8G\K�KQLVD]W]^WH=2AFqFGJA�ema

Ii<n»{`VA"Z�· ?~»rA�S@W]D�· ?>e�AF?\? � ������ � b>`HK-K�d(=2S�e�A�qF=@I�=@A�XQD�P�_H`(^]?U=@I�?>=@?>LVK�=YX�qC?U_H=YZ�K�P8EHS�a

¾F¾ ¹ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_HS@A�XHKMe�A�O(=2XHq�A&L�A�X�OFK�WnZ�E�G�X�]a~�BXtA�=2G\_HS2AFXHKC=@?se�AFO[=2XHq�AmZ�EHG\X�Z\`HG\DFEHq/`�A�I�=2GJI�EHS@A�G4LVK�X�W�l~=YZ�`±A�?�_VK�K�W�DFP ¹ ¾F¾�O[e��"`HG�a�7kZ4e&D"dFKi?`HD/G�=2��D/X[Z\A�S2S2^nDFX�SY^�u�=�a KFa2o�=�Zi· ?RXHD�ZRegD"d(=2XHqCD/GBAFI�I�K�S2K�GJA"Z\=YX�qCW]D"l~X(l�AFG\WDFGREH_(l�AFG\W�a�7!X�DFGJW]K�G~Z\Dne�A�O/KZ\`HKCZ\EHG�XrZ\`HKn_�S2AFXHKCL�AFXHO]?sA"Z ³ ¾ �&P8G�D/e Z\`HKn`HD/G�=2��D/X[Z\A�SR58=�a K/aYo�=YZ\?6l~=2XHq[?sA�G\K�Z\=Y_H_NK�W�A"Z ³ ¾ �&Z\D�Z�`�K`HD/G�=2��D/X[Z\A�S�l~=�Z\`CZ�`�KB`H=2qF`n?�=@W]KRA*l>A*^6P8G\DFe Z�`HK�I�K�X/Z\K�G�D�PpZ\`HKcZ\EHG�X�a��R?�?�EHe&KRAFSYSVZ�`�KcP8DFGJI�KcZ�`HK�A�=2G�I�AFXK��(K�GUZ�DFX&Z\`HKR_�S2AFXHKs5 Z\`HKMA�K�G\D]W]^(X�A�e&=@I~S2=�P Z$<;A/I$Z\?;_VK�G�_NK�XVW]=2I�EHS@A�G\SY^gZ�DsZ�`HKRl~=YX�q/?�a�»{`�A�Z�=@?;Z�`HKRG\A/W]=YEV?DFP�Z\`HK6I�=2G\I�SYK � ������ � ¡RG\A*l�AsP8G\K�K-LND]W]^nW]=@A�q/G\AFema

¾F¾ ¹ h/P8EHS2S�¾/¾ ³ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�ujG�D[AFWQL�A�XHO(=2XHqgP8DFG\esEHS@A³ a ��K�I�A�E�?�KCG\D/A/W�P8G�=@I$Z\=YD/X�=2?gd"A�G\=@A�LHS2KCl~=YZ�`�l�K�A�Z�`HK�G5�W]=Y_�_H=YX�q�S2D"l l~=�Z\`�GJA�=2X�A�X�W�Ki?U_NK�I�=2AFSYS2^r=2I�KQAFX�W?�XHD"lB<$o[G\D/AFWgK�XHqF=2XHK�K�G\?;W]DFX�· Z�S2=2OFK~Z\D6G�K�SY^gDFX&P8G\=@I$Z�=2DFXx5,A�XVW&l�KRegKiA�XC?UZ\A�Z�=@I>P8G�=@I$Z\=YD/XC`HK�G�K*<�Z�D6_�G�D"d(=@W]KAFX[^�DFP;Z\`HKCI�K�X/Z\G�=2_NK�Z\AFS�P8DFGJI�K4Z�Dme�A�O/Kgd/K�`H=@I�S2K�?&5,DFGMdFK�T�`H=@I�S2K�?MA/?Ml�K&E�?�K�W�Z�D�?\A*^�=YXrb�K�XHXHKi?�?�K�K*<Bq/DAFG�D/EHX�W�LNK�X�W�?�a6b>`(E�?RZ�`�K�^mZ�K�X�W�Z�DL�A�XHOZ\`HK4G\D/A/WH?�?UDnZ�`�A�Z�q/G\A*d(=YZ:^AFX�W�Z\`HK&XHDFG\e�A�S�P8DFGJI�KsDFP�Z�`�KG\D/A/WC?UE�_H_HS2^nA�S2S�DFG~A�S2e&D/?UZ>AFSYS�D�P�Z�`HK-I�K�X[Z�G\=Y_NK�ZJA�SNP8DFGJI�K�=YP�Z�`�K�d/K�`H=@I�S2K�qFD(K�?>A"Z�Z�`�K�_�G�Ki?�I�G�=2LVKiWn?�_VK�K�Wpa��GJA*d(=�Z:^m=@?R_�G\A/I$Z�=@I�AFSYS2^m=YX(d"A�G\=@A�LHS2K4A/?BP,AFG-AF?�I�A�GJ?�A�G\K4I�D/X�I�K�G�X�K�W�AFX�W�E�X�W]K�GMXHD/G�e�AFS�I�=YGJI�EHe�?UZ\AFX�I�Ki?Z\`HKRG\D/A/WC?�`HDFEHS@WC`VA�GJW]SY^g��K��nA"Z~A�S2S�XHD4e�A�ZUZ�K�G�l~`VA"Z>XHDFG\e�A�SVP8DFGJI�K�=2?>W]K�e&AFX�W]KiWCD�P�=�Zia�b>`(E�?�q/G\A*d(=YZ:^AFX�WCZ\`HK-XHD/G�e�A�S�P8D/G\I�K-I�A�XLNK-G�K�SY=2K�WQDFX�a

 BD"l�_HG\DFL�AFLHS2^MAFSYS[O(=YXVWH?�D�PVI�DFX�?�=2WHK�GJA"Z�=2DFXV?�q/DB=2X/Z\D�WHK�?�=Yq/XH=YX�qBG\K�A�S[L�AFXHO(=YXHqVo"LHE]Zj=2X6Z�`�K�=@W]K�AFSY=2��KiWI�AF?�K�D�PcA�I�=2G\I�EHS@A�G6LNK�X�Wrl~=YZ�`�I�A�GJ?-e&D"d(=YXHq�A�ZsAm�H�]K�Wr?�_VK�K�W�AFX�WrDFXHS2^�q/G\A*d(=YZ:^Fo�P8G�=@I$Z\=YD/X�o�AFX�W�Z�`�KXHD/G�e�AFS�P8D/G\I�K4AFI�Z�=2XHqCZ\`HK�G\Ks=@?MAn?�=Ye&_HS2K4P8DFG\esEHS@A&P8DFGRZ�`�K4L�AFXHO(=YX�qQA�X�qFS2K6Z�`VA"ZMG�KiW]E�I�Ki?cP8G\=@I$Z�=2DFX±58=�a K/aYoP8G\=2I�Z�=2DFX�AFSYD/XHq&Z�`HKsG�D[AFWm?UE�GUP,A/I�K ���� �� ��� � ¦ ��� � ��Z�D�Z\`HK6d/K�`H=@I�S2KF· ?c=2X�?UZ\A�X[ZJA�XHK�DFE�?cWH=YG\K�I�Z�=2DFXDFP�e&D�Z\=YD/XV<;Z�D���K�G\D�aA[<n�R?�?�EHe&K�AxI�A�Gg=2?&q/DF=2XHqxAFG�D/EHX�WtAxI�=YGJI�EHS@A�GgLNK�X�WtD�P�G\A/W]=YEV? A"Z�AxE�XH=�P8D/G�e ?�_NK�K�W � at¡RG\A*l

� �1��� � � �� � �fA�X�W � �� � ¦&� � A"�]K�?-Z�D�e�A�O/K�EH_�AP8G�K�KCLND(WH^�W]=@A�q/G\AFe l~=YZ�`rZ�`�KnI�AFGAx_NDF=2X/Z&e�AF?\?&A"ZgZ�`HK�I�K�X[Z�K�Gia�¯�AFG�O�Z�`�KmWH=YG\K�I�Z�=2DFX�DFPcZ�`�KLVA�XHO(=2XHq�DFPBZ�`�KQG\D/A/WpuC=�a K/aYo�A�S2=YX�KZ\`�A"Z6G\EHX�?MAFSYD/XHqnZ\`HK�G\D/AFWx?UE�GUP,A/I�KFa&b>`HK&L�AFXHO(=YXHq�AFXHqFS2K � � � ��� =2?�Z\`HK�A�XHq/SYK&DFP�G\D/AFW�P8G�D/e�Z�`�K� �1��� � � �� � �Bap¯�A�G\OZ�`HK&W]=2G�KiI$Z�=2DFX�Z�`�A�Z�Z\`HK&I�K�X[Z\G�=2_VK�Z\AFS�P8D/G\I�Ks_NDF=2X/ZJ?�=YX�uRG�K�e&K�esLNK�GRZ�`�KI�K�X[Z�G\=2_VK�Z\A�S�P8DFGJI�KM=2?cXHD�ZBAFX[^Q_�A�G�Z�=@I�E�S2AFG�P8D/G\I�KFuj=YZB=@?>Z�`HK6?�EHe}D�P�Z�`HKsA/I$Z\E�A�S�P8D/G\I�K�?~=2XZ�`HK-_HS@A�X�KDFPBZ\`HKmEHXH=YP8DFG\e I�=2G\I�EHS@A�G&e&D�Z�=2DFX�at cD"l�=YX�WH=2I�A"Z�KZ\`HK�qFGJA*d(=�ZJA"Z�=2DFXVA�S�P8D/G\I�KAFX�W±A�XHDFZ�`HK�G4P8D/G\I�Kl~`�=2IJ`�l�K&l~=2SYS�A:EV?:ZsI�A�S2S�Z\`HKCI�D/X[Z\AFI�ZRP8D/G\I�K �� � u�Z�`HK�I�DFX[Z\A/I$ZMP8DFGJI�Kg_VD/=YX[ZJ?-A"Z6A�XrA�XHq/SYK � ��� � � �� �P8G\DFe�Z�`HK � �� � ¦&� �caNb>`HK6I�D/X[Z\AFI�Z>P8DFGJI�KMP8DFGcZ�`HK-LND�Z�Z�DFe D�P�Z�`�KMZ�=2G�Ki?~=2?~Z�`HK6d/K�I�Z�DFGc?�EHe}D�PZ\`HK&XHDFG\e�A�S�P8DFGJI�KgA�X�W�Z�`HK4P8G\=2I�Z�=2DFX�AFS�P8D/G\I�KFa ��E]ZMZ�`�KgI�DFX[Z\A/I$Z�P8DFGJI�K4I�A�XxLVK�A�X(^�I�D/X[Z\AFI�ZRP8D/G\I�KZ\`�A"ZcI�A�E�?�K�?�?UD/e&K�Z�`�=YXHqsZ�DgqFDgG�D/EHX�W&Z\`HKMLVK�X�Wpa�b>`(E�?�Z�`�K�I�DFX[Z\A/I$Z�P8DFGJI�KRWHK�?\I�G\=Y_]Z\=YD/XnA�_�_HSY=2K�?�Z\DP8D/G\I�K�?M=2X[Z�K�G\X�AFS�Z�DmZ�`�KCI�A�GMZ\`�A"Z4e&AFOFK&_�AFGUZJ?MD�P>=�Z6q/DG\DFE�X�W�Z\`HKCLNK�X�WxZ\D[DVu6KFa q�a2opZ\`HKnI�D/X[Z\AFI�ZP8D/G\I�KMDFXQZ�`HK6?�K�A�Z>DFP�Z\`HK6W]G\=Yd/K�G>DFG>Z\`HKMZ�K�X�?�=YD/XnP8D/G\I�KMA/I$Z\=YXHq&D/XQZ\`HKMP8EH����^nW]=@I�K/a

LN<¤]=YX�I�K6l�K6`�A*dFK6A/?�?�EHe&K�WZ\`�A"ZBZ�`HKgI�A�GB=2?BqFDF=2XHq�=2X�EHXH=YP8DFG\e I�=YGJI�E�S2AFGce&D�Z�=2DFX�AFG�D/EHX�WQZ�`�K6LVK�X�Wpol~`VA"Z�K�dFK�G6P8DFGJI�Ki?-e�A�O/K�?6E�_�Z�`HKI�D/X/ZJAFI�Z6P8DFGJI�K�5,KFa q�a2o�P8G�=@I$Z\=YD/X�o�XHDFG\e�A�S;P8DFGJI�KFo�Z\K�X�?�=YD/XV<6AFG�KnEH_Z\D�Z�`HK A:DFL±D�PMI�AFE�?U=2XHq�Z�`HK�EHX�=�P8D/G�e I�=YGJI�EHS@A�G&e&D�Z\=YD/X�atb>`�KmI�DFX[Z\A/I$ZgP8DFGJI�KQZ�EHG\X�?&D/X�LNK�I�AFE�?�KDFZ�`HK�G�l~=@?�KcZ�`�KRI�AFG�l�DFE�S2W�_�E�?U`n=YX[Z�D4Z�`�KBG\D/AFWCDFG�?�S2=2W]K�DB�mDFG>?�DFe&K�Z\`H=YX�q�aj¤(DFS2dFKBP8DFG�Z�`HKMA�XHq/SYKBD�PI�DFX[Z\A/I$Z~P8D/G\I�KMP8G�D/e Z�`�K6dFK�GUZ\=2I�A�S � ��� � � �� � =YXmZ\K�G\e�?~D�P � 5,dFK�`�=2I�SYKs?�_NK�K�WV<$o 5,I�EHG\dFK-GJAFW]=2E�?J<$o�AFX�W

Page 36: Introductory Physics Problems David J. Jeffery Department of

³ � v�`�AF_]Z�a ¹  cK�l>Z�DFX�· ?~¸�A*lc?~A�X�W¡B^(X�AFe&=2I�?~7U7

�a������� � ¿~K�e&K�e4LVK�G-Z�`�KnI�S@AF?\?Me�A�X[Z�GJAHu �� � ��� $ � ���=@?6A�S2l�A*^]?RZ�G\EHKCAFX�W�=�Zs=@?6AFSYl>A*^]?BZ\G�E�KI�DFe&_NDFXHK�X/Z~L(^QI�DFe&_NDFXHK�X/Zia

Ii<¤]`HD"l Z�`VA"Z =�P � � � � � =@? AFW A:E�?UZ�KiW Z\D LVK K�h[E�AFS Z�D � ��� � � � � �$o�Z�`�K I�DFX[Z\A/I$Z P8DFGJI�K =2?���� �� ��� � ¦ ��� � � Z�DQZ�`HKgG�D[AFW�?�EHG�P,AFI�KFa6��=Yd/K�X�Z\`�A"Z�� � � � � $ � ��� � � � � �Jopl~`VA"ZR=@?RZ�`HK&?�=Y��KDFP�Z\`HKMP8G\=2I�Z�=2DFX�AFS�P8DFGJI�KMDFXQZ�`HKMZ\=YG\K�?�Z\`�A"ZBI�DFX[Z�G\=2LHE]Z�Ki?�Z�DgZ�`�K6I�DFX[ZJAFI$Z>P8D/G\I�K��m»{`(^��

WV<n»{`VA"Zc=@?�Z�`HK-A�_�_HG�D/_HG\=2A�Z�KRP8DFG\esEHS@A6P8D/G � � � � �s?�E�IJ`QZ�`�A�Z�Z\`HKMP8G\=2I�Z�=2DFXQP8DFGJI�KM=2?>X�K�dFK�G~I�A�S2S2K�WQEH_VD/XZ\Dn`HK�SY_xI�A�EV?UKsZ�`HKgI�A�GBZ�DQqFDC=2X[Z�DnE�XH=�P8D/G�e�I�=YGJI�EHS@A�GRe&D�Z�=2DFX ��7kPjP8G\=2I�Z�=2DFX�=@?RXHK�d/K�GRI�A�S2SYKiW�EH_NDFX�oI�A�XQ=�Z~K�d/K�G�P,A�=2SNZ�D&?UEH_�_HSY^QAFW]Kih/EVA"Z�KBP8DFGJI�KRZ�DgOFK�K�_CZ\`HKMI�A�G>=2XnEHX�=�P8D/G�e I�=YGJI�EHS@A�G�e&D�Z\=YD/X �m»{`�A�ZP8D/G\I�KMDFG>P8DFGJI�Ki?>W]DC?UE�_H_HS2^�Z�`HK6I�K�X[Z�G\=2_VK�Z\A�S�P8DFGJI�K�DFXZ�`HK6I�A�G>=2XQZ\`H=@?cI�A/?UK �

K*<n»{`VA"Z�· ?>Z\`HK-L�A�X�O[=2XHq�A�X�qFS2KRP8D/G ¹ ¾je&= �*`HG~AFX�WnLNK�XVWQGJAFWH=YE�?M�i¾F¾jema

¾F¾ ¹ h/P8EHS2S�¾/¾�µ/¾/¾ ³&³ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj_�?�K�EVW]D�TkG�D/SYS2=2XHqsP8G\=@I$Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� 5,£BA�T\�/��µVu � ¼ _V<�o/Z\K�G\e&=YX�AFSpdFK�SYD]I�=YZ:^

µ�a~b>`HK�G�K�=2?QA�SYD]I�DFe&D�Z\=Yd/K�D�P-e�AF?\?���¾ � O(q�DFX�A�S2K�d/K�SBZ�GJAFIJO�a�b�D�e&D"dFK�=�ZJ?UK�S�P-=YZI�AFX{K��]K�G�ZQArP8D/G\I�K� � � ����$ ¶ ¾/¾F¾� �D/XwZ�`HK�Z�GJAFIJO�o~A�X�W{?�D�o>D�PsI�DFEHGJ?�KFo�Z�`HK�Z�GJAFIJOtI�A�X{K��(K�GUZnZ�`HK�?�AFegK�LVAFIJO±DFXwZ�`�KS2D]I�DFe&DFZ�=2dFKFa�b>`HK�?�KmP8DFGJI�Ki?�A�G\K�=YXwP,A/I$Zn?UZ\A�Z�=@ImP8G�=@I$Z\=YD/XwD�P-l~`HK�K�S2?CDFX±Z�GJAFIJO�AFX�W±Z�GJAFIJO�DFXwl~`HK�K�S2?A/?�?�EHe&=YX�q&Z�`HK�G�K-=@?cXHDQ?US2=Y_�_H=YX�q�u;LND�Z\`mP8DFGJI�Ki?cA�G\KM_�A�GJA�S2SYK�SpZ�DCZ�`HK-Z\G\A/IJO�ujZ�`HK4?:ZJA"Z�=@IMP8G\=2I�Z�=2DFXP8DFGJI�K-D/XZ\`HKsZ\G\AF=YXx_VD/=YX[ZJ? ��� Z�`HK&W]=2G�KiI$Z�=2DFXxD�P�Z\G\AF=YX�egDFZ�=2DFX�a-b>`HK�G�Kg=@?RAFS2?�DQAQG�D/SYS2=2XHq�P8G\=2I�Z�=2DFX�P8D/G\I�KsD/X�Z�`�KZ\G\AF=YXl~`HD/?�KMe�A�qFX�=�Z\E�W]K-=@?>L[^CZ�`HKMP8D/G�e4EHS2Am5,l~`H=2IJ`m7$· e A:E�?UZce�A�O(=2XHq&EH_V<

� � � � � � $ � � �

l~`HK�G�K � $ � � ¶ �w��¾ ��� ? � �Q=@?�ArI�DFXV?:ZJA�X[Z�o � =2?&S2D]I�D/egDFZ�=2dFKe�AF?\?�o�A�X�W � =@?�SYD]I�DFe&D�Z\=Yd/K?�_VK�K�Wpa¿~D/SYS2=2XHq&P8G�=@I$Z\=YD/Xm=2?RA�XHDFZ�`HK�G~O[=2X�WmDFP�P8G\=2I�Z�=2DFX�58X�D�ZR?UZ\A�Z�=@I�o�X�D�ZcO(=YX�K�Z�=@I�<�oVAFX�W=�ZB_NDF=2X[Z\? � � � � � ���Z\D�Z�`HKQW]=YG\K�I�Z�=2DFX�DFP�e&D�Z\=YD/X�am7kZ�· ?s?�DFG�Z6D�PcW]EHKCZ�D�AFX�DFL,A:KiI$Z6`�A*d(=2XHqmZ�D�G\DFS2S�D/E]ZsD�P>Z\`HKnW]K�_HG�Ki?�?�=2DFX=YZ\?�D"l~X�l�K�=2qF`[ZR=@?MI�AFE�?U=2XHqA�X�W�Z�DnD"d/K�GJI�D/egK6Z�`HK&W]=@?:Z\DFG�Z�=2DFX�DFP�Z�`HKgl~`HK�K�S@?RS2=2OFK�l~=@?�K4I�AFE�?�K�W�L(^mZ�`�KD/L,A:K�I�Z�· ?>D"l~XQl�K�=2qF`[Z�aA[<C»{`VA"Zm=2?nZ�`HK�AFI�I�K�S2K�GJA"Z\=YD/X{D�P6S2D]I�DFe&DFZ�=2dFK)A:E�?UZ�A"ZnZ\`HK�=2X�?UZ\AFX/Z=�Z�?UZ\A�G�Z\?ne&D"d[=2XHq�P8G�D/e�G\K�?UZ�

������ � »�G\=�Z\KgW]D"l~X �� ����� $ � ��ml~=�Z\`�Z\`HKgA/I$Z\E�A�S�P8DFGJI�Ki?R?�`HD"l~X�K��]_HSY=@I�=YZ�S2^�A�XVW�?�_VKiI�=@A�S2=Y��KsP8D/GZ\=Ye&K-��K�G\D�a

LN<n»{`VA"Z&=2?4Z�`�KQZ\K�G\e&=YX�AFS�d/K�S2D]I�=YZ:^�DFPcZ�`�KS2D]I�D/egDFZ�=2dFKQ=YX�Z�`HKSY=2e&=�Z&Z\`�A"ZgZ�=2e&Kq/D(K�?sZ�D�=YX]�VXH=�Z:^�������� � »�G�=YZ�KMW]D"l~X �� � ��� $ � ��gl~=YZ�`CZ\`HKMAFI$Z\E�A�SNP8D/G\I�K�?;?�`HD"l~XCK��]_HSY=@I�=YZ�S2^CA�XVW�G�K���K�I�Z�D/XCl~`�A�Z`VA�_H_NK�X�?BAF?>dFK�SYD]I�=�Z:^�=2X�I�G\K�A/?UKi?�a

Ii<Qb>`�Kg?�K�I�DFX�W�S2A*l�l~=YZ�`�Z�`HKgP8DFGJI�Ki?Bl~G\=YZUZ�K�X�K��(_�SY=@I�=YZ�S2^�=2?MAW]= �NK�G�K�X/Z\=2AFS�K�h[E�A"Z\=YD/X�P8DFGMd/K�S2D(I�=�Z:^�A/?P8E�X�I$Z\=YD/X�D�PRd*AFG�=@A�L�SYK�Z\=Ye&K/ar� W]= �NK�G�K�X[Z�=@A�S>K�h[E�A�Z�=2DFX�LNK�=2XHqxAFX�Kih/EVA"Z�=2DFX�P8DFG&A�P8EHX�I�Z�=2DFX�Z�`�A�ZI�DFX[Z\AF=YXV?~W]K�G\=Yd"A�Z�=2dFK�?�DFP�d"A�G\=YD/E�?>DFGJW]K�G\?�D�P�Z�`HKMP8E�X�I$Z\=YD/X�a�b�D�?�DFS2dFK-A&W]= �NK�G�K�X/Z\=2AFSpK�h[E�A�Z�=2DFX=2?�Z\D�VX�W�Z�`HKnP8EHX�I�Z�=2DFX�AF?sA�X�K��]_HS2=@I�=YZ6P8EHX�I�Z�=2DFX�D�P>Z\`HKCd"A�G\=2AFLHS2KFam¯�A�X(^Fo�e�A�X(^�_�`[^]?�=2I�A�S�_�G�D/LHSYK�e�?I�DFe&K-W]D"l~XQZ�DC?�DFS2d[=2XHq&W]= �NK�G�K�X/Z\=2AFS�K�h[E�A�Z�=2DFX�?�a�7!XnZ\`H=@?cI�A/?UK/o]dFK�G\=YP8^�Z�`�A�Z

� $ � ��� ����� �� � � ���� �

5U� ,������ <

=@?RZ�`HK&K��(_�SY=@I�=YZ6?UD/SYE]Z\=YD/X�DFP�Z�`HK�W]= ��K�G\K�X[Z�=@I�AFS�Kih[E�A"Z\=YD/X�u � � =@?�AFXx=2XH=YZ�=@A�S�dFK�SYD]I�=�Z:^�A�ZRZ\=Ye&K&��K�G�DVa»{`VA"Zc=@?�Z�`HK6W]= ��K�G\K�X[Z�=@A�S�Kih[E�A"Z\=YD/XAFX�WQ?�DFS2E]Z\=YD/XQ=YP � � � ����$�¾ �

¾F¾ ¹ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u���E�=2WmG\K�?�=2?UZ�=2dFKRP8DFGJI�K� ª�¬"¨ �V«������V¬ ��­�� |HG�T\� ¶�³ a�7�`HDF_NK�Z�`H=@?~=@?cAgqFD(D]WC��XVA�S�h[EHK�?UZ�=2DFX�a

¶ a~|�S2EH=2W G\K�?�=2?UZ�=2dFK�P8DFGJI�K�?rAFG�K±I�DFe&_HS2K��fAFX�W `VA�GJW�Z�DzZ�G\K�A�Z�=2X qFK�X�K�GJA�S&W]K�?�_H=YZ�K±LVK�=YXHq EHL�=2h[EH=YZ�D/E�?�ab>`HG\DFE�qF`HD/E]ZQ`H=@?UZ�DFG\^{_NK�DF_�SYK�`�A*dFKxD�P Z\K�X A:E�?:Z�W]KiA�SYZl~=YZ�`zZ�`�K�e L(^{G\K�S2^[=2XHqtDFX�K��]_VK�G�=2K�X�I�KFa��BXAF_H_HG\D*�(=2e�A"Z\KnP8D/G�e4EHS2Axl~=YZ�`wAxl~=@W]Kmd"A�S2=2WH=�Z:^�P8D/G&Z�`HK�e�AFqFXH=YZ�E�WHKDFPB��E�=2WtG�Ki?U=@?UZ�=2dFKQP8DFGJI�KmDFX±G�=2qF=@WLND]W]=YKi?~=@?

��5 � < $ � � � � � �

Page 37: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ¹  BK�l>Z\DFX�· ?~¸�A*lc?~AFX�WQ¡R^(X�A�e&=@I�?~7�7 ³/³

5�|HG�T\� ¶�³ <�o�l~`HK�G�K&Z\`HK�P8D/G\I�K&AFSYl>A*^]?M_VD/=YX[ZJ? � � � � � ��� Z�D�Z�`HKnWH=YG\K�I�Z�=2DFXrD�P>e&D�Z�=2DFX�o � =2?-LND]W]^�· ??�_VK�K�Wpo�� AFX�W ��A�G\K4I�DFX�?UZ\AFX[Z\?MW]K�Z\K�G\e&=YXHKiW�=2X�AQdFK�G�^�I�DFe&_HS2K���l>A*^L(^mZ\`HKs�VEH=2W�A�XVW�Z�`�KgLND]W]^�· ??�`�A�_NKFo>?�EHGUP,A/I�KX�A"Z\EHG\KFo�AFX�WtG�K�S2A�Z�=2dFKmW]K�X�?�=YZ:^�W]=@?:Z\G�=2LHE]Z\=YD/X�o�L�E]ZCXHD�Z&Z\`HK�LVD]W]^�· ?&e�AF?\?�awb>`HK�G\Km=2?XHDW]K�_NK�XVW]K�X�I�K4D/X�e�AF?\?RLVKiI�A�EV?UKsZ�`HK4��EH=@W�G\K�?�=2?UZ�=2dFK6P8DFGJI�Ks=@?MAnI�DFX[Z\A/I$ZBP8D/G\I�KFaM¯�AF?\?c=@?�opD�P;I�D/EHGJ?UK/o=2e&_VD/GUZJA�X[Z>Z�D�e&D�Z\=YD/XQ=2XmG�Ki?U=@?:Z\=Yd/KB�VEH=2W�?�oHL�E]ZB=YZcK�X[Z�K�G\?�Z�`�G�D/EHqF`QZ�`HK-q/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�KMAFX�W � ��CD�P�� � ��� $ � ��Na� cD�Z\K���A�X�W�� A�G\K-A�S2l�A*^]?�qFG\K�A�Z�K�G�Z\`�A�XmDFG>Kih/EVA�SpZ\Dg��K�G\D�aA[<Q¤]OFK�ZJIJ` ��5 � <MAF?-AP8EHX�I�Z�=2DFXrD�P � A/?�?�EHe&=YX�q � AFX�W���A�G\K&LVDFZ�`rqFG\K�A�Z�K�G�Z\`�A�Xr��K�G�DVaC cDFZ�K&Z�`�K_�`[^]?�=2I�A�S�G�K�qF=2DFX{=@?nl~`�K�G\K ��� ¾�u�DFXHS2^w_HSYDFZQZ\`�A"ZG�K�qF=2DFX�a 7:W]K�X[Z\=�P8^wZ:l�D�W]= �NK�G�K�X[Zd/K�S2D(I�=�Z:^G\K�q/=Ye&Ki?�a&¡BK�Z�K�G�e&=2XHK�A�X�K��]_HG\K�?\?U=2DFX�P8DFG-AmIJ`�A�GJAFI�Z�K�G\=@?:Z\=2IsdFK�S2D]I�=YZ:^mP8DFGMZ\`HK&Z�GJA�X�?�=YZ�=2DFX�LNK�Z:l�K�K�X?�e�A�S2S�A�XVWsS@A�G\qFK>dFK�SYD]I�=�Z:^-G\K�q/=Ye&K�?�a�»{`�A"Z�=@?�Z�`HKcP8DFGJI�K � � ��A�ZjZ�`HK>Z\G\AFX�?U=YZ�=2DFXgdFK�SYD]I�=�Z:^�� �������� �b>`�K�G\K-=2?~X�D&AFL�?�DFS2E]Z�K-G\EHS2KMP8DFGcW]K�Z�K�G\e&=YX�=YXHqCIJ`VA�GJAFI$Z\K�G\=2?UZ�=@IRd*AFSYE�K�?�a;|HD/Gc=YXV?:ZJA�X�I�K-=YXZ�`�=2?cI�AF?�K-A?�=2eg_�SYKgd"A�S2EHK6Z\`�A"Z-A�S2SYD"lc?�AC^/K�?$y*XHDQW]K�I�=2?�=YD/X�A�LNDFEHZ�l~`�A�ZRG\K�q/=Ye&K6Z\`HKgdFK�S2D]I�=YZ:^m=2?�=2X�l�D/EHS@W�LNKAF_H_HG\DF_HG\=@A"Z�K/a

LN<¤HA*^gl�KB`VA*dFKBAsLVD]W]^�DFP�e&A/?�? ��=YXQA-��EH=@W�Z\`�A"Z>DFLNK�^]?�DFEHG���EH=@WCG\K�?�=@?:Z\=Yd/K~P8DFGJI�KRS2A*l-a�b>`HK�LVD]W]^=@?>I�D/eg_�SYK�Z�K�S2^C?�EHG�G\DFE�X�W]K�WCL[^&Z\`HK���EH=@WnAFX�W�Z\`HK-I�DFX[Z\K��(Z�DFP�Z�`�K�?�^]?:Z\K�e =@?;Z\`HK-�;AFGUZ\`�· ?�?�EHGUP,A/I�K/ab>`�K�G\KQA�G\KCZ\`HG\K�KCP8D/G\I�K�?4DFX�Z\`HKLVD]W]^�u�Z\`HKn�VEH=2W�G�Ki?U=@?UZ�=2dFKCP8D/G\I�KFojq/G\A*d(=YZ:^Fo�A�X�W�Z�`HKLHEHD"^[A�X�I�^P8D/G\I�K � � � ��� a�b>`�KBLHEHD"^[A�X�I�^6P8D/G\I�Kc=2?�A�X�E�_[l>A�GJW�I�D/X[Z\AFI�Z�P8DFGJI�KRI�A�EV?UKiW&L[^gZ\`HKBd"A�G\^(=YX�q-_HG�Ki?�?�EHG\K=2X�Z\`HK6�VEH=2W�aM� ?�=Ye&_HS2Kg��KiWHA�XHO/K�X�58Z�`HD/EHqF`[Z$<cK��(_NK�G\=2egK�X[Z�A�S2S2D"lc?c^FD/EmZ�DQ��X�WmZ\`HK4P8DFG\esEHS@A�P8D/GZ\`HK�LHEHD"^[A�X�I�^mP8DFGJI�K/a�7!e&AFqF=2XHK�AmI�S2D/?�K�Wr?UE�GUP,A/I�Kg=YX�Z�`�K���EH=@WxZ�`�A�Z6=2?-K��HAFI$Z\SY^x?U`�AF_VKiW�S2=2OFK&Z�`�KLND]W]^�=2Xxh[EHKi?:Z\=YD/X�a4b>`HK4��EH=@Wx=2?MA"Z-G\K�?UZ&5,KFa q�a2opSY=2OFKge&D�Z\=YD/XHSYKi?�?�l>A"Z\K�G�=YX�qFS@AF?\?\<�uc=�a K/aYopZ\`HKg��EH=@W=@?M=2Xx`(^]W]G\D/?UZ\A"Z\=2I4K�h[EH=2S2=YLHG\=2EHema&��GJA*d(=�Z:^m_HEHS2S@?-W]D"l~XxD/X�Z\`HK&��EH=@W�=2X�?�=2WHKg^/DFEHG-I�SYD[?UKiW�?�EHGUP,A/I�K/oL�E]Z-Z�`�A�Z6K�X�I�SYD[?UKiW���E�=2WrW]D(K�?�X�· Z6e&D"dFKFa& cD"l ?�A*^�Z\`HK&LVD]W]^�· ?-dFD/SYE�egKgl>AF?�� A�X�W�Z�`�K&��EH=@Wp· ?WHK�X�?�=�Z:^nl�A/?����� � �]aj»{`�A"Zc=@?�Z�`�KRP8D/G�e4EHS@AsP8D/G�Z�`HK-LHE�D"^/A�XVI�^&P8DFGJI�K�DFXQZ�`�K-LVD]W]^������(_�S2AF=YXQ^FDFE�GG\K�A/?UD/XH=2XHq�a

Ii<Q¸�K�Z6E�?6XHD"l ?\A*^�Z\`�A"Z-Z\`HKCLHEHD"^[A�X�I�^�P8DFGJI�K&=@?-XHK�qFS2=Yq/=YLHS2K ��A�XVWxA�P Z�K�G4A�S2SjZ�`HK�l�DFG\O�=2X�_�A�G�ZC58LV<Z\D(D�a�»{`�A�Z4=@?6Z\`HKnK��]_HG�Ki?�?�=2DFX�P8DFGsZ�`HKmAFI�I�K�S2K�GJA"Z\=YD/X ��DFP~Z�`HKQLVD]W]^r=2X���EH=@W�AF?4A�P8EHXVI$Z�=2DFX�D�P� ��� ¦ ���� � EHX�WHK�G�Z�`HKRP8DFGJI�KRD�P�qFGJA*d(=�Z:^&A�XVW���EH=@WCG\K�?�=@?:Z\=Yd/K~P8DFGJI�K ��¤]A*^gZ�`HK�LVD]W]^�?UZ\AFGUZJ?�A�Z� � �A�Z�Z\=Ye&K � $�¾BA�XVW6A�S2SYD"l�K�W�Z\`HK�XsZ�DRegD"d/K�P8D/G�K�dFK�G�AF?�Z�`HK�qF=2dFK�X-P8DFGJI�Ki?�W]K�Z�K�G\e&=YX�KFa�¤]OFK�ZJIJ`=YZ\?MA/I�I�K�SYK�G\A�Z�=2DFX���A�XVW�dFK�SYD]I�=YZ:^ � l~=YZ�`�AF?cP8EHX�I$Z\=YD/X�?�D�P � � � a�b�A�O/K � � � � � � ��� A/?_ND/?�=YZ�=2dFKFa�b>`HKs?�OFK�ZJIJ`HK�?~AFG�KML�A/?UKiWnD/Xm^FDFE�Gch/EVA�S2=�ZJA"Z�=2dFK-E�X�W]K�GJ?UZ\A�XVW]=YX�qgDFP�l~`VA"ZcesEV?:ZB`VA�_H_NK�X�u^/DFEmW]DFX�· Zc`�A*d/K�AFX(^CK��]_HS2=2I�=�ZB?�DFS2E]Z\=YD/X�?�P8DFG�CAFX�W � AF?�P8E�X�I$Z\=YD/X�?>D�P�Z�=2e&KFa

WV<mv�D/X[Z�=2X[E�=YXHqQl~=�Z\`�Z�`�K4_�AFGUZ&5,Ii<BI�AF?�KFoV��X�WmZ\`HKsP8D/G�e4EHS@A&P8DFGRZ�`HK4Z�K�G�e&=2X�A�S�dFK�SYD]I�=�Z:^D�PjZ\`HK4LND]W]^Fa��D/ECl~=2SYSNqFK�Z;Z:l�Ds?UD/SYEHZ�=2DFX�?�aj°RX�KB=@?;EHX�_H`(^(?�=@I�A�S�u�l~`�=2IJ`CD/XHKRAFX�W�K��]A/I$Z\SY^gl~`(^4=@?;=YZ>EHXH_H`(^]?U=@I�AFS �b>`�K-EHXH_H`(^]?U=@I�AFS�?UD/SYEHZ�=2DFXmI�K�G�Z\AF=YX�SY^n?\A"Z\=2?U��Ki?;Z\`HK-K�h[E�A�Z�=2DFX^FD/EQD/L]Z\AF=YXHKiW=�Z~P8G\DFema

K*<n»{`VA"Z4AFG�K�E�?�K�P8E�S�P8DFG\esE�S2A/?MP8DFG-Z\`HK�Z\K�G\eg=2X�AFS;dFK�SYD]I�=�Z:^x=YX�I�AF?�K�?MD�P~d/K�G\^x?�e&AFSYS�A�X�Wrd/K�G\^�S@A�G\qFK� d*AFSYE�K�?�� cD�Z\K A:E�?UZ4?�K�ZUZ\=YX�q � $�¾�A�X�W � $� =@?MZ\D[D�K��(Z�G\K�e&KFo�A�XVW�W]D(K�?�X�· Z4qF=2dFK�E�?�K�P8EHSP8D/G�e4EHS@AF?�a ������ � |HDFG � �����Fo

+ � � � � � � �� � �

Page 38: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� �Z*I>a1 ;<*IH�� >a145\c:6/&A>�,�� ?A5��

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾(º6h[e4EHS�ZB¾/¾F¾���¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_�A�G�Z�=@A�SpK�XHK�G\qF^CWHK���XH=YZ�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¹F¹

�Fa �\¸�K�Zi· ?_HS@A*^ �]1J� D+�"����# 1 |HD/G �(��¾/¾Ho~Z\`HK�A�X�?�l�K�Gn=@?�ut=YZ�`�AF?QLVK�K�X W]K�?\I�G\=2LVKiW�AF?QZ\`�A"Z�_HG\DF_NK�G�Z:^wD�P?�DFe&K�Z\`H=2XHqgZ�`�A�ZcK�X�AFLHSYKi?�Z�`�A�ZB?UD/e&K�Z�`�=YXHqgZ\DCW]D&l�D/G�O�a �»{`�A�Zc=2? oH�BSYK����

A[<�=YX�K�d(=�ZJA�LH=2S2=�Z:^ LV<�XHDF=@?�K Ii<�Z\K�X�?�=2DFX W�<�q/G\A*d(=YZ:^ Ki<�K�XHK�G\qF^

¾F¾(º6h[e4EHS�ZB¾/¾F¾[��¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�XHK�G\qF^CI�DFX�?�K�G\d"A"Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TUº��

�]a~b>`HKMZ\D�ZJA�SpK�X�K�G\qF^�D�PjA&I�S2D/?�K�W?U^]?UZ�K�e 58=�a K/aYoNA&?U^]?UZ�K�e�l~`H=2IJ`mXHDFZ�`H=2XHq&K�X[Z\K�GJ?>DFG~S2K�A*dFKi?\<;=@?�uA[<>I�D/X�?UK�G�d/K�Wpa LV<>A�X�XH=Y`�=YS@A"Z\K�Wpa Ii<>I�G\K�A�Z�K�W�a W�<>I�D/esLHE�?UZ�KiWpa K*<;K�d(=2?\I�K�G\A�Z�K�W�a

¾F¾(º6h[e4EHS�ZB¾/¾F¾ ³ ¾4�Q���Me&D]W]K�GJA"Z\K�e&K�egD/G�^�u�K�X�K�G\qF^�XHKiI�K�?\?�=�Z:^nAFX�Wm?UEH��I�=YK�X�I�^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

³ a~£RA*d[=2XHqRK�XHD/EHqF`4K�XHK�G�q/^RP8D/GjABq/=Yd/K�X A:D/LsDFG�Z\G\AFX�?:P8D/G�e�A�Z�=2DFXMZ�`VA"ZjG�Kih[EH=YG\K�?�A�I�K�G�Z\AF=YX4A�e&DFEHX[Z�D�P�K�XHK�G\qF^=@? o]LHE]Z � � P8DFG>Z\`HK<A:DFLmDFG�Z\G\AFX�?:P8D/G�e�A�Z�=2DFX�a

A[<�X�K�I�Ki?�?\A�G\^ )[?�E]�CI�=2K�X[Z LV<�?�E]�CI�=2K�X[Z*)(XHKiI�Ki?�?\A�G\^ I�<�=2XHK�d(=YZ\A�L�SYK )[X�K�I�Ki?�?\A�G\=2SY^�?�D WV<`VA�G\egD/XH=2DFE�?*)]I�K�G\K�e&D/XH=YD/E�? Ki<�P8D/G�L�=2WHWHK�X )�Agq/=Yd/K�X

¾F¾(º6h[e4EHS�ZB¾/¾F¾Fµ/¾C�&���MK�A/?U^�e&K�egD/G�^�ujEHX�=�ZcDFP�K�X�K�G\qF^Fo(Z\`HK<A:DFE�SYK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a~b>`HKs¤]7;EHXH=YZBDFP�K�X�K�G\qF^nAFX�WnDFP�l�DFG\O�=@?�Z�`HK/uA[<�A:D/EHSYK�5��(<$a LV<�XHK�l>Z�DFX}5, R<�a I�<�OFK�S2d(=YX}5,²6<$a WV<�L�A/?�?�=YX�q�Z�`�DFG\_ 5��~<$a K*<Z\G�E �&K�`(EHX[Z�K�G65�bc<$a

¾F¾(º6h[e4EHS�ZB¾/¾H�i¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujl�DFG\O&P8DFG\esEHS@AsP8DFGcA�I�D/X�?UZ\A�X[Z�P8DFGJI�K� ª�¬"¨ �V«������V¬ ��­�� b>`H=2?cl�A/?;P8D/G~l�KiA�O[TkDFX]TkdFKiI$Z�D/G\?�I�S@AF?\?

¶ a~� I�DFX�?UZ\AFX[Z�P8D/G\I�K ��}A/I$ZJ?-DFX�AmLND(WH^xl~`H=2S2K&Z�`�A�ZsLVD]W]^�e&D"dFKi?-A�W]=2?UZ\AFX�I�K��aQ¸�K�Z ��sA�XVW � ��LNKZ\`HK-P8DFGJI�K6I�DFe&_NDFXHK�X/ZJ?~_�AFG\AFSYS2K�S�AFX�W_VK�G�_NK�XVW]=2I�EHS@A�Gio�G\K�?�_VKiI$Z�=2dFK�SY^/o]Z�DCZ�`HKsWH=YG\K�I�Z�=2DFXmD�Pje&D�Z\=YD/X�a�b>`�Kl�DFG\O�� WHDFXHKMDFXQZ�`�K-LVD]W]^QL[^nZ�`HKMP8D/G\I�KR=@?~q/=Yd/K�XL[^�uA[<�� $ �����aLN<�� $ ������aIi<�� $ �����aWV<�� $ �� � � ��aK*<�� $ �� �� ������a

¾F¾(º6h[e4EHS�ZB¾/¾H�/��¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujl�DFG\O&P8DFG\esEHS@AsP8DFGcA�I�D/X�?UZ\A�X[Z�P8DFGJI�K

Page 39: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia�º ²M=2XHK�Z\=2IM�;XHK�G\qF^CAFX�W»xD/G�O ³[¶

¹ a~��I�D/X�?:ZJA�X[Z�P8D/G\I�K ���AFI�Z\?�DFXnAsLVD]W]^&l~`H=2S2KBZ\`�A"Z�LVD]W]^�e&D"dFKi?;A4W]=2?UZ\AFX�I�K���� a�b>`�KBl�DFG\O � W]D/XHKBD/XZ\`HK-LVD]W]^QL(^�Z�`HKMP8D/G\I�KM=2?~q/=Yd/K�XQL[^�uA[<�� $ �� ����� aLN<�� $ ��&aIi<�� $ �������� aWV<�� $ ���� ������ � aK*<�� $ �������� ��� � a

¾F¾(º6h[e4EHS�ZB¾/¾H�*��¾C� ³ �MK�A/?U^�e�A�Z�`�u�l�DFG\O�S2=�P Z\=YXHq� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½/¶ T ³

º(a~£BD"l�esEVIJ`l�DFG\O�=@?~W]DFXHK-S2=YP Z�=2XHqCA��¾F¾�O[q4SYD[AFWx��¾je�l~=�Z\`HDFE]ZBA/I�I�K�S2K�GJA"Z�=2DFX �A[< ½F¼ ¾F¾>�Vo LV<���¾/¾>��o Ii<���¾/¾F¾>�Vo W�<���¾>�Vo Ki< ½/¼ ¾>�Va

¾F¾(º6h[e4EHS�ZB¾/¾/�F¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�W]K���XH=YZ�=2DFXmO(=YX�K�Z�=@I�K�XHK�G�q/^¼ a~²M=2XHK�Z\=2IMK�XHK�G\qF^�=@?�u

A[<�Z\`HK-K�X�K�G\qF^CDFP�_ND/?�=�Z\=YD/X�uj=�ZJ?>P8DFG\esE�S2A4=2?B²-� $ � ��aLN<CZ\`HK-K�X�K�G\qF^CDFP�e&D�Z\=YD/X�uj=�ZJ?�P8DFG\esEHS@Ag=2?B²-� $ � ��aIi<CZ\`HK-K�X�K�G\qF^CDFP�e&D�Z\=YD/X�uj=�ZJ?�P8DFG\esEHS@Ag=2?B²-� $ 5U� ���/< � � �FaWV<CZ\`HK-K�X�K�G\qF^CDFP�_ND/?�=�Z\=YD/X�uj=�ZJ?>P8DFG\esE�S2A4=2?B²-� $ 5U� ���/< � � �FaK*<n`�K�A"ZcK�XHK�G\qF^/a

¾F¾(º6h[e4EHS�ZB¾/¾/�/��¾4� ¶ µ&e&D]W]K�GJA"Z\K�e�A�Z�`�u�P8G\=2I�Z�=2DFXO(=YS2SY=2XHqC²-�� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½/¶ T ½

½ a~�ze&D"d[=2XHq4DFL,A:KiI$Z>`�AF?�=YX�=�Z\=2AFS�� $ ��¾/¾>�sAFX�WC=@?�?UEHL3A:K�I$Z\K�WCZ�D&A-P8G\=2I�Z�=2DFXCP8D/G\I�KBDFP��j �AFX�WCX�D4DFZ�`HK�GP8D/G\I�K�?�a�£BD"l�P,AFGcW]D(K�?�Z�`�K-DFL,A:KiI$ZcqFDgLNK�P8DFG\K6I�D/e&=YXHqgZ\D&A&?UZ�D/_ �

A[<���¾/¾jema LN<~��ema I�<��i¾F¾F¾�ea W�< ¶ ¾jema Ki<>¾jema

¾F¾(º6h[e4EHS�ZB¾/¾ ³ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]K���XH=YZ�=2DFXm_ND"l�K�G��¾Ha>»�DFG\OC_NK�G~EHXH=YZcZ\=Ye&K-DFG~K�XHK�G\qF^&Z\G\AFX�?UP8DFG\egKiWC_NK�GcE�XH=�Z~Z\=Ye&K-=@?�u

A[<C_ND"l�K�GiaLN<ne&=2qF`[Z�aIi<nD(D/eg_�`�aWV<Q?UZ�G\K�X�q�Z�`�aK*<n_VA*^Fa

¾F¾(º6h[e4EHS�ZB¾/¾ ³ ¾/��� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu;?�EHXHS2=Yq/`/Z~_ND"l�K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½F½ T\�"º

�F�Fa>7kPc^/DFE�I�D/EHS@W�I�AF_]Z�EHG\KC=YZgAFSYS�P8DFG4E�?UK�P8EHS�l�D/G�O�o�Z�`HKQK�XHK�G�q/^�?�EHXHS2=Yq/`[Z4W]K�S2=2dFK�GJ?-Z\DxA�?\h[E�A�G\KCe&K�Z\K�G4D�Pq/G�D/EHX�W�l�DFE�S2W�G�EHXr?�K�dFK�G\AFS�D/G\WH=YX�AFG�^mS2=Yq/`[ZML�EHSYLV?�a&b>`HK&_VD"l�K�G�_NK�G6?\h/EVA�G\Kse&K�Z\K�G6W]K�SY=2dFK�G�KiW�L(^�Z�`�K¤(E�XQZ\D&Z�`HK-q/G�D/EHX�Wn=2?~DFP�D/G\W]K�G�u

A[<���»�a LV<��i¾j»�a Ii<���¾F¾/¾j»�a W�<��i¾"!�»�a K*<���¯�»�a

¾F¾(º6h[e4EHS�ZB¾/¾ ³ ¾�µg� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVujLVD"^nG�EHX�XH=YX�qgE�_m?UZ\AF=YGJ?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½F³ T!� ³

�i�]a~�BX�=2W]KiA�S ¶ ¾jO(q&LVD"^QG�E�X�?~EH_�Ag��=2qF`[ZBDFP�?:ZJA�=2G\?>DFP ¶ e�=2X ¶ ?cA"Z�A�I�DFXV?:ZJA�X[ZcG\A�Z�K/a�£c=@?c_ND"l�K�GcD/E]Z�_HEHZA:E�?UZ~Z�D�l�DFG\OCA�q[A�=2X�?UZ�q/G\A*d(=YZ:^�=2?�u

A[< ¶ ¾j»�a LV<�µ ½ ¾j»�a I�< ½/¼ ¾j»�a W�<-��¾"!�»�a Ki<���¯�»�a

Page 40: Introductory Physics Problems David J. Jeffery Department of

³F¹ v�`�AF_]Z�a�º ²M=YX�K�Z�=@IM��XHK�G�q/^CA�X�W»�DFG\O

¾F¾(º6h[e4EHS�ZB¾/¾ ³ ��¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu�XHD&e�AFI�G�D[?�I�DF_H=@Icl�DFG\OnW]D/XHK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½/¶ T\�

� ³ a~� _VK�G\?�DFX�`�DFS@WH?s�i¾jO(qCqFG\DFEV?UK6A�ZM� � ¾je�A�LND"dFK6Z�`HK4qFG\DFEHX�WP8D/G ³ ¾�?�aR£cD"l e4E�IJ`�e�AFI�G�D[?�I�DF_H=@I-l�DFG\O=@?cW]D/XHK��

A[< ¹ ¾/¾>��a LV<~�F¾>�Va I�< ³ ¾F¾>�Va W�< ¹ ¾���a K*<>¾>��a

¾F¾(º6h[e4EHS�ZB¾/¾�µ[¾F¾C� ³ �MK�A/?U^�e�A�Z�`�u�l�DFG\O�S2=�P Z\=YXHq�D[?:Z\G�=@IJ`� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½F³ T!�H�

��µ�a~b>`HK-l�DFG\OCW]D/XHKM=2?~S2=YP Z�=2XHqCA ³ ¾jO(qgD/?UZ�G\=2IJ`nZ�DCAg`HK�=2qF`[Z~D�P ³ ¾�e l~=�Z\`HDFEHZBAFI�I�K�S2K�GJA"Z\=YD/Xn=@?~A�LNDFE]ZiuA[< ½ ¾/¾F¾>�Va LV< ½ ¾/¾>��a Ii< ³ ¾/¾>��a W�< ³ ��a K*<�µ ¶ ¾F¾>�Va

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾(º6h/P8EHS2S�¾/¾F¾H�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujl�DFG\OCA�X�W²-��Fa ��D/EmAFG�K�_HE�?�`H=2XHqCA ¹ ¾jO(qgLHS2D(IJOQAFI�G\D/?\?>A4P8G�=@I$Z\=YD/XHSYKi?�?~?�EHG�P,AFI�K �{l~`H=2IJ`Q=2?cXHD&egKiA�XQP8K�A�Zc=YXm=YZ\?�K�SYP:a

A[<)��D/E�K��]K�G�ZB�i¾F¾� wDFPNP8D/G\I�K~=YXCZ�`HKBWH=YG\K�I�Z�=2DFX�D�Ppe&D�Z\=YD/XCA�X�W&_�E�?U`&Z\`HKBL�SYD]IJO6P8D/G ³ ¾jema�£BD"lte4E�IJ`l�DFG\O�`�A*d/K�^/DFEW]DFXHK-D/XnZ\`HK-LHS2D]IJO �

LN<Q�R?�?�EHe&=2XHqQ^/DFE�?:ZJA�G�ZRZ\`HK4L�SYD]IJOmP8G\DFe�G\K�?UZMAFX�W�XHDD�Z\`HK�G�P8D/G\I�K�?�AFI$Ziopl~`�A"Z-=@?RZ�`HKg��X�AFS�O[=2XHK�Z�=@IK�XHK�G\qF^QA�X�WQdFK�SYD]I�=YZ:^CDFP�Z�`�K-LHSYD]IJO��

¾F¾(º6h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujl�DFG\OCW]DFX�K�D/XmLHSYD]IJOCD/XQ=2X�I�SY=2XHK� ª�¬"¨ �V«������V¬ ��­�� 5,£BA�T\� ¶ º]uY� ¹ Ki<

�]a~b>`HK�G�KR=2?;P8G\=2I�Z�=2DFXHS2K�?\?;L�SYD]IJO&D�P�=@I�KRD�P ¶ ¾jO(q-DFXnAFXC=YXVI�S2=YXHK�D�P ³ ¾ ��a���l�DFG\OFK�G;_HE�?�`HK�?;Z�`HK�LHS2D]IJOgE�_CZ�`�K=2X�I�S2=2XHK6A"ZcA�I�D/X�?UZ\A�X[Z>dFK�SYD]I�=YZ:^CDFP ³ e���?�aA[<C»{`VA"Zc=@?�Z�`HK-_ND"l�K�G~DFE]Z\_HE]Zs5,=�a KFa2oHGJA"Z�KMDFP�l�DFG\OCW]DFX�Ki<�L(^CZ�`�K-l�D/G�O/K�G �LN<n»{`VA"Zc=@?�Z�`HK-_ND"l�K�G~DFE]Z\_HE]ZcL(^Cq/G\A*d(=YZ:^ �Ii<n»{`VA"Zc=@?�Z�`HK-_ND"l�K�G~DFE]Z\_HE]ZcL(^�Z\`HK-XHDFG\e�A�S�P8D/G\I�K��»{`(^��

¾F¾(º6h/P8EHS2S�¾/¾/��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�ujd*AFG�=@A�L�SYK�P8DFGJI�K/o]_�A"Z\`m=YX[Z�K�qFGJA�S³ a~b>`HK�G�KM=@?cA4P8DFGJI�K�5,A4P8D/G\I�KR�VK�S@W�<�qF=2dFK�XQL(^

�� $�5 � � � � ��� � � <�l~`HK�G�K/� � A�X�W����sAFG�K-I�DFX�?UZ\AFX/ZJ?�ajb>`HG\DFE�qF`CZ\`H=@?>��K�S@WmA�XDFL,A:KiI$Zce&D"dFKi?�P8DFS2SYD"l~=2XHq�Ag_�A"Z\`q/=Yd/K�XQL[^

� $ 5 � � � � � � � <�l~`HK�G�K � � A�X�W � � A�G\KBI�D/X�?UZ\A�X[ZJ?�AFX�W � =@?�As_�A�Z�`C_VA�GJA�e&K�Z\K�G�Z�`�A�Z�l�KBe&=2qF`[Z>A/?;l�K�S2SpI�AFSYSVZ�=2e&KFaj»{`�A�Z=@?�Z\`HK�qFK�X�K�GJA�SHK��(_�G�Ki?�?�=YD/X&P8DFG�l�D/G�OgW]DFX�KR?UZ\A�G�Z�=2XHqsP8G�D/efZ\=Ye&K���K�G\D�a ������ � ��DFECl~=2S2SV`�A*d/K~Z�DgW]D4AFX=2X[Z�K�q/G\AFS�a ��E]Z~Z\D&WHDg=YZ�o�^FDFE�· S2Sp`�A*dFK�Z\D&IJ`VA�XHq/KRZ\`HK-=2X/Z\K�q/G\A�Z�=2DFXnd"AFG�=@A�LHS2K�P8G�D/e � Z\D � a

Page 41: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� BC?A;71)>W;<*[&AN � >a145\c:6 &A>�, ¥ ? >�ER145\()&:;<*[?T> ?A@ � >a145\c:6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾ ¼ h[e4EHS�ZB¾/¾F¾/¾ ¼ �&�-µ&K�A/?U^�e&K�egD/G�^�u�I�DFX�?�K�G\d"A"Z�=2DFXQD�P�K�XHK�G�q/^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�Fa>7!XZ�`�K-_H`(^(?�=@I�?�o(Z�`HK6I�DFX�?�K�G\d"A"Z�=2DFXQD�P�K�XHK�G�q/^Ce&K�A�XV?>K�XHK�G�q/^NuA[<p?�`HDFEHS@W]X�· Z�LNK;l>AF?UZ�KiWMDFX6I�A�GJ?�a LV<p=@?�XHK�dFK�G�W]Ki?:Z\G�D"^/K�Wpa Ii<p=@?�XHK�dFK�G�I�G\K�A�Z�KiWpa W�<�=2?X�K�dFK�GcI�G\K�A�Z�K�WQDFG~W]Ki?:Z\G�D"^/K�Wpa K*<�=2?~_NK�G\_NK�Z�EVA�S2SY^I�G\K�A"Z\K�Wpa

¾F¾ ¼ h[e4EHS�ZB¾/¾F¾���¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujEHX�=Yd/K�GJ?UKMI�D/X�?UK�G�d"A�Z�=2DFXnDFP�K�XHK�G\qF^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½ �"T ¶

�]a>7kP�Z�`HK�E�XH=Yd/K�GJ?UK&AF?-Al~`HD/SYK&=@?-AmI�S2D/?�K�W�?�^]?:Z\K�emo�Z\`HK�X�I�EHG�G\K�X[ZM_H`(^]?U=@I�AFSjS2A*l�Z\K�S2S2?6E�?�Z�`�A�Z6=�ZJ?�Z�DFZ\A�SK�XHK�G\qF^�=@?�u

A[< ³ ¾>�Va LV< I�DFX�?�K�G\dFKiWpa I�< X�D�Z I�D/X�?UK�G�d/K�Wpa WV<�DFXHS2^ O(=2XHK�Z\=2I�K�XHK�G\qF^/aK*<>?UD/e&K�Z�=2e&K�?~I�DFX�?�K�G\dFKiWpa

¾F¾ ¼ h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�uj_ND�Z\K�X[Z�=@A�SpK�XHK�G\qF^nWHK���XH=YZ�=2DFX³ a~9�DFZ�K�X[Z\=2AFSNK�XHK�G\qF^n=2?�u

A[<�Z\`HK-K�X�K�G\qF^CDFP�_ND/?�=�Z\=YD/X�uj=�ZcK��]=2?UZ\?�P8D/G~XHDFX�I�DFX�?�K�G\d"A"Z\=Yd/KBP8D/G\I�K�?�aLN<CZ\`HK-K�X�K�G\qF^CDFP�_ND/?�=�Z\=YD/X�uj=�ZcK��]=2?UZ\?�P8D/GcI�DFXV?UK�G�d"A"Z\=Yd/KBP8D/G\I�K�?�aIi<CZ\`HK-K�X�K�G\qF^CDFP�e&D�Z\=YD/X�uj=�ZJ?�P8DFG\esEHS@Ag=2?B9;� $�5:� �F�F< � � ��aWV<CZ\`HK-K�X�K�G\qF^CDFP�_ND/?�=�Z\=YD/X�uj=�ZJ?>P8DFG\esE�S2A4=2?B9;� $�5:� �F�F< � � ��aK*<n`�K�A"ZcK�XHK�G\qF^/a

¾F¾ ¼ h[e4EHS�ZB¾/¾H�/��¾4�Q� ³ e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�_�A�Z�`�?~AFX�WmAgI�DFX�?�K�G\d"A"Z\=Yd/KBP8D/G\I�Kµ�a~b>`HKMl�DFG\OCW]DFX�K-L[^QAgI�DFX�?�K�G\d"A"Z\=Yd/KcP8DFGJI�KMD/XAFXQD/L,A:K�I�Z>l~`�=YS2KMZ�`HKMD/L,A:K�I�ZcegD"d/K�?�DFXmAg_�A"Z\`QLNK�Z:l�K�K�XZ:l�D&K�X�W_NDF=2X/ZJ?>=2?�uA[<������ �� ��� ��fDFP�Z\`HK-_�A"Z\`���� ¦ � �4� ����� LNK�=2XHq�=YXVW]K�_NK�X�WHK�X[ZcD�P�Z�`HK-K�X�W_VD/=YX[ZJ?�aLN<'� �� ��� �� D/XnZ\`HK-_�A"Z\`�aIi< ����� �� ��� �� D�PpZ�`�Kc_�A"Z\`�o��� ¦ �� Z�`�A�Z;=YZ�W]D(K�?�W]K�_NK�XVW�DFX&Z\`HKBK�X�W�_NDF=2X/ZJ?B5,=�a KFa2o/D/XZ\`HK-_ND/?�=�Z\=YD/XQ=2X�?U_�A/I�KMD�P�Z�`�K-K�X�W_NDF=2X/ZJ?\<�a

WV<'� �� ��� �� D/XnZ\`HK-_�A"Z\`�oHLHEHZ � � DFXZ�`HK-K�X�WQ_VD/=YX[Z\?�aK*<nKih[E�A�S�Z\D&Z�`HK-_�A�Z�`SYK�XHq�Z\`�a

¾F¾ ¼ h[e4EHS�ZB¾/¾H�*��¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l�D/G�O[Tk_VDFZ�K�X/Z\=2AFS�K�XHK�G�q/^&P8DFG\esEHS@A¶ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�u ��� $ , � a �

A[<C»{`VA"Zs=@?MZ�`�K�P8DFG\esEHS@AmG\K�S@A"Z�=2XHq � � � �� � � � K�XHK�G\qF^xIJ`�A�XHq/K&=YX�A�I�DFX�?�K�G\d"A"Z�=2dFKgP8D/G\I�K&��K�S@WZ\Dml�D/G�O�W]D/XHK&L(^�Z�`HKCI�DFX�?�K�G\d"A"Z\=Yd/K6P8DFGJI�K�5,=�a KFa2o�l~`�A�Z-=2?�Z\`HK�l�D/G�O[Tk_VDFZ�K�X/Z\=2AFS�K�XHK�G�q/^mP8DFG\esEHS@A/<�o�BSYK�� �

LN<n»{`VA"Zc=@?~|�A�GJAFW�A*^N· ?�S2A*l-oH�BSYK�� �Ii<n»{`VA"ZBA�G\K-I�AF_�AFI�=�Z\DFGJ?�o(�cS2K�� �WV<n»{`VA"Zc=@? � � � XHD�o]XHD�l>A�=YZ � ��� l~`�A"Zc=@?>EHXH=@I�D/G�XmI�=2G\I�EHS@A�G~e&D�Z\=YD/X�oH�cS2K�� �

Page 42: Introductory Physics Problems David J. Jeffery Department of

³F¼ v�`�AF_]Z�a ¼ 9�D�Z\K�X[Z�=@A�Sp��X�K�G\qF^CA�XVW�v�D/X�?�K�G\d*A�Z�=2DFXQD�P��;XHK�G\qF^

K*<n»{`VA"Zj=2?�Z\`HK�P8DFG\esEHS@ARG�K�S2A�Z�=2XHq������ � ¦ K�XHK�G�q/^-IJ`�A�XHq/K�=2X&A�I�DFX�?�K�G\d"A"Z\=Yd/K�P8DFGJI�K���K�S2WsZ�DMl�DFG\OWHDFXHKML(^CZ\`HK6I�D/X�?UK�G�d"A�Z�=2dFKRP8DFGJI�K&58=�a K/aYoVl~`�A"Z~=@?>Z�`HK-l�DFG\O[T�O(=2XHK�Z\=2IRK�X�K�G\qF^&Z�`�K�DFG\K�eC<�oH�cS2K�� �

¾F¾ ¼ h[e4EHS�ZB¾/¾/�F¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uje&K�IJ`VA�XH=@I�AFSNK�XHK�G\qF^QW]K���X�=�Z\=YD/X¹ a~¯�KiIJ`�A�X�=2I�A�SpK�X�K�G\qF^�=@?>Z�`HK6?�EHe DFP�O(=2XHK�Z\=2I-AFX�WQ_VDFZ�K�X[Z\=2AFS�K�XHK�G�q/^Fa�7kZc=2?BAgI�DFX�?�K�G\dFKiWnh[E�AFX/Z\=�Z:^�u

A[<nAFSYl>A*^]?�aLN<nl~`�K�XHK�dFK�G~=YZc`�A/?>LVDFZ�`mO(=YXHK�Z�=@I-A�X�WQ_ND�Z�K�X[Z�=@A�S�K�XHK�G\qF^CI�DFe&_VD/XHK�X[ZJ?�aIi<n=YPjA�S2SpZ�`HK�P8D/G\I�K�?�Z�`VA"ZBW]D&XHK�Zcl�D/G�OCAFG�K�� � � ¦ � � � �� � � � � saWV<n=YPjA�S2SpZ�`HK�P8D/G\I�K�?�Z�`VA"ZBW]D&XHK�Zcl�D/G�OCAFG�K ¦ � � � � � � � � 4aK*<nl~`�K�XHK�dFK�G~=YZc=@?>_VD[?U=YZ�=2dFK/a

¾F¾ ¼ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�DFX�?�K�G\d"A"Z�=2dFKBP8DFGJI�KMK��HAFeg_�SYKi?º(a~b>l�D�I�DFXV?UK�G�d"A"Z\=Yd/KBP8D/G\I�K�?>A�G\KFu

A[<C_ND"l�K�G~A�X�We&=2qF`[Z�aLN<nq/G\A*d(=YZ:^CA�X�WQO(=YX�K�Z�=@I�P8G\=2I�Z�=2DFX�aIi<nq/G\A*d(=YZ:^CA�X�WQl�DFG\ONaWV<nq/G\A*d(=YZ:^CA�X�WnZ�`�K6?U_HG\=2XHqgP8DFGJI�KFaK*<nl�DFG\OCA�XVWnZ\`HK6?�_HG�=2XHq4P8DFGJI�K/a

¾F¾ ¼ h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujXHD/X�I�D/X�?�K�G\d*A�Z�=2dFKBP8DFGJI�KMK��HA�e&_HS2K¼ a~�BXK��HA�e&_HS2K�DFP�X�DFX�I�DFX�?�K�G\d"A"Z�=2dFKBP8DFGJI�KM=@?�u

A[<CO(=2XHK�Z\=2I�P8G\=@I$Z�=2DFX�aLN<nq/G\A*d(=YZ:^FaIi<CZ\`HK-S2=YXHKiA�G>P8D/G\I�KFaWV<nl�DFG\O�aK*<n_ND"l�K�Gia

¾F¾ ¼ h[e4EHS�ZB¾/¾ ¶ ¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u�K�XHK�G\qF^CI�DFX�?�K�G\d"A"Z\=YD/X½ a~�fLHG�=@IJO`�AF?Be&A/?�?s��O(q�ac� W]DFq�58P8G�D/e�A A:DFOFK6Z�`�A�Z�?�DFe&KsWHA*^7$· S2S�Z�K�S2S�^FDFEN<~W]G\DF_�?cZ�`HK4LHG�=@IJOr58l~`H=@IJ`=YZcl�A/?�`HDFS@W]=2XHq4=2Xm=�ZJ?>e&DFE]Z\`V<R��emaj»{`�A"Z~=@?�Z�`HK-O(=2XHK�Z\=2I�K�X�K�G\qF^�D�P�Z�`HKMLHG\=@IJO�A:E�?:ZcLNK�P8D/G�KM=YZ~`H=�ZJ?>Z�`�Kq/G�D/EHX�W � ������ � b>`�K6I�A�S@I�E�S2A�Z�DFG>=@?c?�EH_VK�GU�VEHDFE�?�aA[< ½ a ¼ l>A"Z�Z\?�aLN< ½ a ¼ q/K�e�?�aIi< ½ a ¼ XHK�l>Z�D/X�?�aWV< ½ a ¼ A:D"l~S@?�aK*< ½ a ¼ A:D/EHSYKi?�a

¾F¾ ¼ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�XHK�G�q/^nA�XVWn`HKiA"Z��¾Ha~�BegK�G�=@I�AFX*��K�X AUAFeg=2X�b>`HD/eg_V?UD/Xw5,K�XHX�DFLHS2K�W�A/?s��GJA"Pc¿~EHegP8DFGJW�<�5U�*º ¶�³ ��� ¼ ��µ[<�opl~`H=2SYKQK�e&_HS2D"^FK�WrA/?

W]=2G\K�I$Z\DFG�D�P�Z\`HK���A*d"AFG�=@A�XCAFG\?�K�X�AFS�o/XHD�Z\=2I�K�WCZ�`�A�Z�=2XQLNDFG\=2XHq4I�A�XHXHD/X�58L�E]Z~XHD�Z~I�AFE�?U=2XHqsI�A�XHX�DFXnK�XHX(EH= <Z\`�A"Z�Z\`HK;LNDFG\=2XHq~e&D�Z�=2DFX6AFX�W�P8G\=2I�Z�=2DFX-?UK�K�e&K�W�Z\Dc_HG\D]W]E�I�K;EHXHS2=Ye&=YZ�K�WsA�e&DFEHX[ZJ?pD�P]`HKiA"Z�a�£cK;I�DFX�I�SYEVW]K�WpuA[<C`�K�A"Zcl>AF?>A&?�EHL�?UZ\A�XVI�KMD�P�l~`H=@IJ`QZ\`HK�G\K-I�D/EHS2WQDFX�SY^QLVK6?�D4e4E�IJ`mD�P�=YX�A�X(^CD/L,A:K�I�Z�aLN<CZ\`�A"Zc`�K�A"Z~l>AF?>?�DFe&K�`HD"lzqFK�XHK�GJA"Z\K�WCL(^Ce&DFZ�=2DFXmA�X�WnP8G�=@I$Z\=YD/X�a�b>`H=@?cI�D/X�I�S2E�?�=YD/XnS@A"Z\K�G~S2K�WnZ�D&Z�`�K

G\K�I�DFq/XH=�Z\=YD/X�DFP;`HK�A�Z6AF?MA�XHDFZ�`HK�G�P8DFG\e D�P�K�XHK�G�q/^QZ\`�A"ZsI�DFEHS@W�LNKCI�D/X(dFK�G�Z�KiWmP8G\DFe D/GMI�DFX(dFK�GUZ\K�W=2X[Z�De&K�IJ`�AFXH=2I�A�S�DFGMIJ`HK�e&=@I�AFS�K�XHK�G\qF^/aMb>`�=2?�K��(Z\K�X�W]KiW�Z\`HKgI�DFX�I�K�_]ZMD�P�I�DFXV?UK�G�d"A"Z\=YD/X�D�P;K�XHK�G\qF^P8G\DFe�egK�G�K�SY^QI�DFXV?UK�G�d"A"Z\=YD/XnDFP�e&K�IJ`VA�XH=@I�AFSpK�XHK�G�q/^Fa

Ii<CZ\`�A"Zj`HKiA"Zj`�A/WsXHD�G\K�S@A"Z�=2DFXsZ�DMe&D�Z\=YD/XgAFX�W6P8G\=@I$Z�=2DFXgA�X�W4l>AF?�?UD/e&K�`HD"l�?�_NDFX[Z\AFXHK�D/E�?US2^MqFK�XHK�GJA"Z\K�WL(^nI�A�XHX�DFX�a

WV<CZ\`�A"ZBI�A�XHX�DFXmI�DFE�S2WQLVKMZ\`HK-_HS2EHGJA�SpD�PjI�AFXHXHD/X�a

Page 43: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ¼ 9�D�Z�K�X[Z�=@A�Sp��XHK�G�q/^CA�X�W�v�D/X�?UK�G�d"A�Z�=2DFXnDFP��;XHK�G\qF^ ³/½

K*<CZ\`�A"Z�Z�`HKRLH=2K�G\q/A�G�Z�K�X�?j=2Xn¯�EHX�=2IJ`Cl�K�G\Kce4E�IJ`CLNK�ZUZ\K�G�Z�`�AFX�Z�`�KcZ\A*d/K�G\X�?j=2X ��D/?UZ�D/XCA�X�WgZ\`�A"Z~¤]A�e�RWHA�e�?�o�_VA"Z�G\=2D�ZUT�P8DFE�X�W]=2XHq�T�P,A"Z\`HK�GMXHDFZ:l~=�Z\`�?:ZJA�X�WH=YXHqVo�I�DFEHS@W�`�A*dFK&S2K�A�G\X[Z6AZ�`H=2XHq�D/GMZ:l�D�A�LNDFEHZL�G�K�l~=YXHq&LNK�K�G�a

¾F¾ ¼ h[e4EHS�ZB¾/¾[º�¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�Z\EHG�X�=YXHq&_NDF=2X[Z\?�F�Fa~�BX-DFL,A:KiI$Z�=@?�Z�GJA�_�_VKiW-A�X�W�e&D"d(=YXHqcAFG�D/EHX�W�=2X6?UD/egKjO(=2X�WMD�P(_ND�Z�K�X[Z�=@A�SFl�K�S2S�up=�Zi· ?�A>LVD/EHX�WM_�AFGUZ\=2I�SYKjl�KF· W

?\A*^Faj»{`�A�ZRA�G\K�Z�`HD[?UK6?�_NK�I�=@A�S�_VD/=YX[Z\?BI�A�S2S2K�WQl~`HK�G\KMZ�`HKsO[=2XHK�Z�=@IMK�XHK�G�q/^CD�P�Z�`HKs_�A�G�Z�=@I�S2KMegD/e&K�X[Z\AFG�=2SY^q/D[Ki?�Z�D&��K�G�D��»{`(^QA�G\KRZ�`HK�^Q?�D&I�A�S2SYKiW �A[<nb�EHG\XH=2XHqQ_NDF=2X[Z\? �{?�DmI�A�S2S2K�W�LNK�I�A�E�?�Kgl~`HK�X�An_�AFGUZ\=2I�SYKgG\K�AFIJ`�K�?RDFXHK/op=�Z-esEV?:Z-I�D/egK4Z�DG\K�?UZMAFX�WG\K�d/K�GJ?UKMW]=2G�KiI$Z\=YD/X�a

LN<¤(Z\A�L�SYK6?UZ\A�Z�=@IRKih[EH=YS2=2LHG�=2EHe}_VD/=YX[Z\? ��?UD�I�AFSYS2K�WQLNK�I�AFE�?�K�l~`�K�X�Ag_�A�G�Z�=@I�S2KMG�KiAFIJ`HKi?�D/XHKM=�ZB?UZ�D/_�?�aIi<¤(Z\A�L�SYK�?:ZJA"Z\=2I K�h[EH=2S2=YLHG\=2EHe _VD/=YX[ZJ? ��?UD I�AFSYS2K�W LVKiI�A�EV?UK l~`HK�X A _VA�G�Z�=@I�S2K G\K�A/IJ`HK�?zDFXHK =YZA/I�I�K�S2K�GJA"Z�Ki?�a

WV<Q�BX�?UZ\A�L�SYK�?UZ\A�Z�=@ItKih[EH=YS2=2LHG�=2EHe _VD/=YX[Z\? ��?UD�I�AFSYS2K�W LNK�I�AFE�?�K±l~`�K�X A�_�A�G�Z�=@I�S2KwG�KiAFIJ`HKi?xD/XHK{=YZA/I�I�K�S2K�GJA"Z�Ki?�a

K*<Qb�EHG\XH=2XHqf_NDF=2X[Z\? �{?�DfI�AFSYS2K�W�LNK�I�A�E�?�K�DFPmZ�`HKz��S2e �\b>`HK�b�EHG\XH=YX�q 9�DF=2X[Z ��?UZ\AFG�G\=YX�qf¤(`H=2G�S2K�^¯�AFI�S@A�=2XHK/oH�cXHXHK �>AFX�I�G\D�P ZioHA�X�W¯�=2O[`VA�=2S �>A�G\=2?�`HX(^(OFD"d�a

¾F¾ ¼ h[e4EHS�ZB¾/¾ ¼ ¾F¾C� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu�_NK�G�P8K�I$ZcLVA�S@A�X�I�K�?\I�AFSYK�i�]a>»{`(^ I�A�X�· Z�A _HGJAFI�Z�=@I�A�S�LVA�S@A�X�I�Kw?\I�AFSYKwK�dFK�G�LNK{=2X _VK�GUP8KiI$Z�EHX�?UZ\AFLHS2K�?:ZJA"Z�=@IwK�h[EH=2S2=YLHG\=2EHe l~`HK�X

L�AFS2AFX�I�=2XHq��A[<n BD�Z\`H=YX�q�=2?>_NK�G�P8K�I�Z�aLN<Q�;dFK�G�^[Z�`�=YXHqg=@?~_VK�GUP8KiI$ZiaIi<Qb>`�K�G\Kn=@?gAFSYl>A*^]?6?�DFe&KCP8G\=2I�Z�=2DFX�AFS;P8D/G\I�KCZ\`�A"Z&e�A�OFKi?6Z\`HKL�A�S@A�X�I�Kn_ND/?�=�Z\=YD/X�oj`HD"l�K�d/K�Gio�?�S2=Yq/`/Z\SY^e&K�Z\AF?UZ\AFLHS2K4D/GRZ\`HK�?�I�A�S2K4X�K�dFK�GMG�KiA�S2SY^�L�AFS2AFX�I�Ki?�uBZ�`HK&_NK�G�Z�EHG\L�A�Z�=2DFX�?�A:E�?UZ-qFG\D"l ?UDm?US2D"l~S2^mZ�`�A�ZD/XHK�I�A�X6e�AFOFK;ABegKiAF?�EHG\K�e&K�X[Z�LNK�P8D/G�K;Z�`HK�^�LNK�I�DFe&K;D/L(d[=2DFEV?�a�°BP�I�DFEHGJ?�KFoiZ�`HK�SYKi?�?�Z�`�K�?UZ\AFLH=YS2=2��=2XHqP8G\=@I$Z�=2DFX�AFX�WCZ\`HK-S2K�?\?�Z�`HK-_NK�G�Z�EHG\L�A�Z�=2DFX�?�o(Z�`HK � � � �K��]A/I$Z\SY^nAge�AF?\?~I�AFXmLVK6W]K�Z�K�G�e&=2XHK�Wpa

WV<Qb>`�K�G\Kn=@?gAFSYl>A*^]?6?�DFe&KCP8G\=2I�Z�=2DFX�AFS;P8D/G\I�KCZ\`�A"Z&e�A�OFKi?6Z\`HKL�A�S@A�X�I�Kn_ND/?�=�Z\=YD/X�oj`HD"l�K�d/K�Gio�?�S2=Yq/`/Z\SY^e&K�Z\AF?UZ\AFLHS2K4D/GRZ\`HK�?�I�A�S2K4X�K�dFK�GMG�KiA�S2SY^�L�AFS2AFX�I�Ki?�uBZ�`HK&_NK�G�Z�EHG\L�A�Z�=2DFX�?�A:E�?UZ-qFG\D"l ?UDm?US2D"l~S2^mZ�`�A�ZD/XHK�I�A�X6e�AFOFK;ABegKiAF?�EHG\K�e&K�X[Z�LNK�P8D/G�K;Z�`HK�^�LNK�I�DFe&K;D/L(d[=2DFEV?�a�°BP�I�DFEHGJ?�KFoiZ�`HK�SYKi?�?�Z�`�K�?UZ\AFLH=YS2=2��=2XHqP8G\=@I$Z�=2DFX�AFX�WCZ\`HK-S2K�?\?�Z�`HK-_NK�G�Z�EHG\L�A�Z�=2DFX�?�o(Z�`HK�� � ��K��]A/I$Z\SY^nAge�AF?\?~I�AFXQLNK6W]K�Z�K�G\e&=YX�K�Wpa

K*<Q BD�DFXHKMl>A�X[Z\?�Z\D�a

¾F¾ ¼ h[e4EHS�ZB¾/¾ ½ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u;¤]£M°�P8D/Gc?Ue�A�S2S�_NK�G�Z�EHG\L�A�Z�=2DFX�?� ³ a>7kPNDFXHK�e�A�OFKi?�A�?�E]�CI�=2K�X[Z�S2^6?Ue�AFSYS]W]=2_HS@AFI�K�e&K�X[Z�P8G�D/e ?:ZJA�LHS2K�?UZ\A�Z�=@I;Kih[EH=YS2=2LHG�=2EHe DFPVA�S2e&D/?UZ�AFX(^M?�^]?:Z\K�e

Asl~=�Z\`n?Ue&D(D�Z\`C_ND�Z�K�X[Z�=@A�S�K�XHK�G\qF^4P8EHX�I�Z�=2DFXA�X�WgZ\`HK�XQSYK�Z;Z�`�KR?�^(?UZ�K�e�K�dFD/SYd/K~=YXQ=2?�DFS@A"Z\=YD/X�o�Z\`HKR?�^]?:Z\K�el~=2SYS�A�_H_HG\D*�]=Ye�A�Z�KFuA[<nA&?�=Ye&_HS2K-`�AFG�e&DFX�=2I�D/?\I�=2S2S2A�Z�DFGiaLN<QAFXAFXH`�AFG�e&DFX�=2I�D/?\I�=2S2S2A�Z�DFGiaIi<QA4Z\G\A*d/K�S2=YXHqgl>A*dFKFaWV<QAFXQE�X�?:ZJA�LHS2K-K�h[EH=2S2=YLHG\=2EHe}?�^]?:Z\K�emaK*<QAgd/K�I$Z\DFG>��K�S2W�a

¾F¾ ¼ h[e4EHS�ZB¾���¾/¾F¾4� ¶�¶ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVujqF=2G�SpD/XA&?�l~=YX�q&²-�>y"9��� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½/¶ T\� ½

��µ�a~��qF=2G\SVD/XQAg?Ul~=2XHqgD/?\I�=2SYS@A"Z\K�?�LVK�Z:l�K�K�XnLNK�=2XHqC��e�DB��Z\`HK�qFG\DFEHX�Wnl~`HK�G\KR?�`HKM=@?�A�Z A�XVW���eD ��Z�`HK-q/G�D/EHX�Wnl~`HK�G\KM`HK�GB?�_NK�K�WQ=@? aj»{`VA"Zc=@?>`HK�G~e�A"�]=2esEHe ?U_NK�KiW �

A[<xegD"d(=2XHq�)mS2D"l�Ki?:Z )�¾je��"?�a LN<�G�Ki?:Z )S2D"l�K�?UZ*)�¾je��"?�a I�<�G\K�?UZ*)m`H=2qF`HKi?:Z )���e��"?�aWV<�G�Ki?:Z )]`H=Yq/`HK�?UZ*)N� � µ�e��"?$a K*<�G�Ki?:Z )]`H=2qF`HKi?:Z )Hµ � µ�e��"?$a

Page 44: Introductory Physics Problems David J. Jeffery Department of

µ/¾ v�`�AF_]Z�a ¼ 9�D�Z\K�X[Z�=@A�Sp��X�K�G\qF^CA�XVW�v�D/X�?�K�G\d*A�Z�=2DFXQD�P��;XHK�G\qF^

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾ ¼ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujq/G\A*d(=YZ:^&9��tZ�DC²-�co]?�_�A�X�XHK�G�Fa ��D/EW]G\DF_mA&� � ¾jO(qg?�_�A�X�XHK�G�Z�DgP8G\=YK�X�W?:ZJA�X�W]=2XHqgDFXQZ�`HK-q/G�D/EHX�Wnl~`H=2IJ`���¾�e LVK�SYD"l{Z\`HK6W]G\DF_Q`HK�=2qF`[Z�a¤(`�K-l~=YS2S�I�A�Z\IJ`QZ�`HK6?�_�AFXHXHK�GM� � ¶ e}A�LND"dFKRZ�`HK-q/G�D/EHX�WpaA[<C»{`VA"Z�· ?>Z\`HK-l�D/G�OCWHDFXHKML(^nq/G\A*d(=YZ:^g=2XZ�`HK6WHG�D/_ �LN<n»{`VA"Z�· ?>Z\`HK6IJ`�A�X�qFK�=YXmqFGJA*d(=�ZJA"Z\=YD/X�A�SN_VDFZ�K�X/Z\=2AFS�K�X�K�G\qF^�=2XQZ\`HK6W]G\DF_ �Ii<Q�R?U=2XHqA�X�K�XHK�G\qF^mI�D/X�?UK�G�d"A�Z�=2DFX�I�AFS2I�EHS2A�Z�=2DFX��VX�WmZ�`�Kg?�_VK�K�W�DFPjZ�`HK&?�_�A�XHX�K�GRA/?c=YZ�G\K�A/IJ`HK�?c^FDFE�GP8G\=2K�X�Wp· ?~`�AFX�WH?�a

¾F¾ ¼ h/P8EHS2S�¾/¾H�F�i¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVuj=2WHK�A�S�I�SY=2esL�=YXHq�]a~b>`H=@?>qFE�^n¡RAFXH=2K�S���D(D]W]l~=YXm=2Xx� ½F¼ �R?\I�A�S2K�WnZ�`�Ks¤(K�AFG\?<��EH=2S2W]=2XHq&=2X�v�`H=@I�AFqFDgE�?�=YXHq�?�E�I$Z\=YD/XI�EH_�?~AFX�We&K�ZJA�S�I�SY=2_�?�a�b>`HKMLHEH=2S2WH=YXHq�=@?~µ/µ ³ e `H=2qF`�a�¸�K�Zi· ?>q/EHK�?\?>`HKM`�A/WAge�AF?\?>D�P;º"¾�O[qVaA[<C7kP;¡�A�X�l�A/?cA�X�=@W]KiA�S�I�SY=2esLNK�G&58=@W]KiA�S�=2X�Z\`HKs_H`(^]?�=2I�?B?�K�X�?�Ki<�oV`HD"l e4E�IJ`�LVD]W]^�IJ`HK�e&=2I�A�S�K�XHK�G\qF^WH=2W`HK-K��(_NK�XVWQq/K�Z�Z�=2XHqgZ�D&Z�`�KMZ�DF_ ��£cK-?UZ\A�G�Z�KiWCP8G\DFe}G�Ki?:ZcAFX�WnK�X�W]KiWA�ZcG�Ki?:Z �

LN<n7kP�`HK/· W&A:E�?UZBI�S2=Ye4LVKiWQZ�`HK6?UZ\AF=YGJ?�o]`�D"l�esEVIJ`QLND]W]^QIJ`HK�e&=2I�A�SpK�X�K�G\qF^�l�DFEHS@W`�A*dFK�E�?�K�W=2WHK�A�S2S2^ �Ii<n»{`(^W]=2W`HKM_HG\DFLVA�LHS2^CE�?�K-A4S2D�Zce&D/G�K�Z�`VA�XZ�`HK-=@W]KiA�S�A�e&D/EHX[Z>DFP�LND]W]^nIJ`HK�e&=2I�A�SpK�X�K�G\qF^��

¾F¾ ¼ h/P8EHS2S�¾/¾/��¾/¾ ³�¶ ¾g`�A�GJWnZ�`H=2XHO(=YX�q�u�W]G\DF_H_NK�WmI�D(I�DFX(E]ZcI�D/e&_HG�Ki?�?�K�?�?�_HG�=2XHq³ a~� I�D]I�DFX(E]Z6DFP�e�A/?�?s� � ¾�O[qm=@?sW]G\DF_�_VKiW�P8G\DFe G�Ki?:ZsA�Z4Am`HK�=Yq/`/Z � � A�LND"dFKgZ�`�K�Z�D/_�DFPcA�Xr=2WHK�A�S�58=�a K/aYoe�AF?\?�SYKi?�?J<$o � �� � ¦&� �Bo;EHX�I�DFe&_HG\K�?\?UKiWw?U_HG\=2XHqrl~=�Z\`�?U_HG\=2XHq�I�DFXV?:ZJA�X[Z ¶ ¾/¾�  �"enazb>`�K�I�D]I�D/X(E]Z?UZ�=@IJO]?MZ�DmZ\`HK&Z�D/_�D�P�Z�`HKC?�_HG\=YXHq�A�P Z�K�G6S2AFX�W]=2XHq�aQb�AFOFKgZ�`HKCZ�DF_rDFP�Z\`HKCEHX�I�DFe&_HG\K�?\?UKiWx?�_HG\=YX�qmZ�D�LNKZ\`HKR��K�G\DsS2K�d/K�S�a�b>`�K�?�_HG\=YXHq4G�KiAFIJ`HKi?;A4e�A"�]=Ye4EHe I�D/eg_�G�Ki?�?�=YD/XCD�P�� � $��F¾ � ¾�I�e�LNK�P8DFG\KBLNK�q/=YX�XH=YX�qsZ\DG\K�LNDFEHXVWpa�b>`HKM_HG\DFLHS2K�e =@?~K�X/Z\=YG\K�S2^���TkW]=2e&K�X�?�=2DFX�AFS�aA[<nb�D�Z�`HKm_NDF=2X[ZCD�PRe�A��(=2esE�e I�D/eg_�G�Ki?�?�=YD/X�`HD"l}esE�IJ`±l�D/G�Orl>AF?&W]D/XHKmL[^�Z�`HK�?�_HG\=YXHq�DFXtZ�`�KI�D]I�DFX(E]Z�A�X�W&L(^4Z�`HK�I�D]I�D/X[EHZ;DFX&Z\`HKR?�_HG\=YXHq�� ������ � |�=2X�W&Z�`�KBl�DFG\O4W]D/XHKcL(^sZ\`HKR?�_HG\=YX�qM��G\?UZ�a

LN<n»{`VA"Zc=@?�� � �Ii<n7kP~Z\`HKQI�D]I�DFX(E]Z4l�A/?6G\K�S2K�AF?�K�W�P8G\DFe Z:l~=@I�KCZ\`HKn`�K�=2qF`[Z6P8DFE�X�W�=2X�_�A�G�ZQ5,LV<n5,=�a KFa2o�P8G\DFe � ��� ����� $� � ��� � � � <$o�`HD"l e4E�IJ`�l�DFE�S2W�Z�`HKr?U_�G�=2XHqwI�DFe&_HG\K�?\?� ������ � |�AFI�Kx=YZ�oM^/DFE�`�A*d/K�Z\D±?�DFS2dFK�Ah[E�A/W]GJA"Z�=@IRP8DFG � � a

WV<n»{`VA"Zj=2?�Z\`HK>_H`(^]?U=@I�AFS(?�=2qFXH=Y�VI�AFX�I�K�D�PVZ�`HK>_ND/?�=�Z\=Yd/K>?�DFS2E]Z\=YD/X6Z�DRZ�`�Kch/EVAFW]GJA"Z\=2I;K�h[E�A"Z\=YD/XsD/L]Z\AF=YXHKiW=2Xm_�A�G�Z65,W�< �

¾F¾ ¼ h/P8EHS2S�¾/¾/�]�i¾ ³�¶ ¾g`�A�GJWnZ�`H=2XHO(=YX�q�u�b�A�GJh/E�=YX�¤(EH_NK�G\LHE�?~D[?�I�=YS2S@A"Z�Ki?� ª�¬"¨ �V«������V¬ ��­�� ¡BEHS2S�h[EHKi?:Z\=YD/X�uj`�AF?>X�Dg_�EHX�IJ`HS2=YX�KFa

µ�a~²MXHD"l~=2XHqx=�ZCl~=2SYScWHDxXHDr`�AFG�e 5,DFG&qFD(D]W�<s^FD/EtW]G\DF_±^FD/EHGgI�A"ZCb�A�GJh/E�=YXw¤(EH_NK�G\LHE�?gP8G\DFe G\K�?UZ4P8G\DFeA�`HK�=Yq/`/Z � � D/X[Z�D�A � �� � ¦&� � ?�_HG�=2XHqVa±b�A�GJh[EH=YX±`�A/?&e&A/?�? ��a{b>`HK�?U_�G�=2XHqr=2?&e�A/?�?�SYKi?�?&AFX�W��� � ��58=�a K/aYo�?�AFX�?4WH=2?\?U=2_�A�Z�=2DFXV<6l~=�Z\`t?�_HG�=2XHq�I�DFXV?:ZJA�X[Z���A�X�W�e�A/?�?�SYKi?�?4_HS@A"Z�P8DFG\e D/X�Z\`HKnZ\DF_�D/Xl~`H=@IJ`rb�AFG\h[EH=2X�S@A�X�W�?�agb>`HK�?U_HG\=2XHqQ=@?�=YX�=�Z\=2AFSYS2^�A"Z-G\K�?UZ�l~=YZ�`�=YZ\?M_HS@A"Z�P8DFG\e A"ZMZ�`�K&?�_HG\=YX�q�· ?B=2X[Z�G\=YX�?�=@IKih/E�=YS2=YL�G�=2EHe _ND/?�=�Z\=YD/X�u�l�K-W]K���XHK�Z�`�KM?�_HG\=YX�q�· ?�=2X[Z�G\=YXV?U=@IBKih[EH=YS2=2LHG�=2EHe _ND/?�=YZ�=2DFXQZ�DgLVKMZ\`HK � $�¾gS2K�d/K�S�a°RX{S@A�X�WH=YXHq�D/X±Z�`HK�?U_HG\=2XHq�_HS@A"ZUP8D/G�emo~b�A�GJh/E�=YXwqFG\=2_�?�=YZQA�X�Ww`�DFS@WH?�DFX±Z\=Yq/`/ZnP8DFG�Z\`HK�G\K�?UZCD�PMZ�`�K_HG\DFL�SYK�eajb>`HKR_HG\DFLHS2K�e =2?�K�X[Z\=YG\K�S2^Q��TkWH=Ye&K�XV?U=2DFX�AFS�a � � � � b>`�=2?�h[EHK�?UZ�=2DFXnI�DFEHS@W&LNK�A-e4EHSYZ�=YT�_�AFqFK�G=2X�AsZ\K�?UZce&=2?�K-K�Xm?�I�(K�X�KFaA[<®REVA�S2=�ZJA"Z�=2dFK�SY^�l~`�A�Z�=@?�q/DF=2XHqcZ\DB`�AF_H_NK�X6Z\DRb�A�GJh[EH=YX4A"P Z�K�G�`�K�=@?�D/X-Z�`�K�?�_HG\=YXHqBP8DFG�Z�`HK�P8DFG\K�?�K�KiA�LHS2KP8EHZ�EHG\K��

Page 45: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ¼ 9�D�Z�K�X[Z�=@A�Sp��XHK�G�q/^CA�X�W�v�D/X�?UK�G�d"A�Z�=2DFXnDFP��;XHK�G\qF^ µV�

LN<Q�R?U=2XHq±I�DFXV?UK�G�d"A"Z\=YD/X{D�PsK�XHK�G\qF^±l~G\=�Z\K�W]D"l~XzA�X�Kih/EVA"Z�=2DFX�G�K�S2A�Z�=2XHq � � A�XVWwZ�`HK�_ND/?UZUTkS2AFX�W]=2XHqb�A�GJh[EH=2X{_�A�GJA�e&K�Z\K�GJ?�dFK�SYD]I�=�Z:^ � AFX�Ww`HK�=Yq/`/Z ��afb�AFG\h[EH=2X�A�XVWw_HS2A�ZUP8D/G�e I�D/X�?UZ�=YZ�E]Z\KxA�_NDF=2X[Z_VA�G�Z�=@I�S2K�DFP�I�DFEHGJ?�KFa

Ii<¤]DFS2dFK~P8D/G ��AF?�AMP8EHX�I�Z�=2DFXnDFP � AFX�W � � aj|HG\DFe�A-_H`(^]?U=@I�AFS�_NK�GJ?U_NK�I�Z�=2dFK45,XHD�Z�A:E�?UZ�A-e�A"Z\`HK�e�A�Z�=@I�A�SD/XHKi<�oHl~`(^nA�G\K�Z�`HK�G�K�Z:l�D�?UD/SYE]Z\=YD/X�?�

WV<��=2dFK�Z\`HK-K��]_HG\K�?\?U=2DFXV?;P8D/G>Z�`HKMZ\EHG\XH=YX�q�_VD/=YX[Z\?>DFP�b�A�GJh[EH=2X�· ?�D[?�I�=YS2S2A�Z�=2DFX�?�aK*<��=2dFK6Z�`HK4K��]_HG\K�?\?U=2DFXmP8D/GRb�A�GJh/E�=YX�· ?cKih[EH=YS2=2LHG�=2EHe `HK�=2qF`[Zia ������ � b>`�=2?R=2?Rl~`HK�G�K-Z\`HKsX�K�ZBP8D/G\I�KD/Xb�A�GJh[EH=2XQ=@?~��K�G�DVa

P\<7kPjA&WHA�e&_H=2XHq&P8D/G\I�KR=@?>Z�E�G�XHKiWDFX�oHA�Zcl~`�A"Z~`HK�=Yq/`/Z~l~=2SYS�b�AFG\h[EH=2XI�DFe&K�Z�D�G\K�?UZ�a

¾F¾ ¼ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujLNDFS2S�l�K�K�d(=2S���^(=YXHq&D ��=Yq/SYD(D¶ a~� LNDFS2Spl�K�K�d(=2SpD�P�e�A/?�? � =@?~?U=YZUZ\=YX�qgD/XnZ\DF_D�P�A4`�K�e&=2?�_H`HK�G�=@I�AFSp=Yq/SYD(DgD�P�G\A/W]=YEV?��4aj�BX=2X]��X�=�Z\K�?�=Ye�A�S_NK�G�Z�EHG\L�A�Z�=2DFXm?:ZJA�G�Z\?>`H=2e}?�SY=@W]=2XHq�W]D"l~Xm?:ZJA�G�Z�=2XHqgP8G�D/e�?U_NK�KiW��K�G\D�ajb>`HK-=2qFS2D(D4=@?>P8G\=2I�Z�=2DFXHS2K�?\?�aA[<n|�=2X�WCAFXgK��]_HG�Ki?�?�=2DFXgP8DFG�`�=2?�?U_NK�KiW&DFX&Z�`�Kc=Yq/SYD(D6A/?�AMP8EHX�I�Z�=2DFX�DFPpAFXHqFS2K �-DFX&Z\`HKc=2qFS2D(D-egKiAF?�EHG\K�WP8G\DFe Z�`HK-d/K�G�Z�=@I�A�SpEV?U=2XHq�I�D/X�?UK�G�d"A�Z�=2DFXnDFP�e&KiIJ`�A�XH=@I�AFS�K�XHK�G�q/^Fa

LN<Q��Z&?UD/e&KC`HK�=2qF`[Zm58e&K�A/?UEHG\K�W�P8G\DFe Z�`�KnqFG\DFE�X�W�<�Z\`HKQLNDFS2S;l�K�K�d(=YS���^]?6D �tZ\`HKn=2qFS2D(D�a�|�=YXVW�Z�`�KK��]_HG�Ki?�?�=2DFX�P8D/GBZ\`H=2?M`�K�=2qF`[Z�a ������ � b>`H=@?�=2?�_HE�G�K�SY^�ACP8DFGJI�K&A�X�AFSY^]?�=2?R_HG\DFLHS2K�ema4v�DFXV?U=@W]K�GRZ�`�KX�DFG\e&AFS�P8D/G\I�KnDFX�Z�`HKLVD/SYS�l�K�K�d(=2S�AFX�W�XHDFZ�KnZ�`�A�Z4Z\`HKnGJAFW]=@A�S�5,I�DFe&_VD/XHK�X[Z&D�P\<4AFI�I�K�SYK�G\A�Z�=2DFXr=2?=2X�?UZ\AFX/ZJA�XHK�DFE�?�S2^4q/=Yd/K�XCL(^ � $ , � � � A:E�?UZ>A/?�P8D/G�E�XH=�P8D/G�e I�=YGJI�EHS@A�G�e&D�Z�=2DFXQK�d/K�X�l~`HK�X � =2?�XHDFZI�DFX�?UZ\AFX[Z�_HG\D"d(=2WHK�WMZ\`�A"Z =@?jI�DFXV?:ZJA�X[Z�a�¿~K�I�A�S2S � =@? A:E�?:Z�Z\`HK�Z\A�X�qFK�X[Z\=2AFS[?�_VK�K�Ws=YX4Z�`H=@?�K��]_HG\K�?\?U=2DFX�a

¾F¾ ¼ h/P8EHS2S�¾/¾ ³ �i¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujLVD/SYS�l�K�K�d(=YS�?UZ\A*^(=2XHq4D/Xm=Yq/SYD(D¹ a~b>`�A�Z�K�q/G�K�qF=2DFE�?�=YX�?�K�I�Z�Z�`�K;LNDFS2SFl�K�K�d(=2SFDFP(e�A/?�? �f=@?�L�A/IJOBD/XMZ�`HK;Z�DF_-DFPH`H=@?�`HK�eg=@?�_H`HK�G\=@I�A�SFP8G�=@I$Z\=YD/XHS2K�?\?=2qFS2D(D�ajb>`H=@?>Z�=2e&K-`HK-=2?>q/DF=2XHqgZ�D�?�SY=@W]K6W]D"l~X`�A�X�qF=2XHq&DFX[Z�D�AgSY=YZUZ\SYKsqFG\D[D"d/KcZ\`�A"ZcG\EHX�?~?UZ�GJA�=2qF`[ZcW]D"l~XZ\`HK-=Yq/SYD(D�?�SYD/_VK/u�Z\`H=@?>Z�=2e&K-`HK-l�D/X�· Z��V^nDB��aA[<nb>`�K~G\A/W]=YEV?�D�PNZ�`HK~=2qFS2D(D�=@?�AFq/A�=2X��zA�X�W �M=@?�Z�`HKcAFXHqFE�S2AFG�_ND/?�=YZ�=2DFX&D�PNZ�`HK~l�K�K�d(=YS]e&K�A/?UE�G�KiW6P8G\DFeZ\`HK � � � ¦ � �cap��=Yd/KsA�XmK��(_�G�Ki?�?�=YD/XP8DFGB`�=2?R?U_NK�KiW � A/?cA&P8EHX�I�Z�=2DFX�DFP �CAF?\?UEHe&=2XHq�Z\`�A"ZB`�K?UZ\AFGUZJ?�o]X�D�Z~P8G\DFe G\K�?UZ�o]LHEHZcl~=�Z\`m?�_NK�K�W � � a ������ � ��W]=@A�q/G\AFe eg=2qF`[Z~`HK�SY_�a

LN<Qb>`�K>AFXHqFE�S2AFG�?�_NK�K�W4D�PVZ�`HK>l�K�K�d[=2S]=@? � � ��� � $ � ���4a���=Yd/K�Z�`HK>K��]_HG\K�?\?�=YD/X6P8DFG � � � � � AF?�ARP8EHX�I$Z\=YD/XDFP ��a��B?cA&?�=Ye&_HS2=��NI�A"Z\=YD/XQS2K�Z�� � $ � � ���ga

Ii<Qb>`�K � � � � � K��]_HG\K�?\?U=2DFXm=@?�oN=2XmP,AFI$ZiopACW]= �NK�G�K�X/Z\=2AFS�Kih/EVA"Z�=2DFXmP8D/G �nA/?BA&P8E�X�I$Z\=YD/X�D�PjZ\=Ye&KFaB7kZR`�A/?X�DnA�X�AFSY^[Z\=2I-?�DFS2E]Z�=2DFX�AF_H_�A�G\K�X[Z\SY^ �{SY=2OFK6?�D�e�A�X(^QW]= ��K�G\K�X[Z�=@A�S�K�h[E�A"Z\=YD/X�?>Z\`�A"ZRWHK�?\I�G\=YLNK6G\K�A�SYTkSY=YP8K_�G�D]I�Ki?�?�K�?�a~� X(EHe&K�G\=@I�A�S�?UD/SYEHZ�=2DFX�=@?�oN`HD"l�K�dFK�G�oV?:Z\G\AF=Yq/`/Z�P8DFG\l�AFG\W�a ��E]Z�=YX�?UZ�KiAFW�DFP�?UD/SYd(=2XHq�P8DFG��A/?�P8EHX�I�Z�=2DFX�D�P�Z�=2e&KFo�SYK�Z�· ?6?�DFS2dFK4P8DFG-Z\=Ye&K � AF?MP8EHXVI$Z�=2DFXrDFP �mdFK�G�^xI�G\E�W]K�S2^Fa�7!X(d/K�G�Z�Z\`HK � � � � �K��]_HG�Ki?�?�=2DFXCZ\D�qFK�Z~AFXQK��]_HG�Ki?�?�=2DFXCP8D/G � � � � �Ha�¯�A�O/KBZ\`HK6A�_�_HG�D*�]=2e�A"Z�=2DFX

� �� ��� �� �

l~`�K�G\K � �wesEV?:Z�LNK�=YX � � � � � � ��aR��=Yd/K�XzZ�`�A�Z�� $ �je A�X�W�� � $ � � ��� $ ��G\A/W �"?$o¦ � �4� �� � Ki?:Z\=Ye�A�Z�K6Z\`HK&?US2=2WHK�T!W]D"l~X�Z�=2e&K � � � � � � � T � � � �CZ\`�A"Z�Z�`HKgl�K�K�d(=2S�ZJA�O/K�?BZ�DnG\K�A/IJ`�Z�`�Kq/G�D/EHX�Wpa

WV<n7kP�� � $�¾Ho]`�D"l�S2DFXHq&=2XQZ\`HK-=@W]K�AFS�I�AF?�KMl�D/EHS@Wn=YZ~Z\AFOFKMl�K�K�d(=2S�Z�D�?US2=@W]K6W]D"l~XQZ�`HK-=2qFS2D(D �»{`(^��

¾F¾ ¼ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�¡R=YX�qFDC?�SY=@W]K�?>D/XA&S2D(DF_QP,A�S2S2?>D ��XHDFZº(a~¡R=YX�qFDCZ\`HK&WHA�G\K�W]K�d(=YS�W]DFqVo�?UZ\AFGUZ\=YX�q�P8G�D/e � � �o�?�SY=@W]K�?�W]D"l~X�ACP8G�=@I$Z\=YD/XHS2K�?\?cZ\G\A/IJOnP8G\DFe�A�X�=YXH=YZ�=@A�S`HK�=Yq/`[Z � � a�b>`�KcZ�GJAFIJO4LVKiI�D/egKi?;S2K�d/K�SNA"Z � ${¾�o[W]D(Ki?�A6I�=YGJI�E�S2AFG;S2D[D/_]T�Z�`HK�T�S2D(DF_&D�P�GJAFW]=2E�?�4o(A�XVW&Z�`HK�Xq/D[Ki?jS2K�dFK�SVA�Z � $�¾6A�q[A�=2X�a � � � � b>`H=2?�h[EHK�?UZ�=2DFXCI�DFEHS@W&LVK�AMesEHSYZ�=YTk_�A�q/K�G�=2XnA�Z�Ki?:Z�e&=2?�KcK�XC?\I�(K�XHK/a

Page 46: Introductory Physics Problems David J. Jeffery Department of

µ[� v�`�AF_]Z�a ¼ 9�D�Z\K�X[Z�=@A�Sp��X�K�G\qF^CA�XVW�v�D/X�?�K�G\d*A�Z�=2DFXQD�P��;XHK�G\qF^

A[<C»{`VA"Zc=@?~¡B=2XHqFDV· ?B?U_NK�KiWQA�ZBA�X(^C`HK�=Yq/`/Z �nA/?�?�EHe&=2XHq&`HK6?:ZJA*^]?�D/XZ�`HKMZ\G\A/IJO �LN<Q|�=2X�WgABq/K�XHK�G\AFSFK��]_HG\K�?\?�=YD/X-P8DFG�Z�`�K�XHD/G�e�AFSFP8D/G\I�K�D/X4¡R=YXHq/DBl~`HK�X4`�K�=@?�DFX6Z\`HK>SYD(D/_sAF?�ABP8EHX�I$Z\=YD/X

DFP�Z\`HKsAFXHqFS2K �gLNK�Z:l�K�K�X�A&qFK�X�K�GJA�SpGJAFW]=@A�Spd/K�I$Z\DFG~A�XVWnZ\`HK6GJAFW]=@A�Spd/K�I�Z�DFG~_NDF=2X[Z�=2XHq&Z�D&Z\`HKMZ�D/_mD�PZ\`HKMSYD(D/_�a�b>`HKMDFXHS2^�d"A�G\=2AFLHS2KR=2XnZ\`HKMP8EHX�I�Z�=2DFXm?U`�DFEHS@WnLNK �Ha ������ �  BD�Z�K�Z\`�A"Z>Z�`�K�e�AFqFXH=YZ�E�WHKDFPjZ�`HK4G\A/W]=@A�S;5�I�DFe&_NDFXHK�X[ZBD�P\<RAFI�I�K�SYK�G\A�Z�=2DFXm=2?B=YXV?:ZJA�X[Z\AFXHK�D/E�?US2^nq/=Yd/K�X�L(^�� $ � � � A:E�?UZ�A/?~P8D/GE�XH=�P8D/G�e I�=2G\I�EHS@A�G>e&D�Z�=2DFXK�d/K�Xl~`HK�X � =@?>XHDFZBI�DFXV?:ZJA�X[Z�_�G�D"d(=@W]K�WnZ�`�A�Z =@?cI�D/X�?UZ\A�X[Zia�¿cK�I�AFSYS �=@?�A:E�?UZ�Z\`HK4Z\A�X�qFK�X[Z\=2AFS�?�_VK�K�W�=YX�Z�`H=@?MK��]_HG\K�?\?U=2DFX�AFX�W�Z\`HK&W]=YG\K�I�Z�=2DFXxD�P�Z\`HK4GJAFWH=2AFS�A/I�I�K�SYK�G\A�Z�=2DFX=@?>Z\D"l�AFG\WCZ�`HK6I�K�X[Z�K�G�a

Ii<Q|�DFG�l~`VA"Z �M=2?jZ�`HKcX�DFG\e&AFS(P8DFGJI�K~K��(_�G�Ki?�?�=YD/X4?�e�A�S2SYKi?:Z �n»{`VA"Z;=@?�Z�`�KcXHDFG\e�A�S(P8D/G\I�K>A�ZjZ�`H=@?;AFXHqFS2K��WV<n»{`VA"ZR=@?BZ�`HKgI�DFXVW]=�Z\=YD/X�Z�`VA"ZBZ\`HKgXHDFG\e�A�SpP8D/G\I�KsXHDFZRqFDnSYKi?�?cZ�`�AFX���K�G�DnAFX(^[l~`�K�G\K-DFX�Z\`HKsS2D(DF_ �

»{`VA"Zc`�AF_H_VK�X�?~=YP�=YZBW]=@WqFDgSYKi?�?>Z\`�A�X��K�G�D��K*<¤HA*^ � � $ ¶ ¾je�A�X�WtZ�`�K�G\A/W]=2E�?&D�PMZ�`�K�SYD(DF_w=@?n��¾�eaz¡BD(K�?n¡B=2XHqFD�?UZ\A*^�DFX±Z�`HK�SYD(DF_ � 5,�WHK�e&DFX�?UZ�GJA"Z\=YD/XQ=@?>XHK�K�W]KiWpoHXHDFZ A:E�?:ZBAg^/K�?>DFG>XHDCAFX�?�l�K�G�a <

¾F¾ ¼ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�AFXH`�A�G\e&DFXH=@I�D/?\I�=2SYS@A"Z\DFG¼ a ��D/EmAFG�K�qF=2dFK�XAFXQD[?�I�=YS2S@A"Z�D/G>D�P�e&A/?�? ��D/LVK�^(=YXHq�AFXmAFXH`�AFG�e&DFX�=2IRD/?\I�=2SYS@A"Z\DFG-5,�B°M<;P8D/G\I�K�S@A*l

�����~5��< $�,� � , � � � l~`HK�G�K ��A�X�W � A�G\Ks_ND/?�=�Z\=Yd/K4I�DFX�?UZ\AFX/ZJ?�a � � � � b>`�=2?Mh[EHK�?UZ�=2DFXxI�DFE�S2W�LNK&Ane4EHS�Z\=�Tk_�AFqFK�GR=YX�A�Z\K�?UZe&=@?UK-K�X?\I�(K�XHKFaA[<C»{`VA"Z~=2?�Z\`HKMl�D/G�O� ��� WHDFXHKML(^&Z�`HK-�B°zP8D/G\I�KBl~`HK�XnZ\`HKMD/?\I�=2SYS@A"Z\DFG�=2?>e&D"dFKiW&P8G\DFe�Z�`�K�D/G�=2qF=2XZ\DCA&qFK�XHK�GJA�Sp_NDF=2X[Z�� � �������� � ��DFE�l~=2SYS�`VA*dFK�Z�DCW]DCAFXm=YX[Z�K�qFGJA"Z\=YD/X�a�¿~K�e&K�esLNK�Gcl~`H=@IJ`ml�A*^Z\`HKMP8DFGJI�KM_NDF=2X[Z\?~A�XVWQl~`�=2IJ`l�A*^CZ�`HK-D[?�I�=YS2S2A�Z�D/G�=@?>e&D"d(=YXHqVa

LN<¤HA*^4Z\`�A"Z�Z�`�KRD[?�I�=YS2S2A�Z�D/G�LNK�P8D/G�K�A�X�WQA"P Z�K�G�=YZ~`�AF?�LNK�K�XQe&D"dFK�WCl�A/?�A�Z�G\K�?UZ�a�»{`�A"Z>l>AF?;Z�`HKMl�DFG\O� � � �4WHDFXHKRL[^gZ\`HK�AF_H_HS2=YKiW&P8DFGJI�KBZ�`�A�Z�I�A�E�?�K�W&Z\`HK�egD"d/K�e&K�X[Z �Q�R?�?�EHe&K�DFXHS2^gZ�`HK�A�_H_HS2=2K�W�P8D/G\I�KAFX�WQZ�`HK6�B° P8DFGJI�K-AFI�Z�a

Ii<n»{`VA"ZB=@?~Z\`HK6K��]_HG\K�?\?�=YD/XnP8D/G~Z�`HK4�B°�_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^ �����t=YP�Z�`HKsDFG\=Yq/=YX=2?RIJ`HD/?�K�XZ\D�LVK6��K�G\D_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^ �

WV<¤HA*^rZ�`�A�ZgZ\`HK�G\KmA�G\KQXHD�XHD/X�I�D/X�?UK�G�d"A�Z�=2dFK�P8D/G\I�K�?&A�X�W�l�KqF=2dFKQZ�`�Km�B°�A�X�=2XH=YZ�=@A�S~e&K�IJ`VA�XH=@I�AFSK�XHK�G\qF^nD�P Caj»{`�A"Zc=@?~=YZ\?>e&K�IJ`�AFXH=@I�A�SpK�XHK�G\qF^ � � � � � A"ZcA�S2S�S@A"Z\K�G>Z�=2e&K�?�

K*<n»{`VA"ZC=@?&Z�`HK�e�A��(=2esE�e�?�_VK�K�WtZ�`�A�Z�Z�`HK�D[?�I�=YS2S@A"Z�D/G�I�A�Xw`�A*d/KQq/=Yd/K�XtZ�`�A�ZC=�ZQ`�AF?&e&K�IJ`VA�XH=@I�AFSK�XHK�G\qF^ �m»{`HK�G�K-W]D(K�?>=YZcG\K�AFIJ`QZ�`�=2?~e�A��(=2esE�e�?U_NK�KiW �

P\<»{`VA"Z6=@?MZ�`HK�e�A��(=2esE�e W]=@?U_HS@AFI�K�e&K�X[Z � ���� Z�`�A�Z-Z�`HKC�B° I�A�Xrq/K�ZMP8G�D/e�Z�`�KCDFG\=Yq/=YX±58=�a K/aYo�Z�`�KAFe&_HSY=YZ�EVW]K�D�P�Z�`HK�D[?�I�=YS2S2A�Z�=2DFXV<Rq/=Yd/K�X�e&KiIJ`�A�XH=@I�AFSjK�XHK�G�q/^ �a ������ � ¤(D/SYd/K4P8D/G�� ���� $ � ������VG\?UZ�a

q(<C7kP � ����&=@?�?UD?Ue�A�S2S�Z�`�A�ZBZ�`�K&��X�WmZ�K�G�e�=2X�Z�`�Kg�B° _ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^QK��]_HG�Ki?�?�=2DFX�=@?BXHK�qFS2=Yq/=YL�SYK/oAF_H_HG\D*�]=Ye�A"Z\K�S2^�l~`�A"Z~O(=2X�WD�PjA�XD/?\I�=2SYS@A"Z\DFG~W]D&l�KM`�A*d/K��

Page 47: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� UW6FE�;71_= E ?T@ BC&A57;<*-H N[1_E &A>�, � *I>S1)&:5 � ?T=!1_>2;<d�=

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾F¾ ½ h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�K�X[Z�K�G~D�P�e�A/?�?~W]K���XH=YZ�=2DFX�Fa~b>`HK6I�K�X[Z�K�G~D�P�e&A/?�?>=@?>Z\`HKFu

A[<C_ND/?�=YZ�=2DFX]Tkl�K�=Yq/`[Z�K�Wne&K�A�Xme�AF?\?>D�P�Z�`HK6AFXmDFL,A:KiI$Z�aLN<nD/L,A:K�I�ZUTkl�K�=Yq/`[Z�K�Wne&K�A�Xme�AF?\?>D�P�Z�`HK-_ND/?�=YZ�=2DFX�aIi<ne&KiA�XD�P�e&A/?�?~AFXQl�K�=2qF`[Z\K�WQDFL,A:KiI$Zc_ND/?�=�Z\=YD/XQDFP:aWV<ne�A/?�?UT�DFGio(_VK�G�`�AF_�?>e&DFG\KM_HG�KiI�=@?UK�SY^/o(Z�`HK6WHK�X�?�=�Z:^[Tkl�K�=Yq/`[Z�K�Wne&K�A�Xm_ND/?�=�Z\=YD/XQDFP�AFXQD/L,A:K�I�Z�aK*<Q?�=2eg_�SYK6I�K�X[Z�K�G~D�P�Z\`HK-DFL3A:K�I$Zia

¾F¾ ½ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�K�X/Z\K�G~DFP�e�AF?\?�o]G�K�P8K�G\K�X�I�KBP8GJA�e&K�]a~b>`HK6I�K�X[Z�K�G~D�P�e&A/?�?-5,=�a KFa2oH=YZ\?cA/I$Z\E�A�Sp_H`(^]?�=2I�A�Sp_ND/?�=�Z\=YD/XQ=2X�?U_�A/I�KMG\K�S@A"Z�=2dFKRZ�D�_�`[^]?�=2I�A�S�DFL3A:K�I$ZJ?\<�=@?�u

A[<nA4P8EHXVI$Z�=2DFXmDFP�Z\`HK6I�D(DFGJW]=2X�A"Z\K�?�^]?:Z\K�emaLN<n=2X�W]K�_VK�X�W]K�X/ZRD�P�Z\`HK6I�D(D/G\W]=2X�A�Z�K-?U^]?UZ�K�eaIi<QWHK�_NK�X�W]K�X[ZcDFXZ�`HK6I�D(DFGJW]=YXVA"Z�KM?�^(?UZ�K�emaWV<nLND�Z\`m=YX�WHK�_NK�X�W]K�X[ZBD�P�A�X�WmA4P8EHX�I�Z�=2DFXmD�P�Z�`HK6I�D[D/G\WH=YX�A�Z�K-?�^(?UZ�K�emaK*<nX�K�=YZ�`HK�Gc=YXVW]K�_NK�X�WHK�X[ZcD�P�XHDFGcA4P8EHXVI$Z�=2DFXmDFP�Z�`�K6I�D(DFGJW]=2X�A"Z\KM?�^]?:Z\K�ema

¾F¾ ½ h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�K�X/Z\K�G~DFP�e�AF?\?�o ³ T!WQ?�^(ege&K�Z�G\^³ a>7kPjA�XDFL,A:KiI$Zc=@?~?U^(e&e&K�Z\G�=@IM=YX ³ W]=2e&K�X�?�=YD/X�?�o]=�ZJ?cI�K�X/Z\K�G~DFP�e�AF?\?>esE�?UZcLNKFu

A[<CD/E]Z\?�=@W]K-D�P�Z�`HK-D/L,A:K�I�Z�aLN<nX�K�=YZ�`HK�Gc=YXV?U=@W]KMXHDFG~D/E]Z\?�=@W]KMZ�`HK-D/L,A:K�I�Z�aIi<QA�Z-Z�`HK&_NDF=2X[ZsA�LNDFE]Z6l~`H=@IJ`xZ�`HK�D/L,A:K�I�ZM=@?6?�^(ege&K�Z�G\=2Ig=2X��QDFP�Z\`HKCW]=2egK�X�?�=YD/X�?�o�LHE]Z6XHDFZ6=YX�Z�`�K³ G\W�a

WV<QA�Z-Z�`HK&_NDF=2X[ZsA�LNDFE]Z6l~`H=@IJ`xZ�`HK�D/L,A:K�I�ZM=@?6?�^(ege&K�Z�G\=2Ig=2X±�&DFP�Z\`HKCW]=2egK�X�?�=YD/X�?�o�LHE]Z6XHDFZ6=YX�Z�`�KDFZ�`HK�GB�]a

K*<QA�Z~Z�`HK-_NDF=2X[ZcA�LNDFE]Zcl~`H=@IJ`QZ�`HK-D/L,A:K�I�Zc=2?~?�^(ege&K�Z�G\=2IM=2XAFSYS ³ DFP�Z\`HK6W]=2egK�X�?�=YD/X�?�a

¾F¾ ½ h[e4EHS�ZB¾/¾ ³ ��¾4� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�I�K�X/Z\K�G~DFP�e�AF?\?� ª�¬"¨ �V«������V¬ ��­��  cD�ZcL�G�=2SYS2=@A�X[Z~_HG�D/LHS2K�e

µ�a~b>`HK6I�K�X[Z�K�G~D�P�e&A/?�?>DFP�AFXQD/L,A:K�I�Z~=2?~KiAF?�=YS2^�P8D/EHX�W=�P�Z�`�K-DFL,A:KiI$Z~=2?�u

A[<n?�^(e&egK�Z�G\=2I6=YX ��� � esE]Z\E�A�S2SY^_NK�G\_VK�X�W]=@I�EHS@A�G�W]=YG\K�I�Z�=2DFX�?cSY=2OFK/oHP8DFGRK��HA�e&_HS2KFoVA�G�KiI$ZJA�XHq/EHS2AFGL�SYD]IJO�a

LN<Q?�^(e&egK�Z�G\=2I�=2X � � esE]Z\E�A�S2SY^�_VK�G�_NK�X�WH=2I�EHS2AFG�W]=YG\K�I�Z�=2DFX�?�o�LHE]Z�XHD�Z�=2X�Z\`HK�Z�`H=2GJW�WH=YG\K�I�Z�=2DFX_NK�G\_NK�X�W]=@I�E�S2AFG>Z�D&Z�`�KM��G\?UZ>Z:l�DVa

Ii<Q?�^(e&egK�Z�G\=2Ig=2X � � W]=2G�KiI$Z\=YD/X�o�LHE]Z4XHD�Z-=2XxZ:l�DmesE]Z\E�A�S2S2^�_VK�G�_NK�XVW]=2I�EHS@A�G6W]=2G�KiI$Z\=YD/X�?�Z�`�A�ZsA�G\K_NK�G\_NK�X�W]=@I�E�S2AFG>Z�D&Z�`�KM��G\?UZ~DFXHK/a

WV<QI�DFe&_HS2K�Z\K�S2^n=2G�G\K�q/EHS2AFG�aK*<ne�A/W]KMDFE]ZcDFP�l~`H=2_H_NK�WmI�G\K�AFema

¾F¾ ½ h[e4EHS�ZB¾/¾ ³ ��¾C� ¶&³ K�A/?U^&Z\`H=2XHO(=YXHqVu;I�K�X[Z�K�G~DFP�e�AF?\?�oH?U^(e&e&K�Z�G\=@I�?�_H`HK�G�K

Page 48: Introductory Physics Problems David J. Jeffery Department of

µFµ v�`�AF_]Z�a ½ ¤(^]?:Z\K�e�?>D�Pj9jA�G�Z�=@I�S2K�?>AFX�WQ¸�=YX�K�A�Gc¯�DFe&K�X[Z�E�e

¶ a~b>`HK�I�K�X/Z\K�G�D�P�e�AF?\?�DFP�?�_H`HK�G\KcDFP�G\A/W]=YEV?��l~=YZ�`nA4W]K�X�?�=YZ:^gq/=Yd/K�XCL(^ � $ � �&5,l~`HK�G\K =@?�Z\`HKBGJAFWH=2AFSI�D[D/G\WH=YX�A�Z�K*<;=@?~A"ZiuA[< $����F�]aLN< $���� ³ aIi< $�¾HaWV< $ ³ �gaK*< $z���ga

¾F¾ ½ h[e4EHS�ZB¾/¾�µ[¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujD]WHWnP8EHX�I�Z�=2DFXmD"dFK�G�K�dFK�XQG\K�q/=YD/X¹ a~b>`HK-=2X[Z�K�qFGJA�S�D�PjA�XD]WHWQP8EHX�I$Z\=YD/XmD"dFK�G~A&?�^[e&e&K�Z\G�=@I�G�K�qF=2DFXA�LNDFE]Z~Z\`HK-DFG\=Yq/=YXQ=2?BA�S2l�A*^]?�u

A[<nAFXQD]WHWQP8EHXVI$Z�=2DFX�aLN<QAgXHD/X]Tk��K�G\DgK�dFK�XnP8E�X�I$Z\=YD/X�aIi<nX�DFX]Tk��K�G�DVaWV<nX�K�q/A�Z�=2dFK/aK*<n��K�G\D�a

¾F¾ ½ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�D]WHWQP8EHX�I$Z\=YD/XmD"dFK�G>K�dFK�XG\K�qF=2DFX� ª�¬"¨ �V«������V¬ ��­�� A A:K�DF_�AFG\WH^C_HG\DFLHS2K�e

º(a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�u�?NK�G�DVa �A[<C»{`VA"Zc=@?>SYKi?�?>Z\`�A�X�oH�cS2K�� �LN<n»{`VA"Zc=@?�Z�`HK-=2X[Z�K�q/G\AFSpD�P�A�XmD]WHWCP8E�X�I$Z\=YD/X�D"dFK�G>A�?�^[e&e&K�Z\G�=@I�G�K�qF=2DFXA�LNDFE]Z~Z\`HK-DFG\=Yq/=YX�o(�BSYK�� �Ii<n»{`VA"Zc=@?�Z�`HK-=2X[Z�K�q/G\AFSpD�P�A�XmK�d/K�XQP8EHX�I$Z\=YD/XmD"dFK�G~A&?�^[e&e&K�Z\G�=@I�G�K�qF=2DFXmA�LNDFE]Z>Z\`HK-DFG\=Yq/=YX�oH�cS2K�� �WV<n»{`VA"Zc=@?>DFXHK/o��cS2K�� �K*<n»{`VA"Zc=@?>XHD�ZBA&I�D/qFX�A�Z�KMl�DFGJW�Z�DCI�=Y_�`HK�GioH�cS2K�� �

¾F¾ ½ h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu�`�AFXHqFK�G>I�K�X[Z�K�G~D�P�e&A/?�?¼ a>»{`HK�G�K/o�G\DFE�qF`HS2^�?�_VKiA�O(=YX�q�o�=@?MZ\`HKnI�K�X[Z�K�GsD�P>e&A/?�?6D�P~A�I�D/A�Z6`�A�X�qFK�G � ������ � 7!e�A�qF=2XHK�S2K�Z�Z�=2XHq�=YZ`�AFXHqP8G�D/e Z:l�D�W]= �NK�G�K�X/Z-P8G\K�K�_�=Yd/D�Z-_VD/=YX[ZJ?�u-Z\`H=@?6=@?-I�A�S2S2K�WrA���K�WHAFXHOFK�X±58Z�`HD/EHqF`[Z$<MK��]_NK�G\=Ye&K�X[Z6=2X_H`(^]?�=2I�?~?U_NK�AFONa�7kP�^FD/EAFG�X�· Z~=YX�A4Z�Ki?:Zce&=@?UK-K�X�?�I�(K�XHK/o(^FDFEmI�D/EHS@WQA/I$Z�EVA�S2SY^nWHD4Z\`HK-K��]_NK�G\=Ye&K�X/ZiaA[<n��Z~Z\`HK-K�XVWQDFP�Z\`HK-`HD(DFO�aLN<Q��Z~Z\`HKMZ�D/_mD�P�Z\`HK-`HD(DFO�aIi<Q��Z~Z\`HK-S2K�P ZcK�XVWQDFP�Z\`HKMZ�G\=@A�XHq/EHS2AFG>SYD(DF_�aWV<Q BD"l~`HK�G\KR?�=2X�I�KMA4I�K�X[Z�K�G>D�P�e�AF?\?�esE�?UZ>LVKM_H`(^]?U=@I�AFSYS2^&=YXV?U=@W]KMA�XnD/L,A:K�I�Z�Z\D4LNK-A4I�K�X[Z�K�G>D�P�e�AF?\?�aK*<m°R`�o�?UD/e&K�l~`HK�G�K�XHD�ZB?�D4P,A�G~P8G\DFe Z\`HK-e&=2W�W]SYK-G\K�q/=YD/XnDFP�Z\`HKMZ�G\=2AFXHqFE�S2AFG�S2D(DF_�a

¾F¾ ½ h[e4EHS�ZB¾/¾ ¹ ��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�`�A�X�qF=2XHq�I�K�X[Z\K�G~D�P�e�AF?\?½ a �\¸�K�Zi· ?�_HS@A*^��]1J� D+�"����# 1 |HD/G �(��¾/¾Ho/Z�`HK-AFX�?Ul�K�G>=@?�u�7kP�DFXHK�`�AFXHq/?>AgG�=2qF=@WCD/L,A:K�I�Z>P8G�D/e AsP8G\K�K�SY^&Z\EHG\XH=YX�q_H=2dFDFZ-_VD/=YX[ZsA�XVWxS2K�ZJ?M=�ZsI�DFe&K&Z�D�?UZ\AFLHSYK�?UZ\A�Z�=@I&K�h[EH=2SY=2LHG\=YEHemo�Z�`HKCI�K�X[Z�K�G-D�P>e&A/?�?M=@?-W]=2G�KiI$Z\SY^�LNK�S2D"lZ\`HKs_H=2dFDFZR_NDF=2X[Z�aBb>`(E�?�opI�K�X[Z\K�GBDFP�e�AF?\?BI�AFX�LVKsP8DFEHXVWmP8G�D/e Z�`HK4=YX[Z�K�G\?�K�I�Z�=2DFX�DFPjZ:l�DCS2=2XHK�?BZ�`HG\DFE�qF`Z\`HK&DFL,A:KiI$ZMZ�`�A�Zs?:ZJA�G�ZMA�ZMZ:l�D_VD/=YX[ZJ?ME�?UKiWxA/?M_H=2dFD�ZM_NDF=2X/ZJ?-A�X�W�Z�`VA"Z-qFD=YX�Z\`HK�W]=YG\K�I�Z�=2DFXxZ�`HG\DFE�qF`Z\`HKsD/L,A:K�I�ZcZ�`�A�ZRl>AF?cWHD"l~X[l>A�GJWl~`HK�X�KiAFIJ`�DFP�Z\`HKs_NDF=2X[Z\?Bl�A/?~Z�`�K6_H=2dFD�ZR_VD/=YX[Z�aRb>`HK6e&K�Z\`HD]WmP,A�=2S2?=YP�Z\`HKMZ:l�Dg_�=Yd/D�Z~_VD/=YX[ZJ?cA�X�WnZ�`�K6I�K�X[Z\K�G~D�P�e�AF?\?�`�A�_H_NK�XZ\D�LVK6I�DFS2SY=2XHK�AFG�a �A[<C»{`VA"Zc=@?~A�XmK�e&_H=2G�=@I�AFSpe&K�Z�`�D(WQP8D/G>��X�W]=2XHq�qFGJA*d(=�ZJA"Z\=YD/X�A�SVZ�D/G\h[EHK/oH�cS2K�� �LN<n»{`VA"Zc=@?~AgZ�`HK�DFG\K�Z�=@I�AFS�egK�Z�`HD]WP8D/G>��X�W]=2XHq&qFGJA*d(=2A�Z�=2DFX�AFS�Z\DFGJh/E�KFoH�cS2K�� �Ii<n»{`VA"Zc=@?>qFGJA*d[=YZ\A�Z�=2DFXnZ�DFGJh[EHKFoH�BSYK�� �WV<n»{`VA"Zc=@?~A�I�K�X[Z\K�G~D�P�e�AF?\?�oH�BSYK����K*<n»{`VA"Zc=@?~A�XmK�e&_H=2G�=@I�AFSpe&K�Z�`�D(WQP8D/G>��X�W]=2XHq&Z�`�K6I�K�X[Z\K�G~D�P�e�AF?\?>D�PjA4G\=2qF=@WnD/L,A:K�I�Z�oH�cS2K�� �

¾F¾ ½ h[e4EHS�ZB¾/¾[º�¾F¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu�`HD(DF_mI�K�X[Z�K�G~DFP�e�AF?\?��¾Ha>»{`HK�G�KM=@?>Z�`�K6I�K�X[Z\K�G~D�P�e�AF?\?>D�PjA4`�D[D/_ �

Page 49: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia ½ ¤(^]?UZ�K�e&?>DFP�9jAFGUZ\=2I�SYKi?>A�X�W¸�=2XHK�AFGc¯�DFe&K�X/Z\EHe µ ¶

A[<n��Z~Z\`HK-K�XVWQDFP�Z\`HK-`HD(DF_�aLN<Q��Z~Z\`HKMZ�D/_mD�P�Z\`HK-`HD(DF_�aIi<Q��Z~Z\`HK-S2K�P ZB?�=2W]K-DFP�`HD(D/_�aWV<Q BD"l~`HK�G\KR?�=2X�I�KMA4I�K�X[Z�K�G>D�P�e�AF?\?�esE�?UZ>LVKM_H`(^]?U=@I�AFSYS2^&=YXV?U=@W]KMA�XnD/L,A:K�I�Z�Z\D4LNK-A4I�K�X[Z�K�G>D�P�e�AF?\?�aK*<m°RXQZ�`�K6A"�]=2?>DFP�Z\`HK-`HD(DF_�a

¾F¾ ½ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj=2X[Z�K�G\X�AFS�P8DFGJI�K�_�A�=2G�l~=@?�KMI�A�X�I�K�S@A"Z\=YD/X�F�Fa>»{`(^QWHDg=2X[Z�K�G�X�AFS�P8DFGJI�Ki?>XHD�ZcA ��K�I�Z~Z�`HK6I�K�X[Z�K�G~D�P�e&A/?�?~A/I�I�K�S2K�GJA"Z�=2DFXQD�PjA&?U^]?UZ�K�e �

A[< ��KiI�A�EV?UK�Z�`�K�^nI�A�X�I�K�S�D/E]Z~=YXZ�`�G�K�K�?�DFe&K�?�aLN<#��KiI�A�EV?UK�Z�`�K�^nAFG�K-A�S2Sp��K�G�DVaIi<#��KiI�A�EV?UKMl�K�A:EV?:Zc=2qFXHD/G�KRZ�`�K�emaWV<#��KiI�A�EV?UK�Z�`�K�^nI�A�X�I�K�S�D/E]Z~_�A�=2G�l~=@?�KFaK*<#��KiI�A�EV?UK�Z�`�K-K��(Z�K�G�X�AFSNP8DFGJI�K-I�AFX�I�K�S2?�Z\`HK�e}DFE]Zia

¾F¾ ½ h[e4EHS�ZB¾/¾ ¼ ��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�K�X/Z\K�G~DFP�e�AF?\?~W]K���XHK�W�i�]a �\¸�K�Zi· ?�_HS2A*^ �(1J��D3�����"# 1 |�DFG �(�i¾F¾�o*Z�`HKBAFX�?�l�K�G�=@?�u�b>`HK~e�A/?�?UT�l�K�=2qF`[Z\K�WsA*d/K�GJA�q/K;_ND/?�=�Z\=YD/XgDFP�AFX&DFL,A:KiI$Z�u

AFXnDFL3A:K�I$Z�LVK�=YX�qgAFX[^C?�_NK�I�=Y��KiWn?�K�Z>D�P�e�A"Z\K�G\=2AFSVe�A/?�?�K�S2K�e&K�X[ZJ?�ajb>`H=@?�_VD[?U=YZ�=2DFX�· ?�AFI�I�K�S2K�GJA"Z\=YD/XCDFLNK�^�· ?�� � ��� $ � ��Cl~`HK�G�K �� � ��� =2?>Z\`HK-XHK�ZcK��(Z�K�G�X�AFS�P8DFGJI�KMAFI�Z�=2XHq&DFXZ�`HK-D/L,A:K�I�Z�a �A[<C»{`VA"Zc=@?�Z�`HK6I�K�X[Z�K�G�o��BSYK�� �LN<n»{`VA"Zc=@?>LVDFZUZ�D/e�K�X�Wpo��BSYK����Ii<n»{`VA"Zc=@?�Z�`HKMZ\DF_mK�X�W�o��cS2K�� �WV<n»{`VA"Zc=@?>SYK�P ZBK�X�W�o��cS2K�� �K*<n»{`VA"Zc=@?�Z�`HK6I�K�X[Z�K�G~D�P�e&A/?�?�oH�cS2K�� �

¾F¾ ½ h[e4EHS�ZB¾/¾ ¼/½ ¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�W]K���XH=YZ�=2DFXmD�P���T!Wne&D/egK�X[Z�EHe� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ³ a~¸�=YXHKiA�G~e&DFe&K�X/Z\EHemoHDFG�A:E�?UZBe&DFe&K�X/Z\EHe P8D/Gc?U`HD/GUZio(P8DFGcA&D/XHK�T!W]=2egK�X�?�=YD/X�A�Sp?�^(?UZ�K�e =@?~qF=2dFK�XQL(^�uA[<�� $ � � � a LV<�� $ � � ��a I�<�� $ 5U� �F�F< � � � a W�<�� $ 5U� �F�F< � � a Ki<�� $ � � a

¾F¾ ½ h[e4EHS�ZB¾/¾ ¼/½ ���&� ³ K�A/?U^�e&K�egD/G�^�uje&DFe&K�X/Z\EHe =@?~XHDFZcK�XHK�G�q/^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½F³ T\� ¶

��µ�a~¸�=YXHKiA�G~e&DFe&K�X/Z\EHe�=@? � � CuA[<�A _�`[^]?�=2I�A�S�h/EVA�X[Z�=YZ:^Fa LN<�W]K�_VK�X�W]K�X[Z DFX�d/K�S2D(I�=�Z:^/a I�<�A O(=2X�W�D�P�K�XHK�G\qF^/aWV<>W]K�_NK�X�WHK�X[ZcDFXme�AF?\?�a K*<�qF=2dFK�XQL(^�� $ � � P8D/G~DFXHK�TkWH=Ye&K�XV?U=2DFX�AFS�I�A/?UKi?�a

¾F¾ ½ h[e4EHS�ZB¾/¾ ¼/½ µg� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�²-�wIJ`�A�XHq/K�AFX�WQegD/e&K�X[Z�EHe IJ`�A�X�qFK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½ µFT\� ³

� ¶ a>7kP�Z�`HK-O(=2XHK�Z\=2IMK�XHK�G\qF^�DFP�AFXQD/L,A:K�I�Zc=2?~WHDFEHLHS2K�W�o]Z�`HK-S2=2XHK�AFG~egD/e&K�X[Z�EHe}IJ`�A�XHq/K�?>L(^nA4P,AFI�Z�D/G~D�P:uA[< + �(a LV<~�Ha I�<�� ���]a W�<�� � + �(a K*<��Fa

¾F¾ ½ h[e4EHS�ZB¾/¾ ½ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�W]K���XH=YZ�=2DFXmD�P�e&DFe&K�X[Z�E�e� ¹ a~¸�=YXHKiA�G~e&DFe&K�X/Z\EHemoHDFG�A:E�?UZBe&DFe&K�X/Z\EHe P8D/Gc?U`HD/GUZio]=2?cqF=2dFK�XL(^�u

A[< �� $ � � �� aLN< �� $ �� � ��aIi< �� $f5:� ���/< � � � aWV< �� $f5:� ���/< � �� aK*< �� $ � �� a

¾F¾ ½ h[e4EHS�ZB¾���¾/¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�I�DFX�?�K�G\d"A"Z�=2DFXQD�P�egD/e&K�X[Z�EHe

Page 50: Introductory Physics Problems David J. Jeffery Department of

µ ¹ v�`�AF_]Z�a ½ ¤(^]?:Z\K�e�?>D�Pj9jA�G�Z�=@I�S2K�?>AFX�WQ¸�=YX�K�A�Gc¯�DFe&K�X[Z�E�e

�*º(a~|�DFGcA&?U^]?UZ�K�e�=@?UD/S2A�Z�K�WCP8G�D/e�K��[Z\K�G\X�A�SNP8D/G\I�K�?�o]egD/e&K�X[Z�EHemuA[<C=@?~XHDFZcI�DFXV?UK�G�d/K�WpaLN<n=@?cI�DFX�?�K�G\dFKiWpaIi<n=@?~��K�G\D�aWV<n=@?~XHK�dFK�G���K�G\D�aK*<n=@?cAFSYl>A*^]?;XHK�q/A�Z�=2dFKFa

¾F¾ ½ h[e4EHS�ZB¾���¾���¾C�&���MK�A/?U^�e&K�egD/G�^�ujD/_VK�G\A�Z�=2DFXnDFP�G\D]IJOFK�Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½ �"T ½

� ¼ a~b>`HK-D/_VK�G\A�Z�=2DFXQD�PjA4G\D]IJOFK�Z�=2X�?U_�A/I�KM=@?>L�AF?�K�WDFX�uA[<�I�DFX�?�K�G\d"A"Z�=2DFXMDFPHSY=2XHK�AFG�e&DFe&K�X/Z\EHema LN<�I�DFX�?�K�G\d"A"Z�=2DFXMDFP�A�XHq/EHS2AFG�e&DFe&K�X[Z\EHema Ii<�A:K�ZP8E�K�S�_HE�?�`H=2XHq�DFX�Z\`HKwd*A/I�EHE�ea W�<�?UZ\AFG�S2=2qF`[Zx_HG\K�?\?�EHG�K/a Ki<�G�E�XHXH=2XHq�AFXf=2X[Z�K�G\X�AFSZ\G�KiAFW]e&=2SYS�a

¾F¾ ½ h[e4EHS�ZB¾��F�i¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�G�D]IJO/K�Z�Z�`HG\E�?UZ~P8DFGJI�K� ½ a~b>`HKMP8D/G\I�K�Z�`�A�Z~A/I�I�K�S2K�GJA"Z�Ki?>A4G\D]IJOFK�Z>=2XZ�`HK-d"A/I�EHEHe�D�Pj?U_�A/I�KM=@?�u

A[<�Z\`HKMP8DFGJI�KMDFP�Z�`�K-d*A/I�EHE�eaLN<CZ\`HKMP8DFGJI�KMK��(K�GUZ\K�WQL(^�Z�`HK-K9A:K�I�Z�K�WQP8EHK�S�D/XnZ\`HK-G�D]IJO/K�Z�u�Z�`�K ��� � � P8DFGJI�K/aIi<CZ\`HKMP8DFGJI�KMK��(K�GUZ\K�WQL(^�Z�`HK-K9A:K�I�Z�K�WQP8EHK�S�D/XnZ\`HK-G�D]IJO/K�Z�u�Z�`�K ��� � � � P8D/G\I�KFaWV<CZ\`HKMP8DFGJI�KMDFP�S2=Yq/`/Zc_�G�Ki?�?�EHG\KFaK*<CZ\`HK6|HD/G\I�KFa

¾F¾ ½ h[e4EHS�ZB¾��i�F¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�I�DFX�?�K�G\d"A"Z�=2DFXQD�P�egD/e&K�X[Z�EHemo�b>`�DFG��¾Ha~b>`HK4e&=Yq/`/Z:^mb>`HD/GB=@?cZ\G\AF_H_VKiW�=2X�Z�`HK4K�Z\K�G\X�A�S�d"AFI�E�EHe�D�P�qFGJA*d(=�Z:^[T�P8G�K�K-?U_�A/I�K6l~=YZ�`�XHD�Z\`H=YX�qCZ�DQ_HE�?�`

D/X�a>��E]Zc`HK-?UK�K�?~�R?Uq[A�GJWnq/SY=YZUZ\K�G\=YXHq � � ��� ��aH£BA*d(=YX�qsZJA�OFK�XQ=2X[Z�G\D]W]E�I$Z\DFG\^C_H`(^]?U=@I�?>=2Xm`H=@?>^FDFE�XHq´R=YO(=2XHq�W�A*^(?�o"`HK�G�KiA�S2=Y��K�?�Z�`�A�Z�`�K�l~=2SYSH?�D/AFG�?UZ�GJA�=2qF`[Z�Z\D��R?Uq[A�GJW-=YP:o�l~=�Z\`gA*l�K�?�DFe&K;?UZ�G\K�X�q�Z�`�o"`HK;Z\`HG\D"lc?`H=@?~`�AFe&egK�G�uA[<C^/DFX�WHK�GiaLN<QAFX[Z�=YT�^/DFX�W]K�G�aIi<QAFX(^Cl~`H=@IJ`Ql>A*^FaWV<nS2K�P ZiaK*<n=2X�Ag_�A�GJA�LNDFS2=2I�A�GJI�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾F¾ ½ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�I�K�X[Z�K�G~D�P�e�A/?�?>=2X[Z�K�q/G\A�Z�=2DFXQD�P�G�D]W�Fa ��D/E�`�A*d/K4Ax��T!W]=Ye&K�X�?U=2DFXVA�S�DFL,A:KiI$ZMD�P�S2K�X�q�Z�` �NuB=�a K/aYo�AnXHDFXHT�EHX�=�P8D/G�e�G\D]Wpa67kZ�· ?�SY=2XHKiA�GMW]K�X�?�=YZ:^�58=�a K/aYoe�AF?\?>_NK�G~EHXH=YZBS2K�XHqFZ�`V<�=@?>qF=2dFK�XQL(^

� $ � �

.

l~`HK�G�K � =2?MAmI�D/X�?:ZJA�X[Z�o 0 =2?-AFX�=2X[Z�K�q/K�G � ¾Ho�A�X�W�Z�`HK�D/G�=2qF=2X�=@?-A"Z-DFXHK&K�X�W�DFP;Z\`HK&G�D]Wpag|�=2X�WxZ�`�KI�K�X[Z�K�G~D�P�e&A/?�?�DFP�Z\`HK-G�D]Wpa

¾F¾ ½ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�I�K�X[Z�K�G~DFP�e�A/?�?�=2X/Z\K�q/G\A�Z�=2DFXD�P�I�EHLNK�]a ��D/E�`�A*dFKCI�EHLNKnl~=YZ�`�?�=2WHK�?6DFP~SYK�XHq�Z\` �Vaxb�AFOFK�DFX�KnI�D/G�XHK�G-Z�DxLVKCZ�`HKQDFG\=Yq/=YXrD�PBA�?:ZJA�X�WHAFG\W ��T �[T �I�D[D/G\WH=YX�A�Z�KM?U^]?UZ�K�ea�|�DFGcI�DFX(dFK�XH=YK�X�I�K/o]?UX(EHqgZ�`�K6I�EHLNK-=YX[Z\D&Z�`HK6AFSYSp_ND/?�=�Z\=Yd/K-I�D(DFGJW]=2X�A"Z\K�D]I�Z\A�X[ZiaA[<n�R?�?�EHe&=2XHqCW]K�XV?U=YZ:^C=@?>qF=2dFK�XL(^CZ\`HKMP8DFG\esEHS@A

�N5 � � ��[< $ � � � �

Page 51: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia ½ ¤(^]?UZ�K�e&?>DFP�9jAFGUZ\=2I�SYKi?>A�X�W¸�=2XHK�AFGc¯�DFe&K�X/Z\EHe µ]º

5,l~`HK�G\K � =@?�A6I�D/X�?:ZJA�X[ZJ<;I�AFS2I�EHS2A�Z�K~Z\`HKBS2D]I�A�Z�=2DFXCDFPNZ\`HKMI�K�X[Z\K�G;DFP�e�AF?\?�D�P�DFPpZ�`HK�I�EHLNKFa ������ �b>`�K�?UD/SYE]Z\=YD/Xw=YX(dFD/SYd/K�?4Z�G\=2_HSYK�=2X[Z�K�qFGJA"Z�=2DFXV?�o�LHE]ZnXH=@I�KmZ\G�=2_HS2K�=YX[Z\K�qFGJA"Z\=YD/X�?�o;XHDFZnAxXVAF?UZ:^�DFX�K�?�av�AFS2I�EHS@A"Z�K�Z\`HKMZ�DFZ\A�Spe�A/?�?���GJ?UZ�a

LN<Q BD"l�Z�`�A�Z�^FD/E�· d/K�I�E]Z�^FDFE�GpZ�K�K�Z�`�o"SYK�Z�· ?�qFD>P8D/G�Z\`HK;I�E�G\?�K�D�P]q/K�XHK�G\AFSY=YZ:^BAF?�es^RDFS@W�P8G�=2K�X�Ws|HGJA�X�I�K�?\I�DEV?UKiWnZ\D�?�A*^/a��R?�?�EHe&=2XHq�W]K�X�?�=YZ:^n=@?>qF=2dFK�XL(^�Z�`�KMP8DFG\esEHS@A

�N5 � � ��[< $ � �

.��� ���

5,l~`HK�G\K � =2?>AsI�DFX�?UZ\AFX[Z�A�XVW 0 o �xo]A�XVW���A�G\Kc_ND/?�=�Z\=Yd/KBD/G���K�G\D6=YX[Z\K�qFK�G\?J<�I�A�S@I�EHS@A"Z\KcZ\`HKRS2D]I�A�Z�=2DFXDFP�Z\`HK6I�K�X[Z�K�G~DFP�e�AF?\?>D�P�Z�`�K6I�EHLNKFa

¾F¾ ½ h/P8EHS2S�¾/¾/�F�F¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�?UEH_NK�G\=2eg_ND/?�K�W?�^[e&e&K�Z\G�^�v�¯³ a ��D/Et`�A*d/KQAr?�_H`HK�G\KD�PRGJAFWH=YE�? ��I�DFe&_HS2K�Z�K�SY^tI�DFX[ZJA�=2XH=YX�qxAr?U_�`HK�G\=2I�A�S>`HD/SYS2D"l D�P�G\A/W]=YEV? � �gatb>`�KI�K�X[Z�K�G�DFP�Z�`�K�`�DFS2SYD"l�=@?�SYD]I�A"Z�KiW � ��P8G\DFe�Z\`HK-I�K�X/Z\K�G>D�P�Z�`HK-?�_H`HK�G\KFa�¤(=2X�I�KRZ\`HK�`HDFS2SYD"l�=2?>I�D/e&_HSYK�Z�K�SY^I�DFX[Z\AF=YXHKiW�� � � ���Facb>`HKsWHK�X�?�=�Z:^D�PjZ\`HKs?�_H`HK�G�K6=@?BAnI�DFXV?:ZJA�X[Z �x5,K��HI�K�_]ZBDFP;I�DFE�G\?�K-=YXmZ\`HKs`�DFS2SYD"ll~`HK�G�KM=YZ\?~��K�G\D[<�a�¸�D]I�A"Z\K�Z�`HK6I�K�X[Z�K�G~D�P�e�A/?�?�a

¾F¾ ½ h/P8EHS2S�¾/¾ ³ ¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVu�I�D/X�?UK�G�d"A�Z�=2DFXnDFP�e&DFe&K�X/Z\EHe� ª�¬"¨ �V«������V¬ ��­�� P8G\AFqFe&K�X[Z�=2XHq�?�`HK�S2S

µ�a~��?�`HK�S2S~D�PBe�A/?�? � =@?�A"Z�A�I�K�G�Z\AF=YXt=YX�?UZ\AFX[Zg=@?&K��HAFI�Z�S2^�=YX±`HD/G�=2��D/X/ZJA�S���=2qF`[Z�l~=�Z\`±?�_VK�K�W � =YXtZ�`�K_ND/?�=�Z\=Yd/K��HT!W]=2G�KiI$Z�=2DFX�a;��ZcZ�`VA"ZB?\A�e&K-=YXV?:ZJA�X[Z~Z�`HK4?U`HK�SYS�K��]_HS2D(WHK�?>=2X�?:ZJA�X[Z\AFXHK�D/E�?�SY^C=2X[Z�D ³ P8GJA�q/egK�X[Z\?�uZ:l�D�P8GJA�q/egK�X[Z\?4`�A*dFKQ��K�G\D �wdFK�SYD]I�=�Z:^/ojDFXHKQqFDF=2XHq�?:Z\G\AF=Yq/`/ZgEH_�ojZ\`HKD�Z�`�K�G&?:Z\G\AF=Yq/`/Z&W]D"l~X )�Z�`HK ³ GJWP8GJA�q/egK�X[Z�opl~`H=@IJ`x`VAF?�e�AF?\? � � o3A:E�?:Z6A�Z�Z\`HK&=YXV?:ZJA�X[Z6A"P Z�K�GMK��]_HS2D/?�=YD/XxI�D/X[Z�=2X[E�K�?�=YXxZ�`�K ��WH=YG\K�I�Z�=2DFXl~=YZ�`mDFX�SY^C=YZ\?���dFK�S2D]I�=YZ:^CXHD/XH��K�G�DVaA[<C»{`VA"Zc=@?�Z�`HK���TkW]=2G\K�I$Z\=YD/XmdFK�S2D]I�=YZ:^ � � D�P�Z�`HK ³ G\WnP8GJA�qFe&K�X/Z �LN<Q£BD"l�P,AFGcW]D(K�?~=YZcqFDg=�P�=YZB?:ZJA�G�Z\?~Ag`HK�=2qF`[Z�� � AFLVD"d/KMA4�VA�Z~_HS2AF=YX�A/?�?�EHe&=YX�qgX�D&AF=YG~G\K�?�=@?:ZJA�X�I�K��Ii<#�/E�?UZ�A�P Z�K�G�Z�`HK�K��]_HS2D/?�=YD/X�oil~`�A"Z�esE�?UZ�Z\`HK�Z\D�Z\AFS �[T!W]=YG\K�I�Z�=2DFX-e&DFe&K�X/Z\EHe LVK�D�P(Z�`�K�Z:l�D~P8G\AFqFe&K�X[ZJ?Z\`�A"Zcl�K�X[Zc?UZ�GJA�=2qF`[Z~EH_�A�X�WW]D"l~X �

¾F¾ ½ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³&³ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�I�DFX�?�K�G\d"A"Z�=2DFXQD�P�e&DFe&K�X[Z�E�e�=2XmAgLND/A�Z� ª�¬"¨ �V«������V¬ ��­�� LVD[A"ZUT!²M=2XHq�Tk^FD/En?U^]?UZ�K�e

¶ a ��D/EHGcW]DFq�²M=2XHq ��Ag?U`HK/o]LHE]ZB?�DFe&K�`�D"l{Z�`�A�Zcl�A/?UX�· Z~DFL(d(=2DFE�?�LNK�P8DFG\K�Z�`HK-_�EH_H_H=2K�?-5 �J°RDF`�oHA�G\X�· Z>Z\`HK�^?�l�K�K�Z\`HK�AFGUZJ?�a �/< �w=@?;D/XQA4SYD/XHq6�NA"ZUTkLND�ZUZ\DFe&K�WQLND/A"Z-5:�i¾je =2XnS2K�XHqFZ�`QZ�DgLVKM_HG\K�I�=2?�Ki<;DFXAs_HS@AFI�=2WnS2AFOFK/a²M=2XHqMXHD"l�e4E�?\I�S2K�?�=2X&A�Z ½ ¾jO(q��w^/DFE6e4E�?:ZjXHDFZ�`�A*dFK�LNK�K�X�S2=@?:Z\K�XH=2XHqMl~`HK�X&`HK�GjqFGJA�X�W�?U=2G�K~��G\D/?\?�£RA�X�?Z\`HKM¤(Z�a,��K�G\X�A�GJW�l>AF?�LVK�=YXHqgA�=2G�KiW � �U`HK�I�DFE�S2W�`VA�EHSpA�X¤]�c´4a �&��DFE�o(AFS2?�D6D/XCZ�`�KRLND/A�Z�o(`HD"l�K�dFK�G�o[A�G\KAM_NK�Z\=�Z\K ¶ ¾jO(q��wl~`H=@IJ`se�AFOFK�?�D/_VK�XH=2XHqMZ�`HKRW]D(DFGjl~`HK�Xg^/DFEgqFK�Z�`HDFe&K>P8G\DFefl�DFG\O�oF²M=2XHqMOFK�K�XH=2XHq A:E�?:Z=2X�?�=2W]K/o�=YZ\?�D"l~X&W]K�e&DFXV?:Z\G\A�Z�=2DFX6=2X&e&A/I�G\D/?\I�D/_H=2I�I�D/X�?UK�G�d"A�Z�=2DFX6DFPVe&DFe&K�X[Z\EHema�b>`HK>LND/A�Z�=@? ¹ ¾�O[qVup=�Zi· ?e�AFWHKsD�PjZ\`�A"Z�SY=2qF`[Z�T�l�K�=2qF`[ZB?UZ�E,�rZ�`VA"ZBZ\`HK4A/?:Z\G�D/X�A�EHZ\?BA�Z�K6D/X�Z�`�K4¯�D(DFX�ac7kZ�=@?~P8D/G�K�TkA�P ZR?�^[e&e&K�Z\G�=@I�u=�a K/aYo�=�ZJ?�I�K�X[Z�K�GMD�P�e�A/?�?�=@?RK��HAFI$Z\SY^�e&=@WH?�`H=Y_V?�ag�B?\?UEHe&K4Z�`HK�G�K&=@?�XHDnP8G\=@I$Z�=2DFX�LNK�Z:l�K�K�X�Z�`HK&LND/A�ZMAFX�WZ\`HK-l�A�Z�K�G�aA[<n�RI$Z��Fo>¤]I�K�XHKm7$u�b>`HKmLVD[A"Z&=2?�A�Z�G�Ki?:Z�58D/GgK�dFK�XtLNK�I�A�S2egKiW�<$um²M=2XHq�· ?gegDFZ�=2DFXHS2K�?\?m5 Z\`�A�XHO[P8EHS2S2^]<A�Z-Z�`HK�LND"l�58LND"l~l�D"l �*< )�^FD/E�AFG�K�A�Z-Z�`HKC?UZ�K�G�XrS2=YO/K�l~=@?UK&K�XBA:D"^[=2XHq�ALHG\K�A"Z\`HK�GiaQv�A�S@I�E�S2A�Z�K&Z�`�KI�K�X[Z�K�GjD�PNe&A/?�?�DFP�Z�`�K�Z\D�ZJA�S]LND/A"Z�Tk²M=2XHqFT�^/DFEs?�^]?:Z\K�e E�?�=2XHqBZ\`HKc?UZ�K�G\X4A/?�Z�`HK>D/G�=2qF=2X4AFX�W4A/?�?�EHe&=2XHqK�dFK�G�^[Z�`�=YXHq&=@?M��T!W]=2egK�X�?�=YD/X�A�SpA�S2DFX�q4Z\`HK-S2K�XHqFZ�`D�P�Z�`HK-LND/A�Z�

LN<Q�RI$ZM�Fo]¤]I�K�XHK�7U7$u(²M=YXHq4=YXQAs?�E�WHW]K�XQA"Z�Z\A/IJO4DFP�X�A�E]Z\=2I�A�S�A�X]�]=2K�Z:^&XHK�K�WH?�?UD/e&KBS2D"d[=2XHqsAFX�Wpo]A"P Z\K�G�AL�G�=2K�P�A�X�WQ=YXVI�DFXV?UKih/E�K�X[Z�=@A�S�A/I�I�K�SYK�G\A�Z�=2DFXC_�`�AF?�KFo]LNDFEHXVWH?�Z�D"l>A�GJWC^/DFEQA�Z ¹ � ¾je��"?�G�K�S2A�Z�=2dFKRZ�DgZ�`�KLND/A�Z�uMZ\`H=2?�o�DFP�I�DFEHGJ?UK/o�?�`HDFEHS@WxLVK�, ¹ � ¾je���?R=YP�Z�`HK&_ND/?�=�Z\=Yd/KCW]=YG\K�I�Z�=2DFX�=2?-A�P ZUT�Z�DFT�P8D/G�K/a4»{`�A�Z6=2?Z\`HKMLVD[A"Zi· ?>d/K�S2D(I�=�Z:^�G\K�S@A"Z\=Yd/KcZ\D4Z\`HKMl�A�Z�K�G�X�D"l �»{`�A"Z~=@?>^FDFE�G�d/K�S2D(I�=�Z:^�G\K�S@A"Z\=Yd/KBZ\DgZ�`HKMl>A"Z�K�G�»{`VA"ZB=@?c²M=2XHq�· ?>dFK�SYD]I�=YZ:^CG\K�S@A"Z\=Yd/KRZ\D&Z�`HKsl�A�Z�K�G �m»{`�A�ZB=@?>Z�`HK-LND/A�ZUT!²M=YX�q�Tk^FDFE?U^]?UZ�K�e· ?cI�K�X[Z�K�GDFP�e�A/?�?>d/K�S2D(I�=�Z:^�G\K�S@A"Z\=Yd/K�Z�DgZ�`HK-l>A"Z\K�G �mb�AFOFK�Z�`�K6A"P ZUT�Z�DFT�P8D/G�KMW]=2G�KiI$Z\=YD/XA/?>_VD[?U=YZ�=2dFK/a

Page 52: Introductory Physics Problems David J. Jeffery Department of

µ ¼ v�`�AF_]Z�a ½ ¤(^]?:Z\K�e�?>D�Pj9jA�G�Z�=@I�S2K�?>AFX�WQ¸�=YX�K�A�Gc¯�DFe&K�X[Z�E�e

Ii<Q�RI$Zn�/o�¤HI�K�X�KC7U7�7$u�²M=2XHq�e�A�OFKi?6A�I�D/e&_HSYK�Z�K�SY^�=YX�K�S@AF?UZ�=@I�I�DFS2S2=2?�=YD/Xrl~=�Z\`�^FDFE�A�Z6Z�`HKQ?:Z\K�G\X�us=�a K/aYo?�`HKC?UZ�=@IJO]?MZ�D�^/DFErl~=YZ�`�A�W]K�K�_�o�l�AFG�e P8K�K�S2=2XHq � �%��K�S@A*^�²M=2XHq�o ��K�S@A*^ 1 � �R?�?�EHe&=YX�q�^FDFE�W]D/X�· ZAFSYS;Z�=2_�L�A/IJO[l>A�GJW�=YX[Z\D�Z�`HKW]G\=YXHO�o�l~`�A�Z4A�G\K&Z�`HKQdFK�SYD]I�=YZ�=2K�?sD�Pc^/DFE�o�²M=YX�q�o�Z�`HKnLVD[A"Z�ojAFX�WrZ�`�KLND/A�ZUT!²M=YX�q�Tk^FDFEQ?U^]?UZ�K�e I�K�X/Z\K�G~DFP�e�AF?\?>XHD"l �m�j�]_HS@A�=2X�a

¾F¾ ½ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\D(IJO/K�Z~?U_NK�KiW=YX�?�_�AFI�K¹ a~¸�D/?UZW]K�K�_�=2X{Z\`HKxd/DF=@W{D�P4K�Z�K�G�XVA�SR?�_�A/I�K�Z\`HK�G\K�=2?A�G\D]IJOFK�ZQ=YX�A�X�=2XHK�G�Z�=@A�SRP8GJA�e&KFa 7kZ�· ?mA"ZQG\K�?UZ�a¤(EVWHW]K�X�SY^g=�Z�K�XHq/=YXHKi?���G\K~K"A:K�I�Z�=2XHq-P8EHK�SVA�Z;A-I�DFXV?:ZJA�X[ZjZ�`HG\E�?UZ;?U_NK�KiW�58=�a K/aYo[A-I�D/X�?:ZJA�X[Z�G\K�S@A"Z�=2dFK>d/K�S2D(I�=�Z:^l~=YZ�`mG\K�?�_VKiI$Z~Z�DgZ\`HK-G�D]IJO/K�ZJ<�aA[<C»{`VA"Z6=@?�Z�`HK�q/K�XHK�G\AFS�P8D/G�e4EHS@AnP8D/GMZ�`HK�GJA"Z\=YDD�P>=2XH=�Z\=2AFSje�AF?\?�Z�D��X�AFS�e�AF?\? � � � � =2XxZ\K�G\e�?MD�PZ\`HK-GJA"Z�=2D&D�P���X�A�S�dFK�S2D]I�=YZ:^&Z�D&Z\`HG�EV?:ZcD/G�K��]`�A�E�?UZB?�_VK�K�W � ��� ���� � �

LN<n»{`VA"Zc=@?�Z�`HK-e�AF?\?>GJA"Z�=2D&=�P�Z�`�KM��X�A�SpG\D]IJOFK�Z~?�_NK�K�W=@?>K�h[E�AFS�Z�D&Z�`�K-K��]`�A�EV?:Zc?�_VK�K�W �Ii<n»{`VA"Zc=@?�Z�`HK-e�AF?\?>GJA"Z�=2D&=�P�Z�`�KM��X�A�SpG\D]IJOFK�Z~?�_NK�K�W=@?>K�h[E�AFS�Z�D&Z:l~=@I�K�Z�`HK-K��]`�A�E�?UZc?U_NK�KiW �

¾F¾ ½ h/P8EHS2S�¾/¾[º"¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\D]IJOFK�Z~S@A�EHXVIJ`º(a~�wG\D]IJOFK�Z�D�P�=YX�=�Z\=2AFS]e&A/?�?�� � ¾ �g��¾ � O(qM=2?jAFLVD/E]Z�Z�DMS@A�EHX�IJ`gdFK�GUZ\=2I�A�S2SY^-l~=YZ�`&I�D/X�?UZ\A�X[Z�Z�`�G�E�?UZjDFG�K��]`�AFE�?UZ?�_VK�K�W � ��� ��� � � $ �i¾F¾/¾je��"?$a��R?�?�EHe&K-A�=2G~G�Ki?U=@?:ZJA�X�I�KR=@?~XHK�qFS2=Yq/=YL�SYK/aA[<n¸�K�Zi· ?-A/?�?�EHe&KgA�ZRZ\=Ye&K���K�G\DCZ�`VA"ZMZ�`HK&G\D]IJOFK�ZM`�A/?�A:EV?:Z-K�X�DFEHq/`�Z�`�G�E�?UZMP8DFGJI�K4Z�D�I�AFX�I�K�S�qFGJA*d[=YZ:^�u=�a KFa2o�Z�`HKgZ�`�G�E�?UZMP8DFGJI�K4K�X[Z�=2G�K�SY^�G\K�_�S2A/I�K�?BZ�`�K4XHD/G�e�AFS�P8D/G\I�K4?�EH_H_NDFG�Z�=2XHqQZ�`HK&G\D(IJO/K�Z�DFX�Z\`HKg_�AFWpa»{`VA"Z�G\A�Z�KQD�PBe�AF?\?&IJ`�A�X�qFKne4E�?UZ4Z\`HKmG�D]IJOFK�Z4`�A*d/Kn=2X�Z\`H=@?gI�AF?�K�� ������ � »�G\=�Z\KmWHD"l~X�Z�`�KKih[E�A"Z\=YD/XQDFP�e&D�Z\=YD/XAFX�W?UD/SYd/KRP8D/G~e�AF?\?~IJ`�A�XHq/KRGJA"Z\KFa

LN<n»{`VA"ZcGJA"Z�KMDFP�e�AF?\?~IJ`�A�X�qFKMesE�?UZ>Z�`HK-G\D]IJOFK�Z>`VA*dFKRZ�DCAFI�I�K�SYK�G\A�Z�KMA"Z~µ nA�Z�Z\=Ye&K-��K�G\D �Ii<n»�G\=�Z\KBW]D"l~X&Z�`�KcK�h[E�A�Z�=2DFX�D�Ppe&D�Z\=YD/XCA�q[A�=2XgAFX�W�?UD/SYd/K>P8DFG�AFI�I�K�S2K�GJA"Z\=YD/X �gAF?�A-P8EHX�I$Z\=YD/XCD�P�Z\=Ye&KFa�R?�?�EHe&K&Z�`VA"Zse�AF?\?-IJ`�AFXHqFK&GJA"Z�K�=@?6AmI�D/X�?UZ\A�X[Zn5,l~`H=2IJ`r=2e&_HSY=2K�?6Z�`�A�Z-Z�`HG\E�?UZ6=2?4I�D/X�?:ZJA�X[ZJ<�AFX�W?�DFS2dFKCP8DFGsd/K�S2D]I�=YZ:^�A/?4AmP8E�X�I$Z\=YD/X�D�P~Z\=Ye&K/a ������ � »xG\=YZ�Kne�A/?�?4AF?��r5 � < $ � � � 5 � � � � � < � ol~`�K�G\K � � =@?>=YXH=YZ�=@A�S�e&A/?�?�a

WV<Q�R?�?�EHe&=2XHqrZ�`HK�qFGJA*d[=YZ:^�=@?�XHK�qFS2=Yq/=YLHS2KFo>E�?�KmZ�`�K�G�Ki?UE�S�ZCDFPM_VA�G�Z�5,I�<&Z�D�?�DFS2dFKP8DFG�Z\`HK�Z\=Ye&K � =YZZJA�O/K-Z�DQG�KiAFIJ`mK�?\I�AF_VK6d/K�S2D]I�=YZ:^x�/� � ��O(e ��?����R?UKsZ�`HK4e�AF?\?cGJA"Z�K4IJ`�A�XHq/KMP8DFEHXVW�=YX�_�A�G�Z458LN<$a ��^K�d"A�S2E�A"Z\=YXHq � AF?\?UKi?�?�=YP�q/G\A*d(=YZ:^-=2?�=YX&P,A/I$Z�XHK�qFS2=Yq/=YLHS2K��£BD"lte4E�IJ`&e&A/?�?�`VAF?�Z\`HKcG\D(IJO/K�Z�S2AFEHX�IJ`HKiW=2X�AFIJ`H=2K�d(=2XHqgK�?\I�A�_NKMdFK�SYD]I�=YZ:^��

Page 53: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p4o ¥ ? N-NI*-EG*[? >�E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H�i¾4h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=2WHK�A�S�I�DFS2S2=2?�=YD/XQW]K���XHKiW�Fa �\¸�K�Zi· ?&_�S2A*^ �]1J� D+�"����# 1 |HDFG �]��¾/¾Ho�Z�`�K�A�X�?�l�K�G4=@?�um�BXt=2X[Z�K�G\A/I$Z�=2DFXtLVK�Z:l�K�K�XtZ:l�DrD/Gge&D/G�KLVD]W]=2K�?l~`HK�G�KBZ�`HKR=YX[Z\K�GJAFI$Z\=YD/X&P8DFGJI�Ki?;A�G\KR?�Ds?UZ�G\DFXHq4A�X�WCWHEHG\A�Z�=2DFXC?�D4?�`HDFG�Z�Z\`�A"Z>DFXHS2^4Z�`HK�=YX[Z\K�GJAFI$Z\=YD/X&P8DFGJI�Ki?LNK�Z:l�K�K�X�Z�`�K4LND]W]=YKi?RAFG�Kg?U=2qFX�=��VI�A�X[Z�WHEHG�=2XHqnZ�`HKg=YX[Z\K�GJAFI$Z\=YD/X�u~D�Z\`HK�GRP8DFGJI�Ki?~Z\`�A"Z-A�G\=2?�K-P8G\DFe ?�DFEHGJI�Ki?K��[Z\K�G\X�A�S�Z�DQZ�`�K4=2X[Z�K�GJAFI�Z�=2DFX�I�A�X�LNKgXHK�q/SYKiI$Z�KiW�W]E�G�=2XHqCZ\`HKg=YX[Z�K�G\A/I$Z\=YD/X�a-°BP Z\K�XxZ�`HKg=2X/Z\K�GJAFI�Z�=2DFX�I�AFXLNK6G\K�q/AFG\WHK�WmAF?~=2X�?UZ\AFX/ZJA�XHK�DFE�?cDFXZ�`HKsZ�=2e&Ks?�I�A�S2K-D�P�Z�`�K6K�d/DFS2E]Z�=2DFXmD�P�Z\`HK4?�^]?:Z\K�e�DFPjLVD]W]=2K�?BLVK�P8DFG\KAFX�WQA�P Z�K�G~Z�`HK-=2X[Z�K�G\A/I$Z�=2DFX�a �A[<C»{`VA"Zc=@?>SY=2XHK�AFG~e&DFe&K�X[Z�E�eoV�cS2K�� �LN<n»{`VA"Zc=@?>EHXH=YP8DFG\e}I�=2GJI�EHS@A�G>e&D�Z\=YD/X�o��cS2K�� �Ii<n»{`VA"Zc=@?>_HG�D/_VK�G~e&D�Z�=2DFX�o��cS2K�� �WV<n»{`VA"Zc=@?~A&l�K�K�OCK�X�Wn=2X�¸�A/?>´jK�q/A/?�oH�BSYK�� �K*<n»{`VA"Zc=@?~A�Xm=2WHK�A�S�I�DFS2SY=@?�=YD/XQ=2Xm_H`(^(?�=@I�?�oH�cS2K�� �

¾H�i¾4h[e4EHS�ZB¾/¾/�F¾F¾4�4µn�4e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=Ye&_HEHS@?�K6W]K���X�=�Z\=YD/X�]a~�BX=2e&_HEHS@?UK ���=2?�u

A[<n?�=2eg_�SY^nZ�`HK6?�EHe DFP�Z\`HK-e&DFe&K�X[Z�E�e}I�D/e&_VD/XHK�X[Z\?>DFP�Age&DFe&K�X/Z\EHe�d/K�I�Z�DFGiaLN<QA4P8D/G\I�K�D/XAFXmDFL,A:KiI$Z>Z�=2e&K�?>Z\`HKMZ�=2e&K � � =YZBAFI$ZJ?>DFXQZ�`HK-D/L,A:K�I�Z�u

�� $ �� � � �7kP�Z�`�KMP8DFGJI�KM=2?>X�D�ZBI�D/X�?UZ\A�X[Z658l~`�=2IJ`�AFI�Z�E�AFSYS2^�Z\`HK-E�?�E�A�S�I�AF?�K�=2XmI�DFS2S2=2?�=YD/X�?�P8DFG~K��HA�e&_HS2Ki<$oHZ�`HK�X

�� $�����

���5 � <�� �

l~`�K�G\K�Z�`HKQ=YX[Z\G�K�q/A�S�=2?sD"dFK�G � � axb>`HKI�DFXVI�K�_HZsD�Pc=2e&_HEHS@?UKQ=2?sE�?UKiW�e�A�=2XHS2^xP8D/G4?UZ�G\DFXHqVo�?�`HD/GUZ�TWHEHG\A�Z�=2DFX&P8D/G\I�K�?B5,=�a KFa2o[=Ye&_HEHS@?�=Yd/KcP8DFGJI�Ki?\<�?UE�IJ`CA/?jZ\`HD/?�KcZ\`�A"Z;D]I�I�EHG�=YXnI�DFS2SY=@?�=YD/X�?;AFX�W&K��]_HS2D/?�=YD/X�?�a7kP>Z\`HKnD/XHSY^ � � � ���� � ¦&� ���� � � � � � � ¦ �� P8DFGJI�K�=@?sAFXr=Ye&_HEHS@?�=Yd/K�P8DFGJI�K/o�Z\`HK�XrP8G\DFe BK�l>Z\DFX�· ?B�"XVWnS@A*l

�� $�� ��

���5 � <�� � $�� ��

� ��� � � � $ � �� u

=�a KFa2o ��xKih/EVA�S@?;Z\`HK6IJ`�AFXHqFKM=2Xe&D/egK�X[Z�EHe}D�P�Z\`HK-DFL3A:K�I$ZiaIi<QA&?�E�WHW]K�X�W]K�?�=YG\KFaWV<CZ\`HK-DF_�_VD[?U=YZ�KMD�PjA�XK��]_HE�S2?�KFaK*<QAFXmK ��K�I$ZRE�?UKiWZ�DCW]G\=2dFK-A�X�=2e&_HEHS@?UK-K�XHqF=2XHKFa�7kPj^FDFE�G~l�AFG�_�W]G\=Yd/K�P,A�=2S2?cAFX�Wm^FD/EAFG�K-D/Xm=Ye&_HEHS@?�KAFX�W ³ ¾�o ¾/¾F¾6S2=2qF`[ZUTk^FKiA�GJ?�P8G\DFe�¿c=Yq/K�S ¼ o(Z�`HK�X=YZ�· ?>Z\=Ye&KMZ�D&q/K�ZcDFEHZ�Z\`HK6I�AFG\WQq/AFe&K�?�a

¾H�i¾4h[e4EHS�ZB¾/¾ ³ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�I�DFX�?�K�G\d"A"Z�=2DFXQD�P�egD/e&K�X[Z�EHe³ a>7!X�AnI�DFS2S2=2?�=YD/X�oHZ\`HKs=2e&_HEHS@?U=2dFK6P8DFGJI�K�?RA�G\K-=YX[Z\K�G\X�A�S�Z�DCZ\`HKs?�^]?:Z\K�e�D�P�I�D/SYS2=@W]=YX�qCDFL,A:KiI$ZJ?�u�=�a KFa2oNZ�`HK�^WHDXHDFZc?UEHe�Z�D�AgXHK�Z~P8D/G\I�KRD/XnZ\`HK6?�^(?UZ�K�ema��B?\?UEHe&=2XHq&K��(Z�K�G�XVA�S�XHK�Z~P8D/G\I�KRD/XZ�`HK-?�^(?UZ�K�e P8DFG>Z\`HK6?�`HDFG�Z

Page 54: Introductory Physics Problems David J. Jeffery Department of

¶ ¾ v�`�AF_]Z�a~�i¾}v�DFS2S2=2?�=YD/X�?

W]E�G\A�Z�=2DFXD�P�Z�`HKsI�DFS2SY=@?�=YD/XQ=@?~=2X�?U=2qFX�=��VI�A�X[ZcI�D/eg_VA�G\K�WnZ�D&Z�`�K-=YX[Z�K�G�XVA�SpP8D/G\I�K�?�o(Z�`HK�X�L[^Q cK�l>Z\DFX�· ?B��X�WS@A*l�Z\`HK�G\KM=2?~X�D&IJ`VA�XHq/K�=2XQZ�`HKMZ\D�Z\AFS�e&DFe&K�esZ�EHe}D�P�Z�`HK6?�^]?:Z\K�ema�b>`H=@?>egKiA�X�?~Z�`�A�Z�u

A[<�Z\D�ZJA�SpO(=YX�K�Z�=@IMK�X�K�G\qF^�� ��I�DFXV?UK�G�d/K�W�Z\`HG\DFEHq/`CZ�`�K6I�DFS2S2=2?�=YD/X�aLN<CZ\D�ZJA�Spe�AF?\? � �rI�DFX�?�K�G\dFKiW�Z�`�G�D/EHqF`QZ�`HK6I�DFS2SY=@?�=YD/X�aIi<CZ\D�ZJA�Spe&DFe&K�X[Z\EHe � ��I�DFXV?UK�G�d/K�W�Z\`HG\DFEHq/`nZ\`HK6I�D/SYS2=2?�=2DFX�aWV<CZ\D�ZJA�Spe&DFe&K�X[Z\EHe�=@? � � I�D/X�?�K�G\dFK�WCZ�`HG\DFE�qF`QZ�`HK6I�DFS2SY=@?U=2DFX�aK*<CZ\D�ZJA�Spe�AF?\?>=2? � � I�DFXV?UK�G�d/K�W�Z\`HG\DFEHq/`nZ\`HK6I�D/SYS2=2?�=2DFX�a

¾H�i¾4h[e4EHS�ZB¾/¾�µ[¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�DFe&_HS2K�Z�K�SY^n=YXHK�S2A/?:Z\=2IMI�DFS2SY=@?U=2DFXµ�a>7!X�A�X=@W]K�AFS�I�DFe&_HS2K�Z\K�S2^n=2XHK�S@AF?UZ�=@IMI�D/SYS2=2?�=2DFX�u

A[<�Z\D�ZJA�SpO(=YX�K�Z�=@IMK�X�K�G\qF^C=@?~I�D/X�?UK�G�d/K�WpaLN<CZ\`HK6I�D/SYS2=@W]=YX�qgD/L,A:K�I�Z\?>LNDFEHXVI�K-DB�xK�AFIJ`QD�Z\`HK�GiaIi<CZ\D�ZJA�Spe&DFe&K�X[Z\EHe�=@? � � I�D/X�?�K�G\dFK�W�aWV<CZ\`HK6I�D/SYS2=@W]=YX�qgD/L,A:K�I�Z\?~?UZ�=@IJO�Z�D/qFK�Z�`HK�G�aK*<CZ\`HK6I�D/SYS2=@W]=YX�qgD/L,A:K�I�Z\?>`�A*d/KMXHD&`�A�=2G�a

¾H�i¾4h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujL�AFSYSpLNDFE�X�I�Ki?>DB��l>A�S2S¶ a~��LVA�S2S�`H=YZ\?cA&l>A�S2S�l~=YZ�`�A�Xm=2X�I�=@W]K�X[ZRAFXHqFS2KMD�P ³ ¾��Me&K�AF?�EHG\K�WnP8G�D/e}A&XHD/G�e�AFS�Z�D&Z�`�K6l�AFSYS�a�v�D/X�?U=@W]K�GZ\`HK&XHDFG\e�A�SjAF?MA_VD/SYK/u�AFXHqFS2K�?�e&K�A/?UE�G�KiW�P8G\DFe�Z\`HK&_VD/SYK�A�G\Ks_NDFS@A�G-AFXHqFS2K�?*)pZ�`�D/?�K&AFG�D/EHX�W�Z�`HK&_NDFS2KAFG�K-A���=Ye4E]Z�`VA�S�A�X�qFS2K�?�a�b>`�K�LVA�S2S�G�K�LVD/EHX�WH?~A�Z~_VD/S2AFGcA�XHq/SYK/uA[< ³ ¾ �Q=2XtAx_HS2AFXHK �� � �� ��� � ¦ ��� � ��Z�DxZ�`�KQD/XHKWHK���XHKiW�L(^rZ\`HKm=YX�I�=2WHK�X[Zg_VA"Z�`wA�XVW�Z�`�KX�DFG\e&AFS�a

LN< ³ ¾ � oHLHE]Zc=2X�A4GJA�XVW]DFe�AF��=2esE]Z\`�A�S�WH=YG\K�I�Z�=2DFX�aIi< ¹ ¾ ��oHLHE]Zc=2X�A4GJA�XVW]DFe�AF��=2esE]Z\`�A�S�WH=YG\K�I�Z�=2DFX�aWV< ¹ ¾ �Q=2XtAx_HS2AFXHK �� � �� ��� � ¦ ��� � ��Z�DxZ�`�KQD/XHKWHK���XHKiW�L(^rZ\`HKm=YX�I�=2WHK�X[Zg_VA"Z�`wA�XVW�Z�`�K

X�DFG\e&AFS�aK*< ³ ¾ ��=2XZ�`HK-_HS@A�X�K � � ��� � L[^CZ�`HK-=2X�I�=@W]K�X/Zc_VA"Z�`�AFX�WCZ\`HK-XHD/G�e�A�S�a

¾H�i¾4h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu�=@W]K�X[Z�=@I�AFSpe�AF?\?UKi?�I�DFS2SY=@W]K¹ a~b>l�D�=2WHK�X[Z�=@I�AFS�_NDF=2X/ZRe&A/?�?�K�?cK�S@AF?UZ�=@I�A�S2S2^nI�D/SYS2=2WHK6=YX�Am��TkWH=Ye&K�XV?U=2DFX�AFS�?�K�Z�E�_�a~¯�AF?\?c��`�A/WmdFK�SYD]I�=YZ:^ �LNK�P8D/G�KgZ�`�K&I�DFS2SY=@?�=YD/XxA�XVW�d/K�S2D(I�=�Z:^���K�G\DmA"P Z�K�G�a&¯�A/?�?���· ?Md/K�S2D]I�=YZ:^�l�A/?R=2XH=YZ�=@A�S2SY^���K�G\DmA�X�W�A"P Z\K�GMZ�`�KI�DFS2SY=@?U=2DFX=YZcl�A/?�uA[< � aLN<� � aIi< , � aWV< ,B� � aK*<Q?UZ�=2S2S���K�G�DVa

¾H�i¾4h[e4EHS�ZB¾/¾[º�¾F¾4�Q� ¶ e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�G\K�S@A"Z�=2dFK�dFK�SYD]I�=�Z:^CG\EHS2Kº(a>7!X�A��T!W]=2egK�X�?�=YD/X�A�S�K�S@AF?UZ�=@IMI�D/SYS2=2?�=2DFXQZ�`HK-=2XH=YZ�=@A�S�AFX�WC�VX�A�S�G\K�S@A"Z\=Yd/KRd/K�S2D]I�=YZ�=2K�?~A�G\KMG�K�S2A�Z�KiWnL(^�u

A[< � � � ��� $ � �� � � �LN< � � � ��� $�� � � � � �Ii< � � � ��� $ ,B� � � � � �WV< � � � ��� $�5:� ���/< � � � � �K*< � � � ��� $ , � � � � �

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

Page 55: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia~��¾}v�D/SYS2=@?U=2DFX�? ¶ �

¾H�i¾4h/P8EHS2S�¾/¾H��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu��cX�W]K�G\WHDFq�A�X�WQLHEHS2S2K�Z~��E]��Fa~|�K�l XHD"l G�K�e&K�esLNK�GR�cX�W]K�G\WHDFq�oVLHE]Z�DFX�I�K6`HK6l>AF?~L�=YqCD/X�¤]A"Z\EHGJWHA*^ne&DFG\XH=2XHq�o�SYD/XHqCLNK�P8DFG\K4¤]I�D(DFLH=2K¡RD(D �{`HKF· ?j?:Z\=YS2S+��=2q�u�=YZ�· ?�Z�K�SYK�d(=2?�=YD/XsZ\`�A"Zi· ?�q/D�Z�Z�K�X&?�e&AFSYS�a�¸�K�Zi· ?jA/?�?�EHe&K~�cX�WHK�GJW]DFqMl>AF?�=YX(d(EHS2XHK�GJA�L�SYK/oAFS�Z\`HDFEHq/`Q7>I�AFX�· Z>=2XP,AFI�ZcG�K�egK�esLNK�GiaA[<n�t?UE�L]T�d(=2SYS@A�=2X ��A�GJIJ`]Tkd[=2S2S2AF=YX�?�`VA*d[=2XHqcL�=Yq/qFK�G�W]DFq[?�Z�DR=Ye&_NDFEHXVW �±Z\G�^]?�Z�DRegD"l�Z\`HK>v�AFXHX(^-v�AFXH=YX�KWHD"l~X l~=�Z\` A�`�A�=2S&D�PnL�EHSYS2K�ZJ?�u LHEHS2SYK�Z�e�A/?�? � $ ³ q�ogLHEHS2S2K�ZrSYK�XHq�Z\`���I�eogLHEHS2S2K�Z�?U_NK�KiW� $ ¹ ¾F¾�e ��?$o�LHE�SYS2K�Z&G\A�Z�KD�P~��G\K � $ ¶ ¾/¾�LHE�SYS2K�ZJ?4_NK�G&e&=2X[EHZ�KFa��R?�?�EHe&=2XHq�Z\`HKQL�EHSYS2K�ZJ? A:E�?:ZLNDFE�X�I�K6D ��Z�`�K6=Ye&e&D"d"A�LHS2K6£cK�G�D/=2I-£BDFEHXVWP8DFS2SYD"l~=2XHq�A�XmK�S@AF?UZ�=@I-I�D/SYS2=@?U=2DFX�o�l~`�A"ZB=@?>Z\`HKsA*dFK�G\AFqFKP8D/G\I�K�Z�`HK�^CK��]K�G�Z~DFX`H=2ea��R?�?�EHe&K-A��T!W]=Ye&K�X�?U=2DFXVA�Sp?UK�Z�EH_mA�XVWCZ\`�A"Z~Z\`HKMG�K�LVD/EHX�W?U_NK�KiWQ=@?�Z�`�K?\A�e&K-AF?�Z\`HK-=2X�I�=@W]K�X[ZB?�_VK�K�WmA�S2LNK�=YZc^FDFE?U`�DFEHS@WO[X�D"lzAF?>e4E�IJ`LVKiI�A�EV?UKM`HK/· ?~=2e&e&D"d*AFLHS2KFa

LN<Q BD"l ¦ � �4� � � K�?UZ�=2e�A"Z�K4Z�`�KgA*d/K�GJA�qFKMP8D/G\I�KsK��(K�GUZ\K�W�L[^mD/XHKsLHE�SYS2K�Z-DFX�=Ye&_�A/I$Z-W]EHG\=YXHqQZ�`�K=2e&_�AFI�ZCZ�=2e&K�� � =YZ\?�K�SYP:a b�D�WHDrZ�`H=@?C^/DFE±XHK�KiW � � � � A�X�W � � � �ro�A�XVWt^/DFE{A�S2G\K�AFWH^O(XHD"l � � � �raV7!X�D/G\WHK�G~Z\DnqFK�Z � � � �roV^/DFE�XHK�K�WZ�DI�D/X�?U=@W]K�GcZ�`�Ks=2eg_VAFI$Z�_HG\D(I�K�?\?�acb>`�KA/I$Z\E�A�Sj_HG\D]I�Ki?�?�=@?M=Ye&e&K�X�?�K�S2^�I�DFe&_HS2K���A�XVW�LNK�^/DFX�Wx^FD/EHG-?�I�DF_NK4Z\D�I�DFXV?U=@W]K�GM=2X�WHK�Z\AF=YS�u-?U`�D(IJOl>A*dFKi?;l~=2S2Sp_�AF?\?�Z�`HG\DFEHq/`nZ\`HKMLHEHS2SYK�ZBA�X�Wn=�Zce�A*^&P8GJA�q/egK�X[Z�ajb>`HK�G\K�P8D/G�KBZ�`H=2XHOQD�P�AgI�G\E�W]KMe&D]W]K�SZ\`�A"Z�?U`HD/EHS@WmLVK4DFGJW]K�GcDFPje&AFqFXH=YZ�EVW]K6qFD(D]Wpa>�B?\?UE�egK6Z�`HK4L�AFIJOQK�X�WmDFPjZ�`HK6L�EHSYS2K�Z�=2?BEHX�AB�NKiI$Z�KiWL(^mZ\`HK&=Ye&_�A/I$Z-D�P>A�X(^�_�A�G�Z\?RD�P�Z�`HK&LHE�SYS2K�Z6A�`�K�AFW�D�P�=�Z6A�XVW�Z�`VA"Z-DFX�I�KsZ\`HK&=Ye&_�A/I$Z-D]I�I�EHG\?RP8D/GZ\`HKnLVAFIJO�K�X�Wpo�Z\`HKn=2e&_�AFI�ZsK�d/K�X[Zs=@?sD"d/K�Giab>`H=@?4_H=2I�Z�EHG\KnI�K�G�Z\A�=2XHS2^�I�A�XHX�D�ZsLNKnG\=Yq/`[Z6=YX�WHK�Z\AF=YSLNK�I�A�E�?�K�?U`�D(IJO�l�A*d/K�?Rl~=YS2S�_HG\DF_�AFq/A�Z�K6Z\`HG\DFEHq/`�Z\`HK�LHEHS2SYK�Z6l~`HK�X�=YZ6=Ye&_�A/I$Z\?�a� cK�dFK�G�Z�`�K�S2K�?\?�o�=YPD/XHK&=Ye�AFqF=2XHK�?RZ�E�G�XH=2XHqmA�S2S�Z�`HK�I�DFe&_HS2=2I�A"Z�KiW�_�G�D]I�Ki?�?�K�?RDB��opZ\`HK�X�_H=@I$Z�E�G�K&e�A*^�LVK�e&D/G�KgDFGMS2K�?\?G\=2qF`[Z�amb>`HD/?�KCI�D/e&_HSY=@I�A�Z�KiWx_�G�D]I�Ki?�?�K�?sI�A�X�· Z6Z\D�ZJA�S2SY^�W]DFe&=2X�A"Z\K�Z�`HKnLVK�`�A*d(=YD/G6A�X�Wr=2X�A�X(^xI�AF?�KZ\`HK�^�AFG�K~S2=YO/K�S2^sZ\D6LNKRW]K�Z�K�G\e&=YX�K�W&Z\Ds?UD/e&KBW]K�q/G�K�K~L(^gIJ`�AFG\A/I$Z\K�G\=2?UZ�=@I>SYK�XHq�Z\`CA�X�WCdFK�S2D]I�=YZ:^4?\I�AFSYKi?DFP~Z�`HKQ_HG\DFLHS2K�emugZ�`HKi?UKn=YX�I�SYEVW]KCZ\`HKnLHE�SYS2K�Z&SYK�XHq�Z\`�A�XVWrdFK�S2D]I�=YZ:^Fa�b>`�=2?sG�K�_HS2A/I�=2XHq�DFPBI�DFe&_HS2K��G\K�AFSY=YZ:^CL(^nI�G�E�WHK-egD]W]K�S2?~Z�`�A�ZBI�DFX[ZJA�=2XQKi?�?�K�X[Z�=@A�S�IJ`VA�GJAFI$Z\K�G\=2?UZ�=@I�?�D�P�Z�`�K-LVK�`�A*d(=YD/G~=2?~A&_ND"l�K�GUP8E�SZ\K�IJ`HX�=2h[EHK-=2Xm_H`(^(?�=@I�?>A�X�WK�S2?�K�l~`HK�G�K/a

Ii<Q¡RGJA*l�AM?�IJ`HK�e�A"Z�=@I�_HSYDFZ�D�PNLHEHS2SYK�Z�P8D/G\I�K~AF?�ARP8EHX�I$Z\=YD/X4DFP�Z\=Ye&KcA�XVWs=2X�I�S2E�W]K~A�S2=YXHK�P8D/G�Z�`HK~A*dFK�G\AFqFKP8D/G\I�KFa

¾H�i¾4h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujqFD/A�Z\?�o]I�DFe&_HS2K�Z\K�S2^n=2XHK�S@AF?UZ�=@IMI�D/SYS�a� ª�¬"¨ �V«������V¬ ��­�� qFD/A�Z\?>¿~=@IJ`[Z�`HDFP8K�X�A�X�W¯�AFXHXHD]IJO

�]a~¿~=@IJ`[Z�`HDFP8K�XmA�X�WQ¯�A�X�XHD]IJOCA�G\KBZ:l�D4q/D/A�Z\?�l~=�Z\`Qe�AF?\?�K�?�µ/¾jO(qgA�X�W ¶ ¾jO(q�o(G\K�?�_VKiI$Z\=Yd/K�S2^Fa�b>`HK�^nIJ`VA�G\qFKKiAFIJ`�DFZ�`HK�G4`�K�AFW]T�D/X�DFX±A�=@I�^�_NDFXVW �{AFe�A���=2XHq/SY^�Z�`�K�^�?UZ\A*^�EH_HG\=2qF`[Z�o�L�E]Z�qFD/A�Z\?gA�G\KQ?�EHG\K�Tk`HD(D�P��KiWpa�/E�?UZ�LNK�P8D/G�K�=Ye&_�A/I$Z~¿~=@IJ`/Z\`HD�P8K�XQ=@?�e&D"d[=2XHqgA"ZM��¾ � ¾je��"? �w`HK/· ?�l>A*^&DFE]Z>D�P�I�DFX[Z�G\DFS ��A�X�WC¯�A�XHXHD]IJO�· ?e&D"d(=YX�q&A�Z/, ¶�� ¾jeny"?�aj°RX=Ye&_�A/I$Z~Z\`HK�^QSYD]IJOC`HD/G�XV?>SY=YZ�K�G\AFSYS2^�58=�a KFa2o�?:Z\=2IJOCZ�DFq/K�Z\`HK�G$<$aA[<C»{`VA"ZcO(=YXVWQDFP�I�DFS2SY=@?U=2DFX`�A/?>D(I�I�EHG\G\K�W �'��K-AF?>_HG\K�I�=2?�K-AF?>_ND/?\?U=2LHS2KFaLN<n»{`VA"Zj=2?�Z\`HKcI�K�X[Z�K�G�DFPVe�AF?\?�dFK�S2D]I�=YZ:^-D�PVZ�`HKc¿~=@IJ`[Z�`HDFP8K�X]T!¯�AFXHXHD]IJO6?U^]?UZ�K�e A:E�?:Z�LNK�P8D/G�K~AFX�WsA�P Z�K�G

Z\`HK6I�D/SYS2=@?U=2DFX �Ii<Q�R?�?�EHe&=2XHq�Z�`VA"ZsZ\`HKQI�D(K��CI�=2K�X[ZsDFPcO[=2XHK�Z�=@I�P8G\=2I�Z�=2DFX � � � ��LVK�Z:l�K�K�X�q/D/A�ZsA�X�Wr=@I�KQ=2?4¾ � � ³ o�l~`�A�Z=@?MZ\`HKnW]=@?U_�S2A/I�K�e&K�X/Z6DFP>Z�`HKCE�XH`�A�_�_[^�¿~=@IJ`/Z\`HD�P8K�X]T!¯�A�XHX�D(IJOx?U^]?UZ�K�e P8G�D/e Z\`HKC=2eg_VAFI$Zg?U=YZ�K&Z\Dl~`�K�G\K�=YZB?UZ�DF_V?>egD"d(=2XHq �

¾H�i¾4h/P8EHS2S�¾/¾/�]�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�Z:l�D&DFL,A:KiI$Z\?~I�DFS2SY=@W]KMK�S@AF?UZ�=@I�AFSYS2^³ a~b>l�D�D/L,A:K�I�Z\?&I�D/SYS2=2WHKQK�S2A/?:Z\=2I�A�S2SY^r=2XtAt��T!W]=Ye&K�X�?U=2DFXVA�S>?UK�Z�EH_�a�b>`�Kn��GJ?UZg`�A/?ge&A/?�? � � $ ��O(qxAFX�W=2XH=YZ�=@A�S�d/K�S2D(I�=�Z:^ � � � $ ¹ e��"?-AFX�WxZ�`HKn?�K�I�DFX�W�o�e�AF?\? � � $ ¼ O(q�A�X�W�=2XH=�Z\=2AFS�dFK�SYD]I�=�Z:^ � � � $ ³ e��"?�a»{`�A�ZBA�G\K�Z�`HKM��XVA�SpdFK�SYD]I�=�Z\=YKi? �

¾H�i¾4h/P8EHS2S�¾/¾ ³ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu>�FEH_�=�Z\K�Gc?�SY=2XHq/?�`HDFZ>K�X�I�D/EHX[Z�K�Gµ�a~ BD"l{^FDFECI�A�X�· Z-5 Z�D4qFD(D]WCA�_�_HG�D*�]=2e�A"Z�=2DFXN<�_HE�?�`nDFG�_HEHS2S�DFXn?�_�AFI�KFa ��E]Z�D/XHKRI�A�X�ZJA�O/KBAs?�l~=YX�q4A�LNDFEHZA�I�K�S2K�?UZ�=@A�S�LND]W]^Fa�b>`�=2?se&AFXHK�E�dFK�Gs=YX� R�R¤]�BK�?�KC=@?sI�AFSYS2K�W�A�?US2=YX�q/?�`HD�Z6K�X�I�D/EHX[Z�K�Gia�¤]A*^�l�KC`�A*d/K�A

Page 56: Introductory Physics Problems David J. Jeffery Department of

¶ � v�`�AF_]Z�a~�i¾}v�DFS2S2=2?�=YD/X�?

?�_�AFI�K6_HG\DFLNK-DFX/�/EH_H=YZ�K�G�· ?cD/G�LH=YZ\AFS�_�A�Z�`�D/_H_VD[?U=YZ�K6Z�D �/EH_H=YZ�K�G�· ?ce&D�Z\=YD/X�acb>`HK6_VA"Z�`�I�A�X�LNKsG\K�q[A�GJW]K�WA/?R?UZ�GJA�=2qF`[ZBS2=YX�K4D"d/K�GcZ\`HK&W]=2?UZ\AFX�I�Kg?�I�A�S2KsDFP;DFEHG�_HG\DFLHS2K�emaMb>`HKg_HG�D/LVK4e�AF?\?B`�A/? � $���¾/¾F¾jO(qCAFX�W�/EH_H=YZ�K�G�`VAF? �

�� $ � � ¼/½F¼/¼ �6�i¾�� �HO(q � ³ � ¼ �;AFGUZ\`se�AF?\?UKi?�a�b>`HK>_HG�D/LVK�dFK�SYD]I�=�Z:^ � � � � � � � $ ,-�i¾jO(e ��?

AFX�W �/EH_H=YZ�K�G�· ?�d/K�S2D]I�=YZ:^ ��� � $ � ³ � ��O[e���?$u�LND�Z\`sdFK�SYD]I�=�Z\=YKi?�AFG�K�G�K�S2A�Z�=2dFK�Z\DBZ\`HK~¤(EHX�· ?�G�Ki?:Z�P8G\AFe&KFa�b>`�K

K�X�I�D/EHX[Z�K�G>=@?�_HS2AFXHXHKiWQ?�E�IJ`CZ\`�A"ZioH=YP�A�S2S�qFD(K�?�l�K�S2S�o[Z\`HKM_HG�D/LVK-W]D(Ki?R� ¼ ¾ � ?�l~=YX�q&AFG�D/EHX�W �/EH_H=YZ�K�G658=�a K/aYoA��cT�Z\EHG�XN<$aQ¿cK�q/AFG\WH=YXHqZ\`HKCK�XVI�DFE�X/Z\K�G6A/?6Ar��T!W]=2egK�X�?�=YD/X�A�SjK�S2A/?:Z\=2I�I�DFS2SY=@?U=2DFX�l~`�A�Z6=2?6Z�`HK�D/E]Z�q/DF=2XHq_HG\DFLNK-?U_NK�KiW �� BD"lzl~`(^nW]D(Ki?~ B�R¤H��E�?�K�?~?�SY=2XHq/?�`HDFZ~?�`HDFZ>K�X�I�D/EHX[Z�K�G\?����=Yd/K�Z:l�D&G\K�AF?�DFXV?�a

¾H�i¾4h/P8EHS2S�¾/¾�µ/¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�Z�K�K�X�A�q/K�GJ?�o]?�^(ege&K�Z�G\=2I�A�S�I�D/SYS�a¶ a~b�K�K�X�A�q/K�GJ?jDFX�=@I�K��±Z\`H=YXn=2I�K �{K�AFIJ`&DFP�e&A/?�? ¶ ¾jO(q�o[?US2=@W]K~Z�D/qFK�Z�`HK�G�A�XVW�I�S2=YXHqVajb>`HK�^&A�G\K~LVDFZ�`Ce&D"d(=2XHqA�Z ³ e ��?�_HG�=2DFG�Z\D4Z\`HK-I�D/SYS2=2?�=2DFX�aj�cXDFS@WI�D]W]qFK�G>D�Pjº ¶ O(qse&D"d(=YX�qgA�Zc�je ��?�Z�`HK�XmI�DFS2SY=@W]Ki?�l~=YZ�`Z\`HK�eAFX�WZ�`HKsl~`HDFS2K6I�D/XHqFS2DFe&K�GJA"Z\K�Z�`HK�X�I�DFe&Ki?>Z�DCA�W]KiAFW�?UZ�D/_�a�»{`VA"ZB=@?>Z�`�KsA�XHq/SYK-LNK�Z:l�K�K�XmZ�`HKs=YXH=YZ�=@A�Sd/K�S2D(I�=�Z:^ndFK�I�Z�D/G\?�D�P�Z�`HKMZ:l�DgZ�K�K�X�AFqFK�GJ?�a ������ � ��W]=2AFqFGJA�e e&=2qF`[Z~`HK�S2_�a

¾H�i¾4h/P8EHS2S�¾/¾ ¶ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujLHEHS2SYK�ZBI�DFS2S2=2W]=2XHq&l~=YZ�`�_HS@A�XHO¹ a~���i¾jq-LHEHS2S2K�Z�=@?�?�`HD�Z�dFK�G�Z�=@I�AFSYS2^sE�_[l>A�GJW&A"ZB�i¾F¾/¾je��"?Ja �FEV?:Z�A�P Z�K�G���G\=YX�q-=�Z;_VAF?\?UKi?�?:Z\G\AF=Yq/`[ZjZ�`HG\DFEHq/`�A�i¾jO(q4_HS@A�X�OCG�Ki?:Z\=YX�q&A/I�G\D/?\?>AgI�DFEH_�SYKMD�P�GJA"P Z�K�G\? �wZ�`HKMG\D[DFP�`�A/?UX�· ZcLNK�K�X�A/WHW]K�WQ^FK�Z�a�b>`HK-L�EHSYS2K�ZcG\=@?UKi?Z\DCA4e�A��(=2esE�e `HK�=2qF`[Z~D�P ¶ ¾/¾je A�LND"dFKRZ�`�K-G\A�P Z�K�GJ?~A"P Z\K�G~q/DF=2XHqgZ�`HG\DFEHq/`CZ\`HK-_HS@A�XHO�a��B?\?�EHe&K-XHD�A�=2GG\K�?�=2?UZ\AFX�I�K�A�X�WnK��HAFI�ZR��TkW]=2e&K�X�?�=2DFX�AFSY=YZ:^Fa ������ � b>`HKMI�DFS2S2=2?�=YD/XCl~=YZ�`QZ�`HK�_HS@A�XHO�=@? � � fAFXCK�S@AF?UZ�=@I�aA[<C»{`VA"Z�=@?pZ\`HK�LHEHS2S2K�Z�· ?�d/K�S2D]I�=YZ:^c=Ye&e&K�WH=2A�Z�K�S2^MA"P Z�K�G�Z\`HK;I�D/SYS2=@?U=2DFX�l~=�Z\`-Z�`�K�_HS@A�XHOg58=�a K/aYo*=2ege&KiW]=2A�Z�K�SY^A�P Z�K�G~=�Zc`�A/?>K��]=YZ�K�WQZ\`HK-_HS@A�XHOH<��

LN<n»{`VA"Z�=2?gZ\`HKm_HS@A�XHO�· ?&dFK�S2D]I�=YZ:^�=Ye&e&K�WH=2A�Z�K�S2^�A�P Z�K�GgZ\`HK�I�DFS2S2=2?�=YD/Xz5,=�a KFa2o�=2e&e&K�W]=@A"Z\K�S2^�A"P Z\K�G&Z�`�KL�EHSYS2K�Zc`VAF?>K��]=YZ�KiWnZ\`HK-_HS@A�XHOH< �

Ii<Q£BD"l�`H=2qF`�W]D(Ki?�Z�`HK-_HS@A�X�OCG�=@?�KMAFLVD"d/KR=YZ�· ?~=2XH=YZ�=@A�S�_ND/?�=�Z\=YD/X �WV<mv�AFS2I�EHS@A"Z�K�Z\`HK-LHEHS2SYK�Z�· ?c?�_VK�K�Wl~`HK�Xm=YZcG�K�Z�EHG\X�?~AF_H_HG\D*�(=2e�A"Z\K�S2^4Z\D&Z�`HK-q/G�D/EHX�WnSYK�dFK�S�aK*<n»{`(^Q=2?>=YZRWHAFXHqFK�G�D/E�?�Z\D&��G\K�L�EHSYS2K�ZJ?B?UZ�GJA�=2qF`[Z>EH_m=YX[Z�D&Z\`HK6A�=2G �m|�=2GJ?:ZBA/?�?�EHe&KMXHD�A�=2G~G�Ki?U=@?:ZJA�X�I�KAFX�Ww?U`�D"l L(^t?�^[e4LVD/SY=@ImI�AFS2I�EHS2A�Z�=2DFX±l~`HK�Z\`HK�G&Z\`HK�G\K�Z�E�G�X]T�Z�DFTk��A�G�Z�`tdFK�S2D]I�=YZ:^�=@?�WHA�XHq/K�G\DFE�?gD/GX�D�Z�a� BK��(ZcAF?\?UE�egK�Z\`HK�G\KM=2?~AF=YG>G\K�?�=2?UZ\AFX�I�KMA�X�WA�G\qFE�KRl~`HK�Z�`HK�G>Z�`HKMG\K�Z\EHG�XHT�Z\D�T!�;A�G�Z�`ndFK�S2D]I�=YZ:^�=2?W�A�XHq/K�G\DFE�?�DFG~X�D�Z�a ������ � v�DFX�?�=2WHK�G�P,A�S2SY=2XHq�`�AF=YS@?UZ�DFX�K�?�a

Page 57: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 pAp �L?:;7&:;<*[?T> Q

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H�/��h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujGJAFW]=@A�XV?�=2X�A&I�=2G\I�SYK�Fa~£BD"l�e�A�X(^CGJAFW]=@A�XV?�AFG�K�Z\`HK�G\KM=YX�A&I�=2G\I�SYK �

A[< �jaLN<���jaIi< ³ �jaWV< ³/¹ ¾��"aK*< ³/¹ ¾�a

¾H�/��h[e4EHS�ZB¾/¾/�F¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�G�DFZ\A�Z�=2DFX�AFSNO(=2XHK�e�A�Z�=@IMK�h[E�A"Z\=YD/X�?�]a~b>`HK-G\D�ZJA"Z\=YD/X�A�S�O(=YX�K�e�A"Z\=2I�K�h[E�A�Z�=2DFX�?�u

A[<C`VA*dFKMXHD&G�Ki?UK�esLHS@A�XVI�KRZ�D&Z�`�K�S2=2XHK�AFG~O[=2XHK�e&A�Z�=@IMK�h[E�A�Z�=2DFX�?�aLN<QAFG�KMK��]A/I$Z\SY^�Z\`HKs?\A�e&K-AF?�Z\`HK6S2=YXHKiA�G~O(=2XHK�e�A"Z\=2IMKih[E�A"Z\=YD/X�?�o]K��HI�K�_HZ~Z�`�A�Z~Z�`HKsAFXHqFE�S2AFG�O(=2XHK�e�A�Z�=@I

Kih[E�A"Z\=YD/X�?>G�K�S2A�Z�K � ��� ��� � ��G\A�Z�`HK�G>Z�`�AFXQS2=2XHK�AFG~d*AFG�=@A�L�SYKi?�aIi<QAFG�KMK��]A/I$Z\SY^�Z\`HKs?\A�e&K-AF?�Z\`HK6S2=YXHKiA�G~O(=2XHK�e�A"Z\=2IMKih[E�A"Z\=YD/X�?�o]K��HI�K�_HZ~Z�`�A�Z~Z�`HKsAFXHqFE�S2AFG�O(=2XHK�e�A�Z�=@IKih[E�A"Z\=YD/X�?>G�K�S2A�Z�K�� ��� � �}GJA"Z\`HK�G>Z\`�A�XmA�X�qFEHS@A�G~d"A�G\=@A�LHS2K�?�a

WV<QWHDgX�D�ZBA�S2S2D"l{P8DFGBAFXHqFE�S2AFG>A/I�I�K�S2K�GJA"Z�=2DFX�aK*<n=2X�I�SYE�WHKMZ�DFGJh[EHK�Z�K�G�e�?�a

¾H�/��h[e4EHS�ZB¾/¾ ³ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujG\D�ZJA"Z�=2DFXVA�S�_HG\=YX�I�=Y_�SYKi?³ aBv�S@AF?\?U=@I�AFS�G�DFZ\A"Z\=YD/X�A�S�e&K�IJ`VA�XH=@I�?>_HG\=2X�I�=2_HS2K�?~A�G\KFu

A[<n?�K�I�DFX�W�A�G\^ _�G�=2X�I�=2_HS2K�?{W]K�G�=2dFKiW P8G\DFe Z\`HK P8EHX�W�A�e&K�X[Z\AFS�S2A*lc?±DFP�I�S@AF?\?�=2I�A�Sme&K�IJ`�AFXH=2I�?�58=�a K/aYo BK�l>Z\DFX�· ?>Z�`�G�K�K�S@A*lc?J<$a

LN<n=2X�W]K�_VK�X�W]K�X/Z�_ND/?UZ�EHS@A"Z\K�?�I�DFe&_HS2K�Z\K�S2^-EHXHG\K�S@A"Z\K�WMZ\DcZ�`�K;P8EHXVWHA�e&K�X[ZJA�S[S2A*lc?�D�P�I�S2A/?�?�=2I�A�S/egKiIJ`�A�X�=2I�?5,=�a KFa2o� BK�l>Z�D/X�· ?>Z�`HG\K�KMS@A*lc?\<�a

Ii<Q?�K�I�DFX�W�A�G\^�_HG�=2X�I�=Y_HS2K�?~WHK�G\=Yd/K�WnP8G�D/e�h[E�A�X[Z�E�e�e&K�IJ`�AFXH=@I�?�aWV<QAFSYS>q/G�D[?�?4A�_H_HG\D*�]=Ye�A�Z�=2DFX�?4W]K�G\=Yd/K�W�P8G�D/e Z�`HKQP8EHX�WHAFe&K�X[Z\AFS~S2A*lc?4D�PRI�S2A/?�?�=@I�A�S�e&K�IJ`�AFXH=@I�?m58=�a K/aYo

 BK�l>Z\DFX�· ?>Z�`�G�K�K�S@A*lc?J<$aK*<n=2X�W]K�_VK�X�W]K�X/Zio�LHE]Z4d/K�G\^�A�_�_HG�D*�]=2e�A"Z�K/o�_ND/?UZ�EHS@A"Z\K�?6I�DFe&_HS2K�Z\K�S2^xEHX�G�K�S2A�Z�K�WxZ\D�Z�`HKCP8EHX�WHAFegK�X[Z\A�SS@A*lc?>D�P�I�S@AF?\?U=@I�AFS�egKiIJ`�A�X�=2I�?-58=�a K/aYo� BK�l>Z\DFX�· ?>Z�`�G�K�K�S@A*lc?J<$a

¾H�/��h[e4EHS�ZB¾/¾�µ[¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�Z\DFGJh/E�K�W]K���XH=YZ�=2DFXµ�a~b�DFGJh[EHKM=2?�u

A[<�Z\`�A"Z~Z\`H=2XHq�5 P8D/G~S2A/IJOCD�P�A&LVK�ZUZ�K�G~l�D/G\WV<;X�K�K�WHK�WQP8DFGcAFXAFXHqFEHS@A�G � ��� ¦ �����Z\D&K��]=2?UZ�aLN<CZ\`�A"Z~Z\`H=2XHq�5 P8D/G~S2A/IJOCD�P�A&LVK�ZUZ�K�G~l�D/G\WV<�Z\`�A"ZBI�A�XmI�AFE�?UK-AFXHqFEHS@A�G �C¦&¦ � � � � � �raIi<CZ\`HK6?\A�e&K-AF?~A�X�qFEHS@A�G~AFI�I�K�SYK�G\A�Z�=2DFX�aWV<CZ\`HK6?\A�e&K-AF?~A�X�qFEHS@A�G>dFK�SYD]I�=�Z:^/aK*<QAge&=2XHDFG ��G\=�Z\=2?�`mG�D]IJOC?UZ\A�G~DFP�Z\`HK ¹ ¾�· ?�u�Z�`HKMP,AF=YG\`�A�=2G\K�Wn¯�DFXHO/K�KFa

¾H�/��h[e4EHS�ZB¾/¾ ¶ ¾F¾C� ¶ �4K�A/?U^&Z\`H=2XHO(=YXHqVu�XHD&XHK�Z~Z�DFGJh[EHKM=YXmKih/E�=YS2=YL�G�=2EHe

Page 58: Introductory Physics Problems David J. Jeffery Department of

¶ µ v�`�AF_]Z�a~�/�f¿~DFZ\A"Z\=YD/XQ7

¶ a~b>`HK�G�K/· ?~AFXQD]WHW]Tk?�`�A�_NK�WQDFL3A:K�I$Zc?�=�Z�Z�=2XHq&DFXmA4Z\A�L�SYK/aj7kZ�· ?>XHD�Z~G\D�Z\A�Z�=2XHq�)]=YZ�· ?>XHDFZ�Z\G\AFX�?�S2A�Z�=2XHq�u�=YZ�· ?�A:E�?:Z?�=�Z�Z�=2XHq�a�b>`�K � fZ�D/G\h[EHKMDFXQZ�`�=2?~D/L,A:K�I�ZBAF?>e&K�A/?UE�G�KiW�P8G\DFe}AFX(^�DFG\=Yq/=YXmA"ZcA�S2S�e4E�?:Z~LNKFuA[<C=2X]��X�=�Z\KFaLN<n��K�G\D�aIi<n=2X�I�A�S@I�EHS@A�LHS2KFaWV<Q¾ � ¶  �eQaK*<QAge&=2XHDFG ��G\=�Z\=2?�`mG�D]IJOC?UZ\A�G~DFP�Z\`HK ¹ ¾�· ?�u�Z�`HKMP,AF=YG\`�A�=2G\K�Wn¯�DFXHO/K�KFa

¾H�/��h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ �4K�A/?U^&Z\`H=2XHO(=YXHqVu;�cGJIJ`H=2e&K�W]Ki?¹ a~�BG\IJ`H=2e&K�W]Ki?R5�� ¼ º�� �]�H�i� �cv><c5 Z\`HKMW]=2?\I�D"d/K�G\K�GjDFPpZ�`HK�S2A*lwDFPpZ�`HKRSYK�dFK�G$<�?\A�=@W�?�DFe&K�Z\`H=YX�qsS2=YO/K �Uq/=Yd/Kce&KAgS2K�dFK�G~SYD/XHq&K�XHD/EHqF`�oHAsP8E�S2I�G�EHe 5,A&?�EH_H_NDFG�Z~P8DFGcAgSYK�dFK�GJ<�oHA�X�WA&_HS@AFI�K�Z\D&?UZ\AFX�Wpo�AFX�WQ7�l~=2SYS�egD"d/KFuA[<nA4��KiA"��aLN<CZ\`HK6�;AFGUZ\` �HaIi<QAg`HD/G\?�K�Z�D�W]G\=YX�Ox5,A�P Z�K�G~SYKiAFW]=2XHq&=�Z~Z\D�l�A�Z�K�GJ< �HaWV<QAge�A�XZ\D&WHG�=2XHO��HaK*<QAge&=2XHDFG ��G\=�Z\=2?�`mG�D]IJOC?UZ\A�G~DFP�Z\`HK ¹ ¾�· ?�u�Z�`HKMP,AF=YG\`�A�=2G\K�Wn¯�DFXHO/K�K���a

¾H�/��h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ��MK�A/?U^&Z\`H=2XHO(=YXHqVu�G\D�Z\A�Z�=2DFX�AFSpA�X�AFSYD/q/?º(a~b>`HK>G\=Yq/=2W]T�LND]W]^FoF?�=2XHqFS2K�T!A"�]=@?�G\D�ZJA"Z\=YD/X�A�S(A�X�AFSYD/q/?�D�PN=YX�K�G�Z�=@A�S]e�AF?\?>5 ��<$o/ BK�l>Z\DFX�· ?��"X�W4S@A*lz5 �� $ � ��]<$oe&DFe&K�X/Z\EHe 5 �� $ � �� <�o�A�X�WnZ�GJA�XV?US@A"Z\=YD/X�A�S�O(=YX�K�Z�=@IMK�X�K�G\qF^�5�²-� $ �

�� � �i<>A�G\KFo]G\K�?�_VKiI$Z�=2dFK�SY^�u

A[<CG\D�ZJA"Z\=YD/X�A�S�=YX�K�G�Z�=@A�5��(<$o�Z\`HKxG\D�ZJA"Z\=YD/X�A�SM cK�l>Z�DFX�· ?��"XVW�S@A*l 5�� $�����<$oMA�XHq/EHS2AFGQe&D/egK�X[Z�EHe5� $� ��<$oHAFX�WG�DFZ\A�Z�=2DFX�AFSNO(=2XHK�Z\=2IMK�XHK�G\qF^�5�²-� $ �

�� � ��<�a

LN<nG\D�ZJA"Z\=YD/X�A�S�=2XHK�GUZ\=2A�5�[<�o�Z\`HKsG\D�ZJA"Z\=YD/X�A�S� BK�l>Z\DFX�· ?R��X�WmS2A*l 5���$�����<�o�AFX�W�A�X�qFEHS@A�Gce&D/egK�X[Z�EHe5� $� ��<$a

Ii<CZ\`HK&G�DFZ\A�Z�=2DFX�AFS� BK�l>Z�D/X�· ?M��X�WxS2A*l�5�� $�� ��<$o�A�XHq/EHS2AFGBe&DFe&K�X/Z\EHe 5� $�����<�o�A�X�WxG\D�Z\A�Z�=2DFX�AFSO(=2XHK�Z\=2IMK�XHK�G\qF^�5�²-� $ �

�� � ��<�a

WV<ne�A/?�?R5 ��<$o/Z�`HK�?:ZJA"Z�=@Ic BK�l>Z�D/X�· ?���X�W&S2A*l�5�¾�$�¾/<�o[AFXHqFE�S2AFG�dFK�SYD]I�=YZ:^Q5 ��<$o]A�XVW&G�DFZ\A"Z\=YD/X�A�S�O[=2XHK�Z�=@IK�XHK�G\qF^x5,²-� $ �

�� � ��<�a

K*<nl~=YZ�`�DFE]ZBI�SYKiA�GcW]K���XH=YZ�=2DFX�?�a

¾H�/��h[e4EHS�ZB¾/¾ ¼ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�qFGJA*d(=�ZJA"Z�=2DFXVA�SVZ�DFGJh[EHK¼ a �\¸�K�Zi· ?>_�S2A*^ �]1J� D+�"����# 1 |HD/G �(�i¾F¾Ho[Z\`HK6A�X�?�l�K�G�=2?�uj=�ZJ?>Z�D/G\h[EHKMA�LNDFEHZ~AFX(^CDFG\=Yq/=YXI�AFXQLNK6I�AFS2I�EHS2A�Z�KiWQA/?=YP�AFSYS�Z\`HK-DFL3A:K�I$Zi· ?ce&A/?�?�l�K�G\KMSYD]I�A�Z�KiWQA�Z~Z�`HK6I�K�X[Z�K�G~D�P�e�A/?�?�a �A[<C»{`VA"Zc=@?~A�I�DFX[ZJAFI$Z>P8D/G\I�KFo]�cS2K�� �LN<n»{`VA"Zc=@?�P8G�=@I$Z\=YD/X�o��cS2K�� �Ii<n»{`VA"Zc=@?~AgZ�K�XV?U=2DFXQP8DFGJI�K/oH�cS2K�� �WV<n»{`VA"Zc=@?~A&XHDFG\e�A�SNP8DFGJI�K/oH�cS2K�� �K*<n»{`VA"Zc=@?>qFGJA*d[=YZ:^Fo]�BSYK����

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H�/��h/P8EHS2S�¾/¾F¾ ½ ¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVuje&DFe&K�X[ZcA�G\e�Fa~b>`HK-q/K�XHK�G\AFS�G�EHS2K�P8DFG>Z\DFGJh/E�K�=@?

�� $ � � �� �£BD"l�K�dFK�GioHZ\`HK�G\Ks=@?MAC?�=Ye&_HS2K4G\EHS2K6Z\`�A"ZM_HG\D"d[=@W]Ki?cA�X�A�SYZ�K�G\X�A�Z�=2dFK6l>A*^QDFP;I�AFS2I�EHS2A�Z�=2XHq�Z\`HK4e�AFqFXH=YZ�E�WHKDFP�Z\`HKMZ�D/G\h[EHK/a�b>`H=2?cG�EHS2K-=@?~_�A�G�Z�=@I�E�S2AFG�S2^�E�?�K�P8EHS�l~`�K�X�I�AFS2I�EHS2A�Z�=2XHq&Z�`�KMZ�DFGJh[EHK�P8DFG>P8D/G\I�K�?>=2SYS2E�?UZ�GJA"Z�KiWD/Xm�"TkW]=2e&K�X�?�=2DFX�AFS�W]=2AFqFGJA�e�?�a�b>`HKMe�A�q/XH=YZ�E�W]K-DFP�Z\`HKMZ�D/G\h[EHKMG\K�I�AFSYSp=@?

� $ ��?�=2X �

Page 59: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia~�F�f¿cD�Z\A�Z�=2DFX7 ¶/¶

l~`HK�G�K ��=@?MZ\`HKnA�X�qFS2K�LVK�Z:l�K�K�X�Z�`HKnG\A/W]=YEV?6A�X�WxP8D/G\I�K�dFK�I�Z�D/G\?�an¡RG\A*l�AmqFK�XHK�GJA�SjGJAFW]=2E�? � P8G\DFe AFXD/G�=2qF=2XmZ�DnAn_VD/=YX[Z�l~`HK�G\KsA&P8D/G\I�K ���=2?�A�_�_HSY=2K�W�aBb>`HK�X���X�W�AFX�DFL(d(=YD/E�?�SY^QG�K�SYK�d*AFX[ZRW]=@?U_HS@AFI�K�e&K�X[ZBD/XZ\`HKB�VqFEHG\K~Z�`VA"Z>`�AF?�e�A�qFX�=�Z\E�W]K ?�=YX ��a�b>`�=2?�W]=@?U_HS@AFI�K�e&K�X[Z>=2?�I�AFSYS2K�W�Z�`HK�e&DFe&K�X[Z�AFG�e�5�£B¿�»wT:� ³ ¾/<�a|�=2X�W]=2XHqnZ\`HKse�AFqFXH=YZ�E�WHKsD�PjZ\`HKgegD/e&K�X[Z�AFG�e DFX�AQW]=@A�qFGJA�e D�P Z\K�X�S2K�A/WH?BZ�DQ?�=2eg_�SYKgI�A�S@I�E�S2A�Z�=2DFX�P8D/GZ\`HKMZ�D/G\h[EHK/a

¾H�/��h/P8EHS2S�¾/¾F¾H�i¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj7:?:T!£c=2S2W�A4D/XQd(=2X(^[S�G�KiI�DFGJW�]a>7:?UTk£B=YS@WHA�Z�`HKmS@AFW]^(LHE�q�=@?&DFXtAxd(=YX(^(S>G�KiI�D/G\W�?�_H=2XHXH=2XHqrA"Znº ¼ G�_Hemat¤]`HK�?:ZJA�G�Z\?gA"Z&Z�`HKmI�K�X[Z�K�G�AFX�W?�=��(TkSYK�qFq/K�W]S2^ml�AFSYO]?�G\A/W]=@A�S2SY^�D/E]Z:l�AFG\W�as��Z ¹ I�e�P8G\DFe�Z\`HK�I�K�X/Z\K�Gio�7:?UTk£B=YS@WHA?UE�W�W]K�XHS2^�?�SY=@W]Ki?MDB��Z�`�KG\K�I�DFGJWpa�»{`�A�Zc=2?>Z\`HKs?UZ\A�Z�=@I�P8G�=@I$Z\=YD/XmI�D(K��CI�=2K�X[ZBLNK�Z:l�K�K�X`�K�GBAFX�WQZ�`HK6G\K�I�DFGJW �m»{`�A�ZB=@?>Z�`HKsO[=2XHK�Z�=@IP8G\=2I�Z�=2DFX�I�D(K���I�=YK�X[Z>=YP�^FDFEmI�AFXWHK�Z�K�G�e&=2XHK-=YZ�

¾H�/��h/P8EHS2S�¾/¾H��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�W]D/EHLHS2K-=YXVI�S2=YXHK/oHG\D�Z\A�Z�=2DFX�AFS�=YXHK�GUZ\=2A³ a ��D/E�`�A*d/KxA�Z�G\=2AFXHqFEHS@A�GLHS2D]IJO±l~`�=2IJ`zqF=2dFK�?Q^FD/E�Z:l�D�=2X�I�S2=2XHK�W�?US2DF_NK�?�a�¤(S2DF_NKt��=@?A�Z � � Z�DtZ�`�K`HD/G�=2��D/X[Z\A�S>A�XVWt?�SYD/_VK��xA"Z � � awb>`HKmO(=YXHK�Z�=@IQP8G�=@I$Z\=YD/X±I�D[K��CI�=2K�X[Z\?&A�G\K � � � AFX�W � � � P8DFG�?�SYD/_VKi?�AFX�Wx�HopG�Ki?U_NK�I�Z�=2dFK�S2^Fa���D/Ex`VA*dFK4AQ_HEHS2S2K�^�A"Z�Z�`�K&AF_VK���A�X�WxAn=@W]KiA�S�ope&A/?�?�S2K�?\?BG\DF_NKgI�DFXHX�K�I$Z\=YX�qnZ:l�DLHS2D]IJO]?�o(DFX�KRD/XnK�A/IJ`Q?�SYD/_VK/ajb>`HKMG�D/_VK�=2?�ZJA�E]ZcA�XVWC=@?�_VA�GJA�S2SYK�SVZ\D4KiAFIJ`?US2DF_NKFajb>`HKM?US2DF_NK&�RL�SYD]IJO�`�A/?e�AF?\? � � A�XVWZ�`HKs?�S2DF_NK4�]oVe&A/?�? � � a>b>`�K6G�D/_VK-D"d/K�G>Z\`HK6_HEHS2S2K�^mW]D(K�?cX�D�ZR?�SY=2_�A�XVWnZ\`HKs_�EHSYS2K�^`�A/?G\D�ZJA"Z�=2DFXVA�S�=2XHK�GUZ\=2A �mAFLVD/E]ZR=YZ\?�A"�]=@?BA�XVW�G\A/W]=2E�? a-b>`HK4A��]SYK6DFP�Z�`�Ks_HEHS2S2K�^m=2?BP8G\=2I�Z�=2DFXHS2K�?\?�a ��SYD]IJO��?�SY=@W]Ki?~EH_Z�`HK6?�S2DF_NKMAFX�W'��SYD]IJOQ�g?�SY=@W]K�?BW]D"l~XnZ\`HK6?�SYD/_VK/a�v�A�S2S�LVDFZ�`Z�`�K�?�K6W]=YG\K�I�Z�=2DFX�?>_ND/?�=YZ�=2dFKFa ��D/EO(XHD"l AFSYS�Z�`�KQd"A�G\=@A�LHS2K�?4K��HI�K�_]ZgZ�`HK�AFI�I�K�SYK�G\A�Z�=2DFX�D�PBZ�`HKmLHS2D]IJO(?gA�S2DFX�q�Z�`�K?�SYD/_VKmA�XVW�Z�`�KnZ\K�X�?�=YD/XP8D/G\I�K�?>=2XQZ\`HKMZ:l�D4G\K�q/=YD/X�?�D�P�Z�`HK-G\DF_NKFaA[<n¡RGJA*ltZ\`HKcP8G\K�KRLVD]W]^�W]=@A�q/G\AFe�?�P8DFG�Z�`HKRLHS2D(IJO]?�A�X�WCAFX�W&l~G\=�Z\KRW]D"l~X�Z\`HK�=2G;Kih[E�A"Z\=YD/X�?�DFP�egDFZ�=2DFX�a»{`(^I�A�X�· Z~^FD/E?�DFS2dFK�P8D/GcAFI�I�K�S2K�GJA"Z\=YD/XCXHD"l �

LN<n»{`VA"Zc=@?�Z�`HK-G\D�ZJA"Z�=2DFXVA�SpK�h[E�A�Z�=2DFXD�P�egDFZ�=2DFXQP8DFG~Z\`HKM_HEHS2SYK�^��Ii<Q BD"l ?�DFS2dFKP8D/G�Z�`HK�qFK�X�K�GJA�S~K��]_HG\K�?\?�=YD/XtDFPMA/I�I�K�SYK�G\A�Z�=2DFXt=YXwZ\K�G\e&?CD�P�Z�`HK�O(XHD"l~XV?�u�=�a KFa2o>?\A�XV?Z\K�X�?�=2DFXP8DFGJI�Ki?�a

WV<¤]_VKiI�=@A�S2=Y��KMZ�`HK-q/K�XHK�G\AFSNK��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK6I�AF?�KMl~`HK�G\K � � � $ � � � ${¾�aK*<¤]_VKiI�=@A�S2=Y��KMZ�`HK-q/K�XHK�G\AFSNK��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK6I�AF?�KMl~`HK�G\K � � $�¾ ��aP\<�¤]_VKiI�=@A�S2=Y��KMZ�`HK-q/K�XHK�G\AFSNK��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK6I�AF?�KMl~`HK�G\K � � $�¾ �MAFX�W � � $ ½ ¾���aq(<Q¤]_VKiI�=@A�S2=Y��KMZ�`HK-q/K�XHK�G\AFSNK��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK6I�AF?�KMl~`HK�G\K � � $ � � $ ½ ¾ ��a`N<¤]_VKiI�=@A�S2=Y��KMZ�`HK-q/K�XHK�G\AFSNK��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK6I�AF?�KMl~`HK�G\K � ${¾�a= <n»{`(^w=@?CZ\`HK�q/K�XHK�G\AFSBK��]_HG\K�?\?�=YD/X{l�K�WHK�G\=Yd/K�W{l~G\DFXHqrP8D/GnZ\`HKxI�AF?�K�l~`HK�X�Z�`�KxAFI�I�K�SYK�G\A�Z�=2DFXw=2?X�K�q/A�Z�=2dFK �»{`�A"ZB?�=Ye&_HS2K6W]K�e&AFG\IJ`�K�I�DFG\G�KiI$Z\?�Z\`HK-K��]_HG\K�?\?U=2DFX �

¾H�/��h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u���Z:l�D[D]Wp· ?>e�AFIJ`H=2XHK/o]G�DFZ\A"Z\=YD/X�A�S�=2XHK�G�Z�=@Aµ�a ��D/EQ`�A*d/K�AFX��Z:l�D(D]Wp· ?�e�AFIJ`�=YXHK/ujA4_�EHSYS2K�^nl~=�Z\`QZ:l�D&WHA�XHq/SY=2XHqgLHS2D(IJO]?�a ��S2D]IJO���`�AF? � � $�¾ � ¶ ¾F¾jO(qAFX�W�L�SYD]IJOz��`�AF? � � $ ¾ � ¶ ��¾jO(q�a}b>`HKr_HEHS2SYK�^�`�AF?me�A/?�? � � � $ � � ¾jO(q±AFX�WzK ��K�I$Z\=Yd/KrG\A/W]=YEV? $�¾ � ¾(º"¾jema�b>`HKMG�D/_VKM=@?~e�AF?\?US2K�?\?�aA[<n�R?�?�EHe&KCZ\`HK_HEHS2SYK�^�=@?sP8G�=@I$Z\=YD/XHSYKi?�?s=YXtG�K�q/AFG\WxZ�D�Z�`HKG\DF_NKFa�»{`�A�Zg=@?sZ�`HKAFI�I�K�S2K�GJA"Z\=YD/X�D�P~Z�`�KL�SYD]IJOn?�^]?:Z\K�e ��¤[ZJA�G�Z�=2XHqgP8G�D/e G�Ki?:Z~`HD"lzSYD/XHq�W]D(K�?~=YZ~Z\AFOFKRP8DFG~Z\`HKMLHS2D(IJO]?�Z\D�egD"d/K4��e �

LN<Q BD"l�AF?\?UEHe&KmZ\`HK�XHDFTk?�S2=Y_�I�DFX�W]=YZ�=2DFXwP8D/G�Z�`�K�G\DF_NK�A�X�W±Z\`�A"ZQZ�`HKx_HEHS2SYK�^±A��(S2K�=@?�P8G\=2I�Z�=2DFXHS2K�?\?�a��?:Z\=Ye�A�Z�KCZ\`HKnG\D�ZJA"Z\=YD/X�A�S�=2XHK�GUZ\=2A�D�P~Z�`�Kn_HEHS2S2K�^�AF?\?UE�eg=2XHq�=YZ4=@?gA�EHXH=YP8DFG\e W]=@?UO�a��BX�?Ul�K�G4Z�`�Kh[EHKi?:Z\=YD/X�?�P8G\DFe _�AFGUZ65�A/<�=2XQZ\`H=@?cI�A/?UK/a

¾H�/��h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujS2SYXHS�W]D(DFGcA�XVWCZ\DFGJh/E�K� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿~T!��µ ¶ u ¶�³ _V<

Page 60: Introductory Physics Problems David J. Jeffery Department of

¶�¹ v�`�AF_]Z�a~�/�f¿~DFZ\A"Z\=YD/XQ7

¶ a~b>`HK�?U`�=YK�S2WQW]D(DFG;DFP�Z�`�KBXHK�E]Z�G\DFX�Z\K�?UZ�P,A/I�=2SY=YZ:^�A"Z>¸�A*l~G\K�X�I�KB¸�=2dFK�G�e&DFG\KB RA"Z�=2DFXVA�SV¸�A�LNDFGJA"Z\DFG\^Q58l~`�K�G\KZ\`HK�^�W]K�?�=Yq/X�Z\`HK�LVD/esL�?J<�=@?�o�A/I�I�DFGJW]=YX�qnZ\Dm£RA�S2=2W�A*^�¢�¿~Ki?UXH=@IJO�opZ�`�K�l�D/G�S@Wp· ?Re&D[?:Z-e�AF?\?U=2dFKg`H=2XHqFKiWW]D(D/G�u6e�A/?�?-µ/µ \¾F¾F¾�O[qVopG�DFZ\A�Z�=2DFX�AFSj=YXHK�GUZ\=2A�AFLVD/E]Zs=YZ\?s`H=YX�qFKCA"�]=@? ¼ � º ���i¾��pO(q�e �Fo�W]D(DFGsl~=2W(Z\`�� � µe&K�Z\K�GJ?�aj�R?�?�EHe&=YX�q6��K�G�D-P8G\=@I$Z�=2DFX�o/l~`�A�Z�I�DFX�?UZ\AFX/Z;P8DFGJI�Kc_NK�G\_VK�X�W]=@I�EHS@A�G�Z�DsZ�`HK�W]D(DFG�A"Z;=YZ\?�DFE]Z\K�G�K�W]q/K=@?>=2?>X�K�K�WHK�WnZ�DgegD"d/KBZ\`HK-W]D(DFG ½ ¾ � =YXr��¾;? ��v�DFE�S2WQ^FD/EnDF_NK�XQZ�`�=2?~W]D(D/G�»�DFEHS@WQ^FDFEQl�AFX[Z�Z\DgD/_VK�XZ\`H=2?BW]D(DFG �

¾H�/��h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujG\D�ZJA"Z�=2DFXVA�S�K�XHK�G�q/K�Z\=2I�?�o]I�AFGcI�GJA�XHO]?�`�A"P Z¹ a~� I�AFG�I�G\AFXHO]?U`�A�P ZBG\D�Z\A�Z�=2XHqnA�Zg� ¶ ¾F¾CG�_He Z\G\AFX�?:P8K�G\?BK�XHK�G�q/^P8G�D/e}Z\`HK&I�A�G�K�X�qF=2XHK6Z\DCZ�`�K4l~`HK�K�SjA"�]S2KA�Zº*µ � ¹ O(» 5,DFG���¾/¾j`H_V<�a{»{`�A"Zi· ?gZ\`HK�A*d/K�GJA�qFKnZ�D/G\h[EHKmD�PRZ�`HK�I�G\AFXHO]?U`VA"P Z� »{`�A"Zi· ?&Z\`HK�A*dFK�G\AFqFK � ��� �� � � �� �1� ¦ �D�PpZ\`HKRI�G\AFXHO]?U`�A�P Z;DFX&Z\`HKRWHG�EHe�5,DFG;l~`VA"Z�K�dFK�G;DFX�KBI�AFSYS@?jZ\`�A"Z�Z�`H=2XHqsD/XZ\`HK6A"�]S2KRZ\`�A"Z~Z\`HK6I�GJA�X�O(?�`�A�P Z�Z\EHG�XV?\<>A/?�?�EHe&=YX�qg=YZc`�A/?>G\A/W]=YEV?~¾ � ��¾jema

¾H�/��h/P8EHS2S�¾/¾�µ[�F¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj`HDFS2SYD"l�?U_�`HK�G\KM=YXHK�GUZ\=2Aº(a~b>`HK-G\D�ZJA"Z\=YD/X�A�S�=2XHK�G�Z�=@AgD�P�A�?�DFS2=@WnEHX�=�P8D/G�e�?�_H`HK�G�K-AFLVD/E]ZBA�XmA"�]=@?�Z�`HG\DFEHq/`Q=YZ\?BI�K�X[Z\K�G~D�P�e�AF?\?>=2?

� $ �¶ � �

l~`HK�G�K � =@?>=YZ\?~e�AF?\?~A�XVW =2?>=YZ\?cG\A/W]=YEV?�aA[<C»{`VA"Zc=@?�Z�`HK-e�AF?\?>D�Pj?�_H`HK�G\KMD�P�EHXH=YP8DFG\e}W]K�X�?U=YZ:^ � �LN<n»{`VA"Z6=@?MZ�`HKnG�DFZ\A"Z\=YD/X�A�S�=2XHK�G�Z�=@AmD�P~Am?U_�`HK�G\=2I�A�S�?�`HK�S2S�DFP�D/E]Z�K�G6G\A/W]=2E�? � o�=2XHXHK�G6G\A/W]=2E�? o�AFX�WE�XH=�P8D/G�e W]K�XV?U=YZ:^ � �Ii<¤HA*^�Z�`�A�Z � $ � � a�»{`�A�Zc=2?~Z�`HK-G\D�ZJA"Z�=2DFXVA�S�=YX�K�G�Z�=@A4DFP�Z\`HK6?�`HK�S2SpZ�D��i?:Z~D/G\W]K�G~=YX�?�e�A�S2S � a

������ � �B?�=YXHq&Z\`HK-LH=2XHDFe&=@A�S�Z\`HK�D/G�K�e�A�X�WmW]G\DF_`H=2qF`HK�G>DFGJW]K�G>Z\K�G\e&?�aWV<n»{`VA"Zc=@?�Z�`HK-e�AF?\?�Z�`�K6?U`HK�SYS�Z�Dm��?UZcDFGJW]K�G>=2X � �K*<n»{`VA"Zc=@?�Z�`HK-G\D�ZJA"Z�=2DFXVA�Sp=2XHK�G�Z�=@AgD�P�A&W]= ��K�G\K�X[Z�=@A�S2SY^nZ�`H=2Xm`HDFS2S2D"l�?U`�K�S2S�D�P�e�AF?\? � A�X�WQG\A/W]=2E�? �

¾H�/��h/P8EHS2S�¾/¾�µ��i¾g� ¶ ¾ge�A"Z�`Z\`H=YX�O[=2XHqVu�?U_H=2XHXH=2XHq&EH_Z�`�K6�;A�G�Z�`� ª�¬"¨ �V«������V¬ ��­�� W]K�e&=2EHG�q/K-¡BK�eg=2EHG\qFK-¡RK�e&=YD/EHG\qFD/?

¼ a ��D/EAFG�KRZ�`HK-¡RK�e&=2EHG�q/K ��9�S@A"Z\D�· ?;e4^/Z\`H=@I�A�S�o]LHE]ZcX�D�Z>Z�K�G�G\=YL�SY^�G\K�?�_VD/X�?�=YLHS2KFo]AFGUZ\=��VI�K�G>D�P�Z�`HKMEHX�=Yd/K�GJ?UK/a£RA*d[=2XHq&A:E�?UZsI�DFXV?:Z\G�E�I�Z�KiW�Z�`�KC�;A�G�Z�`±58e�AF?\? ¶�� ½ º ����¾����pO(qDFG-?�D�)�GJAFWH=YE�?�_HG\DFLVA�LHS2^ ¹F³ º"¾jO(eC<$op^/DFEO(XHD"lz^FDFEQXHK�KiWCZ\D�qFK�Z>=YZc?U_�=YXHX�=YXHq��wDFZ�`HK�G�l~=@?�K�=YZ~l�D/EHS@W A:E�?UZB?�=�Z~Z\`HK�G\KMqFK�Z�Z�=2XHq�A�S2Sp`HD�Z~D/XQD/XHK-?U=@W]KFa��D/E���q/EHG\KFo�D �VTk`�A�XVW]K�W]S2^Fo;Z�`�A�Z ¼F¹ µ[¾F¾mZ\=Ye&Ki?gZ�`HKZ�=2e&KmD�P ½ � ½ � ¹F³ �*º/º"¾D/?\I�=2SYS@A"Z\=YD/X�?4D�PRS2=2qF`[Z�58D�P�A?�_VKiI�=Y��K�W�l>A*dFK�SYK�XHq�Z\`V<cK�e&=�Z�Z�K�WrL(^�Z\`HKCI�Ki?U=2EHegTJ� ³F³ A"Z\DFe DFEHq/`/ZMZ\D&A:EV?:ZsAFLVD/E]ZsW]D�=YZ-P8DFG6A_VK�G�=2D]WDFP�G\D�ZJA"Z�=2DFX�ac5,¸�A�Z�K�G~=YXH`VA�LH=YZ\AFX/ZJ?~D�P�Z�`�=2?~_�G�=2e&K-G�KiA�SpK�?UZ\A�Z�KMl~=2SYS�I�A�S2S�Z�`�KMZ�=2egK6Z\A�O/K�XL(^ ½ � ½ � ¹F³ �"ºFº�¾D[?�I�=YS2S2A�Z�=2DFX�?�DFP�I�K�?�=YEHe�SY=2qF`[ZBA&?UKiI�D/X�Wpa <A[<C»{`VA"Zn=@?CA�X�qFEHS@A�G�d/K�S2D(I�=�Z:^�=YX{GJAFW]=@A�XV?&_VK�Gn?UKiI�D/X�W±D�P�Z�`HK���A�G�Z�`tP8DFGC^/DFEHGCIJ`�D/?�K�Xw_VK�G�=2D]W±D�PG\D�ZJA"Z\=YD/X �

LN<¤HA*^-^FDFEsqF=2dFK;^/DFEHGJ?�K�SYPHDFXHK�^FKiA�G>58l~`H=@IJ`s^/DFEsO(XHD"lrZ\DRLNK ���6�i¾��p?�Z�D�qFD(D]W6AFI�I�EHGJAFI�^H<�Z�DM?�_H=YX4Z�`�K��A�G�Z�`4EH_sP8G\DFe�G\K�?UZ�Z�D�^FD/EHGjIJ`HD/?�K�X-�VX�A�SHAFXHqFEHS@A�G�P8G\K�h[EHK�XVI�^Fa�»{`�A�Z�=@?�Z�`�K>AFXHqFE�S2AFG�A/I�I�K�SYK�G\A�Z�=2DFX��^FDFEl~=2SYS�`VA*dFK�E�?UK6A/?�?�EHe&=2XHq4O/K�K�_ � ¦ � � � � �� �

Ii<#��E]Z�A"P Z�K�G�A~S2DFX�q>Z�`HD/EHqF`[ZUP8E�SN5,=�a KFa2o*d*A/I�AFX/Z$<�_�AFE�?UK/o�^/DFEMG\K�A�S2=2��Kj^FD/EMl~=YS2S/X�K�K�WMO(XHD"lxZ�`�K;G\D�Z\A�Z�=2DFX�AFS=2XHK�GUZ\=2AgD�P�Z�`�K6�;A�G�Z�`Q=�P�^FD/EAFG�K�Z\D&AF_H_HS2^�Z�`�K-G�=2qF`[Z>Z�D/G\h[EHK�Z�D�q/K�Z>Z�`�K-G�=2qF`[ZcAFI�I�K�S2K�GJA"Z\=YD/XCZ\=Ye&KFa BD�Zc`�A*d(=2XHq&W]=2?\I�D"d/K�G\K�W�=2X[Z�K�qFGJA"Z�=2DFX^FK�Z �{^FD/E�· S2S�qFK�Z~AFG�D/EHX�WnZ�D&=YZB?UD/egK-AFK�DFXQDFGcAFXHD�Z\`HK�G��w^/DFEWHK�I�=@W]KQDFX�A�X�K�e&_H=YG\=@I�A�S�e&K�Z�`�D(W�Z�D�W]K�Z�K�G�e&=2XHKCZ\`HKCG\D�Z\A�Z�=2DFX�AFS�=2XHK�G�Z�=@AmP8DFG\esE�S2A�a'��DFE�`�A*d/KCAE�XH=�P8D/G�e�W]K�X�?�=YZ:^�L�A�S2S~D�P�e�AF?\?Q��O[qrA�XVW�GJAFW]=2E�?&¾ � ��ema*��D/EwegKiAF?�EHG\KQG\D�ZJA"Z�=2DFXVA�S�=YXHK�GUZ\=2AxP8D/G^/DFEHGML�AFSYS�AFLVD/E]Z6A�XrA"�]=@?BZ\`HG\DFEHq/`�=YZ\?6I�K�X[Z�K�G�DFP�e�AF?\?�Z�DmLNK�5 ³ � ½F¼ �w¾ � ¾[�F< ����¾ � � O(q�e �Fu�Z�`�KE�X�I�K�GUZJA�=2X/Z:^ ��¾ � ¾/�Q?U`HD"lc?�Z\`HK�G\K�?�EHS�Z-=@?-XHDFZ6K��HAFI�Z�aC�c`�o�^/DFEr?�A*^/opZ�`HK�S@A*lc?MD�P>X�A�Z�EHG\K�58l~`H=@IJ`l�K�G\K�X�· Zc_�AFGUZcDFPj^FDFE�GcI�DFXV?:Z\G�E�I�Z�=2DFX�I�D/X[Z�GJAFI$Z$<�esE�?UZBqF=2dFK6?�=2eg_�SYKMP8D/G�e4EHS2AFKMP8DFGB?�=2eg_�SYKs?�^]?:Z\K�e�?�a

Page 61: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia~�F�f¿cD�Z\A�Z�=2DFX7 ¶ º

¤]DQl~`�A�Z�e4E�?UZRZ\`HK&K��HAFI�Z�G\D�ZJA"Z�=2DFXVA�S�=2XHK�GUZ\=2AnP8DFG\esEHS@ACLNKgP8DFG-ACE�XH=�P8D/G�e W]K�X�?�=YZ:^�?U_H`�K�G\K4A�LNDFEHZAFXA��]=2?�Z\`HG�D/EHqF`=YZ\?cI�K�X[Z�K�G~D�P�e�A/?�?�������� � b>`HK-E�XH=�ZJ?~esEV?:Z~l�DFG\OCDFE]ZcI�DFG\G�KiI$Z�S2^Fa

WV<Q�R?�?�EHe&=2XHq&Z�`HK6��A�G�Z�`Q=2?cAgEHX�=�P8D/G�e�WHK�X�?�=�Z:^?U_�`HK�G\KFo]l~`�A�Z~=2?~=YZ\?cG�DFZ\A"Z\=YD/X�A�S�=2XHK�G�Z�=@A��K*<Q£BD"l�e4E�IJ`Z�DFGJh[EHKRZ�D�^FD/EQX�K�K�WnZ�D�K��]K�G�Z�P8D/G>Z�`�A�Zc^FKiA�G �P\<»{`VA"Zc=@?�Z�`HKM��XVA�S�G\D�ZJA"Z�=2DFXVA�S�O(=YXHK�Z�=@IMK�XHK�G�q/^�D�P�Z�`HK6��A�G�Z�` �q(<n£BD"l�e4E�IJ`ml�D/G�O�`�A*d/KR^/DFEmW]DFX�KM?�_H=2XHXH=2XHq�EH_Z�`�K6�;A�G�Z�` �

¾H�/��h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\D�Z\A�Z�=2DFX�AFS�K�XHK�G�q/K�Z�=@I�?>l~=YZ�`mq/G\A*d(=YZ:^½ a ��D/E�`�A*dFK6A�q/SYD/LVK-DFPjG�DFZ\A"Z\=YD/X�A�S�=YXHK�GUZ\=2A �

�� A�X�WmGJAFWH=YE�?

�� LNK�=2XHqn?�_HEHX�L(^QACG�D/_VK-EHX(l~=2X�W]=2XHq�P8G\DFe

=YZ\?�K�h[E�A�Z�D/G�aj¤]A�=@WCG\DF_NKBq/D(K�?�DFE]Z�`HDFG\=Y��DFX[Z\AFSYS2^4P8G�D/e�Z�`HK�qFS2DFLNKRAFX�WC_�A/?�?�K�?;D"dFK�G�A6_�EHSYS2K�^�5,G�DFZ\A�Z�=2DFX�AFS=2XHK�G�Z�=@A � � � AFX�W�GJAFW]=2E�? � � <BA�X�W�WHA�XHq/SYKi?BW]D"l~X�l~=�Z\`�ACLHS2D]IJOQDFP�e�AF?\? � ��� A"ZBZ\`HKsK�X�WpaMb>`HK4A��]SYKi?DFP�Z\`HK-qFS2DFLNK-A�X�WQ_HEHS2SYK�^QAFG�KRP8G�=@I$Z\=YD/XHS2K�?\?�o]LHEHZcZ�`HK-G\DF_NKMDFXQZ�`HK-q/SYD/LVK-AFX�W_HEHS2SYK�^C=2?cXHD�T!?US2=2_�aA[<C»{`(^mW]D(K�?>Z\`HK6?�^(?UZ�K�e I�DFX�?�K�G\dFK�e&K�IJ`�AFXH=@I�A�S�K�XHK�G�q/^ ��v�DFX�?�=@W]K�GcAFSYSpZ\`HK-P8D/G\I�K�?>Z\`�A"Zce4E�?:ZR_HS2A*^AgG\DFS2KFu�qFGJA*d(=�Z:^/o(XHDFG\e�A�S�P8DFGJI�Ki?�o[Z\K�X�?�=YD/XP8DFGJI�K�?�o]A�X�Wm?UZ\A�Z�=@IBP8G\=@I$Z�=2DFX�a

LN<Q|�G�D/e�K�XHK�G�q/K�Z\=2I�?Rl~`VA"ZM=2?�Z\`HK&K��]_HG\K�?\?U=2DFX�?�_NK�K�WxD�P;Z�`HK&LHS2D]IJO�A"P Z�K�G-=�ZMP,AFSYS@?MAn`HK�=Yq/`[Z � �mP8G\DFeG\K�?UZ��b>`HKMqFS2DFLNKMAFX�W_HEHS2SYK�^nl�K�G\K�A�ZcG�Ki?:ZcA�Z�Z\=Ye&K-��K�G\D4Z\D(D�a

Ii<¤HA*^MZ�`�A�Z�Z\`HK>qFS2DFLNK�AFX�W6_HE�SYS2K�^6I�A�XsLNK�Z�G\K�A�Z�K�W4AF?�Z�`H=2X&?U_H`�K�G\=2I�A�S]?U`�K�S2S�5,e�AF?\? ����$ ¶ O[qVo*G\A/W]=YEV?

�� $�¾ � ³ eC<6A�XVW�A�E�XH=�P8D/G�e WH=2?�O{58e�AF?\? � � � $�¾ � ¶ O(q�o�GJAFW]=2E�? �� $�¾ � ��e�<�ojG�Ki?U_NK�I�Z�=2dFK�SY^/a

v�AFS2I�EHS@A"Z�K�Z\`HK�=2GcG\D�Z\A�Z�=2DFX�AFS�=YXHK�GUZ\=2A/?�aWV<¤HA*^ � � � $�¾ � �jO[q&A�XVW � � $z��emaj»{`�A�Z>=@?>Z\`HK-LHS2D(IJOQ?U_NK�KiWA�Z>Z�`HK-K�X�WD�P�Z�`HKMP,AFSYS �

¾H�/��h/P8EHS2S�¾/¾ ¹ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\D�ZJA"Z�=2DFXVA�SpA�XH`VA�G\egD/XH=@IRD[?�I�=YS2S@A"Z�D/G��¾Ha ��D/ExA�G\K6q/=Yd/K�X�AFX�G�DFZ\A�Z�=2DFX�AFS�D/?\I�=2S2S2A�Z�DFGRD�P�G\D�ZJA"Z�=2DFXVA�S�=2XHK�GUZ\=2A �QD/LVK�^(=YXHqA�X�AFXH`�AFG�e&DFX�=2I-D[?�I�=YS2S@A"Z�D/G

5��B°M<�Z�DFGJh[EHKMS2A*l� ��� 5�N< $ ,� � , � � �

l~`HK�G�K/�QA�X�W � AFG�KM_ND/?�=�Z\=Yd/K-I�DFXV?:ZJA�X[Z\?�aA[<C»{`VA"Z�=@?�Z�`HK~l�DFG\O � ���rW]D/XHK>L[^sZ�`HKc�B°{Z�D/G\h[EHK>l~`HK�XgZ�`HK~D[?�I�=YS2S2A�Z�D/Gj=2?�e&D"dFKiW6P8G\DFefZ�`HK~D/G�=2qF=2XZ\DCA�qFK�XHK�GJA�Sp_NDF=2X[Z ��� �������� � ��DFEml~=2SYS�`�A*dFK�Z\DnW]DCA�Xm=2X[Z�K�q/G\A�Z�=2DFX�a�¿~K�e&K�e4LVK�GBl~`H=@IJ`ml�A*^Z\`HKMZ�D/G\h[EHKM_NDF=2X[Z\?~A�XVWQl~`�=2IJ`l�A*^CZ�`HK-D[?�I�=YS2S2A�Z�D/G�=@?>e&D"d(=YXHqVa

LN<¤HA*^4Z\`�A"Z�Z�`�KRD[?�I�=YS2S2A�Z�D/G�LNK�P8D/G�K�A�X�WQA"P Z�K�G�=YZ~`�AF?�LNK�K�XQe&D"dFK�WCl�A/?�A�Z�G\K�?UZ�a�»{`�A"Z>l>AF?;Z�`HKMl�DFG\O� � � � W]D/XHKnL(^�Z�`�KQA�_�_HSY=2K�W�Z�DFGJh[EHK�Z\`�A"Z�I�AFE�?UKiW�Z�`HKe&D"dFK�egK�X[Z� �R?�?�EHe&KnD/XHS2^xZ\`HKQAF_H_HS2=YKiWZ\DFGJh[EHK-A�X�WnZ�`HK6�B°�Z�D/G\h[EHKMAFI�Z�a

Ii<n»{`VA"ZB=@?~Z\`HK6K��]_HG\K�?\?�=YD/XnP8D/G~Z�`HK4�B°�_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^ � ��� =YP�Z�`HKsDFG\=Yq/=YX=2?RIJ`HD/?�K�XZ\D�LVK6��K�G\D_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^ �

WV<¤HA*^�Z�`�A�ZMZ�`HK�G�K�A�G\KgXHDmXHDFX�I�DFX�?�K�G\d"A"Z\=Yd/KsZ\DFGJh/E�K�?MA�X�Wxl�Kgq/=Yd/KsZ\`HKC�B° AFXx=2XH=YZ�=@A�Sje&K�IJ`VA�XH=@I�AFSK�XHK�G\qF^nD�P Caj»{`�A"Zc=@?~=YZ\?>e&K�IJ`�AFXH=@I�A�SpK�XHK�G\qF^ � � � � �>A"ZcA�S2S�S@A"Z\K�G>Z�=2e&K�?�

K*<n»{`VA"Z�=2?�Z\`HKwe�A"�]=Ye4EHe AFXHqFEHS@A�Gr?�_VK�K�WfZ�`�A�Z�Z�`HKwD/?\I�=2S2S2A�Z�DFGrI�AFXf`�A*d/Ktq/=Yd/K�XfZ�`�A�Zr=YZ�`�A/?e&KiIJ`�A�XH=@I�AFSpK�XHK�G�q/^ �m»{`HK�G�K6WHD[Ki?>=�ZcG\K�A/IJ`CZ\`H=2?ce&A��]=Ye4EHe}AFXHqFEHS@A�G~?�_VK�K�W �

P\<»{`VA"Zs=@?MZ�`�KCe�A"�]=Ye4EHe WH=2?�_HS@AFI�K�e&K�X[Z�� ����QZ�`�A�Z-Z�`HKn�B°�I�AFXrqFK�Z-P8G\DFe Z�`HK�D/G�=2qF=2Xw58=�a K/aYo�Z�`�KAFe&_HSY=YZ�EVW]K�D�P�Z�`HKnD/?\I�=2SYS@A"Z\=YD/XV<RqF=2dFK�X�e&K�IJ`�AFXH=@I�A�SjK�XHK�G\qF^ Ca������� � ¤(D/SYd/KgP8DFG�� ���� $ ��������VG\?UZ�a

q(<C7kP � ���� =@?R?�DQ?�e�A�S2S�Z\`�A"Z�Z�`�K&��X�WmZ�K�G�e�=2X�Z\`HK&�B° _VDFZ�K�X/Z\=2AFS�K�XHK�G\qF^mK��(_�G�Ki?�?�=YD/X�=2?�XHK�qFS2=Yq/=YL�SYK/oAF_H_HG\D*�]=Ye�A"Z\K�S2^�l~`�A"Z~O(=2X�WD�PjA�XD/?\I�=2SYS@A"Z\DFG~W]D&l�KM`�A*d/K��

Page 62: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 pXn �L?:;7&:;<*[?T> Q7Q

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H�*�sh[e4EHS�ZB¾/¾H�i¾F¾4� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuje&K�IJ`�AFXH=2I�A�S�K�X�K�G\qF^nI�DFX�?�K�G\dFKiW�Fa>7!XzZ�`HK�=@W]KiA�S2=Y��K�W�D/L,A:K�I�ZUTkG�D/SYS2=2XHq�T!W]D"l~X]Tk=YXVI�S2=YXHKx?U^]?UZ�K�emo�Z�`�K�G\DFS2S2=YXHq±DFL3A:K�I$Z�=@?m_VK�GUP8KiI$Z\SY^�G\DFE�X�Wf5�AI�^[S2=2X�W]K�G&D/Gg?�_H`HK�G�K*<$ojZ\`HKQD/L,A:K�I�Z&AFX�W�=2X�I�SY=2XHKmA�G\Kn_NK�G�P8K�I$Z\SY^�G\=2qF=@Wpo;A�XVW�Z�`�K�G\KQ=@?&A�P8G\=2I�Z�=2DFX�AFS�P8D/G\I�KZ\`�A"Z�I�A�E�?�K�?�Z\`HK�G\K>Z�D-LNKcXHD6?�S2=Y_H_�=YXHqVa�5�b>`HK~P8G\=2I�Z�=2DFX�AFS]P8DFGJI�K>=@?�AFI�Z�E�AFSYS2^4A-?UZ\A�Z�=@I�P8G�=@I$Z\=YD/X�A�SHP8DFGJI�K~?U=2X�I�K=@W]K�AFSYS2^nA�Z�Z\`HK-_NDF=2X/Z~DFP�I�DFX[Z\A/I$Z�Z�`HK�G�KM=@?~XHD&G�K�S2A�Z�=2dFK�e&D�Z�=2DFXLNK�Z:l�K�K�XDFL3A:K�I$ZcAFX�Wn=2X�I�SY=2XHK6?�EHGUP,A/I�Ki?�a <¯�KiIJ`�A�X�=2I�A�S]K�X�K�G\qF^C5 Z\`HKB?�EHefDFPN_ND�Z\K�X[Z�=@A�S]K�XHK�G\qF^4A�X�W4Z�GJA�XV?US@A"Z\=YD/X�A�S]A�XVW4G\D�ZJA"Z\=YD/X�A�S(O(=YX�K�Z�=@I>K�X�K�G\qF^H<=@?BI�DFX�?�K�G\dFKiWpa~�cX�W�^FK�ZBZ�`HK�G�K6=@?�A&P8G�=@I$Z\=YD/X�A�S�P8DFGJI�K-=@?RWHDF=2XHqCl�DFG\OnDFXmZ\`HKsD/L,A:K�I�Z�a~»{`(^�W]D(K�?�X�· ZBZ�`�KP8G\=2I�Z�=2DFX�AFS�P8DFGJI�K-I�AFE�?�K�S2D/?\?>D�P�e&K�IJ`�AFXH=2I�A�SpK�XHK�G\qF^&Z\D�`HK�A�Z>K�XHK�G\qF^x58=�a K/aYo�WH=2?\?U=2_�A�Z�=2DFXmAF?>=YZc=2?~I�A�S2SYKiW�<��A[<nb>`�K�G\K�=@?~XHK�dFK�G>AFX(^�P8G�=@I$Z\=YD/X�A�Sp`�K�A"Z\=YX�qgl~=YZ�`mG\DFEHXVWQD/L,A:K�I�Z\?�aLN<Qb>`�K�P8G�=@I$Z\=YD/X�A�S�P8D/G\I�KCW]D(K�?-X�D�XHK�Zsl�DFG\O�aQ��DF=2XHq�W]D"l~X�Z\`HKC=2X�I�S2=YX�KFo�Z�`HK�P8G\=@I$Z�=2DFX�P8D/G\I�K�58l~`H=@IJ`

_NDF=2X[Z\?BEH_H`H=2SYS <cWHD[Ki?cXHK�q/A�Z�=2dFK-l�DFG\OCSYD"l�K�G\=2XHqgZ�`HK4DFL,A:KiI$Z\?~Z�GJA�X�?�S2A�Z�=2DFX�AFS�O(=YX�K�Z�=@I-K�XHK�G\qF^�58l~`H=@IJ`LNK�=2XHq =2X�I�G�KiAF?�K�W L(^ q/G\A*d(=YZ\A"Z\=YD/X�A�S�_ND�Z\K�X[Z�=@A�SQK�XHK�G�q/^H<$oCLHEHZt_ND/?�=�Z\=Yd/K�l�D/G�O Z�D =2X�I�G\K�A/?UK{=YZ\?G\D�ZJA"Z\=YD/X�A�S�O[=2XHK�Z�=@InK�XHK�G\qF^/axb>`HKnP8G�=@I$Z\=YD/X�l�DFG\O�I�DFX[Z�G\=YL�E]Z�=2DFX�?4I�AFX�I�K�S�A/?4AxI�A�S@I�E�S2A�Z�=2DFX�l�DFEHS@W?�`HD"l-ac��DF=2XHqCE�_�Z�`HK4=YXVI�S2=YXHK/o�Z\`HK-P8G\=2I�Z�=2DFX�AFS�P8D/G\I�K6=2?R?:Z\=YS2S�EH_H`H=2SYS�oNLHE]ZRX�D"l I�DFX(dFK�GUZJ?~G\D�Z\A�Z�=2DFX�AFSO(=2XHK�Z\=2InK�XHK�G�q/^x=2X[Z�D�Z�GJA�X�?�S2A�Z�=2DFX�AFS�O(=YX�K�Z�=@ICK�XHK�G\qF^w58l~`�=2IJ`�=@?gW]=2?\A�_�_VKiA�G\=YXHq�=YX[Z�DxqFGJA*d(=�ZJA"Z�=2DFXVA�S_ND�Z\K�X[Z�=@A�SVK�XHK�G�q/^H<$a��cq/AF=YX&Z\`HK~P8G\=2I�Z�=2DFX�l�DFG\O4I�DFX[Z�G\=YL�E]Z�=2DFX�?;I�A�XCI�A�X�I�K�SHD/E]Z�aj|�G�=@I$Z\=YD/XCW]=2?\?�=Y_�A�Z�Ki?K�XHK�G\qF^sL[^sZ�EHG\XH=2XHq-=YZ;=YX[Z\D-G\AFX�W]DFe e&=2I�G�D[?�I�DF_H=@I;O(=2XHK�Z\=2IBA�X�Wg_ND�Z�K�X[Z�=@A�SHK�XHK�G\qF^/a�b>`HK~=@W]KiA�S�?UZ\A�Z�=@IP8G\=@I$Z�=2DFXnP8DFGJI�K�W]D(K�?�XHD�Z~W]D4Z�`H=@?�oHA�X�WQ?UDgW]D(K�?�XHD�Z~W]=@?�?�=2_�A"Z\KBK�X�K�G\qF^Fa;°BP�I�DFEHGJ?�KFo[=YXQG�KiA�S2=�Z:^gZ�`�K�G\K=@?jA�S2l>A*^(?�?�DFe&K~?US2=Y_�_H=YX�qMAFX�Wg?UD/egK�XHD/X]T�K�S2A/?:Z\=2I�W]K�P8DFG\e&A�Z�=2DFX4D�PNZ�`HK>LND(WH=YKi?�oFAFX�Wg?UD-?�DFe&K�K�XHK�G\qF^q/K�ZJ?~W]=2?\?�=Y_�A�Z�KiWpa�b>`H=@?~?US2=Y_�_H=YX�qCA�X�WW]K�P8D/G�e�A�Z�=2DFXe&A*^nXHD�ZcLNK-DFL(d(=YD/E�?�Z�DgZ�`�K-K�^FK/a

Ii<Q�RI$Z\E�A�S2SY^�`�K�A"ZgK�XHK�G�q/^x=@?4LVK�=YXHqxZ�E�G�XHKiW�=2X/Z\Dxe�A/I�G\D/?\I�DF_�=2I&O(=2XHK�Z\=2InK�XHK�G�q/^�L(^�P8G\=2I�Z�=2DFX�=2X�Z\`H=2?I�AF?�Ksl~=YZ�`HD/E]ZRG\K"A:KiI$Z\=YD/X�D�P;AFX[^m`HKiA"Z�K�XHK�G�q/^nZ\DQACS2D"l�K�GcZ\K�e&_NK�GJA"Z�E�G�KsZ�`HK�G�e�A�S�G\K�?�K�G\dFDF=2Giacb>`H=2?d(=2DFS@A"Z\K�?�Z�`HKs��X�WCS@A*l�DFP�Z\`HK�G\e&D(WH^[XVA�e&=2I�?�o(LHEHZ~Z�`�A�Z~WHD[Ki?UX�· Zce�A"Z�Z�K�G�=2X�Ase&KiIJ`�A�XH=@I�?>_�G�D/LHSYK�ema

WV<Qb>`�K�P8G\=2I�Z�=2DFX�AFSBP8D/G\I�K ¦&� ��� � ArZ\DFGJh/E�K�A�X�W{P8DFGJI�K�?CZ�`�A�ZmI�A�E�?�K�Z\DFGJh/E�K�?�� � �� I�A�E�?�KWH=2?\?U=2_�A�Z�=2DFX�a

K*<Qb>`�KmP8G�=@I$Z\=YD/X�A�S>P8D/G\I�K�� � � � � ¦&� ��� AxZ\DFGJh/E�KmAFX�WtP8DFGJI�Ki?sZ\`�A"Z�� � � � I�A�E�?�KZ\DFGJh[EHK�? � � ��}I�A�E�?�K-W]=@?�?�=Y_VA"Z�=2DFX�a

¾H�*�sh[e4EHS�ZB¾/¾/�F¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu�G\DFS2SY=2XHqgegDFZ�=2DFXD"dFK�G�ZJA�LHS2K�]a~�{G\DFS2S2K�GB5,=�a KFa2o[A-?�_H`HK�G�K~D/G;I�^(S2=YXVW]K�G$<�XHK�K�WH?�P8G\=@I$Z�=2DFX&Z\D6K�XHP8DFGJI�K>Z�`�KcXHD�T!?�SY=2_�I�DFXVW]=�Z\=YD/X�a ��E]Z;=YZ�W]D(K�?�X�· ZXHK�K�W�P8G�=@I$Z\=YD/X�Z�DOFK�K�_�G\DFS2SY=2XHqA"Z�I�DFX�?UZ\AFX[Z�?�_VK�K�W�A/?B=YZMG�D/SYS@?RAFSYD/XHqnAQSYK�dFK�S�?�EHG�P,AFI�K/a ��D/E�O(XHD"l Z\`H=2?5,=�P�P8DFGcX�DgDFZ�`HK�G~G�KiAF?�DFXV<;LNK�I�AFE�?�K�=YP�=�ZcG\DFS2S2?>D ��Z�`�KMZ\A�L�SYK/o]=�ZiuA[<CO/K�K�_�?~?U_�=YXHX�=YXHqVaLN<Q?UZ�D/_�?~?�_H=YX�XH=YX�q�aIi<nq/D(K�?>=2X/Z\D�A4_VA�GJA�LNDFS2=2IRZ�GJA A:KiI$Z\DFG\^FaWV<nq/D(K�?>=2X/Z\D�Ag?UZ�GJA�=2qF`[Z~S2=YXHKMZ\G\ABA:K�I�Z�DFG\^FaK*<QWHG�D/_�?~?:Z\G\AF=Yq/`[Z>W]D"l~X�a

¾H�*�sh[e4EHS�ZB¾/¾ ³ ¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u�G\D�ZJA"Z\=YD/X�A�Sp cK�l>Z�D/X�· ?c��X�WS2A*l�=YXm_HGJAFI�Z�=@I�K³ a~b>`HK�G�KM=@?cAgXHK�Z~Z\DFGJh[EHKMD�P ³  �e D/XmAFXQD/L,A:K�I�ZBA�LNDFE]ZcA&_�AFGUZ\=2I�EHS@A�G~A"�]=@?>D�P�Z�`HK-D/L,A:K�I�Z�a�b>`HKMDFL3A:K�I$Zi· ?G\D�ZJA"Z�=2DFXVA�S�=YX�K�G�Z�=@AsP8D/G>Z�`H=@?cA��(=@?>=@?M��¾���O[q;e �Faj»{`�A"Zc=@?>Z\`HK6A�XHq/EHS@A�G~AFI�I�K�S2K�GJA"Z\=YD/X �

Page 63: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~�*� ¿~DFZ\A"Z\=YD/XQ7�7 ¶F½

A[< � $ ³ ����¾���G\A/W~? � �"aLN< � $�5U� � ³ < �x�i¾���GJAFW~? � �"aIi< � $�5U� � ³ < �x�i¾ � ��G\A/W~? � �"aWV< � $ ³ ����¾ � ��GJAFW~? � �"aK*< � $ �i¾ � ��GJAFW~? � ��a

¾H�*�sh[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujd/K�I$Z\DFG~AFW�W]=�Z\=YD/Xµ�a~�BXHqFEHS@A�G>e&DFe&K�X/Z\EHe A�XVW�Z�D/G\h[EHKMA�G\KRA/I$Z\E�A�S2SY^�d/K�I�Z�DFGJ?�A�SYZ�`HD/EHqF`Q=YXnZ�`H=@?~I�S@AF?\?�l�K�E�?�E�A�S2SY^�W]KiA�S�DFX�SY^l~=YZ�`xZ�`HK�=YG �FT!I�DFe&_NDFXHK�X[Z\?�l~`H=@IJ`�AFG�Kg?�I�A�S@A�GJ?�asb>`�K&WH=YG\K�I�Z�=2DFX�D�P;Z\`HK�?�K&dFKiI$Z�D/G\?�I�AFXxLNK�W]K�Z\K�G\e&=YXHKiWP8G\DFe Z\`HK�=2GBW]K���XH=YZ�=2DFX�?B?UEH_�_HSYK�e&K�X[Z�KiWQl~`�K�XXHK�I�K�?\?�AFG�^�L(^nA&G\=Yq/`[ZUTk`�A�X�WnG�E�SYK/aA[<C´jKiI$Z\DFGJ?4A/WHW�S2=YO/KQd/K�I�Z�DFGJ?�arb>`�=2?&I�AFX�LNKWHDFXHKqFK�DFe&K�Z\G�=@I�AFSYS2^rDFGgE�?U=2XHqrI�D/eg_NDFX�K�X[Z\?4=YXw?�DFe&KI�D(DFGJW]=YXVA"Z�K-?�^]?:Z\K�ema

LN<n´jKiI$Z\DFGJ?~AFWHW A:E�?UZBSY=2OFK-?\I�AFS2AFG\?�aIi<n´jKiI$Z\DFGJ?~I�A�X�XHD�Z~LNK6AFWHW]KiWmA"ZcA�S2S�a�b>`�KMI�DFX�I�K�_]ZcDFP�A/WHW]=2XHq&dFK�I�Z�D/G\?�=@?~EHX�W]K���XHKiWpaWV<n´jKiI$Z\DFGJ?~AFWHW A:E�?UZBSY=2OFK-?\I�AFS2AFG\? � ��� � ��� ��aK*<n´jKiI$Z\DFGJ?~AFWHW A:E�?UZBSY=2OFK-?\I�AFS2AFG\? � ��� ��� sa

¾H�*�sh[e4EHS�ZB¾/¾ ¶ ¾F¾4�Q�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�ujI�D/X�?�K�G\d*A�Z�=2DFXQD�P�AFXHq�aje&D/egK�X[Z�EHe¶ a ��D/ExA�G\K&²-A"Z�`�K�G\=YX�An»{=�Z�ZC58DFG-¡RDFG\D�Z\`[^�£RA�e&=YS2S�o�²-A�G\K�X�¯�A�qFX(E�?�DFX�oND/GRK�dFK�X �>A�GJA�L�AFG\An�cXHX�¤]I�DFZUZ$<A�Z-Z�`HK�»{=2X[Z�K�G&°RSY^(e&_H=@I�?�aC�~P Z�K�GsK��(KiI�E]Z\=YX�qmA�NA*l~SYKi?�?-h[E�A/W�P8D/SYS2D"l�KiW�L(^�AQ_�`[^]?�=2I�A�S2SY^�=Ye&_ND/?\?U=2LHS2K`HD/G�=2��D/X[Z\A�S�S2K�A�_�op^FDFE�Z�DFGJh[EHKg^FDFE�G\?�K�SYPB58E�?�=2XHqm`HK�AFS �{Z�D(K��*<�=2X/Z\D�AQ?�_H=2X�a ��DFExXHD"lfW]KiI�=@W]KgZ�Dm?U_NK�KiWEH_{^/DFEHG�?�_H=2X 58=2X�I�G\K�A/?UKm^FD/EHG ��<$az¿~K�e&K�e4LVK�G�=2XHqrZ\`�A"ZCl~=YZ�`HD/E]ZQArXHK�ZCK��(Z�K�G�XVA�S~Z\DFGJh/E�KFo>A�XHq/EHS2AFGe&DFe&K�X/Z\EHe 5�� $ ����<c=2?�I�D/X�?UK�G�d/K�W�AFX�W�AF?\?�EHe&=YXHqCZ�`�A�ZBZ�`�K4=@I�KsP8G�=@I$Z\=YD/X�Z�D/G\h[EHK4DFX�^/DFEHGcL�S2A/W]K�?R=2?XHK�qFS2=Yq/=YL�SYK/o/^/DFEnW]Dsl~`�A"Z �������� � b>`�KRe&DFG\KB?�_HG\K�AFW&D/E]Z;P8G\DFe Z\`HK�A��]=2?�A-�H�]K�WnA�e&DFEHX[Z�D�P�e�AF?\?�=@?�oZ\`HK-qFG\K�A�Z�K�G�Z\`HK-G�DFZ\A�Z�=2DFX�AFSN=2XHK�GUZ\=2A�aA[< � ��� ��^FDFE�GcA�G\e&?�=2XZ�D ��� ¦ � � � �^FD/EHG~G�DFZ\A�Z�=2DFX�AFSN=2XHK�GUZ\=2A�aLN< � ��� ��^FDFE�GcA�G\e&?�=2XZ�D1� ¦ � � � �^FD/EHG~G�DFZ\A�Z�=2DFX�AFSN=2XHK�GUZ\=2A�aIi<' � ����� ^FDFE�GcA�G\e&?�D/E]Z~Z�D � ¦ � � � ^FD/EHG>G�DFZ\A�Z�=2DFX�AFSp=YXHK�GUZ\=2A�aWV<' � ����� ^FDFE�GcA�G\e&?�D/E]Z~Z�D ��� ¦ � � � ^FD/EHG>G�DFZ\A�Z�=2DFX�AFSp=YXHK�GUZ\=2A�aK*<#��K�SYS2^���D/_�a

¾H�*�sh[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ µ&e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�Z:l�D&G\DFS2SY=2XHq&I�^(S2=YX�WHK�GJ?¹ a~b>l�D�I�^(S2=YXVW]K�GJ?sDFP~Z�`HK?�AFe&KCe�AF?\?4AFX�W�GJAFW]=2E�?s?UZ\AFGUZsP8G�D/e G\K�?UZgA�Z6Z�`�KnZ\DF_�DFPBA�X�=2X�I�S2=2XHKQAFX�W�G\DFS2SW]D"l~X�ax°RXHKn=@? A:E�?UZgA�Z�`H=2XtI�^[S2=2X�W]G\=2I�A�S;?�`HK�S2S>A�X�W�Z\`HKnDFZ�`HK�Gs=@?4?�DFS2=2W�I�^(SY=2X�W]K�GsD�PcE�XH=�P8D/G�e W]K�X�?U=YZ:^Fa»{`H=@IJ`mG�KiAFIJ`HKi?�Z�`HK-LND�Z�Z�DFe ��� � �A[<n BK�=YZ�`HK�G�aLN<Qb>`�K-G�KiAFIJ`CZ\`HK-LND�ZUZ\DFe A"Z>Z�`HK6?\A�e&K�Z�=2e&KFaIi<Qb>`�K6?U`HK�SYSpD/XHKFaWV<Qb>`�K6?UD/SY=@WnD/XHKFaK*<n7kZi· ?cG\AFX�W]DFe l~`�=2IJ`mDFX�K�G\K�A/IJ`HK�?�Z\`HK-LVDFZUZ\DFe �VG\?UZ�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H�*�sh/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\DFS2SY=2XHq&L�A�S2SpDFX=2X�I�S2=YX�K�Fa~� EHX�=�P8D/G�e ?UD/SY=@WnLVA�S2SpD�P�e&A/?�?~¾ � ¶ O[q&?UZ\A�G�Z�=2XHq4P8G�D/e G\K�?UZcG�D/SYS@?>W]D"l~XAFXm=YX�I�SY=2XHKMD�PjA�X�qFS2K ��$ ³ ¾��"a

A[<n|�=2X�WQZ�`HK-LVA�S2S�· ?~AFI�I�K�S2K�GJA"Z\=YD/X�aLN<n»{`VA"Zc=@?>=�ZJ?>Z�GJA�X�?�S@A"Z�=2DFXdFK�SYD]I�=�Z:^CA�P Z�K�G ³ ¾�?>A�XVWn`HD"l�P,A�G~`�A/?>=�Zcq/DFXHK �

Page 64: Introductory Physics Problems David J. Jeffery Department of

¹ ¾ v�`�AF_]Z�a~�*� ¿~DFZ\A"Z\=YD/XQ7�7

Ii<Q��Z;Z�`HK ³ ¾�?�e�A�G\O-Z�`�KcL�A�S2S�I�DFe&_HS2K�Z�K�SY^4=YX�K�S@AF?UZ�=@I�A�S2S2^4I�D/SYS2=@W]K�?jl~=YZ�`CAML�SYD/LgDFPNq/D(D[K�^s?UZ�E,�D�Ppe�AF?\?¶ � ¾�O[qQG�Ki?:Z\=YX�qmAFX�W�?:Z\E�IJO�DFXrA_H=YKiI�K&D�P�l�A���_�A�_NK�GMDFP�XHK�qFS2=Yq/=YL�SYKge�AF?\?�agb>`HK�L�A�S2SYT�LHS2DFLHT�_�AF_VK�GZ\`HK�Xm?�SY=@W]K�?~�F¾je P8EHGUZ\`HK�G~W]D"l~XnZ�`HK�=2X�I�S2=YX�KMAFX�WnI�DFe&K�?�Z\DgA4?:Z\DF_�aj»{`�A�Z�=@?�Z�`HKMO(=2XHK�Z\=2IBP8G�=@I$Z\=YD/XI�D(K��CI�=2K�X[Z � �6D�P�Z�`HK-_VA�_NK�G>l~=�Z\`Z�`HKM=2X�I�S2=YX�K��m»{`(^nW]D(Ki?�Z�`HK-LHS2DFLm?UZ\A*^CA"Z~G\K�?UZ>A�P Z�K�G~=�Zc?UZ�DF_V? �»{`(^W]D(K�?�X�· Z~=YZB?:ZJA�G�Zce&D"d[=2XHqgL�AFIJOnEH_Z�`HK6?�SYD/_VK/a

WV<Q£BD"l�P,AFG~l�D/EHS2WnZ�`�K-L�A�S2S�TkLHS2DFL]Tk_�AF_VK�G�`VA*dFKMqFD/XHKM=�P � � $�¾ � �

¾H�*�sh/P8EHS2S�¾/¾/��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�¡R=YX�qFD�G\DFS2S2?�DFXmS2D(DF_�]a~¡R=YX�qFDxZ�`HK�WHAFG�KiW]K�d(=2S>WHDFq�=2?gL�A/IJO � A:E�?UZCAFI�I�K�_]Z&=YZ�at£BKm=2?&XHD"l�DFXtAxXHDFTk?�SY=2_�Z\G\A/IJO�A�X�W�`HK�I�EHG\S@?`H=2e�?UK�S�P�=YX[Z�DQA�X�K��]A/I$Z\SY^m?U_�`HK�G\=2I�A�S2SY^m?�^[e&e&K�Z\G�=@I6LVA�S2S�5,LHE]ZMXHD�Z�XHK�I�K�?\?�AFG�=2SY^A�EHXH=YP8DFG\e�W]K�XV?U=YZ:^mDFXHK*<DFP�G\A/W]=YEV? �� � �

�� aM¤(Z\A�G�Z�=2XHq�P8G\DFe � � �o�`HKsG\DFS2S@?BW]D"l~X�Z\`HK6Z\G\A/IJOnP8G\DFe�AFX�=YX�=�Z\=2AFS�`�K�=2qF`[Z � � a�b>`�KZ\G\A/IJOnLNK�I�D/e&K�?cS2K�d/K�S�A"Z � $ ¾�oVW]D(Ki?BACI�=YGJI�EHS@A�GBSYD(DF_HT�Z\`HK�TkSYD(D/_DFP�G\A/W]=2E�? �goNAFX�WZ�`�K�X�q/D[Ki?~S2K�dFK�S�A�Z

� ${¾�A�q[A�=2X�a� cD�Z\K � � ��� AFX�W � A�G\K-W]= �NK�G�K�X/Z~GJAFW]=2=�a

A[<C»{`VA"Zc=@?~¡B=2XHqFDV· ?~Z�GJA�X�?�S2A�Z�=2DFX�AFSp?U_NK�KiWQA�ZBA�X(^C`HK�=Yq/`/Z �nA/?�?�EHe&=2XHq&`HK6?:ZJA*^]?�D/XZ�`HKMZ\G\A/IJO �LN<Q|�=2X�WgABq/K�XHK�G\AFSFK��]_HG\K�?\?�=YD/X-P8DFG�Z�`�K�XHD/G�e�AFSFP8D/G\I�K�D/X4¡R=YXHq/DBl~`HK�X4`�K�=@?�DFX6Z\`HK>SYD(D/_sAF?�ABP8EHX�I$Z\=YD/X

DFP>Z�`HKnAFXHqFS2K ��LNK�Z:l�K�K�X�A�qFK�XHK�GJA�SjGJAFW]=@A�S;dFK�I�Z�D/GsA�X�W�Z\`HKCGJAFW]=@A�S;dFK�I�Z�D/G6_VD/=YX[Z\=YXHq�Z�D�Z\`HK�Z�D/_DFPjZ�`HK4SYD(D/_�A�X�W�GJAFWH=YE�? �ga ������ �  cD�Z\K6Z\`�A"ZRZ�`HK4e&AFqFXH=YZ�EVW]KsDFPjZ�`HK4G\A/W]=2AFS�5�I�DFe&_NDFXHK�X[ZBD�P\<A/I�I�K�S2K�GJA"Z�=2DFX=@?~=YXV?:ZJA�X[Z\AFXHK�D/E�?US2^Cq/=Yd/K�XmL(^'� $ � � � A:EV?:ZRA/?>P8DFGBEHXH=YP8DFG\e}I�=2GJI�EHS@A�G~e&D�Z\=YD/X�K�d/K�Xl~`�K�X � =@?�XHD�Z~I�D/X�?UZ\A�X[Z�_HG�D"d(=@W]K�W�Z�`�A�Z =@?>I�D/X�?:ZJA�X[Z�aj¿~KiI�AFSYS � =2?�A:E�?UZ>Z�`HKRZ\AFXHqFK�X[Z�=@A�Sp?U_NK�KiWC=2XZ\`H=@?~K��]_HG\K�?\?U=2DFXA�X�WQZ\`HK6W]=2G�KiI$Z�=2DFXD�P�Z�`HK-GJAFWH=2AFS�AFI�I�K�S2K�GJA"Z\=YD/Xn=@?�Z�D"l>A�GJW�Z�`�K6I�K�X[Z\K�Gia

Ii<Q|�DFG�l~`�A"Z �n=@?RZ�`HKgXHD/G�e�A�S�P8DFGJI�K4K��]_HG\K�?\?U=2DFX�?�e�A�S2SYKi?:Z �w»{`�A�Z�=@?cZ\`HK&XHDFG\e�A�S�P8DFGJI�KgK��]_HG\K�?\?U=2DFXP8D/G>Z�`H=@?cAFXHqFS2K��

WV<n»{`VA"ZM=2?BZ�`HK&I�D/X�W]=YZ�=2DFX�D/X � � ��� P8DFGRZ�`HKgXHD/G�e�A�S�P8DFGJI�K�� � q/DnS2K�?\?cZ\`�A�X���K�G\DnA�X(^(l~`HK�G�K6D/XZ\`HK-S2D[D/_ �m»{`�A�Zc`�A�_�_VK�X�?>=�P�=YZBW]=2Wq/DgS2K�?\?�Z�`VA�Xm��K�G�D��

K*<¤HA*^ � � $ ¶ ¾je�AFX�WnZ�`HK-GJAFW]=2E�?>DFP�Z�`�K-SYD(DF_m=@?c��¾jemaj¡RD[Ki?c¡R=YXHq/D�?:ZJA*^CDFXQZ�`HK-S2D(DF_ �

¾H�*�sh/P8EHS2S�¾/¾ ³ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�9�=2_H_�AgDFXme&K�G\G�^[TkqFDFT�G\DFEHXVW³ a>»�K�K>9�=2_H_�A�9jAF?\?U=2XHqcG\EHX�?�EH_4Z�DMAc_HS@A*^(qFG\DFEHXVW-e&K�G\G�^[TkqFD�TkG\DFEHX�W�o�=2XH=�Z\=2AFSYS2^6A"Z�G\K�?UZ�o�A�XVW A:EHe&_�?�GJAFW]=@A�S2SY^D/X/Z\DgZ�`HK-G\=YemaA[<C»{`VA"ZR=@?~Z\`HK6Z\DFGJh[EHKs?�`HK6K��]K�GUZJ?BA�LNDFEHZcZ�`HK4G�DFZ\A�Z�=2DFX�AFS�A"�]=@?cD�P�Z\`HKse&K�G\G\^/TkqFDFT�G\DFE�X�W �x¡BD(K�?BZ�`�Ke&K�G�G\^[T�q/D�TkG�D/EHX�W�?UZ\A�G�Z>Z�D�e&D"dFK �

LN<Q9;=Y_�_�A�A�X�WtZ\`HK�e&K�G\G�^[TkqFDFT�G\DFEHXVW�LVDFZ�`�I�A�Xw`�A*dFK�AFXHqFE�S2AFG�egD/e&K�X[Z�EHe A�LNDFE]ZnZ�`HK�e&K�G�G\^[T�q/D�TG\DFE�X�WnA��(=@?�aj¤]`HK-A�X�WnZ�`HKMe&K�G\G\^/TkqFDFT�G\DFE�X�W�A�G\K�I�DFEH_�SYKiW�Z�D/qFK�Z�`HK�G�L(^�Z\`HK-?:ZJA"Z\=2IRP8G\=2I�Z�=2DFX�AFSVP8D/G\I�KLNK�Z:l�K�K�X{`HK�GnP8K�K�ZQA�X�W±Z\`HKx?�EHG�P,AFI�KFa(��EHZQ9�=2_H_�A�I�A�X{W]=2G�KiI$Z\SY^wI�D/X/Z\G�D/S~Z�`�K�G�K�S2A�Z�=2dFK�d/K�S2D(I�=�Z:^LNK�Z:l�K�K�Xx`�K�GJ?UK�S�P�AFX�W�Z�`HK&e&K�G\G�^[TkqFDFT�G\DFEHXVWQL(^�l>A�S2O(=YX�qnDFGMG\EHXHXH=2XHqVuBZ\`[EV?�?�`HK�I�AFXxIJ`�AFXHqFK4Z�`�KI�DFEH_�SY=2XHqRI�DFX�WH=�Z\=YD/X�a�»{`�K�X4?�`HK�=2?�A�Z�G\K�?UZ�D/X-Z�`HK>e&K�G\G\^/TkqFDFT�G\DFE�X�Wpo�?�`HK�A�X�W6Z�`HK�e&K�G\G�^[TkqFD�TkG\DFEHX�WI�DFX�?UZ�=YZ�EHZ�K-DFX�K�G\=2qF=@WnG\D�ZJA"Z�D/G�a ��E]Z~l~`HK�X�?�`HKMe&D"dFK�?�Z\`HK�^I�DFXV?:Z\=�Z\E]Z�K�Z:l�DgG\=2qF=@WnG\D�ZJA"Z�D/G\?�A�LNDFEHZZ\`HK-e&K�G\G�^[TkqFDFT�G\DFEHXVW�A"�]=2?�a¤HA*^t9�=2_H_�A�?UZ\AFGUZJ?�G\EHXHXH=2XHq'A:E�?UZnDFXwZ\`HK�G\=Ye�D�PMZ�`�K�e&K�G\G�^[TkqFD�TkG\DFEHX�W�a�b>`HK�e&K�G\G�^[TkqFD�TkG\DFEHX�W

A��(=@?�=@?�P8G\=2I�Z�=2DFXHS2K�?\?�u�Z�`(E�?CZ�`HK�Z�D�ZJA�SBAFXHqFE�S2AFGCe&DFe&K�X[Z�E�e�DFP�Z\`HK�?�^]?:Z\K�e�AFLVD/E]ZCZ\`HK�A"�]=@?nI�A�XHXHDFZIJ`�AFXHqFK/a��R?U=2XHq&I�D/X�?UK�G�d"A�Z�=2DFXCDFP�A�XHq/EHS@A�G;e&D/egK�X[Z�EHe P8D/G�AFXn=@?UD/S2A�Z�KiWn?�^(?UZ�K�e���X�WQA�XnK��]_HG�Ki?�?�=2DFX�P8D/GZ\`HK6e&K�G\G�^[TkqFDFT�G\DFEHXVWCA�XHq/EHS@A�G�P8G�Kih[EHK�X�I�^ � � =YXmZ\K�G\e�?~D�Pj9�=2_H_�A�· ?>G\K�S@A"Z\=Yd/KMAFXHqFE�S2AFG>P8G�Kih/E�K�X�I�^ � � � � �AFX�W�Z\`HK4G\D�ZJA"Z\=YD/X�A�S�=YXHK�GUZ\=2A/?RAFLVD/E]Z�Z�`HK&A"�]=@?BDFP�9�=2_H_�A � �AFX�WmZ\`HK4e&K�G�G\^[T�q/D�TkG�D/EHX�W � �Ma6 cDFZ�K4Z�`�A�Z� ��� � ��$ � � ,�� ��aIi<��=2dFK�Z�`HKxK��]_HG\K�?\?U=2DFXwP8D/GQ9;=Y_H_VAH· ?���X�AFS�AFXHqFE�S2AFGndFK�SYD]I�=�Z:^±G�K�S2A�Z�=2dFK�Z\D�Z\`HK�q/G�D/EHX�WwE�?�=YX�q�Z�`�K_VA�G�Zs58LV<cG�Ki?UEHSYZ\?�a;»{`VA"ZBl�DFEHS@Wm9�=2_H_�A�· ?>�VX�A�S�AFXHqFE�S2AFG~dFK�S2D]I�=YZ:^nLNK6=2XmZ�`HK-S2=Ye&=YZ\?BZ�`�A�Z � ��� AFX�W � ��� ¾Ha

Page 65: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~�*� ¿~DFZ\A"Z\=YD/XQ7�7 ¹ �

WV<Q9;=Y_�_�AgG�EHXV?~DFXZ�`�K-G�=2e}A�Z ³ � ¾je��"?�G�K�S2A�Z�=2dFK�Z�D&Z\`HK-G\=Yema;b>`HK-GJAFWH=YE�?>DFP�Z\`HK-e&K�G\G�^[TkqFDFT�G\DFEHXVW�=2?³ ea�b>`HK~ZJA�XHq/K�X[Z�=@A�S]G\=2efdFK�SYD]I�=�Z:^4D�PNZ�`HKce&K�G�G\^[T�q/D�TkG�D/EHX�W-=@? ,B� � ¾je��"?�l~`�K�X�9�=2_H_�AM=@?jG\EHXHXH=2XHq�a9;=Y_�_�A�`�A/?6A�e�AF?\?-D�P~µ[¾jO(q�am�B?\?UEHe&=2XHqmZ�`�Kne&K�G\G�^[TkqFDFT�G\DFEHXVW�=@?sAmEHXH=YP8DFG\e W]=2?�O�o�l~`�A"Zs=@?6=YZ\?e�A/?�?�a

K*<n7:?&=YZCA"Z�A�S2S~_VD[?�?�=2LHSYKQZ�`VA"ZC?:ZJA�G�Z�=2XHqxP8G�D/e G�Ki?:Z&G�K�S2A�Z�=2dFKQZ�DxZ�`HKmq/G�D/EHX�W�Z\`�A"Z�LND�Z\`±9;=Y_H_VAxAFX�WZ\`HK&e&K�G\G�^[TkqFD�TkG\DFEHX�W�I�DFEHS@W�LNK�e�AFW]K4Z�D�?�_H=2Xx=2X�Z\`HK�?�AFe&Kg?�K�X�?�K&G�K�S2A�Z�=2dFKsZ�DZ�`HK&q/G�D/EHX�W�?\A�XV?K��(Z�K�G\X�AFS�Z�DFGJh[EHK�?�

¾H�*�sh/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�P,AFSYS2=YX�q�_H=YS2S@A�G~=2X�¤]_�A�G�Z\A� ª�¬"¨ �V«������V¬ ��­��  cK�KiWH?~G\K�l�DFG\O(=YXHqVu�?UZ\AFGUZ~l~=YZ�`�Ag��XH=YZ�K-d/K�S2D(I�=�Z:^�uj?�e&AFSYSpKiA�G�Z�`�h[E�AFOFK

µ�a~��Z\AFSYS�oFZ\`H=2XQ£cK�SYS2K�X�=2IR_H=2SYS@A�G�5,¡RDFG\=2IR?:Z:^(S2Ki<j`VAF?�?:Z\D[D]W�K�G�KiI$Z�P8DFG�� ¶ I�K�X[Z�EHG\=2K�?�=2XQ¤(_VA�G�Z\AHo[XHD"l-o[=�ZJ?�L�AF?�KK�G�D]W]KiWpoH=YZcP,A�S2S2?~P8G�D/e�G\K�?UZ�P8G\DFe�Z�`HKsdFK�G�Z�=@I�AFSpEHX�W]K�G~Z�`�K-P8DFGJI�KMD�P�qFGJA*d(=�Z:^/a�b>`HK-L�A/?UK6?UZ\A*^]?��H�]K�WmAFX�WZ\`HKC_H=2SYS@A�GsP,A�S2S2?6SY=2OFKCG\=2qF=@WxG\D�ZJA"Z\DFG6A�LNDFEHZs=�Zia�b�AFOFK&Z�`�KCL�AF?�KnA/?-LVK�=YX�q�Z�`HKn_H=Yd/D�Zs_NDF=2X[ZQ58D/G6DFG\=2qF=2XV<P8D/G�AFSYS�Z�`HKgG\D�Z\A�Z�=2DFX�AFS�I�A�S@I�EHS@A"Z\=YD/X�?�a��B?\?UE�egK4Z�`�KsL�A/?UK4=2?MA�X�=2W]KiA�S�_H=2dFD�Z�_VD/=YX[Ziuc=�a KFa2oNZ�`HK4Z�`�K4_H=2S2S2AFG=@?RI�DFe&_HS2K�Z\K�S2^mP8G�K�K6Z�DnZ�EHG\X�AFLVD/E]ZRZ\`HKs_�=Yd/D�ZR_NDF=2X[Z�opLHEHZRZ\`HK4_�=Yd/D�ZB_NDF=2X[Z�=YZ\?�K�SYP;=@?c�H�]KiWpa�b>`�KgAFXHqFS2KDFPjZ�`HKg_H=2SYS@A�GRP8G�D/e Z�`HKgEH_(l�AFG\Wm_NDF=2X[Z�=2XHq�� �� � ¦&� ��A"Z�AFX(^QZ\=Ye&Kg=YX�Z�`HK4P,A�S2S�=2?��Ha-�B?\?UE�egK4Z�`�K_H=2S2S2AFG6`�AF?6SYK�XHq�Z\` 0 o�=YZ\?sI�K�X[Z�K�G-D�P~e�AF?\?-=@?-SYD]I�A"Z�KiWrA"Z 0 � � P8G\DFe Z�`HKnL�AF?�KFo�=�ZJ?6e�AF?\?M=2? �xo�A�XVWx=YZ\?G\D�ZJA"Z�=2DFXVA�SN=YXHK�GUZ\=2As=2? �Va ������ � ¡BGJA*l�A6q/D(D(Wn=YX�=�Z\=2AFS�WH=2AFqFGJA�ema � � � � b>`H=@?>h/E�K�?UZ�=2DFXQI�DFEHS@WCLNKMAe4EHS�Z\=�Tk_�AFqFK�G>=2X�AsZ\K�?UZce&=2?�K-K�X�?\I�(K�XHKFaA[<C»{`VA"Zc=@?>=�ZJ?cA�XHq/EHS@A�G~AFI�I�K�S2K�GJA"Z\=YD/X ��DFP�Z\`HK-_H=2SYS@A�GcA/?~A4P8EHX�I$Z\=YD/XmD�P ���LN<Q�R?U=2XHqRZ�`HK�G\D�Z\A�Z�=2DFX�AFSFl�DFG\O[T�O(=2XHK�Z\=2IjK�XHK�G\qF^RZ�`�K�DFG\K�e���XVWsA�X4K��]_HG\K�?\?U=2DFXMP8D/G�Z\`HK>A�XHq/EHS2AFG�d/K�S2D(I�=�Z:^�{DFPjZ�`HK4_H=YS2S@A�Gia ������ � ��D/E�l~=YS2S�`VA*dFKMZ�DA�e&D]W]K�?UZB=2X/Z\K�q/G\AFS�ac�BX�=YX[Z�K�qFGJA�S�K��]_HG\K�?\?U=2DFXm=@?cXHDFZAFXA/I�I�K�_]ZJA�LHS2K�P8EHSYS�A�X�?�l�K�Gia

Ii<Q�R?�?�EHe&KQZ�`HK_H=2SYS@A�G&I�AFX�LVKQZ�G\K�A�Z�KiW�AF?sZ�`H=2X�o�EHXH=YP8DFG\e G\D]W�58G\D�ZJA"Z\=YD/X�A�S�=YX�K�G�Z�=@A�A�LNDFEHZ&AFX�A"�]=@?Z\`HG\DFEHq/`�=YZ\?�I�K�X/Z\K�G�DFP]e&A/?�?�=2?�5:� �]�i�/< � 0 ��<$a�»{`�A"Z�=@?�Z\`HK�?�=Ye&_HS2=Y��K�WMK��(_�G�Ki?�?�=YD/XBP8D/GpZ�`�K;G\D�Z\A�Z�=2DFX�AFS=2XHK�GUZ\=2A�AFLVD/E]ZcZ�`�K6L�AF?�K-=2XmZ�K�G\e�?~D�P � AFX�W 0 DFXHS2^�� ������ � � �R?UKMZ\`HK6_�AFG\AFSYS2K�SYT!A"�]=2?�Z\`HK�D/G�K�ema7kP�Z�`�K-_H=YS2S@A�G~=@?~EHXH=YP8DFG\emo]l~`�A"Zce4E�?:Z 0 � ��Kih[E�A�S �

WV<Q BD"l�E�?�=YX�qsZ\`HKR_VA�G�ZM5,LV<�A�X�Wx5,I�<�AFX�?Ul�K�GJ?�oFl~G\=�Z\KBZ\`HKMK��]_HG\K�?\?U=2DFX�P8D/G �±AF?>A6P8E�X�I$Z\=YD/XnD�P�DFXHS2^ No0 oHAFX�W �Ha;¤(=2X�I�K � $�� � ��� � oHl~`VA"ZcO(=YXVWQDFP�Kih/EVA"Z�=2DFXQP8DFG �&=@?>Z�`�K-K��]_HG\K�?\?U=2DFX A:E�?:ZBWHK�G\=Yd/K�W �K*<Q�BS2A/IJO�o�Z\`HK�G\K;=@?�X�DRA�XVA�S2^/Z\=2I;?UD/SYE]Z\=YD/X6qF=2d(=YX�q �BAF?�A~P8EHXVI$Z�=2DFXsD�P]Z�=2e&K�P8D/G�Z\`HK�W]= ��K�G\K�X[Z�=@A�S[K�h[E�A�Z�=2DFXP8D/G��mDFL]ZJA�=2XHK�W�=2XrZ�`HK�_VA�G�Zn5,W�<-AFX�?�l�K�G�u�Z�`�K�G\K�e&A*^xXHD�Z6LNKCD/XHKFa ��E]Z6l�KF· Wr?:Z\=YS2S;S2=2OFK&Z�Dm�VX�WA�ZRS2K�A/?:ZMACI�G\E�W]K4K�?UZ�=2e&A�Z�K4D�PjZ�`�K6Z�=2e&KsP8D/GBZ\`HKs_�=YS2S2AFGBZ\D�P,A�S2SjW]D"l~X�aB¯�A�OFKsZ�`HKgA�_H_�G�D*�]=2e&A�Z�=2DFX� $ � � � � � � � � � � � o�?UK�Z � � $ � ���Ho�A�X�WxI�AFS2I�EHS2A�Z�K � � P8DFGMA A:EVW]=2I�=YD/E�?-IJ`HD/=2I�KsD�P �Q=2X �B5 �/<$ab>`�K�_�=YS2S2AFG�=@?M��¾�e =2XSYK�XHq�Z\`�ajb>`HKMG�Ki?UEHSYZ>_HG�D/L�A�L�SY^&`�A/?�A/?:Z\G�D/_H`(^]?U=@I�AFSVAFI�I�EHGJAFI�^�u�=�a K/aYo(P,A/I$Z\DFG�D�P��=2?�`�a

Page 66: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � ���Wd�*-N-*-e�5\*-d�= &A>�, � N[&TE�;<*-HJ*[;]6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H� ³ h[e4EHS�ZB¾/¾H�i¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujG\D�ZJA"Z�=2DFXVA�S�K�h[EH=2SY=2LHG\=YE�e�Fa~b�D&LVK-=2XmG�DFZ\A"Z\=YD/X�A�S�Kih/E�=YS2=YL�G�=2EHemo�A�XDFL3A:K�I$Zce4E�?UZ>`VA*dFKFu

A[<C��K�G\D�A�XHq/EHS2AFG>egD/e&K�X[Z�EHemaLN<nX�DFX]Tk��K�G�D&A�XHq/EHS@A�G>e&DFe&K�X[Z�E�eaIi<QI�DFX�?UZ\AFX[Z~AFXHqFE�S2AFG�e&D/egK�X[Z�EHemaWV<nX�DFX]T!I�D/X�?:ZJA�X[Z~A�XHq/EHS2AFG>egD/e&K�X[Z�EHemaK*<nX�Dg`VA�=2G�a

¾H� ³ h[e4EHS�ZB¾/¾/�F¾F¾4� ¶&³ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�?:ZJA"Z\=2I�K�h[EH=2S2=YLHG\=2EHe�]a>7!X � � � ¦ K�h[EH=2S2=YLHG\=2EHemu

A[<�Z\`HK�G\K�=2?>XHD4Z�GJA�XV?US@A"Z\=YD/X�A�SNDFG>G\D�Z\A�Z�=2DFX�AFSNA/I�I�K�S2K�GJA"Z�=2DFX�o/LHEHZ�Z\`HK�G\KMI�A�XQLVK�� � � � �� � d/K�S2D(I�=�Z:^AFX�WmA�XHq/EHS@A�G>dFK�SYD]I�=YZ:^Fa

LN<CZ\`HK�G\K�=@?CXHD�Z�GJA�X�?�S2A�Z�=2DFX�AFS~DFGQG�DFZ\A"Z\=YD/X�A�ScA/I�I�K�S2K�GJA"Z�=2DFX�o�AFX�W � ��Z�GJA�XV?US@A"Z\=YD/X�A�S~D/GnG\D�Z\A�Z�=2DFX�AFSd/K�S2D]I�=YZ:^Fa�7kPp?UZ\A�Z�=@I~K�h[EH=2S2=YLHG\=2EHe K��]=2?UZ\?;=YXCA-?�_VKiI�=Y�VIcG\K�P8K�G�K�X�I�K>P8GJA�e&K/oF=YZ;K��]=@?:ZJ?�=2X � � ��G�K�P8K�G\K�X�I�KP8GJA�e&Ki?>XHD&e&A�ZUZ\K�Gc`HD"l�Z�`HD[?UKMG\K�P8K�G�K�X�I�K�P8GJA�e&K�?�e�A*^CLNK-egD"d(=2XHq�a

Ii<CZ\`HK�G\K�=@?CXHD�Z�GJA�X�?�S2A�Z�=2DFX�AFS~DFGQG�DFZ\A"Z\=YD/X�A�ScA/I�I�K�S2K�GJA"Z�=2DFX�o�AFX�W � ��Z�GJA�XV?US@A"Z\=YD/X�A�S~D/GnG\D�Z\A�Z�=2DFX�AFSd/K�S2D]I�=YZ:^Fa�7kP�?UZ\A"Z\=2I�Kih/E�=YS2=YL�G�=2EHe K��(=@?UZ\?=YX�A±?U_NK�I�=��NIxG\K�P8K�G�K�X�I�KxP8GJA�e&KFoM=YZmK��]=2?UZ\? � � ��� =2XG\K�P8K�G�K�X�I�K�P8GJA�e&K�? � � fe&D"d(=2XHq&l~=�Z\`G\K�?�_NK�I$Z>Z\D&Z�`HK6?�_VKiI�=Y�VI�G�K�P8K�G\K�X�I�K�P8G\AFegK-?�^]?:Z\K�ema

WV<CZ\`HK�G\K-A�G\KMXHDgP8DFGJI�K�?~A�ZcA�S2S�aK*<CZ\`HK�G\K-A�G\KMXHDgZ�DFGJh[EHK�?~A�ZcA�S2S�a

¾H� ³ h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�`�A�X�qF=2XHq�I�K�X[Z\K�G~D�P�e�AF?\?³ a �\¸�K�Zi· ?�_HS@A*^ �]1\��D3�����"# 1 |�DFG �(�i¾F¾�o�Z�`�KMAFX�?�l�K�G;=@?�ujb>`HKMXHK�Z�q/G\A*d(=YZ\A"Z\=YD/X�A�S�Z�D/G\h[EHKRDFXQAFXCDFL3A:K�I$Z~A�LNDFEHZAFX[^QDFG\=Yq/=YXmA"Z�A�S2S�=2?cZ�`HK4?�AFegK6A/?>=�P;AFSYS�Z�`HK6e�A/?�?~DFP�Z\`HK6D/L,A:K�I�ZBl�K�G�K-I�DFX�I�K�X[Z�GJA"Z\K�WmA"Z~Z\`HKsI�K�X[Z�K�GBD�Pe�AF?\?�u�=�a KFa2o

���� ��� $ � � � � � ��

l~`HK�G�K � � ��=@?je&K�AF?�EHG\K�W4P8G\DFe�Z\`HKcDFG\=2qF=2XgAFX�W��6=2?�AME�XH=�Z�dFK�I�Z�D/Gj=YXgZ�`�KcW]=YG\K�I�Z�=2DFX&D�PNZ�`�KcqFGJA*d(=�ZJA"Z�=2DFXVA�SP8D/G\I�KFa�°RXHS2^nl~`�K�X � � ��A�X�W��nAFG�K6AFSY=2qFXHKiWnD/Gcl~`HK�X � � � $z¾&W]D(K�?~Z�`HK6q/G\A*d(=YZ\A�Z�=2DFX�AFSVZ\DFGJh[EHKMd*AFXH=@?U`�ab>`(E�?�P8D/GMAFXxD/L,A:K�I�Z�`VA�XHq/=YXHqQP8G\DFe AnP8G�=@I$Z\=YD/XHS2K�?\?M_H=Yd/D�ZiopK�h[EH=2SY=2LHG\=YEHe DFXHS2^�K��]=@?:ZJ?RP8DFGMZ�`�K&I�K�X[Z�K�GMD�Pe�AF?\?�W]=YG\K�I�Z�S2^-A�LND"dFKFo*D/X�o"DFG�W]=YG\K�I�Z�S2^-LVK�SYD"lrZ\`HK�_H=Yd/D�Zia��cLND"dFK�=2?�EHX�?UZ\AFLHS2K�LNK�I�A�E�?�K�AFX[^M_NK�G�Z�EHG\L�A�Z�=2DFXI�A�E�?�K�?&A�qFGJA*d(=�ZJA"Z�=2DFXVA�S�Z�DFGJh[EHK�A*l�A*^�P8G\DFe Z\`HK�K�h[EH=2S2=YLHG\=2EHema�°RXw=@?�A�XHK�E]Z\G\AFS~K�h[EH=2SY=2LHG\=YE�e ?U=2X�I�KZ\`HK�G\K~=2?;XHD-qFGJA*d(=�ZJA"Z\=YD/X�A�S[Z�D/G\h[EHK~l~`VA"Z�K�dFK�GjZ�`HKBDFG\=YK�X/ZJA"Z\=YD/X4DFPNZ\`HKcD/L,A:K�I�Z�a ��K�SYD"lt=2?�?:ZJA�LHS2Kc?�=YX�I�K~Z�`�Kq/G\A*d(=YZ\A"Z\=YD/X�A�S�Z\DFGJh[EHK6Z\`HK�X�Z\G�=2K�?cZ�DQ_HEHS2S�Z\`HK4I�K�X[Z�K�GBDFP�e&A/?�?BL�AFIJOQZ�DnZ�`HK4K�h[EH=2SY=2LHG\=YE�e _NDF=2X[Z�aR»{=�Z\`AFX[^WHA�e&_H=2XHq�Z\D�O(=YS2S�G\D�ZJA"Z�=2DFXVA�SpO(=YX�K�Z�=@I-K�XHK�G\qF^�58LHE]Z�=YXV?UE]�CI�=YK�X/Z�?:ZJA"Z�=@IMP8G\=2I�Z�=2DFXm=2XmZ�`HK4_H=Yd/D�Zc_NDF=2X[ZZ\D6DF_H_ND/?�KBAFX[^4qFGJA*d(=�ZJA"Z�=2DFXVA�S(Z�D/G\h[EHK*<$oFZ�`HKRDFL,A:KiI$Z;l~=2SYSNI�D/egKcZ�DsA6?UZ\A�Z�=@Ic?UZ\A�L�SYKcKih[EH=YS2=2LHG�=2EHe l~=�Z\`�Z�`�KI�K�X[Z�K�G~D�P�e&A/?�?>W]=2G\K�I$Z\SY^QLVK�SYD"l�Z�`HK-_�=Yd/D�Z�a �A[<C»{`(^W]D(K�?>Z\`HKsI�K�X[Z�K�G~DFPje&A/?�?>DFP�AFXmDFL,A:KiI$Z~Z�K�X�WZ�DCI�DFe&KMZ�D�G\K�?UZBW]=2G�KiI$Z\SY^ �� � � A4P8G\K�K�SY^Z\EHG\XH=YX�q�_H=Yd/D�Z>P8G\DFe l~`H=@IJ`QZ�`HK-D/L,A:K�I�Zc=2?>`�AFXHqF=2XHqVoH�cS2K�� �

Page 67: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~� ³ �;h[EH=2SY=2LHG\=YE�e}A�XVWQ�;S2A/?:Z\=2I�=�Z:^ ¹/³

LN<n»{`(^mW]D(K�?cZ�`HKsI�K�X[Z�K�GcD�Pje�AF?\?~DFPjAFX�DFL,A:KiI$Z~Z\K�X�WmZ\DnI�D/e&KMZ�DCG\K�?UZBW]=2G�KiI$Z�S2^ � ��� fAgP8G\K�K�SY^Z\EHG\XH=YX�q�_H=Yd/D�Z>P8G\DFe l~`H=@IJ`QZ�`HK-D/L,A:K�I�Zc=2?>`�AFXHqF=2XHqVoH�cS2K�� �

Ii<n»{`(^Q=2?�Z\`HK�G\K6A&I�K�X[Z\K�G~D�P�e�AF?\?�oH�BSYK����WV<n»{`(^Q=2?�Z\`HK�G\K6A&I�K�X[Z\K�GioH�cS2K�� �K*<n»{`(^Q=2?�Z\`HK�G\K6AgEHXH=2dFK�GJ?�KFo]�cS2K�� �

¾H� ³ h[e4EHS�ZB¾/¾�µ[¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u;?�=2eg_�SYKMLNK�A�e�Z�D/G\h[EHK-I�AFS2I�EHS@A"Z�=2DFXµ�a~�BXnDFL3A:K�I$Z�D�P�e�A/?�?B��O(qs?U=YZ\?�D/XnA6`HD/G�=2��D/X[Z\A�SVLVKiA�e A"ZM��e P8G\DFe A6_H=2dFDFZ�_NDF=2X[Z�a�»{`�A"Z>=@?�Z\`HKBZ\DFGJh[EHKAFLVD/E]Z~Z�`HK-_�=Yd/D�Z~_VD/=YX[Z~Z\`�A"Z>Z�`�K-l�K�=Yq/`/Z~DFP�Z\`HK-e�AF?\?~I�A�EV?UKi? �A[<��� �emaLN<�� �emaIi< ³  �emaWV<nµ� �emaK*< ½ a ¼  �eQa

¾H� ³ h[e4EHS�ZB¾/¾ ¶ ¾F¾4� ³ �Me&D]W]K�GJA"Z\K�e�A�Z�`�u�Z\DFGJh/E�KMI�A�S@I�EHS@A"Z\=YD/Xnl~=YZ�`�A&LNK�A�e¶ a~b>l�D&DFL,A:KiI$Z\?~AFG�K-?�=�Z�Z�=2XHq�DFXmAgEHXH=YP8DFG\e�`HD/G�=2��D/X[Z\A�S�LNK�AFea�b>`�K-LVKiA�e�G\K�?UZ\?�D/XmAg_H=2dFDFZcA"Zc=YZ\?cI�K�X[Z�K�GDFP�e�AF?\?�a;b>`HK6LNK�AFe�=@?>P8G�K�KMZ�D�G\D�ZJA"Z�K6AFLVD/E]Z~Z�`�K6_H=2dFD�Zia�°RL,A:KiI$Z6�6?�=�ZJ?~DFXZ�`�K6SYK�P ZUTk`�A�XVW?�=@W]K-D�P�Z�`�K_H=2dFDFZ4A"ZgA�W]=2?UZ\AFX�I�K 0 � P8G�D/e Z\`HKn_�=Yd/D�Z�a�°RL,A:KiI$Zg�m?�=YZ\?6D/XrZ�`HKQG�=2qF`[Z�T�`�AFX�Wr?U=@W]KnA�Z4A�W]=@?:ZJA�X�I�K 0 � a��=2dFK�X � � $�� � � oHl~`�A"Z~=@? 0 � =YXZ\K�G\e&?cD�P 0 � �������� � ¡RG\A*l�A&W]=2AFqFGJA�emaA[< 0 � $�� 0 � aLN< 0 � $ 0 � ����aIi< 0 � $ 0 � aWV< 0 � $z� 0 � aK*< 0 � $�¾Ha

¾H� ³ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj=2X�W]K�Z�K�G\e&=YXVA"Z�KMKih/E�=YS2=YL�G�=2EHe}I�AF?�K�?¹ a>7!XAs_HS@A�XVA�G�DFG~�*T!W]=Ye&K�X�?U=2DFXVA�S�I�AF?�KBDFP�?UZ\A"Z\=2IRK�h[EH=2S2=YLHG\=2EHe l~=�Z\`QX�Dg?�_VKiI�=@A�SNG�E�SYKi?�G\K�S@A"Z\=YX�q6P8DFGJI�Ki?�o(I�AFX^/DFEm?UD/SYd/KBP8D/G>P8DFEHGcE�XHO(XHD"l~XnP8D/G\I�K�?>AF?\?�EHe&=YXHq&_NK�G�P8K�I�Z�S2^nG\=Yq/=2WQDFL,A:KiI$ZJ? �A[<n BD�a�b>`HK-?�^]?:Z\K�e�=@? ����� � �'� ��� � �4uH^FD/EnDFX�SY^Q`�A*dFK � �'��Kih/E�=YS2=YL�G�=2EHe�Kih[E�A"Z\=YD/X�?�aLN< ��Ki?�a�b>`�K6?U^]?UZ�K�e�=2?� � �'� ��� � ��?�=YXVI�KM^FD/EQ`�A*d/K� �� �4��K�h[EH=2SY=2LHG\=YE�e�K�h[E�A�Z�=2DFX�?�aIi<Q BD�ajb>`HK�?U^]?UZ�K�e�=@? ����� ����� ��� � �4u[^FDFE�D/XHS2^g`VA*dFK ��� �zK�h[EH=2S2=YLHG\=2EHe�K�h[E�A"Z\=YD/X�?�aWV< ��Ki?�a�b>`�K6?U^]?UZ�K�e�=2?� � �'� ��� � �4u]^FD/EQ`�A*d/K ��� K�h[EH=2SY=2LHG\=YEHe}K�h[E�A�Z�=2DFX�?�aK*<Q BD�a�b>`HK-?�^]?:Z\K�e�=@? ����� � �'� ��� � �4uH^FD/EnDFX�SY^Q`�A*dFK �� �}Kih/E�=YS2=YL�G�=2EHe�Kih[E�A"Z\=YD/X�?�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H� ³ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj`HD/G�=2��D/X[Z\A�S�L�AFS2AFX�I�KiWnLNK�AFe�Fa~� `HD/G�=2��D/X[Z\A�SNLNK�A�e�=2?>L�AFS2AFX�I�KiWnD/XA4_NDF=2X/Zc_�=Yd/D�Z~A"Z � � � � � � $�¾ � ��¾/¾jema�b>`HKMLNK�AFe =2?>E�XH=�P8D/G�e}l~=�Z\`e�AF?\?-¾ � ��O(qQAFX�W�Z�`HKCI�K�X[Z�K�G-D�P�e�A/?�?M=@?-A"Z�� � � � � � � $�¾ � ¶ ¾F¾jemagb>`HK�G\K&=2?-AFS2?�DAm?�=YX�qFS2KgD/L,A:K�I�Z-D�Pe�AF?\?c��O(qgDFXZ�`HK-LNK�AFemaj»{`HK�G\KM=2?>=YZ�

¾H� ³ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK�h[EH=2S2=YLHG\=2EHe�S@AFWHWHK�G�]a~��S@AFWHWHK�G&SYKiA�X�?�AFq/AF=YX�?UZ�A�l>A�S2S~=YXw?UZ\A"Z\=2IKih/E�=YS2=YL�G�=2EHema{¸�AFW�W]K�Gio;l>A�S2S�o�A�X�WtqFG\DFE�X�W�AFG�K_VK�GUP8KiI$Z\SY^G\=Yq/=2W�a�b>`�K�S@AFW�W]K�G~`�A/?�e&A/?�? � � � � � � � oHS2K�XHqFZ�` 0 � ����� � � oVA�X�WI�K�X/Z\K�G>D�P�SYD]I�A"Z�KiWQA�Z 0 � � A�S2DFXHqg=�ZJ?>SYK�XHq�Z\`e&K�A/?UE�G�=2XHqP8G�D/e =YZ\?6L�AF?�KFab>`HKnA�X�qFS2K�LVK�Z:l�K�K�X�Z�`HKnS2A/WHW]K�G4A�X�W�Z\`HK�� �� � ¦&� �f=2?���a ������ �¡RG\A*l�A�q/D(D(W�WH=2AFqFGJA�e e&AFG�O(=2XHq�DFX�AFSYS�_ND/?\?U=2LHS2K-P8DFGJI�Ki?�u�qFGJA*d(=�Z:^/oHZ�`�KsXHD/G�e�A�S�P8DFGJI�Ki?~D�PjZ\`HKsq/G�D/EHX�WAFX�W�l>A�S2S�oNA�X�WmZ\`HK6P8G\=@I$Z�=2DFX�P8DFGJI�K�?cD�PjZ�`�KsqFG\DFE�X�W�A�X�Wml>A�S2S�aB¡BGJA*l�Z�`HK4S2A/WHW]K�GBS2K�A�X�=YXHqCZ�DCZ\`HKsG\=2qF`[Z?�DgZ�`�A�Zcl�K-A�G\K-A�S2S�I�D/X�?U=@?UZ�K�X[Zia

Page 68: Introductory Physics Problems David J. Jeffery Department of

¹ µ v�`�AF_]Z�a~� ³ �;h[EH=2S2=YLHG\=2EHe}AFX�WQ�;S2A/?:Z\=2I�=�Z:^

A[<C»�G\=�Z\KsDFEHZBZ�`�KsK�h[E�A�Z�=2DFX�?BD�P�Kih/E�=YS2=YL�G�=2EHe�=YXVI�S2E�W]=2XHqQAFSYS�_VD[?�?�=2LHSYKsP8DFGJI�Ki?�a �/E�?UZ�?�DCl�KgA�G\KsA�S2S�D/XZ\`HK>?�AFegK�l>A*dFK�S2K�X�q�Z�`MZJA�O/K�Z�`�K�D/G�=2qF=2X-P8DFG�Z\`HK;Z\DFGJh[EHK;Kih/EVA"Z�=2DFX6Z�D�LVK�Z�`�K�I�DFX[Z\A/I$Z�_NDF=2X[Z�LNK�Z:l�K�K�XS@AFW�W]K�GcAFX�Wnq/G�D/EHX�Wpa�»{`(^n=@?�Z�`�=2?cA&q/D(D(WQIJ`HDF=@I�K ��v�A�X^FD/EQD/L]Z\AF=YXK��]_HS2=@I�=YZ~P8DFG\esEHS@A�KM=2XnZ\K�G\e&?DFP�Z\`HK-O(XHD"l~X�?-58=�a KFa2o � � ��� o 0 � � � o 0 � ����� � A�XVW �[<�P8DFG�Z�`HK-X�DFG\e&AFS�P8DFGJI�Ki?�DFP�Z\`HK-qFG\DFEHXVWnA�XVWQl>A�S2S�oAFX�WZ�`�Ks?:ZJA"Z\=2IMP8G\=@I$Z�=2DFXmP8D/G\I�K�?~DFP�Z�`HK6q/G�D/EHX�WmA�XVWml�AFSYS � ������ � 7!X�?�K�Z�Z�=2XHqCEH_�Z\`HK6Kih/EVA"Z�=2DFXV?^/DFEQesE�?UZ>A/W]DF_HZ>?�DFe&KRI�DFX(dFK�X[Z�=2DFX�?�A�LNDFE]Z>l~`H=@IJ`QW]=2G\K�I$Z\=YD/X�?>A�G\KB_ND/?�=�Z\=Yd/KBP8D/G>l~`H=2IJ`nP8DFGJI�Ki?�AFX�Wl~`VA"ZR=@?BZ�`HK4_VD[?U=YZ�=2dFKsZ�DFGJh[EHKsW]=2G\K�I$Z\=YD/X�aB�R?BS2DFXHqQAF?R^FDFE�AFG�K4I�DFXV?U=@?:Z\K�X[ZBK�dFK�G\^[Z�`H=2XHqCl�DFG\O]?~DFEHZZ\`HK6?\A�e&KM_H`(^(?�=@I�A�S2S2^CXHD&e�A"ZUZ\K�G~l~`�A�ZBI�D/X[d/K�X[Z�=2DFXV?�^/DFEmAFW]D/_]Z�a

LN<Q�R?�?�EHe&=2XHq�Z�`HKml>A�S2S�=@?gP8G\=2I�Z�=2DFXHS2K�?\?�o�l~`�A"ZCAFG�KQZ�`HKmK��(_�G�Ki?�?�=YD/X�?sP8DFG&Z�`�KX�DFG\e&AFS�P8DFGJI�K�?gDFPBZ�`�Kq/G�D/EHX�WgA�X�Wgl>A�S2S�o[A�X�W4Z\`HKB?UZ\A"Z\=2I�P8G\=@I$Z�=2DFXgP8D/G\I�K�DFPVZ\`HKcq/G�D/EHX�W ��cG\K>Z�`�K�?�K~=YX[Z�G\=2X�?U=@I>K��]_HG\K�?\?�=YD/X�?P8D/G;Z\`HK�?�KRP8DFGJI�K�?����=2dFK�XCZ�`HKM?:ZJA"Z\=2IBP8G�=@I$Z\=YD/XCLNK�Z:l�K�K�XQDFGJW]=2X�A�G\^4q/G�D/EHX�WCAFX�W�S@AFWHWHK�GJ?;l~`�A�Z�e4E�?UZ`VA�_H_NK�X�AF?��&LNK�I�DFe&K�?>S@A�G\qFK �

Ii<Q�Bq/AF=YXCA/?�?�EHe&K>Z�`HKRl�AFSYS�=2?�P8G�=@I$Z\=YD/XHSYKi?�?�a�¤]A*^6Z\`HKBS@AFW�W]K�G�=@?6A:EV?:Z�DFX&Z�`�KcdFK�G�q/K~D�P�?US2=2_H_H=2XHqsA"Z � � � � �Ha»{`VA"Zc=@?�Z�`HKMP8D/G�e4EHS2A4P8D/G>Z�`HK6?UZ\A�Z�=@I�P8G�=@I$Z\=YD/XI�D[K��CI�=2K�X[ZcD�P�Z�`HK-q/G�D/EHX�W �

WV<Q�R?�?�EHe&=2XHq�Z\`HKQ��D(DFGs=@?4P8G�=@I$Z\=YD/XHS2K�?\?�ojl~`�A�ZgAFG�KnZ�`HKK��]_HG\K�?\?U=2DFXV?-P8DFG4Z�`�KQXHD/G�e�AFS�P8DFGJI�Ki?sDFPcZ�`�Kq/G�D/EHX�WxA�X�W�l�AFSYS�o�A�XVW�Z�`�K&?UZ\A�Z�=@I4P8G�=@I$Z\=YD/X�P8DFGJI�KgD�P�Z�`HK&l>A�S2S ��»{`�A�ZMD/G\WH=YX�AFG�^P8G\=2I�Z�=2DFX�G�E�SYKg=2?d(=2DFS@A"Z\K�WQ=YXZ�`�=2?cI�AF?�K��

¾H� ³ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�b�A�GJh/E�=YXmI�A�Z>D/XmLVKiA�emo]LHG\K�A�O(=2XHqgZ�K�X�?U=2DFX³ a~b�A�GJh[EH=YX�¤(EH_NK�G\LHE�?�Z\`HKCI�A�Z-=2?Ml>A�S2O(=YXHq�AFSYD/XHqA`HD/G�=2��D/X[Z\A�S�LNK�A�e Z�`�A�Z-=2?6A�ZUZJAFIJ`HKiW�Z�D�Al>A�S2S�L[^xAP8G\K�K�SY^sZ�EHG\XH=2XHq�oFP8G�=@I$Z\=YD/XHSYKi?�?�`H=YX�qFKFa�b�A�GJh/E�=YX&`�A/?�e&A/?�? � � � ��AFX�W4Z�`HKBLVKiA�ef`VAF?je�AF?\? � � ajb>`HK~LVKiA�e=@?~XHDFZ>E�XH=�P8D/G�emoHL�E]Zc`�AF?~I�K�X[Z�K�G~D�P�e�AF?\?~A"Z � � � � o]l~`HK�G�K ��=@?�Z�`HK6I�D(DFGJW]=YXVA"Z�KMA�S2DFX�q4Z\`HK-LNK�A�e}l~=�Z\`Z\`HK-DFG\=Yq/=YXmA"Z~Z\`HK-l>A�S2S�a�b>`HK-LNK�AFe�=@?~?UE�_H_VD/GUZ\K�WL(^QAgG\DF_NK�G\K�A/IJ`H=2XHqgP8G�D/e Z�`HK-K�X�WD�P�Z�`HK-LNK�AFe}A�Z� �sZ\D4Z\`HK-l>A�S2S�ajb>`HK-A�X�qFS2KRLNK�Z:l�K�K�XnZ\`HK-G�D/_VKMA�XVWCZ\`HKM`HDFG\=Y��DFX[Z\AFS�=2?��Ha�b>`�K�e�A��(=2esE�e Z�K�X�?U=2DFXQZ�`�KG\DF_NK-I�A�Xm?�EH_H_NDFG�Zc=2? ��� � � � � � a ������ � ¡RG\A*l�AgqFD(D]WQW]=@A�q/G\AFemaA[<nb�A�GJh[EH=2XM?UZ\AFGUZJ?pA"Z�Z\`HKjDFG\=2qF=2XMAFX�W�l�AFSYO]?�D/E]Z:l�AFG\W�a�»{`�A"Z�=@?pZ\`HKjK��]_HS2=@I�=YZ�K��]_HG\K�?\?U=2DFXRP8DFG�b�AFG\h[EH=2X�· ?_ND/?�=YZ�=2DFX ��AF?�P8EHXVI$Z�=2DFXmDFP�Z�`�K-D�Z�`�K�G~d"A�G\=2AFLHS2K�?�

LN<��=2dFK�X � � � � $ ³ � ¾jO(q�o � � $ ��¾jO(q�o � � ��� $ � � ¶ emo � � $�µ � ¾jemo � $ ³ ¾ �Fo;A�XVW ��� � � � � � $�i¾F¾/¾� 6o(l~`�A�Zc=2?>_ND/?�=�Z\=YD/XQl~`�K�G\KRZ\`HK-G\DF_NK-LHG�KiA�O]?�u�=�a K/aYo � � � � � � �

Ii<Q�R?�?�EHe&=2XHq�b�A�GJh/E�=YX�P,A�S2S@?MP8G�D/e Z\`HKCLNK�AFeo�l~`HK�Z�`HK�G6=YZ4LHG\K�AFO(?MD/G6XHDVo�`HD"l P,A�GgW]D(K�?-`�K�P,A�S2S;=2X³ � ¾;? ��B?\?�EHe&K�X�DgAF=YG>G\K�?�=2?UZ\AFX�I�K�A�X�WnqFG\K�A"Z�=YX�=�Z\=2AFSp`HK�=2qF`[Z�aj¡RDFX�· Z~LVDFZ�`HK�G>l�D/G�G\^(=YXHq4A�LNDFE]Z~`HD"l`�K6W]=2?�K�X�q/A�q/K�?�P8G\DFe Z\`HKMZ�`HK-LNK�AFemuj=�Zi· ? A:EV?:ZBA&?�=Ye&_HS2KMP,A�S2S�I�AFS2I�EHS2A�Z�=2DFX�a

WV<n»{`VA"Z�· ?cb�A�GJh[EH=YX�· ?�O(=YX�K�Z�=@IMK�X�K�G\qF^nA�Z ³ � ¾;?>=YXQZ�`HK-_VA�G�Zs5,I�<>?\I�K�X�A�G\=2D �K*<Q¸�E�IJO(=YS2^QI�A"ZJ?BAFI�Z�E�AFSYS2^nG\K�A/IJ`Z�K�G\e&=YXVA�S�d/K�S2D(I�=�Z:^A"P Z\K�GRAFLVD/E]ZR��¾�e}A�XVW��K��Z�`HK�e�?UK�SYd/K�?cAFG�D/EHX�WZ\DnS@A�X�WmD/XmZ�`HK�=YGRP8K�K�Z�u�Z�`�K�^m_VD/EHX�I�KsDFXmZ\`HK4��A�G�Z�`�acb>`�K�^E�?UEVA�S2SY^m?UE�G�d(=2dFK6=2X�P,A�=2GR?�`�AF_VK��wLHEHZ=YZ�· ?~XHDFZBAgG�KiI�DFe&e&K�XVW]K�WI�A�ZcK��]_VK�G�=2e&K�X[Z�uj=�a KFa2o]Z�`HG\D"l~=2XHqsZ\`HK�e}DB�x?�O(^]?�I�G\AF_VK�G\?�a�»{`�=2IJ`mD�P�Z�`�K ��� O(=2X�WH?MDFP�I�D/SYS2=@?U=2DFX�W]D(K�?MDFS@W�b�A�GJh[EH=2Xx`�A*d/Ksl~=YZ�`�Z�`�K&��A�G�Z�` � ��� Z�`HK�W]E�?UZ6`�A/??�K�Z�Z�S2K�W �

¾H� ³ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\DFS2SY=2XHq�AgG�D/SYS2K�G>D"d/K�G~A&?:Z\K�_µ�a~��G\DFS2S2K�G658K�=�Z\`HK�GRA�?U_H`�K�G\=2I�A�S2SY^n?�^(e&egK�Z�G\=2IMLVA�S2S�DFGBA�I�^(SY=2X�W]G\=2I�A�S2SY^Q?U^(e&e&K�Z�G\=@I-I�^(SY=2X�W]K�GJ<�=@?~G\DFS2SYKiWEH_Z\DgAg?:Z\K�_mA�X�WnG�Ki?:ZJ?�AFq/AF=YX�?UZ�=YZ�a�b>`�K�G\DFS2S2K�G�`�AF?�G\A/W]=2E�? ��A�X�Wne&A/?�? ��a�b>`HK�?UZ�K�_Q`VAF?�`HK�=2qF`[Z ��l~=�Z\`� � �ga��fP8DFGJI�K � � � �Q=2?�A�_H_�SY=2K�W�`HDFG\=Y��DFX[Z\AFSYS2^CZ\DnZ\`HKsG\DFS2S2K�GMA"ZR`�K�=2qF`[Z � Z�DQZ�G\^Z�DQ_HE�?�`�Z�`�KsG\DFS2SYK�GD"d/K�G~Z\`HK4?UZ�K�_�aR�fSY=2XHK4WHG\A*l~XmZ\`HG�D/EHqF`mZ\`HK4AF_H_HS2=YKiWmP8DFGJI�Ks_�AF?\?UKi?~Z\`HKsG\DFS2SYK�G�· ?BI�K�X[Z�K�GBDFP�e&A/?�?�ac|�=YXVWZ\`HK~K��]_HG\K�?\?U=2DFXsP8DFG � � � �RZ�`�A�Z6A:E�?:Z�e&AFG�q/=YXVA�S2SY^-S2=�P ZJ?�Z�`�K~G�D/SYS2K�Gia�b>`H=@?j=@?�AM?:ZJA"Z\=2I�K�h[EH=2S2=YLHG\=2EHe ?�=�Z\E�A"Z\=YD/Xl~`HK�G�K&Z\`HKCXHD/G�e�AFS�P8DFGJI�K�D�P�Z�`�KCqFG\DFEHXVW�`�A/?<A:E�?UZsqFD/XHK&Z�D���K�G\D�o�LHE]Z6Z\`HKCG\DFS2SYK�G-=2?6?UZ�=2S2S;e�A�G\qF=2X�A�S2S2^Z\DFE�IJ`H=2XHq�Z\`HKsq/G�D/EHX�Wpa~»{`VA"Z�AFG�K6Z�`HK � � � � d"A�S2EHKi?cP8D/G � $ ¾CAFX�W � $ ��� �������� � ¡BGJA*l�A�qFD(D]WW]=@A�q/G\AFemo[EV?UK-q/K�DFe&K�Z�G\^Fo]A�X�W=@W]K�X[Z\=�P8^nZ�`HK-LNK�?UZc_H=2dFD�Z~_NDF=2X[Z~P8DFGcA4Z�D/G\h[EHK-I�AFS2I�EHS@A"Z�=2DFX�a

Page 69: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � �'5<&)(+*O; 6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H��µgh[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujq/G\A*d(=YZ:^&A�ZUZ\G\A/I$Z\?~AFSYl>A*^]?�Fac��GJA*d(=�Z:^�=@?�u

A[<nAFSYl>A*^]?>A"ZUZ\G\A/I$Z\=Yd/KFaLN<QAFSYl>A*^]?�G�K�_HEHS@?U=2dFK/aIi<nK�=�Z\`HK�GRA"ZUZ\G\A/I$Z\=Yd/KRD/G~G�K�_HEHS@?U=2dFK/aWV<nX�K�=YZ�`HK�GBA"Z�Z�GJAFI$Z\=Yd/KRX�DFG~G\K�_HEHS@?�=Yd/KFaK*<nX�K�=YZ�`HK�G~�V?�`QXHD/G>P8D"l~S�a

¾H��µgh[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�qFGJA*d(=�Z:^CAFX�WQ?UZ�G\E�I�Z�EHG\K�]a �\¸�K�Zi· ?c_HS2A*^��]1\��D3�����"# 1 |�DFG �]��¾/¾Ho]Z\`HKsA�XV?Ul�K�G~=@?�u>b>`H=@?>P8DFGJI�Ks=2?~Ki?�?�K�X[Z\=2AFS�=YX�e�AFO[=2XHq&Z\`HKsS@A�G\qFK�Tk?\I�AFSYK?UZ�G\E�I$Z\EHG\KBD�P�DFL,A:KiI$Z\?M5,D�P�Z\`HKRO(=2X�WCl�K�O[X�D"lB<�P8G\DFe e&=2W�W]SY=2XHq&AF?UZ�K�G�D/=2WH?;Z�Dg?UE�_VK�GUT!I�S2E�?UZ�K�GJ?�D�P�q[A�S@A"�]=YKi?AFX�Wn_NK�G\`�AF_�?>Z�DgZ\`HK-EHXH=2dFK�G\?�K-AF?�l~`HDFS2KFa �A[<C»{`VA"Zc=@?~A�I�DFX[ZJAFI$Z>P8D/G\I�KFo]�cS2K�� �LN<n»{`VA"Zc=@?�P8G�=@I$Z\=YD/X�o��cS2K�� �Ii<n»{`VA"Zc=@?~AgZ�K�XV?U=2DFXQP8DFGJI�K/oH�cS2K�� �WV<n»{`VA"Zc=@?~A&XHDFG\e�A�SNP8DFGJI�K/oH�cS2K�� �K*<n»{`VA"Zc=@?>qFGJA*d[=YZ:^Fo]�BSYK����

¾H��µgh[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u� BK�l>Z�D/X�· ?>S2A*lzD�P�qFGJA*d[=YZ:^³ a~ BK�l>Z�D/X�· ?~S2A*l�D�P�qFGJA*d[=YZ:^&P8DFG>Z\`HKMP8DFGJI�KMK��(K�GUZ\K�WQL(^C_VD/=YX[Zce�AF?\?M�MDFX_VD/=YX[Zce�AF?\?c�4=2?�u

A[< �� ��� $�� � � � � � � � � aLN< �� ��� $���5 � � � � � < � � � � aIi< �� ��� $���5 � � � � � < � �� aWV< �� ��� $���5 � � � � � � < � � � aK*< �� ��� $���5 � � � � � � < � � � a

¾H��µgh[e4EHS�ZB¾/¾ ³ ��¾4�Q� ³ e&D]Wpaje&K�e&DFG\^�u�e�A/?�?~AFX�Wnl�K�=2qF`[ZcA�LND"dFKM�;AFGUZ\`� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ¶�½ T!� ¶

µ�a~�BX�DFL3A:K�I$Z�`�AF?Re�AF?\?��rA�X�W�l�K�=Yq/`/Z��mDFX�Z\`HKg��A�G�Z�`�· ?B?�EHG�P,AFI�KFaB»{`VA"ZM=2?R=�ZJ?�e&A/?�?RA�X�W�l�K�=Yq/`[ZRA"Z-���A�G�Z�`G\A/W]=Y=�AFLVD"d/KBZ\`HK6�;AFGUZ\`�· ?�?�EHG�P,AFI�K��

A[<���AFX�W ���F�]a LV< � ���&AFX�W ���F�]a I�<���A�X�W � � ½ a WV<��xAFX�W ���"µ�a Ki<�� � ½ AFX�W� � ½ a

¾H��µgh[e4EHS�ZB¾/¾�µ[¾F¾C� ³�³ K�A/?U^�e�A�Z�`�u;?UZ�G\K�X�q�Z�`D�P�qFGJA*d(=�Z:^¶ a~�R?U=2XHq� cK�l>Z�DFX�· ?~S@A*l�DFP�q/G\A*d(=YZ:^

�� ��� $� � � � � �

� � �

5�� $ ¹ � ¹ º*µ[¾[º ���i¾ � � �&=2X�e&O]?6EHX�=�ZJ?\<4I�AFS2I�EHS2A�Z�K�Z\`HKne�AFqFXH=YZ�E�WHKnD�P~Z\`HKCP8D/G\I�K�?sLVK�Z:l�K�K�XrZ:l�D ³ O(qD/L,A:K�I�Z\? ³ e�AF_�A�G�Z�ajb>`HK6AFX�?�l�K�G�=@?�u

Page 70: Introductory Physics Problems David J. Jeffery Department of

¹F¹ v�`�AF_]Z�a~��µ}��GJA*d[=YZ:^

A[< ¹ ¾ � � �x�i¾ � � � ���*� �x�i¾ � � �VS2L�aLN<�F¾ � ¾ �x�i¾ � � � �{µ ����¾ � � �VSYL�aIi< ¹ � ¹ º ³ ����¾ � � �N  � � � ³ �x�i¾ � � �VS2L�aWV<� � �/�"µ ����¾ � � �N  ��¾ � ¶ �x�i¾ � � �VS2L�aK*<Q¾ � º"µ�� ����¾�� � �   ��¾ � � ¶ ����¾ � � � SYL�a

¾H��µgh[e4EHS�ZB¾/¾ ¶ ¾F¾4�Q�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�uj?�DFS2=2WA�XHq/SYK-W]K���XH=YZ�=2DFX¹ a~b>`HK6WH=���K�G\K�X[Z�=@A�S�WHK���XH=YZ�=2DFXmDFP�?�DFS2=2WA�X�qFS2K�=@?�u

A[< ��� $ � � �� � � aLN< ��� $ 5 � ���� ��< � � aIi< ��� $ 5 � � �� � � < � � aWV< ��� $ � �� � � aK*< ��� $ ,65 � �� � < � � a

¾H��µgh[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ µ&K�A/?U^&Z\`H=2XHO(=YXHqVujZ:^(_H=@I�A�S�?�DFS2=@WQAFXHqFS2K�?º(a~b>`HK ?UD/SY=@W AFXHqFS2K�?�?UE�L]Z�K�X�W]K�W L[^�A}?U_H`�K�G\KFo�`HK�eg=@?�_H`HK�G\KFo�?�K�e&=YT�`�K�e&=2?�_H`HK�G�K/o�A�X�W WHK�e&=�T!?�K�e&=�T`HK�e&=2?�_H`HK�G�K�58=�a KFa2o�A�XmD]I$ZJA�X[ZJ<�A�G\KFo]G\K�?�_NK�I$Z\=Yd/K�S2^�uA[<n?�D�P ZB?�DFS2=@Wpo]`�A�GJW?UD/SY=@Wpo]`�AFG\W]K�G~?UD/SY=@Wpo�AFX�Wn`VA�GJW]K�?UZc?UD/SY=@WpaLN<nµ ¶ ��o ½ ¾��"o�� ¼ ¾ ��oHA�X�W ³/¹ ¾ ��aIi< ³/¹ ¾ � o�� ¼ ¾ � o ½ ¾ � o�AFX�Wnµ ¶ � aWV<nµ��joV� �jo �joVA�X�W � ���HaK*<�� �F�]o �joV���jo�A�XVWnµ��ja

¾H��µgh[e4EHS�ZB¾/¾[º�¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujq/G\A*d(=YZ\A"Z\=YD/X�A�Sp�MA�EV?�?�·]S2A*l¼ ac�MAFE�?�?�·]S@A*l�P8DFG~q/G\A*d(=YZ:^Fo(l~=YZ�` �#��6G\K�_HG\K�?�K�X[Z\=YXHqgqFGJA*d(=�ZJA"Z\=YD/X�A�SVP8DFGJI�KM_NK�G~EHXH=YZBe�AF?\?�o]=2?�u

A[<�� �# � � � �� $���� � � � � � � � � aLN<�� �# � � � �� $��&aIi<�� �# � � � �� $� � � � � � � � � aWV< � �#�� � � �� $ ,~µ�� ��� � � � � ��� � �FaK*<�� �#�� � � �� $ ,~µ�� ��� � � � � � � � �[a

¾H��µgh[e4EHS�ZB¾/¾ ¼ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�EHXH=YP8DFG\e}?�_H`HK�G�KMqFGJA*d(=�Z:^g��K�S2W½ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�u

�#� $ ����5 , � <��� ��� �

� � )�� �

� � �ga �

A[<C»{`VA"Zc=@?c�MA�E�?\?�·�S2A*l{P8D/G~qFGJA*d(=�Z:^/o(�BSYK�� �LN<n»{`VA"Zc=@?c�MA�E�?\?�·�S2A*l{P8D/G~K�S2K�I�Z�G\D/?UZ\A"Z\=2I�?�oH�BSYK�� �Ii<n»{`VA"Zc=@?~AgZ�K�XV?U=2DFXQP8DFGJI�K/oH�cS2K�� �WV<n»{`VA"Zc=@?~A&XHDFG\e�A�SNP8DFGJI�K/oH�cS2K�� �K*<n»{`VA"Zn=@?&Z�`�K�qFGJA*d(=�ZJA"Z�=2DFXVA�S�P8DFGC_NK�GnEHXH=YZne�AF?\?�58=�a K/aYo�Z\`HK�qFGJA*d(=�ZJA"Z\=YD/X�A�S���K�S2W�<&P8DFGnArEHX�=�P8D/G�eWHK�X�?�=�Z:^?U_�`HK�G\KRDFP�GJAFWH=YE�?��fA�X�We�AF?\?�� o��cS2K�� �

¾H��µgh[e4EHS�ZB¾/¾ ½ ¾F¾4� ³�³ e&D]W]K�GJA"Z\K�e�A�Z�`�u�I�A�S@I�EHS@A"Z\KMI�K�X[Z�G\=YP8EHq/AFSV�VK�S@W��¾Hac��=2dFK�XtZ\`HK�e&K�AFXwG\A/W]=YEV?&D�P�Z�`HK���A�G�Z�` � � $ ¹ � ³ º(�*� ³ �{��¾�!�emo�D/XHKm��X�W�?�Z�`VA"ZCe�A�q/XH=�Z\E�W]K�AFX�W

W]=2G\K�I$Z\=YD/XQDFP�Z\`HK6I�K�X[Z�G\=�P8EHq[A�SNP8DFGJI�KM_NK�GcE�XH=�Zce�A/?�?~A�Z>µ ¶ � W]K�qFG\K�Ki?>XHDFG�Z�`S2A�Z�=YZ�E�WHK6A�G\KFuA[<��z� � µFe���? �R_VK�G�_NK�XVW]=2I�EHS@A�G\SY^C=2X(l�AFG\WnZ�D"l>A�GJW�Z\`HK6�;AFGUZ\`�· ?�A��]=2?�a

Page 71: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~��µ}��GJA*d(=�Z:^ ¹ º

LN< �z� � µ�e��"? �R_VK�G�_NK�X�WH=2I�EHS2AFG�S2^CD/E]Z:l�AFG\WCP8G�D/e Z\`HK-�;A�G�Z�`�· ?~A��(=@?�aIi< ��¾ � ¾/��µ�e��"? �c_NK�G\_VK�X�W]=@I�EHS@A�G\S2^CDFE]Z:l>A�GJW�P8G\DFe�Z�`HK6��A�G�Z�`�· ?>A"�]=@?�aWV< � ½ � ¼ e��"? �R_VK�G�_NK�X�WH=2I�EHS2AFG�S2^CD/E]Z:l�AFG\WCP8G�D/e Z\`HK-�;A�G�Z�`�· ?~A��(=@?�aK*< � ½ � ¼ e��"? �R_VK�G�_NK�X�WH=2I�EHS2AFG�S2^C=2X(l�AFG\WnZ�D"l>A�GJW&Z�`�K6�;A�G�Z�`�· ?~A��(=@?�a

¾H��µgh[e4EHS�ZB¾���¾/¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujq/G\A*d(=YZ:^g=2X�?�=2WHK6A4`�DFS2SYD"l�?U_H`�K�G\K�F�Fa~b>`HK-q/G\A*d(=YZ\A�Z�=2DFX�AFS���K�S2W�5,qFGJA*d(=�ZJA"Z�=2DFXVA�SVP8DFGJI�KM_VK�GcEHXH=YZBe�AF?\?J<;=2X�?�=2WHK6A�I�K�X[Z\G\AFS�I�A*d(=�Z:^�DFP�AFXm=2?�DFS@A"Z\K�W

?�_H`HK�G�=@I�AFSYS2^n?�^[e&e&K�Z\G�=@I�e�AF?\?~W]=2?UZ�G\=2LHE]Z�=2DFX=@?�uA[<n¾�aLN< �# � $ , ��5 � � < � aIi< �#� $ , ��5 � � �*< � aWV< �#� $ , ��5 � � < � aK*<n=2X]��X�=�Z\KFa

¾H��µgh[e4EHS�ZB¾��F�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj²MK�_HS2K�Gi· ?M��?UZ>S@A*l�i�]a~�RI�I�D/G\WH=YXHqgZ\D&²MK�_HS2K�Gi· ?M�i?:Z~S@A*l-o(Z�`HK-D/G�LH=YZ\?>DFP�Z:l�D&qFGJA*d[=YZ\A�Z�=2DFX�AFSYS2^&LVD/EHX�WmI�K�SYKi?:Z\=2AFSpLVD]W]=2K�?BA�G\KFu

A[<CD"d"AFS2?�l~=YZ�`mZ�`�K6I�K�X[Z\K�G~D�P�e�AF?\?>D�P�Z�`HK6?�^]?:Z\K�e�A�Z~A&_NDF=2X[Z>Z�`�A�Zc=2?cA4P8D]I�EV?�P8DFGcKiAFIJ`nD"d"AFS�aLN<Q?\h[E�A�G\K�?�aIi<CZ\G�=@A�X�qFS2K�?�aWV<QI�^(esL�AFS2?�aK*<nK�SYS2=2_�?UKi?>l~=�Z\`Z�`HK6I�K�X[Z�K�G~D�P�e&A/?�?>DFP�Z\`HK6?U^]?UZ�K�e}A"ZcAg_NDF=2X/Z~Z\`�A"Zc=@?cA4P8D]I�E�?�P8D/G~K�A/IJ`QK�SYS2=Y_V?UK/a

¾H��µgh[e4EHS�ZB¾��i�F¾F¾4�Q�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�DFG\LH=YZ\AFS�A�XHq/EHS2AFG>egD/e&K�X[Z�EHe� ³ a~b>`HK6AFXHqFE�S2AFG�e&D/egK�X[Z�EHe}D�P�AFXQD/G�L�=�Z\=YXHq&LND]W]^n=2X�AgI�K�X[Z�GJA�S�P8D/G\I�K-?U^]?UZ�K�e�=2?�u

A[<C_�G�D/_VD/GUZ\=YD/X�A�SNZ�D&GJAFW]=@A�S�WH=2?UZ\AFX�I�K/aLN<QI�DFX�?UZ\AFX[Z�aIi<n=2X(dFK�G\?�K�S2^�_HG\DF_NDFG�Z�=2DFX�AFSVZ\D&G\A/W]=2AFS�W]=@?:ZJA�X�I�KFaWV<n_�G�D/_VD/GUZ\=YD/X�A�SNZ�DgZ\`HK-=YX(d/K�GJ?UK-?\h/EVA�G\KRDFP�GJAFW]=@A�S�W]=@?UZ\A�XVI�KFaK*<Q?�=2X[EV?UD/=2WHAFS�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H��µgh/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�I�A�S@I�EHS@A"Z\K�q&q/G\A*d(=YZ\A"Z\=YD/X�A�S�AFI�I�K�SYK�G\A�Z�=2DFX�FaBv�AFS2I�EHS2A�Z�K&Z\`HKnq/G\A*d(=YZ\A"Z\=YD/X�A�SjA/I�I�K�SYK�G\A�Z�=2DFX �P8D/G-Z�`HKQ�;A�G�Z�`�· ?6?�EHG�P,AFI�K�qF=2dFK�X � $ ¹ � ¹ º*µ[¾[º ����¾ � � �e&O]?cEHX�=�ZJ?�oN�;A�G�Z�`me�AF?\? � � $ ¶�� ½ º"µ[� �r��¾����pO(q�oVA�X�Wme&K�AFX��;A�G�Z�`mGJAFW]=2E�? � � $ ¹ � ³ º(�*� ³ �r��¾�!�ea»{`�A�Zc=2?�Z\`HK-_NK�GJI�K�X[ZJA�qFK-W]= ��K�G\K�X�I�KRP8G\DFe�Z�`HKM�NW]E�I�=@A�S

�� $ ½ � ¼ ¾je��"? �cZ\`�A"Z~=@?cI�D/ege&D/XHSY^nE�?UKiWpa

¾H��µgh/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujq/G\A*d�_ND�Z\K�X[Z�=@A�S�=2X�?U_�`HK�G\=2I�A�Sp?�^[e&e&K�Z\G�^�]ac��=2dFK�XnZ\`�A"Z~Z\`HK-qFGJA*d(=�ZJA"Z�=2DFXVA�SV��K�S@WD�PjA4E�XH=�P8D/G�e W]K�XV?U=YZ:^n?�_H`HK�G\KMD�P�e�AF?\? � A�XVWnGJAFW]=2E�?���=@?

�#�� $�����5 , � <��� ��� �

� � )�� �

� � �go

l~`�A�Z�=2?�Z�`HKBK��]_HG\K�?\?U=2DFX4P8DFGjZ\`HKcq/G\A*d(=YZ\A"Z\=YD/X�A�S(_ND�Z\K�X[Z�=@A�SHK�XHK�G\qF^s_VK�G;EHXH=YZ;e�AF?\? ��5,E�?UEVA�S2SY^&I�AFSYS2K�W4Z�`�Kq/G\A*d(=@A"Z�=2DFXVA�Sp_ND�Z�K�X[Z�=@A�S <��±b�AFOFKsZ�`HK4��K�G\DCDFPjZ�`HKgqFGJA*d(=�ZJA"Z�=2DFXVA�S�_ND�Z\K�X[Z�=@A�S�Z�DQLVKgA"ZR=2X]��X�=�Z:^/a ������ �»rA"ZJIJ`QZ\`HD/?�K-I�D/X�?:ZJA�X[Z\?�DFP�=2X[Z�K�q/G\A�Z�=2DFX�a

Page 72: Introductory Physics Problems David J. Jeffery Department of

¹F¼ v�`�AF_]Z�a~��µ}��GJA*d[=YZ:^

¾H��µgh/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujLHE�=YS@W]=2XHqCA&?UK�S�P TkqFGJA*d(=�ZJA"Z�=2XHq&?U`�K�S2S³ a~ R�R¤]� `�A/? A:E�?UZ�A*l�AFG\W]KiWr^FD/E�A�I�DFX[Z�GJAFI�ZsZ�D�I�D/X�?:Z\G�EVI$Z4=2X�D/G�L�=�Z�A�q/=2AFX/Z&?U_�`HK�G\=2I�A�S>?U`�K�S2S�DFPBe�AF?\?� AFX�WzG\A/W]=YEV? �ga �/E�?UZ�AF?\?UEHe&KxZ�`HK�?�`HK�S2S-=@?Qd"AFXH=2?�`H=2XHqFS2^wZ�`�=YX A�X�W�Z�`VA"Z�K ��K�I�Z�=2dFK�S2^{^FD/E�`�A*d/KZ\DxLHG\=2XHq�Z\`HKme&A�Z�K�G�=@A�S�Z�D�LHEH=2S2W�Z�`HKm?�`HK�S2S�P8G�D/e =YX]�VXH=�Z:^�=2XwA�X�DFZ�`HK�G�l~=@?UKQK�e&_]Z:^�EHX�=Yd/K�GJ?UK/arb>`(E�?q/G\A*d(=YZ\A"Z\=YD/X�A�S�_VDFZ�K�X/Z\=2AFS�K�XHK�G�q/^�D�P�Z\`HK&e&A�Z�K�G�=@A�S�A"ZM=YXH��XH=YZ:^ ��A�XVW�7ce&KiA�XxZ�`HK&W]= �NK�G�K�X/Z\=2AFS�LH=�ZJ?-A�G\K=2X]��XH=YZ�K�SY^?UK�_�A�GJA"Z\K�WnP8G�D/e K�A/IJ`QDFZ�`HK�G �{=@?���K�G\D�ajb>`HKi?UK6AFG�K�G�KiAF?�DFX�AFLHS2KB��GJ?UZUTkDFGJW]K�G>A�_H_�G�D*�]=2e&A�Z�=2DFX�?�aA[<C»{`VA"Z�· ?�Z�`�K&Z�D�ZJA�S�IJ`�AFXHqFKg=2X�_ND�Z\K�X[Z�=@A�SjK�XHK�G\qF^�=2X�I�D/X�?:Z\G�EVI$Z�=2XHqQZ�`HKC?�`HK�SYS � �B?\?UE�egK&S2K�?\?�Z�`�AFXG\K�A/?UD/X�A�L�SY^/oVLHEHZRZ\DQe�A�O/K6Z\`HK&_HG�D/LHS2K�e Z�GJAFI�Z\A�L�SYK/oVZ\`�A"Z6A/?B^/DFE�LHG\=2XHqnEH_�K�A/IJ`�W]= �NK�G�K�X[Z�=@A�S�LH=YZDFPBe�A"Z\K�G\=2AFS�^/DFE�?�e&K�A�Gg=YZ&D/E]Z&D"dFK�GsZ�`HKml~`HD/SYK?U_�`HK�G\KnZ\Dx_�G�Ki?UK�G�d/KnA�?�_H`HK�G�=@I�AFSYS2^�?U^(e&e&K�Z�G\=@Iq/G\A*d(=YZ\A�Z�=2DFX�AFS���K�S2WmA�ZBA�S2S�Z�=2egKi?�a

LN<Q BD"l�l~`�A�Zc=�Pj^/DFEmW]=2WHX�· Zc_�G�Ki?UK�G�d/K�?�_H`HK�G�=@I�AFS�?U^(e&e&K�Z�G\^n=2X�I�D/X�?:Z\G�EVI$Z�=2XHqgZ�`�K6?U`HK�SYS ��»�DFE�S2WQZ�`�KIJ`VA�XHq/K�=2XQZ�D�ZJA�S�_ND�Z\K�X[Z�=@A�SpK�XHK�G\qF^nLVKMZ\`HK6?�AFe&K��

Ii<n»{`VA"Z�WHD[Ki?pZ\`HK;_ND�Z\K�X[Z�=@A�S/K�XHK�G�q/^BqFK�Z�IJ`�AFXHqFKiWM=YX[Z�D����������� � b>`HK�G\K;I�AFX-LVK;XHDRW]K���XH=YZ�K�A�X�?�l�K�Gl~=YZ�`�DFE]Z~?U_NK�I�=�P8^(=2XHq6Z\`HKRI�DFX�WH=�Z\=YD/X�?;K��HAFI$Z\SY^/a ��EHZ�=2e&AFqF=2XHKB^/DFECAFG�KRLHEH=2S2W]=2XHqsZ�`H=@?�?�_H`HK�G�K/o(l~`HK�G\K_�S2AFE�?U=2LHS2^C=@?>Z�`HK-K�XHK�G\qF^�q/DF=2XHq�a

WV<Q¸�K�Z � $���¾ � O[qRA�X�W � $ ³ ¾jema�»{`�A"Z�=@?pZ�`�K�IJ`�AFXHqFKj=2Xs_ND�Z\K�X[Z�=@A�S[K�X�K�G\qF^RWHEHG�=2XHq�I�DFXV?:Z\G�E�I�Z�=2DFX �7:?~?�K�SYP TkqFGJA*d[=YZ\A�Z�=2DFXQD�P�Z\`HK-e�A"Z\K�G\=2AFSpesE�IJ`D�PjA&I�DFXVI�K�G\X=YXZ�`�=2?cI�AF?�K��

¾H��µgh/P8EHS2S�¾/¾ ¹ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujLHE�=YS@W]=2XHqCA&?UK�S�P TkqFGJA*d(=�ZJA"Z�=2XHq&?U_�`HK�G\Kµ�aB°�I�D/X�?:Z\G�EVI$Z�K�EHG;I�D/?�eg=@h[EHK~K��(Z\G\AFDFGJW]=YXVA�=2G�K/o"DFX�I�KcA�q/AF=YX& B��¤]��A*l>A�GJW]KiWs^/DFE&A6I�D/X/Z\G\A/I$Z�Z�D4I�DFXV?:Z\G�E�I�Z=2X�?�_�AFI�KFa�b>`H=@?-Z\=Ye&K=�Zg=2?4A�qF=@A�X[Z�o�EHX�=�P8D/G�e W]K�XV?U=YZ:^�?U_H`�K�G\KCD�P~e�AF?\? � A�XVW�G\A/W]=2E�? �ga��B?\?�EHe&KZ\`�A"Z~K ��K�I�Z�=2dFK�SY^�^/DFEC`�A*d/KcZ\D4LHG\=2XHqsZ\`HK�e&A�Z�K�G�=@A�SVZ�DgLHEH=2S2WnZ�`�KM?�_H`HK�G�KBP8G�D/e =YXH��XH=YZ:^C=YXA�XQD�Z�`�K�G\l~=2?�KK�eg_HZ:^sEHXH=2dFK�G\?�KFa�b>`(E�?jq/G\A*d(=YZ\A"Z\=YD/X�A�S[_ND�Z�K�X[Z�=@A�SHK�XHK�G\qF^6DFPVZ\`HKce�A"Z\K�G\=2AFSHA"Z�=2X]��XH=YZ:^ �{AFX�W&7�egKiA�XgZ�`�KW]= ��K�G\K�X[Z�=@A�S]LH=YZ\?;A�G\K�=2X]��X�=�Z\K�S2^4?�K�_�AFG\A�Z�K�WsP8G\DFe KiAFIJ`gD�Z�`�K�G��w=@?���K�G�DVa�b>`H=@?j=@?jARG\K�A/?UD/X�A�L�SYK���GJ?:Z�T�D/G\W]K�GAF_H_HG\D*�(=2e�A"Z\=YD/X�aA[<nb�D�?UZ\A�G�ZCl~=YZ�`{l~`�A�Zn=2?�Z�`HK�q/G\A*d(=YZ\A�Z�=2DFX�AFS�K�XHK�G\qF^t_VK�GCEHXH=YZne�AF?\? � 5,=�a KFa2o>Z�`�K�qFGJA*d(=�ZJA"Z�=2DFXVA�S_ND�Z\K�X[Z�=@A�S <<A:EV?:Z�A"Z4Z�`HK?UEHG�P,AFI�KCD�PB?�_H`HK�G�=@I�AFSYS2^r?U^(e&e&K�Z�G\=@I�e�AF?\?sW]=@?:Z\G�=2LHE]Z\=YD/X�D�Pce�A/?�? � AFX�WGJAFWH=YE�? � ¯�A�O/K�Z�`�KnI�D/X[d/K�X[Z�=2DFXVA�S;A/?�?�EHe&_]Z�=2DFXV?MZ�`�A�Z ��=@?-Z\`HKn_ND�Z\K�X[Z�=@A�S�W]= �NK�G�K�X�I�KCG\K�S@A"Z\=Yd/KZ\Dt=2X]��X�=�Z:^�AFX�W�=2X]��X�=�Z:^{=@?m?UK�ZZ\Dt��K�G\D�_ND�Z\K�X[Z�=@A�S�a �������� � b>`�=2?m=@?UX�· Zm=YX[Z\K�X�W]KiW�Z\DtLNKrAWHK�G\=Yd"A"Z\=YD/X�a �/E�?UZ6G�=2qF`[Z6W]D"l~XxZ�`HKnI�DFG\G�KiI$ZMK��]_HG\K�?\?U=2DFXxP8G\DFe e&K�egD/G�^�DFG6AmG\K�P8K�G\K�XVI�K&K�h[E�A�Z�=2DFX?�`HK�K�Z�a�°BPjI�D/EHGJ?UK/o[^/DFEmI�D/EHS2WW]K�G�=2dFK�Z�`�K-G�Ki?UEHSYZc?U=2e&_HS2^nK�X�DFEHq/`Q=YP�^/DFEl�AFX[Z�K�WnZ�DVa

LN<n»{`VA"Z>=2?;Z�`HK�W]= �NK�G�K�X/Z\=2AFSpIJ`�A�XHq/Kc=2XCqFGJA*d(=�ZJA"Z�=2DFXVA�SH_ND�Z\K�X[Z�=@A�SNK�XHK�G�q/^ � ��Z\`�A"Z>I�D/egKi?�P8G\DFe�LHG\=2XHqAgW]= �NK�G�K�X[Z�=@A�SNLH=�Z~DFP�e&A/?�? � � P8G�D/e =2X]��X�=�Z:^&Z\DsZ\`HK�?�EHG�P,AFI�KBD�P�Z�`HKM?U_�`HK�G\=2I�A�S2SY^�?�^(ege&K�Z�G\=2IRe�AF?\?WH=2?UZ�G\=YL�E]Z�=2DFX�I�D/X�?�=2W]K�G�KiWC=2Xm_�A�G�Z65,A/< �

Ii<Q BD"l e&AFO(=YXHq�EV?UK6DFP�Z�`HK6_VA�G�Z\?65�A/<cAFX�Wr58LV<BA�X�?�l�K�GJ?�oH^/DFE�I�AFXm��X�WZ\`HK6Z\D�Z\AFS�_ND�Z�K�X[Z�=@A�S�K�XHK�G\qF^IJ`VA�XHq/KQ=2XtA/?�?�K�e4LHSY=2XHq�^FD/EHG4q/=2AFX[Z&?�_H`HK�G�KL(^�=Ye�AFqF=2XH=YX�q�Z�`VA"Z�^FD/E�LHG\=YX�qxEH_tZ�`�KmWH=���K�G\K�X[Z�=@A�SL�=�ZJ?�DFP�e�AF?\?�P8G\DFe�=2X]��XH=YZ:^�A�X�WQAFWHW&Z\`HK�e�Z\D4AsqFG\D"l~=YXHq-E�XH=�P8D/G�e W]K�X�?�=�Z:^C?�_H`HK�G�KBAFX�WC?�e&K�A�G\=2XHqZ\`HK�efK�dFK�XHS2^6D"dFK�G�Z�`�Kc?UEHG�P,AFI�K�l~`�K�X6Z\`HK�^4A�G\G�=2dFK �������� � � ��DFEgl~=YS2S]XHK�K�WsZ�D�K��]_HG\K�?\?�GJAFWH=YE�?�A/?P8E�X�I$Z\=YD/X�D�P�qFG\D"l~=YXHq�e�AF?\? � =2X�DFGJW]K�G�Z�D6WHDMZ�`HKc=2X[Z�K�qFGJA�S�a�¿cA/W]=YEV?�A�X�W4e�AF?\?�A�G\K>XHD�Z;I�DFX�?UZ\AFX[Z\?�a��E]ZBWHK�X�?�=�Z:^n=2?cI�DFX�?UZ\AFX[Z�a

WV<Q BD"l�?�A*^g^FD/ECW]=@W]X�· Z�_HG\K�?�K�G\dFKc?�_H`HK�G�=@I�AFSN?�^(e&egK�Z�G\^4=2XQI�DFX�?UZ�G\E�I�Z�=2XHq-Z�`�K�?�_H`HK�G�KBAFSYLNK�=YZ�Z�`HKB��X�A�S?�_H`HK�G�K~=@?6A:EV?:Z�A/?�?�_VKiI�=Y��K�Wg=2X�^FDFE�G;I�D/X/Z\G\A/I$Zia�7:?�Z\`HKBIJ`�AFXHqFK~=2XgZ�D�ZJA�SV_VDFZ�K�X[Z\=2AFSHK�XHK�G�q/^6Z\`HKB?\A�e&KA/?�P8DFEHXVWQ=2XZ�`HK-_VA�G�Z-5�I�<>AFX�?Ul�K�G �

K*<n»{`VA"ZC=@?&Z�`HK�_VDFZ�K�X[Z\=2AFScK�XHK�G�q/^�D�P�Z�`HKx?U_H`�K�G\Kq/=Yd/K�X � $���¾�� � O(q�A�XVW � $ µ/¾�ea�¿cK�I�AFSYS� $ ¹ � ¹ º*µ[¾[º��x�i¾ � � �B=2XQe&O]?~EHXH=YZ\?�o

P\<»{`VA"Zf=@? Z�`�K e&AFqFXH=YZ�EVW]K D�PwZ�`�K qFGJA*d[=YZ\A�Z�=2DFX�AFS���K�S@W 58l~`H=@IJ` =2?fA�S@?UD Z�`�K qFGJA*d(=�ZJA"Z�=2DFXVA�SA/I�I�K�S2K�GJA"Z�=2DFXN<;A�Z~Z�`HK6?�EHG�P,AFI�K�D�P�^FD/EHG~?U_�`HK�G\K��

Page 73: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~��µ}��GJA*d(=�Z:^ ¹/½

¾H��µgh/P8EHS2S�¾/¾[º"¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj7:WHA&A�X�Wm¡�AFI$Z:^(S� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ³ � ½ <

¶ a~b>`HKR?U_�A/I�KiI�GJA"P Z��MA�S2=2SYK�D-=2?;XHD"lwDFG\LH=�Z\=YX�q �FEH_�=�Z\K�G�AFX�W&DFX&=YZ\?�S2A/?:Z�S2K�q[?;I�=YGJI�A6�F¾F¾/�Ha ��E]Z�=2X�� ½/½F³ DFX�=YZ\?l>A*^gZ�D��FEH_�=�Z\K�Gio]=�Z>e�AFW]KMA6�V^[L(^�DFP�AF?UZ�K�G�D/=2Wn��µ ³ 7:WHA4AFX�WnWH=2?\I�D"d/K�G\K�W&7:WHA4`�AFWQA4?�e�A�S2S�egD(D/Xnl~`H=@IJ``�A/?>LVK�K�XmX�AFegKiWQ¡�AFI�Z:^(S�ac5�b>`HKs�"µ ³ e&K�AFX�?>7:WHAgl>AF?�Z�`�Ks�"µ ³ G\WnAF?UZ�K�G\DF=@WW]=2?\I�D"d/K�G\K�Wpu�AF?UZ�K�G�D/=2Wne�AF?\?Z\K�X�WH?6Z�D�WHK�I�G\K�A/?UKCA/?6AF?UZ�K�G�D/=2W�X(EHe4LVK�G6=YXVI�G\K�AF?�K�?�amb>`HKCX�AFegK�7:W�A�=2?s_HG\DFL�AFLHSY^�P8DFG-Z\`HKCe&DFE�X/ZJA�=2XD"d/K�G\SYD(DFO(=2XHq&b�G\D"^Cl~`HK�G�Ks9jAFG�=@?�e�AFW]K6`�=2?B=YS2S�T�P,A"Z\K�W�IJ`HD/=2I�KFa�¡RA/I$Z:^(S�l>AF?~?�DCI�AFSYS2K�Wm_HG\DFLVA�LHS2^CLNK�I�AFE�?�K=YZ�e&KiA�X�?c��XHqFK�GBD/GBZ\D[K4=YX���G�K�K�OmG\A�Z�`HK�GcZ\`�A�X�P8D/GcZ\`HK4_�G�D[?UD]W]=@IMP8D(D�ZMWHAFI�Z:^[S�u �����4a <m7:WHAn=2?�A�LNDFEHZ¶/¶ O(e A�S2DFXHqm=YZ\?-S2DFX�q�A"�]=2?-AFX�WrA�LNDFE]Z4�/��O(e A�S2DFX�q=YZ�· ?s?�`HD/GUZ6A"�]=@?6AF?-?�K�K�Xr=YXr_HG\DBA:KiI$Z�=2DFX�aC7kZ6=2?sAI�G\A�Z�K�G\K�W�o�_VDFZ\A�Z�D�TkS2=YO/K�G\D]IJO�a�¡�AFI$Z:^(SH`VAF?�A-?\I�AFSYK~?�=Y��K~D�P�� � ¶ O(e A�XVWsZ\`HK~GJAFW]=2E�?jDFPN=YZ\?jD/G�L�=�Z�=@?jD�P�DFGJW]K�G�i¾F¾jO(emaA[<v�D/X�?�=2W]K�G�Ax?�e�A�S2S>?�_H`HK�G�=@I�AFSYS2^�?�^[e&e&K�Z\G�=@IQLVD]W]^�DFPBe�AF?\? � =YX±I�=2G\I�EHS2AFG&DFG\LH=�Z�A�LNDFEHZ&A�S@A�G\qFK?�_H`HK�G�=@I�AFSYS2^�?U^(e&e&K�Z\G�=@IBLND]W]^CDFP�e�AF?\? � aj�B?\?�EHe&K ��=@?>?UDgesE�IJ`?Ue�AFSYS2K�G�Z�`�AFX�� Z\`�A"ZcI�K�X[Z�K�GDFPpZ�`HKRS2AFG�q/KcLND(WH^&I�A�XCLNKRI�DFX�?�=@W]K�G\K�W�A/?�LNK�=2XHq4A�Z;Z�`�KRI�K�X[Z�K�G�D�P�e�A/?�?;D�PpZ�`�KcZ:l�D�TkLVD]W]^&?U^]?UZ�K�ea¡RK�G\=2dFK�Z�`HK-q/G\A*d(=YZ\A�Z�=2DFX�AFSVD/G�LH=YZ\AFS�?U_NK�KiWK��]_HG\K�?\?U=2DFXnP8DFGcA&I�=2G\I�EHS@A�G>DFG\LH=YZ

� � � � � � $� ���

������ � ¿~K�e&K�e4LVK�G~Z�`�K6I�K�X[Z\G�=2_VK�Z\AFS�P8DFGJI�KMG�Kih[EH=YG\K�e&K�X/ZiaLN<Q|�DFG>Z\`HK6?U^]?UZ�K�e D�P�_�A�G�Z65,A[<$o�W]K�G�=2dFK�Z\`HK-K��]_HG\K�?\?U=2DFXnP8DFG>Z\`HK-DFG\LH=YZ\A�S�_NK�G\=YD]WQP8DFGcA&I�=YGJI�EHS@A�G~D/G�L�=�Z

� $ � � � � �+ ��� �

Ii<��=2dFK�X�Z\`�A"ZmZ\`HKrDFG\LH=�ZJA�SM_NK�G\=YD]WzD�Pg¡�AFI�Z:^(S-=2?��[º�`HD/EHGJ?�oRl~`�A"Z�=@?m7:WHAH· ?e&A/?�?� �B?\?UE�egK�A/?AF_H_HG\D*�]=Ye�A"Z\=YD/X�?>Z\`�A"ZMDFG\LH=YZR=@?�I�=YGJI�E�S2AFGRA�XVWmZ�`�A�ZRZ\`HKsLND]W]=2K�?MA�G\K4?�_H`HK�G�=@I�AFSYS2^?�^(e&egK�Z�G\=2IFa�b>`�Kq/G\A*d(=YZ\A�Z�=2DFX�AFS�I�DFXV?:ZJA�X[ZsAFI�I�DFGJW]=2XHqmZ�D�Z�`HKQS2A�Z�K�?UZse&K�A/?UE�G�K�egK�X[Zn5���¾/¾/�/<�=2? ¹ � ¹ º"µ/¾[º ���i¾�� � � =2X¯�²6¤nE�XH=�ZJ?�a

WV<mv�G\E�W]K�SY^�Ki?:Z\=Ye�A�Z�K7:WHAH· ?sd/DFS2EHe&KFa ������ � ¯�AFOFKA�X(^rG�KiAF?�DFX�AFLHSYKQAF?\?UEHe&_]Z\=YD/X�?g^FD/E�XHK�KiW�Z\DAFLVD/E]Zc=YZ�· ?~?U`�AF_VK/a

K*<mv�G\E�W]K�SY^�Ki?:Z\=Ye�A�Z�K�7:WHAH· ?;e&KiA�XQWHK�X�?�=�Z:^/a ������ � b>`HK�¯�D[D/X�· ?R5,=�a KFa2o(Z�`HK-��A�G�Z�`�· ?�e&D(DFX�· ?J<�e&K�AFXWHK�X�?�=�Z:^Q=2? ³/³ µ[¾jO(q �"e � aj7:WHA�· ?>l�DFX�· ZcLNKMZ�`HK6?\A�e&K/o]LHE]Z � ���

¾H��µgh/P8EHS2S�¾���¾F¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�²MK�_HSYK�G�· ? ³ GJWQS2A*l� ª�¬"¨ �V«������V¬ ��­�� _HS2AFXHK�ZJA�G\^CDFG\LH=YZ\AFS�?�_NK�K�W�?

¹ aB°RL]ZJA�=2X Z�`HK�P8DFS2SYD"l~=2XHq�I�=2GJI�EHS@A�G�D/G�LH=YZ�G\K�?�EHSYZ\?�a �R?�?�EHe&K�Z�`�K�e&DFG\K�e&A/?�?�=2dFK�LND(WH^ 5,e&A/?�? ��<m=2?D"d/K�G\l~`HK�S2e&=YXHq/SY^4e&DFG\KBe�AF?\?U=2dFKcZ�`�AFXCZ�`�KRDFZ�`HK�G;LND(WH^Fa�b>`HKRegD/G�KRe�AF?\?U=2dFKcLND]W]^�=@?�Z\`[EV?;d(=2GUZ\E�A�S2SY^�A�ZZ\`HK6I�K�X/Z\K�G~DFP�e�AF?\?>A�X�WQZ\`HK-D�Z\`HK�G~LND]W]^n=@?>d(=YG�Z�E�AFSYS2^�Z\`HK-DFG\LH=YZ�=2XHq&LVD]W]^QDFGc?\A"Z�K�SYS2=YZ�KFaA[<nb>`�K-DFG\LH=�ZJA�Sp?�_VK�K�W

� � � � $� ���

l~`�K�G\K =@?MZ\`HKnD/G�LH=YZ\AFSjG\A/W]=2E�?�a ������ � �R?UKCZ�`HKnI�K�X[Z�G\=2_VK�Z\A�S;P8DFGJI�K�S@A*lfP8D/G6EHXH=YP8DFG\e I�=YGJI�E�S2AFGe&DFZ�=2DFXmA�X�WQZ�`�KMP8DFGJI�KMS2A*l�P8DFG~q/G\A*d(=YZ:^&AFLVD/E]ZBA&?U_�`HK�G\=2I�A�S2SY^C?�^(e&egK�Z�G\=2IMLND]W]^Fa

LN<Qb>`�K-DFG\LH=�ZJA�Sp?�_VK�K�WQP8DFG~_HS@A�X�K�Z\?BA�LNDFE]Z>Z�`�Ks¤(EHXmE�?�=YXHqgZ\`HK6�;AFGUZ\`�· ?~?�_NK�K�WAF?�Z\`HKM�VW]EVI�=@A�S�?�_VK�K�Wpu

� � � � $�� � � ��� O(e��"?

Page 74: Introductory Physics Problems David J. Jeffery Department of

º"¾ v�`�AF_]Z�a~��µ}��GJA*d[=YZ:^

l~`�K�G\K ��=2?RZ�`�K&��A�G�Z�`�· ?�e&K�A�XxDFG\LH=YZ\A�Sj?�_VK�K�W�=YX�O(eCy�? ��?�DFS2dFK6P8D/GM=�Z��{AFX�W ����=@?RZ�`HK&DFG\LH=YZ\AFSGJAFWH=YE�?g=2XtE�XH=�ZJ?&D�PRZ�`HK�AF?UZ�G\DFX�DFe&=2I�A�S�EHXH=YZ�58=�a K/aYo�Z�`HKme&K�AFX±¤(E�X]Tk��A�G�Z�`±W]=2?UZ\AFX�I�K*<$a±�B?�K � $¹ � ¹ º*µ[¾[º �±��¾ � � �ge&O]?6EHXH=YZ\?�o � � � � $ � � ½F¼F½ ���±��¾ � � O(q�ojAFX�W ¯�KiA�X�¤(EHXHTk��A�G�Z�` $ �n�~� $� � µ ½F¹ ����¾ � �Vema

Ii<Qb>`�K�DFG\LH=�ZJA�SB?�_NK�K�WtP8D/Gn?�A�Z�K�SYS2=�Z\K�?CAFLVD/E]Z�Z�`�K��;A�G�Z�`±E�?�=YX�qrZ�`HK�D/G�L�=�ZJA�Sc?�_VK�K�W{A"Z�Z\`HK��;AFGUZ\`�· ??�EHG�P,AFI�KMA/?�Z�`HKM�NW]E�I�=@A�S�?�_NK�K�W�u

� � � � $ � � � � � � ��� T � � � � O(e��"?

l~`�K�G\K � Z�`�KsDFG\LH=YZ\AFS�?�_VK�K�W�A�ZBZ\`HK4��A�G�Z�`�· ?B?�EHG�P,AFI�Ks=YXxO[eny�? ��?UD/SYd/KMP8DFGR=�Z��{AFX�W � � � ��� T � � � � =2?Z\`HK-DFG\LH=YZ\AFSpG\A/W]=YEV?>=YX�EHX�=�ZJ?~D�P�Z�`HK-e&KiA�X��;AFGUZ\`QGJAFW]=2E�?�a��B?�K � $ ¹ � ¹ º*µ/¾(º �r��¾ � � �BegO]?~E�XH=�ZJ?�o� � � � � ��$ ¶�� ½ º"µ[���x�i¾�� �pO[qVoHA�X�W �;A�G�Z�` $ ¹ � ³ º(�*� ³ ����¾�!�ema

WV<Q²MK�_HS2K�Gi· ? ³ G\WnS2A*l� � $

� µ�� ������ �

l~`�K�G\K � =@?>DFG\LH=�ZJA�Sp_NK�G\=YD]Wpa��BX�WmA�S@?UD&W]K�G�=2dFK�Z�`�KMP8DFG\e 7;Z\`H=2XHOn_NK�D/_HSYK-D/EHqF`[Z>Z�D&_HG\K�P8K�G�u

� $� � �+ ��� � � � � �

K*<Q²MK�_HS2K�Gi· ? ³ GJWQS2A*l�?�_NK�I�=@A�S2=2��K�WnP8DFG>Z\`HK-I�A/?UK�D�P�_HS@A�XHK�Z\?>DFG\LH=YZ�=2XHq4Z�`HKs¤(E�XQl~=YZ�`m_NK�G\=YD]WQegKiAF?�EHG\K�W=2Xm^FKiA�GJ?�AFX�WW]=2?UZ\AFX�I�K-e&KiAF?�EHG�KiWC=2X�AF?UZ�G\DFXHD/eg=@I�AFS�EHXH=YZ\?�uj=�a KFa2o

� �� � $ � �� �D/G

� � � $ + � � � �� �

l~`�K�G\K � A�XVW + � A�G\KB�NW]E�I�=@A�S�I�DFXV?:ZJA�X[Z\?�^FD/EQe4E�?UZB?UD/SYd/KBP8D/G�aP\<m²MK�_HS2K�Gi· ? ³ GJW�S@A*l ?U_NK�I�=2AFSY=2��KiW�P8DFGxZ�`�K±I�AF?�K�D�P?�A�Z�K�S2S2=�Z\K�?�DFG\LH=YZ�=2XHq�Z\`HK±��A�G�Z�` l~=YZ�` _VK�G�=2D]We&KiAF?�EHG�KiWn=2X�WHA*^]?>A�X�WmW]=@?:ZJA�X�I�KMegKiAF?�EHG\K�WQ=YXe&K�A�X���A�G�Z�`nGJAFWH=Y=�uj=�a KFa2o

� �� $ � �� � � ��� T � � � �D/G

� ��$ + � � � �� � � ��� T � � � � l~`�K�G\K � A�XVW + � A�G\KB�NW]E�I�=@A�S�I�DFXV?:ZJA�X[Z\?�^FD/EQe4E�?UZB?UD/SYd/KBP8D/G�a

q(<nb>`�Kg¯�D(D/X�· ?R_NK�G\=YD]W�=2XxWHA*^]?BP8G�D/e�²MK�_HS2K�Gi· ? ³ GJW�S@A*l�qF=2dFK�X�Z�`�A�ZM¯�D[D/X�· ?Be&K�AFX�W]=@?:ZJA�X�I�K6P8G\DFeZ\`HK��;AFGUZ\`�=2? ¹ ¾ � ³F³ =YXxegKiA�Xr�;AFGUZ\`�G\A/W]=2=�a6»{`(^�=@?RZ�`HK&d"A�S2EHKgDFL]ZJA�=2XHK�Wx?U=2qFX�=��VI�A�X[Z�S2^�W]= �NK�G�K�X[ZP8G\DFe Z�`HKnegKiA�X�S2EHX�AFG6e&DFX[Z�`�DFP~� ½ a ¶�³ ��WHA*^]?�a ������ � b>`HKnW]=@?�I�G�K�_�A�XVI�^�=@?6e&D/?UZ�S2^�X�D�Z4W]E�KZ\DmZ�`HKQI�=2G\I�EHS2AFG-DFG\LH=YZsA�_H_HG\D*�]=Ye�A�Z�=2DFX�XHDFGMZ\DmZ�`HKC_NK�G�Z�E�G�L�A�Z�=2DFXrK ��K�I�Z\?sD�P�Z�`HKQ¤]EHX�A�X�WrDFZ�`HK�G_�S2AFXHK�ZJ?�a

Page 75: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � � NIda*I,�E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H� ¶ h[e4EHS�ZB¾/¾F¾���¾C� ³ �MK�A/?U^�e�A�Z�`�u;AF=YG>e�AF?\?>=2XmAgG\D(DFe� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ �*T ½

�Fa~b>`HKQW]K�X�?�=YZ:^xDFP~AF=YG4A"Zg�F¾ �CAFX�Ww�CA"Z\e _�G�Ki?�?�EHG\K�=2?n� � �]��O(q��*e � a�5,|HD/G4I�DFe&_�A�G\=@?UD/X�o�l>A"Z\K�GsW]K�X�?�=�Z:^EHXVW]K�G&Z\`HK�?�AFe&KI�DFX�W]=YZ�=2DFXV?&=2? ½/½F¼ O(q��*e � l~`H=@IJ`±=2?&XHKiA�G\SY^rZ\`HKmP8G\K�h[EHK�X[Z\SY^�h[EHDFZ�K�Wz��¾/¾F¾jO(q��*e � a <b>`HK�G�KR=2?>AsG�D(DFe ¶ e�S2DFXHqVo/µ;e l~=@W]K/oHA�X�W ³ e `�=Yq/`C��S2SYKiWCl~=YZ�`A�=2G�a�»{`�A"Z>=@?;Z\`HK�e&A/?�?;D�P�AF=YG�=2XCZ�`�KG\D(DFe �

A[<cº�� � ¹ O(qVa LV<�� � �H��O(q�a I�< ½F½/¼ O(q�a W�<>¾jO(qVa Ki< , ½F½/¼ O(q�a

¾H� ¶ h[e4EHS�ZB¾/¾F¾[��¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA"Z\egD[?U_�`HK�G\=2I�_HG\K�?\?�EHG�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ T ³

�]a~b>`HK-_�G�Ki?�?�EHG\KRDFP�Z\`HK-�;A�G�Z�`�· ?~A�Z�e&D/?�_H`HK�G�KMA"ZBAFX[^nSYK�dFK�Sp=@?~I�AFE�?�K�WQL[^�uA[< Z�`�K l�K�=2qF`[Z D�P Z�`�K D"dFK�G�S2^(=YX�q AF=YG e&A/?�?�a LV< G\K�?�_H=2G\A�Z�=2DFX L[^ S2=Yd(=2XHq Z�`�=YXHq[?�aIi<�K�d"A�_NDFGJA"Z\=YD/XnDFP�?�K�Agl>A"Z�K�G�a W�<�q/S2A/I�=2K�GJ?�a Ki<>?\h/E�=2Wpa

¾H� ¶ h[e4EHS�ZB¾/¾F¾ ¶ ¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_HG\K�?\?UEHG\K�=YX�?UZ�GJA*l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ��T ¶

³ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK-A�X�?�l�K�G>=2?�u�b>`H=@?cI�AFE�?�K�?�l�A�Z�K�G>Z�D&G�=@?�K�=2X�A&?UE�IJO/K�WnDFX�?:Z\G\A*l-a �»{`�A�Zc=2? oH�BSYK����

A[<4`H=Yq/`HK�GgZ\`�A�XwG\D[D/e A�=2G&_HG�Ki?�?�EHG\KQ=2X�?�=2WHKQZ\`HK�?UZ�GJA*l LV<4S2D"l�K�G4Z\`�A�X±G\D[D/e A�=2G&_HG�Ki?�?�EHG\K=2X�?�=2WHKcZ�`�KR?UZ�GJA*l I�<�Z\`HKBK�SYKiI$Z\G�=@I>P8DFGJI�K W�<�Z�`HKRe&AFqFXHK�Z�=@I>P8DFGJI�K Ki<jZ�`HKM?U_NK�KiW�D�PpS2=Yq/`[Z

¾H� ¶ h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u��BG\IJ`H=2e&K�W]Ki?�·]_�G�=2X�I�=2_HS2K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a~�RI�I�D/G\WH=YXHqgZ\D&�BG\IJ`�=Ye&K�WHK�?�o(Z�`HK-LHE�D"^/A�X[Z�P8DFGJI�KM=@?~K�h[E�AFS�Z�D�uA[<�Z\`HK-l�K�=2qF`[Z~D�P�Z�`HK-D/L,A:K�I�Z�aLN<CZ\`HK-l�K�=2qF`[Z~D�P�Z�`HK-D/L,A:K�I�Z~?�EHLHe&K�G�q/K�WQLVK�XHK�A�Z�`Z�`HK6?�EHG�P,AFI�KRDFP�Z\`HKM��EH=@WpaIi<CZ\`HK-l�K�=2qF`[Z~D�P�Z�`HKM��E�=2W=2X�?U=@W]K�Z�`�K-DFL,A:KiI$Z�aWV<CZ\`HK-l�K�=2qF`[Z~D�P�Z�`HKM��E�=2WmW]=@?U_�S2A/I�K�WQL(^�Z�`�K-DFL,A:KiI$Z�aK*<CZ\`HK-GJA"Z�=2D&D�P�Z�`HK6W]K�X�?�=�Z:^QD�P�Z\`HKM��EH=@WQZ�D&Z\`�A"ZcDFP�Z�`�K-DFL,A:KiI$Z�a

¾H� ¶ h[e4EHS�ZB¾/¾H�/��¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu;?�`H=Y_=2Xe&K�G\I�EHG�^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ T ¶

¶ a~|�G�Ki?U`(l>A"Z�K�GCW]K�XV?U=YZ:^t=@?nAFLVD/E]Z�� � ¾/¾jq ��I�e � oc?�K�A*l>A"Z�K�GCW]K�XV?U=YZ:^Fo-� � ¾ ³ q ��I�e � ocA�XVWwegK�G\I�EHG\^tW]K�X�?U=YZ:^Fo��µ�q ��I�e �*a���Z�D"^nLVD[A"Z~��D[A"Z\?>`�=Yq/`HK�G>=2X�u

A[<>A�S2SpD�P�Z�`HK�ea LN<�XHDFXHKMDFP�Z\`HK�ema I�<�?�K�A*l>A"Z\K�Gia WV<�P8G�Ki?U`(l>A"Z�K�G�a K*<�egK�G\I�EHG\^Fa

¾H� ¶ h[e4EHS�ZB¾/¾/�F¾F¾C� ³�³ K�A/?U^�e�A�Z�`�u�L�EHD"^/AFX/Z�P8DFGJI�K

Page 76: Introductory Physics Problems David J. Jeffery Department of

º�� v�`�AF_]Z�a~� ¶ |�SYE�=2WH?

¹ a>»{`�A�Zg=@?4Z�`HKmLHE�D"^/A�X[Z6P8D/G\I�KQD/X�A�I�DFe&_HS2K�Z\K�S2^�?UE�LHe&K�G\qFK�W�DFL,A:KiI$Z&D�PBd/DFS2EHe&K���e � a ������ � b>`�KW]K�X�?�=�Z:^CDFP�l>A"Z\K�G~=@?M��¾/¾F¾jO(q�e ��� aA[<��i¾F¾/¾� 6aLN<��i¾ � �  6aIi< ½ ¼ ¾F¾� saWV<nµ ½ ¾F¾� saK*< ½ � ¼  6a

¾H� ¶ h[e4EHS�ZB¾/¾/�/��¾4� ¶ �Me&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVuj=2I�KM=YXP8EHS2S�I�E�_� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ��TJ�F�

º(a~b>`HK-LVAF?�=2IR��D[A"Z�=2XHq&K�h[E�A�Z�=2DFXl~`HK�XDFX�SY^CD/XHKM��EH=@WXHK�KiWH?�Z�D�LNK6I�D/X�?�=2W]K�G�KiWC=@?

� $ � ��� � � � � � �

l~`HK�G�K � =2?4Z�`�KQe�AF?\?gD�P~Z\`HK��D/A�Z�=2XHq�D/L,A:K�I�Z�o �� � � ��=2?4Z�`�KW]K�X�?�=�Z:^�DFPcZ�`HKQ��EH=@Wpo�A�X�W � � � �s=2?4Z�`�KAFegD/EHX[Z~D�P��VEH=2WmW]=@?�_HS2A/I�KiWCL(^�Z�`�KM��D/A�Z�=2XHq4D/L,A:K�I�Z�a;¤]A*^&Z\`�A"Z~^/DFE`�A*dFKMA&I�EH_D�P�l�A�Z�K�G���S2S2K�WQZ�DgZ�`�KLHG\=2e l~=�Z\`nl>A"Z�K�G�AFX�WnAFXC=@I�KM?�AFeg_�SYKRD�P�d/DFS2EHe&K � A�X�Wne&A/?�? �}��D/A�Z�=2XHqs=2XCZ\`HKMl�A�Z�K�Gia�b>`HKRd/DFS2EHe&KW]=@?�_HS2A/I�KiW�L(^�Z\`HK�=2I�K&=2? � � � � a��~P Z\K�G-Z\`HKC?\A�e&_HS2Kge&K�S�ZJ?-=�ZJ?Me�AF?\?M=2?MEHXVIJ`�A�XHq/K�Wpo�D�P�I�DFEHGJ?�KFo�AFX�W�=YZ\?W]K�X�?�=�Z:^C=@?>Z\`�A"ZcDFP�l>A"Z�K�G�a�¤(DCA�P Z�K�G~egK�S�Z\=YX�q�o�?\A�e&_HS2KM`�AF?>d/DFS2EHe&KFu

A[< � � � � A�XVWgZ�`HK�I�EH_C=@?;��SYS2K�W�Z�D-Z\`HKBLHG\=2e�?UZ�=2S2S�a LV<�� A�XVW&Z�`HK�I�EH_�D"d/K�G���D"lc?�a Ii< ��AFX�WZ\`HKnI�EH_r=2?6I�DFe&_HS2K�Z\K�S2^�EHX]�VSYS2K�Wpa W�<-��K�G\D�A�X�WxZ\`HKCI�EH_r=@?6I�D/e&_HSYK�Z�K�SY^xEHX]��S2SYKiWpa Ki<���K�G\DAFX�WQZ�`HK6I�EH_D"dFK�G���D"lc?�a

¾H� ¶ h[e4EHS�ZB¾/¾ ³ ¾F¾4�4µn�4e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_HG�Ki?�?�EHG\KMl~=�Z\`mWHK�_]Z\`¼ a~b>`HK&K��(_�G�Ki?�?�=YD/X�P8D/G�_�G�Ki?�?�EHG\K4DFP�A�X�=2X�I�D/eg_�G�Ki?�?�=YL�SYK4��EH=@Ww58D�P>W]K�XV?U=YZ:^ �]<MAF?MAQP8EHX�I$Z\=YD/XxDFP>WHK�_]Z\` �5,egKiAF?�EHG\K�WQ_VD[?U=YZ�=2dFK-W]D"l~X(l>A�GJW�<�LNK�S2D"lzA&?�EHG�P,AFI�KM=@?�uA[< � $ � ��� � � � � � � �NaLN< � $ � ��� � � � � � � �� ��aIi< � $ �

�� ��� � � �� � � � ��a

WV< � $ �� � � � ��� � � �� � aK*< � $ � ��� � � � � ��a

¾H� ¶ h[e4EHS�ZB¾/¾ ³ ��¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�uj_HG\K�?\?�EHG�KMA"ZBWHK�_]Z\`�� ¶ e� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

½ a~b>`HK-K��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK-_�G�Ki?�?�EHG\KRDFP�AFXQ=2X�I�D/e&_HG�Ki?�?�=2LHSYK���E�=2Wl~=YZ�`�W]K�_HZ�`m=2?

� $� ��� � � �� � � � � l~`HK�G�K4=2? � ��� � � �� � =@?M?UEHG�P,AFI�Ks_HG\K�?\?�EHG�K/o �=@?B��EH=@WxW]K�X�?�=�Z:^/o $ ½ � ¼   �"O[qQ=2?RZ\`HKsP8D/G\I�Ks_NK�GMEHXH=YZ-e�AF?\?W]E�KsZ\DnqFGJA*d(=�Z:^QXHK�AFGcZ\`HKg��A�G�Z�`�· ?B?�EHG�P,AFI�KFo�A�X�W ��=@?�W]K�_]Z\`�e&K�A/?UE�G�KiW�W]D"l~X(l�AFG\WQP8G\DFe Z�`HK&?�EHGUP,A/I�K/a�B=YGj_HG\K�?\?�EHG�K�A�X�W4l>A"Z�K�GjW]K�X�?�=YZ:^6XHK�AFG�Z�`HK~�;AFGUZ\`�· ?�?�EHG�P,AFI�K�AFG�K�Z�D�qFD(D]W4AF_H_HG\D*�]=Ye�A"Z\=YD/X�o*G�Ki?U_NK�I�Z�=2dFK�SY^/o�i¾ � 9jAC5�A�S2egD[?:ZR�BA"Z\e�<;A�X�Wm�i¾F¾/¾jO(q �"e � ajb>`HKB_HG�Ki?�?�EHG\K~=YXQA"Z�e&D[?U_H`�K�G\K�?�A�Z>� ¶ e =2XCW]K�_HZ�`n=@?;AFLVD/E]Z�u

A[< ³ � ¶ �x�i¾ � A"Z\ea LV<���¾ � A�Z�ema I�<��-A"Z\ema W�<~�]a ¶ A"Z\ea Ki< ³ a ¶ A"Z\ea

¾H� ¶ h[e4EHS�ZB¾/¾�µ[¾F¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu���¾/¾H�/u���¤(_�A/I�K4°�W]^]?\?UK�^��¾Ha>7!X�������� ��� �BD+�F J1)Cc��#*)\)�1�#"oVA/?:Z\G�D/X�A�E]Z~¡�A*d[=@W ��D"l~e�A�Xn��X�WH?c`H=Ye�?�K�SYP�Z\G\AF_H_NK�WQl~=�Z\`HDFE]Z~`H=@?~`HK�SYe&K�Z

=2X�A�?U_�A/I�K&_ND(W�anb>`HKCI�D/e&_HE]Z�K�Gs£BAFS�`�A/?MSYD]IJOFKiW�Z\`HKnW]=2G\K�I$Z-_ND]W(T�Z\D�T!?U_VAFI�K�Tk?�`H=2_�AF=YG\S2D(IJO�a)��D"l~e�A�XW]KiI�=@W]K�?�Z�D ��LHG�KiA"Z\`HK~d"AFI�E�EHe � �wZ�D-qFD-?\A�X�?�`HK�S2e&K�Z;Z\`HG\DFEHq/`g?�_�AFI�K>Z�DsAFX&DFE]ZJ?U=@W]KBAF=YG\SYD]IJO ��A�X�WsZ�`HK�XW]KiA�S�l~=�Z\`�£RA�S�aM»{`[^�WHD[Ki?UX�· Z ��D"l~e&AFX�K��]_HS2D]W]KgWHEHKsZ\DQ`�=2?R=YX[Z\K�G\X�A�S�LVD]W]^�_�G�Ki?�?�EHG\Ks=2X�Z�`�K4XHKiA�G\SY^��K�G\Dg_�G�Ki?�?�EHG\KRDFP�?�_�AFI�K��A[<n£BK-=2?�Z\D(DCh/E�=2IJO�Z\D&K��]_HS2D(WHKFa

Page 77: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ¶ |�SYEH=@WH? º ³

LN<Q£BK-`HDFS@WH?>`H=@?~LHG\K�A�Z�`�aIi<Q£RA�S�`VAF?>XHDFZ~AFX[Z�=@I�=2_�A"Z\K�W'��D"l~e&AFX�· ?�e�AFXHK�EHd/K�G>DFGcA�Z~SYKiAF?UZc`�AF?>XHD�I�DFX[Z�=2XHqFK�X�I�^n_HS2AFX�aWV<¤]`HK�K�G~_HSYDFZcG�Kih[EH=YG\K�e&K�X/ZiaK*<Q¯�D/?UZsD�P>Z�`�KCLVD]W]^�· ?6=2X[Z�K�G\X�AFS�_HG\K�?\?UEHG\K�=@?6?UE�_H_HS2=YKiW�L(^�XHKiA�G\SY^x=YX�I�DFe&_HG\K�?\?U=2LHS2K�5,AFX�W�Z�`HK�G�K�P8DFG\KX�K�A�G\S2^�X�DFX]T!W]K�I�DFe&_HG\K�?\?U=2LHS2Ki<p��EH=@WsA�XVWs?�DFS2=2Wpu�Z�`HKi?UK�_�AFGUZJ?�l�DFX�· Z�K��]_HS2D(WHK�EHXVW]K�GjW]KiI�DFe&_HG\K�?\?�=YD/X�a��Z�SYKiAF?UZ�A/I�I�D/G\WH=YXHqMZ\D4²MEHL�G�=@IJOgAFX�WC�BGUZ\`[E�G~vRaHv�S2AFG�O/KFoFZ�`HKRLVD]W]^CI�A�XCI�D/X[Z\A�=2X�Z\`HKRAF=YG�_HG�Ki?�?�EHG\KZ\`�A"Z<��D"l~e&AFX�esE�?UZ�`VA*dFKc=2X�?�=2W]KR`H=@?;S2EHXHq[?;A�XVW�D�Z\`HK�G�A�=2G�d/K�?\?UK�S2?�a�7kZi· ?�DFXHS2^m� ¶ _V?U=�58_NDFEHXVWH?;_NK�G?\h[E�A�G\K�=YX�IJ`N<�DFGc?�D�a ��E]Zc7�AFSYl>A*^]?�Z\`H=2XHOn`H=@?~KiA�GJ?�e4E�?UZc`�A*dFK-I�GJAFIJO/K�W�S2=2OFK-I�GJA���^Fa

¾H� ¶ h[e4EHS�ZB¾/¾�µV��¾ ³�¶ �M`�AFG\WnZ�`H=2XHO(=2XHq�ujl>A"Z\K�G>SYK�dFK�Sp=YXm_ND[D/S�A�XVWQI�A�XHD(K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ��TJ� ³ � `�AFG\WnZ�`�=YXHO(=2XHqCh[EHK�?UZ�=2DFX�o]LHE]Zce&K�e&DFG\^C`HK�SY_V?

�F�Fa~�BXQK�eg_HZ:^CA�S2EHe&=YX(EHe I�A�XHD(KR��D/A�Z\?�=YXm?Ul~=2e&e&=YXHqg_ND[D/S�a�7kZc?�_HG�=2XHq[?�A4SYKiA�O�A�XVWn?�=YXHO]?�Z�D4Z�`�K�LND�Z�Z�D/ea»�KCAF?\?UE�egK�AF=YG-`�A/?MXHK�q/SY=2qF=2LHS2K�W]K�X�?�=YZ:^Fanb>`HK&EH_V?U`HDFZ6G�Kih[EH=YG\K�?MAmLH=YZ-Z�`�=YXHO(=2XHq�o�LHE]ZsD/XHKg��X�WH?-Z�`�A�ZZ\`HK-_VD(D/S�l�A�Z�K�G�S2K�d/K�S�u

A[<�SYD"l�K�GJ?�a LN<�G�=@?UKi?�a Ii<>?:ZJA*^]?�I�DFX�?UZ\AFX[Z�a W�<�P8G\K�K���K�?�a K*<;LNDF=2S@?�a

¾H� ¶ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u>��K�G\XHD/EHSYS2=pA�X�WmI�DFX[Z�=2X(EH=�Z:^nK�h[E�A"Z\=YD/X�?�i�]a~b>`HK6I�DFX[Z�=2X(EH=YZ:^CK�h[E�A�Z�=2DFXmA�X�WnZ�`HK ��K�G�XHD/EHS2SY=pKih/EVA"Z�=2DFXK��]_HG\K�?\?�u

A[<�Z\`HK4I�DFX�?�K�G\d"A"Z\=YD/X�D�P�� � � ��A�X�WZ\`HK&I�DFXV?UK�G�d"A"Z\=YD/XmD�P�� �1� �� �'� oVG�Ki?U_NK�I�Z�=2dFK�SY^/oV=2X�Z�`�KI�AF?�KMD�P��VEH=2W�?�a

LN<CZ\`HKCI�D/X�?�K�G\d*A�Z�=2DFX�DFP � � � �±AFX�W�Z�`HKCI�DFX�?�K�G\d"A"Z�=2DFX�D�P � �� � �xopG�Ki?U_NK�I�Z�=2dFK�SY^/op=YXxZ�`HKCI�AF?�KDFP��VEH=2W�?�a

Ii<CZ\`HKsI�DFX�?�K�G\d"A"Z�=2DFXD�P � �1� � A�X�WQZ�`�KsI�D/X�?UK�G�d"A�Z�=2DFXD�P � �� � ��oHG\K�?�_VKiI$Z\=Yd/K�S2^FoH=2XZ�`HKsI�AF?�KDFP��VEH=2W�?�a

WV<CZ\`HKMI�DFXV?UK�G�d"A"Z\=YD/XCD�P � � � ��AFX�W�Z\`HKMI�DFXV?UK�G�d"A"Z\=YD/XCD�P � � � �� �4� o/G\K�?�_NK�I$Z\=Yd/K�S2^Fo(=2XCZ�`�KI�AF?�KMD�P��VEH=2W�?�a

K*<CZ\`HKCI�D/X�?�K�G\d*A�Z�=2DFXxD�P � � � ��A�X�W�Z�`�KCI�DFXV?UK�G�d"A"Z\=YD/X�D�P � � CopG�Ki?U_NK�I�Z�=2dFK�S2^Fo�=YX�Z�`�KCI�AF?�KgD�P�VEH=2W�?�a

¾H� ¶ h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ µ&K�A/?U^&Z\`H=2XHO(=YXHqVu;I�D/X[Z�=2X[E�=�Z:^CKih[E�A"Z\=YD/X� ³ a~b>`HKQ?U=2e&_HSYKnK��]_HG\K�?\?U=2DFX�P8DFGsZ�`HKQI�DFX[Z\=YX(EH=YZ:^xKih[E�A"Z\=YD/XxP8D/G6Z\`HK���D"l�D�PcAFX ��� ¦ � � �/� � � � �

��E�=2W=2XmAg_H=2_NKC58DFGcAg�VD"l�Z�E�LVK-l~`H=@IJ`=2?cAg_H=2_NK-D�P�Z�`HK-e&=2X�W�<�=@?

v�DFX�?UZ\AFX[Z $ � �

l~`HK�G�K���=@?MZ�`�KCI�G\D/?\?:T!?UKiI$Z\=YD/X�A�S�A�G\K�AQD�P�Z�`HK�_�=Y_NK�5,A/?�?�EHe&K�Wx_NK�G\_VK�X�W]=@I�EHS@A�GMZ\DmZ�`HK&��D"l W]=2G�KiI$Z�=2DFXN<AFX�W � =@?�Z�`HK���E�=2W?U_NK�KiWx5�AF?\?UE�egKiWnI�DFX�?UZ\AFX/Z>D"dFK�G�Z\`HK-I�G\D/?\?:T!?UKiI$Z\=YD/X�A�SNA�G\K�A/<�ajb>`HK�h[E�AFX[Z�=YZ:^ � � I�AFXLNK6I�AFSYS2K�WnZ�`HK-d/DFS2EHe&K���D"l�GJA"Z\KFa

A[<C7kP � ��� ¦ � � � ��o � � ¦ � � � �jaH7!X�AgZ\=Ye&K � � o�Z�`HKsAFe&DFEHX[ZcD�P�dFD/SYE�egK-DFP���EH=@WZ�`�A�Z`VAF?���D"l�K�WQ_�AF?\?�K�WA4q/=Yd/K�X_VD/=YX[Z~=@? � � ��� � a

LN<n7kP � ��� ¦ � � � ��o � � ¦ � � � �jaH7!X�AgZ\=Ye&K � � o�Z�`HKsAFe&DFEHX[ZcD�P�dFD/SYE�egK-DFP���EH=@WZ�`�A�Z`VAF?���D"l�K�WQ_�AF?\?�K�WA4q/=Yd/K�X_VD/=YX[Z~=@? � �H5�� � � <�a

Ii<n7kP � ��� ¦ � � � �jo � ��� ¦ � � � ��aV7!X�ACZ�=2e&K � � oNZ�`HK&A�e&DFE�X/ZRD�P;d/DFS2EHe&K6D�Pj��E�=2W�Z�`�A�Z`VAF?���D"l�K�WQ_�AF?\?�K�WA4q/=Yd/K�X_VD/=YX[Z~=@? � � � � a

WV<n7kP � ��� ¦ � � � ��o � � ¦ � � � �jaH7!X�AgZ\=Ye&K � � o�Z�`HKsAFe&DFEHX[ZcD�P�dFD/SYE�egK-DFP���EH=@WZ�`�A�Z`VAF?���D"l�K�WQ_�AF?\?�K�WA4q/=Yd/K�X_VD/=YX[Z~=@? � � � � a

K*<n7kP5� � ¦ � � � ��o � � ¦ � � � ��a(7!XAsZ�=2e&K � � o(Z�`HK-A�e&D/EHX[Z>DFP�dFD/SYE�egKMDFP���EH=@WQZ�`�A�Z`VAF?���D"l�K�WQ_�AF?\?�K�WA4q/=Yd/K�X_VD/=YX[Z~=@? � � � � a

¾H� ¶ h[e4EHS�ZB¾/¾[º�¾F¾4� ¶&³ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu>��K�G\XHDFEHS2S2=pK�h[E�A"Z\=YD/X

Page 78: Introductory Physics Problems David J. Jeffery Department of

º*µ v�`�AF_]Z�a~� ¶ |�SYE�=2WH?

��µ�a~b>`HK-?�=Ye&_HS2=Y��K�W!��K�G\XHDFEHS2S2=NKih[E�A"Z\=YD/Xx5,WHEHKMegD/G�K�DFG>S2K�?\?�Z�D&¡RAFXH=YK�S���K�G\XHDFEHS2S2=N=2X��*º ³/¼ <jP8DFG�Z�`HK���D"l�D�PAFX ��� ¦ �1� �/� � � � � ���E�=2W=2XmAg_H=2_NKn58D/GcAs�VD"l�Z�E�LVK-l~`H=@IJ`m=2?~Ag_H=2_NK-D�P�Z�`HK-e&=2X�W�<�=@?

v�D/X�?:ZJA�X[Z $ � � �� � � � � � �

l~`HK�G�K � =@?>_HG\K�?\?UE�G�KR=YXQZ�`HK���E�=2WnP8G\AFe&K�DFP�e&D�Z\=YD/X�o ��� � �R=@?�Z�`�K�O(=2XHK�Z\=2I�K�XHK�G\qF^�_NK�G~EHX�=�Z~e�AF?\?�o]AFX�W

� �Q=2?cZ�`HK4qFGJA*d(=�ZJA"Z�=2DFXVA�S�_VDFZ�K�X/Z\=2AFS�K�XHK�G\qF^n_VK�GBEHXH=YZRe�A/?�?BegKiAF?�EHG\K�WQP8G�D/e}?�DFe&KsI�DFX(dFK�X/Z\=YD/X�A�Sp��K�G\DS2K�d/K�S�a�b>`HKB_HG�Ki?�?�EHG\K�Z�K�G\e��zG\K�_HG\K�?�K�X[Z\?�Z\`HKcK�XHK�G\qF^6_NK�G�EHXH=YZ;e�AF?\?j?:Z\DFG\K�Wg=2X&Z�`HKcI�DFe&_HG\K�?\?U=2DFXgD�P�Z�`�K��E�=2WpaMb>`HKgh/EVA�X[Z�=YZ:^ � � �Q5,XHD�Z\K6Z�`�K4A�LV?UK�X�I�K4D�PjZ�`�K �

�P,AFI$Z\DFG$<~=@?BI�A�S2SYKiWmZ�`HK � � � �/� � � �'� su

=YZs=@?UX�· Z4G\K�AFSYS2^xAm_�G�Ki?�?�EHG\KC?U=2X�I�Kn=�Z4A/I$ZJ?-DFXHS2^�=YXrZ\`HKQW]=2G\K�I$Z\=YD/XrD�P>��EH=@Wre&D�Z�=2DFX�AFX�WrDFX�SY^xDFX�l~`�A�ZZ\`HKse&D"d(=YX�q&��EH=@Wm`H=�ZJ?�oNXHDFZBDFXmZ\`HK6��E�=2Wm=YZ\?�K�SYP:acb>`HK6GJA�e _HG\K�?\?UEHG\KMK��]K�G�Z\?RA&P8DFGJI�K-_NK�GREHXH=YZ�AFG�KiA4D/Xe�A"Z�Z�K�G6XHD�Z6e&D"d(=2XHqml~=�Z\`xZ\`HK&��EH=@Wpab>`HK ��K�G\XHDFEHS2S2=jK�h[E�A"Z\=YD/X�A/?�?�EHe&K�?MX�D�SYD[?�?MDFP�K�XHK�G\qF^mZ\D�`HK�A�ZZ\`HG�D/EHqF`�d(=@?�I�EHDFEV?R58P8G�=@I$Z\=YD/X�A�S <jK.�NKiI$Z\?�A�XVW�XHDsS2D/?\?�D/G;q[A�=2X�?jP8G\DFe�l�DFG\O4W]D/XHKBL(^&DFG�DFX�Z\`HKc��E�=2Wpaj7kZi· ?G\K�AFSYS2^�A`H=Yq/`HS2^�?U=2e&_HS2=���KiW�P8D/G�e4EHS@AHo�LHEHZM=YZs?UZ�=2SYSjl�DFG\O]?R_�G�K�ZUZ:^�l�K�S2S�A"Z-SYKiAF?UZ6h/EVA�S2=�ZJA"Z�=2dFK�SY^�K�dFK�X�P8D/GAF=YG~l~`H=@IJ`=2?~`VA�GJW]SY^QA�X=YX�I�DFe&_HG\K�?\?U=2LHS2K���EH=@WQL(^Ce&D[?:Zc?UZ\A�XVWHA�GJWH?�a��D/E{`�A*dFK�_H=2_NK�l~=YZ�`�?UZ�KiAFW]^[T!?:ZJA"Z�K�=2X�I�DFe&_HG\K�?\?U=2LHS2Km��D"l Z�D�l~`H=@IJ` ��K�G\XHDFE�SYS2=�· ?�Kih/EVA"Z�=2DFX�AFX�W±Z�`�KI�DFX[Z�=2X(EH=�Z:^K�h[E�A�Z�=2DFX�AF_H_HS2^Fa65,¿cK�I�AFSYS�oVZ�`HKgI�DFX[Z\=YX(EH=YZ:^QKih[E�A"Z\=YD/X�=2?Mv�DFX�?UZ\AFX/Z $ � �6o�l~`HK�G\K � =2?B��EH=@W?�_VK�K�WQA�X�W���=@?>I�G\D/?\?:T!?UKiI$Z\=YD/X�A�S�AFG�KiAHa <-7kP�Z�`HKMI�G\D/?\?:T!?�K�I$Z\=YD/X�A�SVA�G\K�A �zD�P�_H=Y_NK�=2? ¦ � � � � ��fAFX�W�C=2X�I�G�KiAF?�K�?�o(Z�`HK�X�u

A[< � A�XVW � � ¦ � � � 4aLN< � � ¦ � � � ��AFX�W � ��� ¦ � � � �jaIi< � � ¦ � � � ��AFX�W � ?UZ\A*^]?>I�DFXV?:ZJA�X[Z�aWV< � A�XVW � ��� ¦ � � � 4aK*< ��� ¦ � � � �nA�X�Wsl~`�A"Z�`�AF_H_VK�X�?�Z�D � I�A�XHX�D�Z�LVK>W]K�Z\K�G\e&=YXHKiW6l~=YZ�`HD/E]Zje&DFG\K;=2X]P8DFG\e�A"Z�=2DFX�a

¾H� ¶ h[e4EHS�ZB¾/¾ ¼ ¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u;I�DFX[Z�=2X(EH=YZ:^CK�h[E�A�Z�=2DFXK��HA�e&_HS2K� ¶ a~b>`HK�I�DFX[Z�=2X(EH=�Z:^�K�h[E�A"Z\=YD/X�P8D/G6A�X�=YX�I�DFe&_HG\K�?\?U=2LHS2Ks�VEH=2W�=2X�A_H=2_NK�DFG���D"l�Z\EHLVK�=@?sv�DFXV?:ZJA�X[Z�$ � �6o

l~`HK�G�K � =@?RI�G�D[?�?UT!?UKiI$Z�=2DFXVA�S�AFG�KiA&D�P�?\A�=@Wm_H=2_VKgDFGB��D"l Z�EHLNK&A�X�W � =@?cZ\`HKs�VEH=2Wx?U_NK�KiWmZ�`�G�D/EHqF`�?\A�=@WI�G�D[?�?UTk?�K�I�Z�=2DFX�AFS�AFG�KiAHucP8D/G6?U=2e&_HS2=2I�=�Z:^ � =@?-AF?\?�EHe&K�W�I�DFXV?:ZJA�X[Z�D"d/K�GRZ�`HK�I�G�D[?�?UTk?�K�I�Z�=2DFX�AFS�AFG�KiAHa67kP�Z�`�KI�G�D[?�?UTk?�K�I�Z�=2DFX�AFSNAFG�KiAsDFP�Agl>A"Z\K�G>_H=2_VK6W]D/EHLHS2K�?�o]Z�`�K6?U_NK�KiWQDFP�Z\`HK-l�A�Z�K�G�u

A[<nWHDFEHLHS2K�?�aLN<nq/D(K�?�Z�D&��K�G\D�aIi<n=2X�I�G�KiAF?�K�?�aWV<n`VA�S2dFK�?�aK*<nq/D(K�?�Z�D&=2X]��XH=YZ:^Fa

¾H� ¶ h[e4EHS�ZB¾/¾ ½ ¾F¾C� ¶�¶ K�A/?U^�KiAF?�^�Z�`�=YXHO(=2XHq�uj_VA�_NK�GcA�XVWQS2=YP Z� ª�¬"¨ �V«������V¬ ��­��  cD�Z~P,AF=YGc?�D�?UD/e&KM?UZ�EVW]K�X[Z\?cl~=�Z\`mWH=2?\A�LH=2S2=�Z\=YKi?�a

� ¹ a~b�A�O/K6Z�`�=2?Mh[EH=2�4A�XVW � ��� �{XHD�o�XHDXHDFZBZ�`VA"Z�a-b�A�O/K6Z�`�=2?Mh[EH=2� �{DFGR?�DFe&Kg?U=2XHqFS2K&?U`HK�K�Z�D�P;_�AF_VK�GR=YP;^/DFEAFG�X�· Zc=2XmA�h[EH=2�6e&=@?UK-K�Xm?\I�(K�XHK��w=2XQ^/DFEHG>�VXHqFK�G\?~l~=YZ�`m^/DFEHG>��X�qFK�GJ?~D/XK�=�Z\`HK�GR?U=@W]K-D�P�DFX�K-D�P�X�A�G\G�D"lK�X�WH?�a�£cDFS@WQZ�`H=@?>K�XVW A:EV?:Z ��� � ^FD/EHG>SY=2_�?cAFX�WQLHSYD"l�A�?:Z\G�D/XHqgqFE�?UZ�a

A[<n BD�Z\`H=YX�q�`�A�_H_NK�XV?�o]LNK�I�A�E�?�K-^FD/E�· d/KRL�SYD"l~XQZ�D(D&`�A�GJWpaLN<Q BD�Z\`H=YX�qC`�A�_�_VK�X�?�oNLNK�I�AFE�?�K-^FDFE�· d/K-LHSYD"l~XmZ\D(Dn?UDFP Z�S2^AFX�Wm^FD/E�· dFK-XHK�dFK�GR?UE�I�I�K�K�W]KiWm=YX�LHS2D"l~=2XHq

E�_mAgL�AFSYS2D(DFX=YXm^/DFEHG>S2=�P8K/aIi< ��D/E�?U_H=YZ�aWV<Qb>`�K-=YX�?UZ�G\E�I�Z�=2DFX�?~AFG�KMEHXH=2X[Z�K�SYS2=Yq/=YL�SYK/aK*<Qb>`�Kg_VA�_NK�GMG�=@?�K�?RLVKiI�A�EV?UKg^FD/E�· d/K4I�G�KiA"Z�KiW�AQ`H=2qF`]T!?U_NK�KiWpopS2D"l>T�_HG\K�?\?�EHG�Ks��DFX�KgAFLVD"d/K6Z�`�K4_�AF_VK�G�ab>`�=2?�=@?�?UD/GUZ�D�PNSY=2OFK>A�=2G�_�S2AFXHK�S2=YP Z�a�°BPNI�D/EHGJ?UK/o"=�PN^FDFE4_HE]Z�Z�`�K�_VA�_NK�G�A�LND"dFK�^FD/EHG�S2=2_�?jA�X�W4LHS2D"l�Z�`�K

Page 79: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ¶ |�SYEH=@WH? º ¶

_VA�_NK�G�G�=@?UKi?~Z\D[DVu�Z�`H=@?cZ\=Ye&KgLVKiI�AFE�?UK6Z�`HKge&D"d[=2XHqnAF=YGR_HE�?�`HK�?RDFXmZ\`HKg_�A�_NK�Gg58=�a K/aYo�GJA�e _HG�Ki?�?�EHG\KA/I$ZJ?>DFXZ�`HKM_�AF_VK�GJ<�o�A�XVWQ?�D�?UD/egK�Z�=2e&K�?cI�DFe&e&DFXm?UK�X�?UKMl�DFG\O]?�K�dFK�XQ=2X��EH=@WWH^[XVA�e&=2I�?�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H� ¶ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu;��EHK�G\=2IJO/KFo]`HK�e&=2?�_H`HK�G�Ki?�o]`HD/G\?�K�?� ª�¬"¨ �V«������V¬ ��­�� v�SY^]W]Ki?�WHAFSYKi?

�FaB°BZ�Z�D�dFDFX&��EHK�G\=@IJOFKR5U� ¹ ¾/� ��� ¹/¼F¹ <V=2X(dFK�X[Z\K�W-Z\`HK~A�=2G�_�EHe&_gAFX�Wsl~G\D�Z\K�ARLVD(D/O6W]K�?\I�G\=YL�=YXHq�`H=@?�=YX(dFK�X[Z�=2DFXAFX�W�K��]_NK�G\=Ye&K�X/ZJ?cZ\`�A"ZMI�D/EHS2W�LVKgW]DFXHK4l~=�Z\`�=YZ�u ; = D�1��$+ 3�1��V�8���� � �#���.$[�F1i.��]�$F+, ����F1 � �F ����Q) D3����+,�5U� ¹ ºF�F<�a�� P,A�e&DFE�?&=2S2SYE�?UZ�GJA"Z\=YD/X{?U`HD"lc?4Z:l�D�Z�K�AFe�?�D�PMK�=2qF`[Z�`HDFGJ?�K�?gZ�G\^(=YX�qxZ\D�?UK�_�A�GJA"Z\KAr_VA�=2G�D�PA:D/=YXHKiWmLHGJAF?\?>`HK�e&=@?U_H`�K�G\K�?�a�¸�K�Z~Z�`HKsSY=2XHK-Z\`HG�D/EHqF`Z\`HK-`HDFGJ?�K�?~A�XVWm`HK�e&=@?U_H`�K�G\K�?~LNKMZ�`HK �HT!A"�]=2?�a�b>`�K`HK�e&=2?�_H`HK�G�Ki?�`VAFW6LNK�K�X4K�d"AFI�EVA"Z�KiWsAFX�WsK��(Z�K�G\X�AFS[AF=YG�_HG\K�?\?UE�G�K�`HK�S@W6Z\`HK�e Z�DFq/K�Z\`HK�Gia�b>`HK>`HK�e&=2?�_H`HK�G�Ki?l�K�G\KcA�LNDFE]Z;A�P8D(DFZ�=YXCW]=@A�e&K�Z�K�Gia�b>`HK~Z�DFZ\AFSH`HDFGJ?�K�P8D/G\I�K~XHK�KiW]K�W ��� ��� � � � � � ��?�K�_�AFG\A�Z�KZ\`HK�`HK�e&=2?�_H`HK�G�Ki?�l�A/?CA�LNDFEHZ�º ¶ ¾F¾� sa � � � � b>`HKxW]=2AFe&K�Z�K�GQAFX�W±Z�DFZ\A�SR`HDFGJ?�KmP8DFGJI�K�d"A�S2EHK�?QA�G\Kd/K�G\^nA�_H_�G�D*�]=2e&A�Z�K/oHA�X�W�?�D�A�X(^nd"A�S2EHKi?cI�AFS2I�EHS2A�Z�KiWQEV?U=2XHq&Z�`�K�e l~=YS2S�LNK6S2=YO/K�l~=@?UK6AF_H_HG\D*�(=2e�A"Z\KFa��cS@?�DEHXVI�K�G�Z\AF=YX[Z\=YKi?�Z�K�XVWnZ\D�LVK-S@A�G\qFKRP8DFG>Z\`HK6W]= �NK�G�K�X�I�KMDFP�XHKiA�G\SY^�Kih[E�A�S�d"AFSYEHKi?�aA[<v�D/X�?�=2W]K�G�Z�`HK �HT!W]=2G�KiI$Z\=YD/X�P8D/G\I�K�?�DFXxDFXHK&`HK�eg=@?�_H`HK�G\Km5 Z�`�K�DFXHK4Z�`�A�Z�· ?MG�D/EHX�W]^�=2XxZ�`HK&_ND/?�=�Z\=Yd/K��TkWH=YG\K�I�Z�=2DFXV<�an|HD/EHGMP8DFGJI�Ki?-AFI$ZiuMZ�`HK�K��(Z�K�G\X�AFS�A�=2GMP8DFGJI�KFo�Z�`HK�=2X[Z�K�G\X�AFS;A�=2GMP8DFGJI�K�5 Z\`HK�d"AFI�EHEHem· ?X�D�Z-I�DFe&_HS2K�Z\Ki<�oVZ\`HKgXHDFG\e�A�S�P8DFGJI�KsDFPjZ�`HKgG\=Ye�D�P;Z�`HKgD�Z\`HK�G�`HK�e&=@?U_�`HK�G\KFopA�XVWmZ�`HKg_HEHS2S�P8DFGJI�K4D�PZ\`HK-`HD/G\?�K�?�aj|HDFG~Kih[EH=YS2=2LHG�=2EHe

¾�$ ��� � � � � � � � � ��� � � � � ��� � �

 BD�Z\K-Z�`�A�ZcZ�`�K6=YX[Z\K�G\X�A�S�_�G�Ki?�?�EHG\KRP8D/G\I�K-=YXmZ\`HK ��TkW]=2G\K�I$Z\=YD/X�DFX�A�W]= �NK�G�K�X[Z�=@A�S�L�=�ZBDFP�?�_H`HK�G�K4A�G\K�A� � =@?

� ��� � � $��� � � � � �� � �� l~`�K�G\K ���=@?�Z�`HK-XHD/G�e�AFS�Z�DgZ�`HK6?�EHG�P,AFI�KMAFG�KiAHa�� LH=YZcD�P�=YX�?�=2qF`[Zc?U`HD"lc?�Z\`�A"Z

��� � � $ ��� � � � � �

l~`�K�G\K � =@?&Z�`�K�G\A/W]=2E�?�D�PMZ\`HK�`HK�eg=@?�_H`HK�G\KFaz»{`�A"ZQ=2?CZ�`HK�K��]_HG�Ki?�?�=2DFXtP8DFG � � � � =YXwZ\K�G\e&?CD�PK��(Z�K�G\X�AFSp_HG�Ki?�?�EHG\K�����K�Z~Z�`HK6?�=Yq/XQDFP � � � � G\=2qF`[Z�a

LN<��=2dFK�X � $�¾ � ¶ P Zn5 P Zg=2?-P8D[DFZ\?�o�P8D[DFZ\?J<$o � � � � $ � � ¾H� ����¾ � 9jAHo�A�X�W � � � ��� � $�º ¶ ¾F¾; 6opl~`�A�Zs=2?��� � � ���B?\?�EHe&KMZ�`HK-`HK�e&=2?�_H`HK�G�Ki?>`�A*dFK�XHK�q/SY=2qF=2LHS2K�Z�`H=@IJO(XHK�?\?�a

Ii<n»�DFE�S2WgZ\`HKc`HD/G\?�K�P8DFGJI�K>`�A*dFK>Z\D-LVKRA�X(^sW]= �NK�G�K�X[Z�Z�D-_HE�SYSNAM`HK�e&=@?U_H`�K�G\K~DB�QAMl>A�S2SH=YPNZ\`HKc=2X[Z�K�G\X�AFS_�G�Ki?�?�EHG\KRl�K�G\K�Z�`HK6?\A�e&K-AF?>=2XZ�`HKMZ:l�D&`HK�e&=@?U_H`�K�G\K�K��]_VK�G�=2e&K�X[Z�����]_HS2AF=YX�a

WV<n´jD/X±��EHK�G�=@IJOFK/· ?s`HDFGJ?�K�?sI�DFEHS@W]X�· Zg?�K�_VA�GJA"Z�KCZ�`HK`HK�e&=@?U_�`HK�G\K�?�a��R?sXVA"Z�E�G\AFS�TkLVD/G�X�I�D"l~qF=2G�S@?6AFX�WI�D"l~LVD"^]?�l~`�A�Zcl�D/EHS2WQ^FD/E?\A*^�u�WH=2W`HK-E�?�Ksv�SY^]W]Ki?�W�A�S2K�?>DFG~_NDFX�=YKi? �����]_HS2AF=YX�a

 M°�b~�cu�¯�^±?�DFEHGJI�Ki?&P8DFGCZ�`H=@?Qh[EHKi?:Z\=YD/X{A�G\K�v�A�GJW]l�K�S2Ss58_�a ½F¼ AFX�W �F�"º�<�o>£R¿�»�o�_�a ³ µ��/o>AFX�W±Z�`�Kv�S2^]W]K�?\WHA�S2KM_�A�q/KFu

`[Z�Z�_�u yFy"l~l~l-a =2e&`�a D/G�q]y*=2e&`Ny*L(lRy"I�SY^]W]K/a `[Z\egS

¾H� ¶ h/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj_�AFG\AFLVD/SY=@IM?UE�GUP,A/I�K�D�P�G�DFZ\A"Z\=YX�qs��E�=2W�]a ��D/Ex`�A*d/K�A�X�=YX�I�DFe&_HG\K�?\?U=2LHS2Ks�VEH=2W�DFP�W]K�X�?U=YZ:^ ��=2X�ALHE�IJOFK�Z�a&b>`HK�LHE�IJO/K�Z-=@?MG�DFZ\A"Z\=YX�qA�ZsA�XHq/EHS2AFG?�_VK�K�W �ca�¡BEHK6Z�D�d(=2?\I�D[?U=YZ:^�Z\`HK-��EH=@Wm`�A/?cI�D/egKMZ\DCA�?:Z\K�A/W]^Q?UZ\A�Z�K-l~`HK�G�K-=YZB=@?cI�DFT�G\D�ZJA"Z�=2XHq&l~=YZ�`mZ�`�KLHEVIJOFK�Ziu~=�a KFa2opK�A/IJ`m��EH=@W�K�SYK�egK�X[Z�=@?BG\D�ZJA"Z\=YXHqnl~=�Z\`xA�X�qFEHS@A�G�?U_NK�KiW �ca�7!X�Z�`HKgG\D�Z\A�Z�=2XHq�P8GJA�e&KsDFP�Z�`�KLHEVIJOFK�Z�Z�`�KR�VEH=2Wn=2?~A�Z�G\K�?UZ�ajb>`HK�LHE�IJO/K�Z�P8G\AFe&KR=@?�o(DFP�I�D/EHGJ?UK/o/XHD/X]Tk=YXHK�GUZ\=2AFS�o(LHEHZ>=YZ~I�A�XQLVK�Z\G�KiA"Z�KiWnA/?

Page 80: Introductory Physics Problems David J. Jeffery Department of

º ¹ v�`�AF_]Z�a~� ¶ |�SYE�=2WH?

AFX�=YXHK�GUZ\=2AFSpP8GJA�e&K6L(^Q=2X[Z�G\D]W]E�I�=2XHq&Z\`HK4I�K�X[Z�G\=�P8E�q/A�S�P8DFGJI�KFa>b>`HK4K��(Z�K�G�X�AFS�A�=2Gc_HG\K�?\?�EHG�K-=@?BA/?�?�EHe&K�WQZ\DLNK6A&I�DFXV?:ZJA�X[Z � � � � aA[<C7!XA6q/K�XHK�G\AFSN?�K�X�?�KBl~`VA"Z~W]Ds^/DFECK��(_NK�I�Z�Z\`HKM?U`�AF_VK�D�P�Z�`HKM?UE�GUP,A/I�KBDFPpZ�`HK�l>A"Z�K�G;Z\D4LNKFa ������ �b�G\^�?�l~=YG\S2=YXHq�l>A"Z\K�G4=YX�A�I�SYKiA�G6q/S2A/?�?�am7!X�A�G\DFEHq/`�h/EVA�S2=�ZJA"Z�=2dFK�l>A*^�=�ZsD/XHS2^xe�A"Z�Z�K�G\?6Z�`�A�ZsZ�`�Kl>A"Z\K�G~=@?>G�DFZ\A�Z�=2XHq�?UD/egK�Z�`H=2XHq&S2=YO/KMAgG\=Yq/=2WQG\D�Z\A�Z�D/G�u�Z�`HK6I�EH_�W]D(K�?�X�· Zc`�A*dFKRZ�D�LNKFa

LN<n»{`VA"Zc=@?�Z�`HK6I�K�X[Z�G\=�P8E�q/A�S�P8D/G\I�KM_VK�GcEHXH=YZce�AF?\?>=YXZ�`�K-G�DFZ\A"Z\=YX�qsP8GJA�e&K��Ii<Q¡RK�G\=2dFK�Z\`HKnK��(_�G�Ki?�?�=YD/X�P8DFG&?:ZJA"Z�=@I�Kih/E�=YS2=YL�G�=2EHe _HG\K�?\?UEHG\K�=2X�Z�`HKQdFK�GUZ\=2I�A�S�WH=YG\K�I�Z�=2DFX �xZ\A�O(=2XHq �_ND/?�=YZ�=2dFKnA/?-EH_(l�AFG\W�am¸�K�A*d/K4Z\`HKQI�DFX�?UZ\AFX[Z6D�P~=YX[Z\K�qFGJA"Z\=YD/XrEHX�W]K�Z�K�G\e&=YX�K�WrP8D/G-Z�`HKQe&DFe&K�X[Z�ug=YZl~=2S2S�W]K�_NK�XVWQD/X A�XVW ��� � ��a

WV<Q¡RK�G\=2dFK�Z�`HK~K��(_�G�Ki?�?�=YD/X-P8DFGj?UZ\A�Z�=@I�Kih[EH=YS2=2LHG�=2EHe _�G�Ki?�?�EHG\K�=2XsZ\`HK>`HDFG\=2��DFX[ZJA�S(W]=YG\K�I�Z�=2DFX e&K�A/?UEHG\=2XHq P8G�D/e Z�`HK>G\D�ZJA"Z�=2DFXgA"�]=@?�a�b>`H=2?�=@?�W]DFX�K�Z\G�KiA"Z\=YXHqRZ�`�K�G\D�ZJA"Z\=YXHqBP8G\AFe&K>A/?�AR?UZ\A�Z�=@I�G\K�P8K�G�K�X�I�K�P8GJA�e&Kl~=YZ�`xACI�K�X/Z\G�=YP8EHq[A�SpP8D/G\I�KFac¸�KiA*dFKMZ\`HK4I�DFX�?UZ\AFX/ZcDFP�=YX[Z\K�qFGJA"Z\=YD/XmEHX�W]K�Z�K�G\e&=YX�K�WP8DFGBZ�`HK4e&DFe&K�X[Z�u=YZ>l~=YS2SpW]K�_NK�X�WQDFX �CA�X�W � � � � a ������ � v�DFX�?�=2WHK�G�Z\`HKM=YX�XHK�G>A�X�WnDFE]Z\K�G�`HDFG\=2��DFX[ZJA�S�_�G�Ki?�?�EHG\K�?�D/XA&I�^[S2=2X�W]K�G~DFP�Z\`H=@IJO[X�K�?\? � A�X�WQe&K�AFXm?�EHG�P,AFI�K�AFG�KiA � � I�K�X[Z�K�G\K�WQDFXQZ�`�K-G�DFZ\A"Z\=YD/XQA��(=@?�a

K*<¤]K�Z�Z\`HK~��K�G�D-S2K�d/K�S]D�P �sZ�D-LNK>Z�`HKc`�K�=2qF`[Z�D�PNZ�`HKc��EH=@W�A"ZjZ�`�K $�¾M_VD/=YX[Zia� BD"ltI�DFesL�=YXHK>Z\`HK~Z:l�D_�G�Ki?�?�EHG\K6K��]_HG\K�?\?U=2DFXV?~l~=�Z\`�Z\`HKsLNDFEHXVWHA�G\^I�DFX�WH=�Z\=YD/X ��5 $�¾ � $ ¾/< $ � � � � oNZ\DC��X�W�_HG�Ki?�?�EHG\KA/?~A4P8EHX�I$Z\=YD/XmD�P A�XVW ��a

P\<mb�A�O/K&Z�`HKW]K�G\=2d*A�Z�=2dFK�DFP ��5 �]<6l~=�Z\`�G�Ki?U_NK�I�Z6Z�D �nA�I�D(DFGJW]=YXVA"Z�K&Z\`�A"ZgG�E�X�?6A�S2DFX�qmZ�`HK?UEHG�P,AFI�KWH=YG\K�I�Z�S2^QD/E]Z:l�AFG\WnP8G\DFe Z\`HKsG\D�ZJA"Z\=YD/XA��(=@?�a>��=2dFK�XmZ�`HK6LNDFE�X�WHA�G\^QI�DFX�WH=�Z\=YD/X�o�l~`�A�ZcesE�?UZ � � ��� �Kih[E�A�S � �������� � ��D/E�W]DFX�· Z�XHK�K�WgK��]_HS2=2I�=�Z�K��]_HG�Ki?�?�=2DFX�?�P8DFG � � � �cAFX�W � � � � �/a���E]Z�^/DFE&W]DMXHK�KiWZ\D�G�K�e&K�esLNK�G�Z\`HK6IJ`�A�=2XmG�E�SYK/a

q(<Q¤]DFS2dFK�P8DFG �nA/?~A4P8EHX�I$Z\=YD/X�D�P a;»{`�A"Zc=@?�Z�`HK6?�`�AF_VK-DFP�Z�`�KM��EH=@W?�EHG�P,AFI�K��

¾H� ¶ h/P8EHS2S�¾/¾ ³ �i¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj_HS@A�X�K�Zc_HG\K�?\?UE�G�K/o(¯�AF?UZ�D]W]DFX³ a~£RA�=2S�?UZ\AFGcdFD"^[A�qFK�G 1 �~P Z\K�GMA�K�DFX�?~DFPjZ�GJA*dFK�SpZ�`HG\DFE�qF`�W]K�K�_�o�WHA�G\OQ?�_�A/I�K6^/DFE�I�D/e&KsA�EH_NDFX�An?:Z\G\AFXHqFK/oXHK�l�l�DFG\S2Wpa�7kZ>=2?�A6_HS@A�X�K�Z�o(Z\`�A"Z�^FD/ECX�A�e&KM¯�AF?UZ�D]W]D/X�o[e&A/W]KBDFP�A�XQA�L�?�DFS2E]Z�K�SY^&=2X�I�D/e&_HG�Ki?�?�=2LHSYKB��EH=@Wl~`H=@IJ`&^FD/EgI�A�S2S�¯�AF?UZ�D]W]D/XH=2EHema�¿~K�e�A�G\O*AFLHS2^FoFAFS�Z\`HDFEHq/`sZ\`HK~_HS@A�XHK�Z�=2?j��EH=@WgAFSYSHZ�`HK~l>A*^Fo�=YZ�=@?jG�DFZ\A�Z�=2XHqS2=YO/K�A4G\=Yq/=2W�G\D�ZJA"Z\DFGiu�K�dFK�G\^&LH=YZ�`�A/?�Z�`HK-?\A�e&KRAFXHqFEHS@A�G�dFK�SYD]I�=�Z:^ �ca � � � � b>`H=2?>h[EHKi?:Z\=YD/XQI�D/EHS@WCLNKAgesE�S�Z\=�Tk_�A�q/K�G~=2XAgZ\K�?UZ~eg=@?�K-K�X�?�I�(K�X�KFaA[<nb>`�K�G\A/W]=2E�?�D�P�¯�A/?:Z\D]W]DFX�=@? � $ � � ¾ �f�i¾���e )xZ�`HK�W]K�X�?�=YZ:^fD�P�¯�A/?:Z\D]W]DFXH=2EHe =2? � $

� � ¾ ����¾ � O(q �"e � aj»{`�A"Zc=@?c¯�A/?:Z\D(WHDFX�· ?�e&A/?�? � �

LN<��=2dFK�X�Z\`HK4G\D�ZJA"Z\=YD/X�A�S�=YX�K�G�Z�=@A�P8DFG\esE�S2ACP8DFGMAnG\=Yq/=2WHSY^mG\D�Z\A�Z�=2XHqnE�XH=�P8D/G�e ?�_H`HK�G�K/o � $�5���� ¶ < � ��ol~`VA"Zc=@?~¯�AF?UZ�D]W]D/X�· ?>G\D�ZJA"Z\=YD/X�A�S�=2XHK�G�Z�=@A��

Ii<Q¯�AF?UZ�D]W]DFX G\D�ZJA"Z\K�?�D/X�I�K�K�dFK�G�^��"µ�a ¾�`HD/EHGJ?�l~`H=@IJ` =2?�Z�`HK�?�AFe&K�AF?�Z�`HK��;A�G�Z�` Z\D l~=�Z\`H=2XK��]_VK�G�=2e&K�X[Z\AFS�E�X�I�K�GUZJA�=2X/Z:^/aM»{`�A"Z-=@?R=YZ\?MAFXHqFEHS@A�GRdFK�SYD]I�=YZ:^ ��=2XxGJAFW]=@A�XV?B_NK�G-?�K�I�D/X�W � ������ �£BD"l�e�A�X(^CGJAFWH=2AFX�?>A�G\KRZ\`HK�G\KM=YX�A�I�=YGJI�S2K��

WV<Q�R?�?�EHe&=2XHq�Z\`HKnq[AF?sI�SYD/E�W�D/E]Z4DFPcl~`H=2IJ`t¯�AF?UZ�D]W]D/XrP8DFG\egKiW�l>AF?6K.�NKiI$Z\=Yd/K�S2^x=@?UD/S2A�Z�KiWrP8G�D/e AFSYSK��(Z�K�G\X�AFS;P8D/G\I�K�?�o�I�A�S@I�E�S2A�Z�K�Z\`�A"Z&q/A/?4I�SYD/E�Wp· ?4AFXHqFEHS@A�G4e&DFe&K�X[Z�E�e A�LNDFE]Zg=�ZJ?gI�K�X[Z�K�G4DFPBe�AF?\? ��������� � »{`�A"Z�=2?�¯�A/?:Z\D(WHDFX�· ?BAFXHqFEHS@A�GBegD/e&K�X[Z�EHe�XHD"l ���cS@?UDVo ��=2?�DFS@A"Z\K�WP8G\DFe�A�S2S�K��(Z�K�G\X�AFSP8D/G\I�K�? �4WHD[Ki?UX�· Zc=2e&_HSY^nZ�`HK6I�SYD/E�WQ`�AFW��K�G�D&A�X�qFEHS@A�G>e&DFe&K�X[Z\EHema

K*<mv�D/X�?�=2W]K�G�AgW]= �NK�G�K�X[Z�=@A�SNLVD*�C=2X�?�=2W]KM¯�A/?:Z\D(WHDFXnA�Z�GJAFW]=2E�? l~=YZ�`e&A/?�? � �xo]`HK�=Yq/`[Z � oVA�X�WQA�G\K�A_NK�G\_NK�X�W]=@I�E�S2AFGRZ\DnZ\`HKgG\A/W]=YEV? � �6a4 cD�Z\K =2?RZ�`�K4GJAFW]=@A�S�I�D(D/G\W]=2X�A�Z�K4AFX�W�=YZ-=YXVI�G\K�AF?�K�?RDFEHZ:l�AFG\WP8G\DFe ¾�A"ZsZ�`HKI�K�X[Z\K�G-Z\D��}A�Z-Z�`HK?UE�GUP,A/I�KFa»{`�A�Zs=2?6Z�`HKW]= �NK�G�K�X/Z\=2AFS�_HG\K�?\?UE�G�K � ��AFI�G�D[?�? � q/DF=2XHqsD/E]Z:l>A�GJW�=YXnZ�K�G�e�?�D�P ��AFX�W�Z\`HKRe�AFqFXH=YZ�E�WHKRDFP�Z�`HKMq/G\A*d(=YZ\A"Z\=YD/X�A�SH��K�S@W�# � 5 <>A�Z ��»�G\=�Z\KZ\`HK-qFGJA*d(=�ZJA"Z\=YD/X�A�SV��K�S@WDFE]ZcK��]_HSY=@I�=YZ�S2^C=2XZ�K�G\e�?~D�P �&o]Z�`�K-G�K�SYK�d*AFX[Z>e�A/?�?�oHA�X�W a

P\<7!X[Z\K�qFGJA"Z\K±Z�`HK�W]= ��K�G\K�X[Z�=@A�SCK��]_HG�Ki?�?�=2DFXf^/DFE P8DFE�X�W =YX Z�`�K�_�A�G�Z�58K*<�A�X�?�l�K�G�Z�D�D/L]Z\AF=YX Z�`�K

Page 81: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ¶ |�SYEH=@WH? º/º

K��]_HG�Ki?�?�=2DFXMP8DFG�Z�`�K�_HG\K�?\?�EHG�K�A"Z�Z\`HK>I�K�X[Z\K�G�D�P�¯�A/?:Z\D(WHDFX�a� cEHe&K�G\=@I�A�S2S2^�K�d"A�S2E�A"Z\K�Z�`�=2?�K��]_HG\K�?\?U=2DFX�a�R?�?�EHe&KMZ�`�Ks?UE�GUP,A/I�KM_HG\K�?\?UEHG\KM=2?c��K�G\D�a� BD�Z\KMZ�`HK6I�K�X[Z�G\=�P8E�q/A�S�P8D/G\I�K6I�AFXQLNK6=2qFXHD/G�KiWpu�A:E�?UZBAF?>P8D/GZ\`HK���A�G�Z�`�58l~`H=@IJ`{¯�AF?UZ�D]W]D/XwG�Ki?UK�esLHS2K�?�=2X{?UD/e&K�G�Ki?U_NK�I�Z\?J<gZ�`HK�I�K�X[Z�G\=YP8EHq/AFS~P8DFGJI�K�=@?�DFX�SY^±A_NK�G�Z�E�G�L�A�Z�=2DFX�aj¿~KiI�AFSYS � $ ¹ � ¹ º*µ[¾[º��x�i¾ � � �B=YX�¯�²6¤nEHXH=YZ\?�a

¾H� ¶ h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�9jA/?�I�A�S�· ?�_HG\=YX�I�=Y_�SYK/oHSY=YP Z�=2XHqCA&I�AFGµ�a ��D/Ex`�A*d/KgAl>A"Z\K�G�T�L�A/?UKiW�`(^]W]G\AFEHS2=2I&?�^(?UZ�K�e l~=YZ�`xZ:l�D�I�=2GJI�EHS@A�GM_H=@?:Z\DFX�?�a&b>`HK���?UZ-DFXHKg=2?&� � ¾;I�e =2XW]=@A�e&K�Z�K�G�A�X�W�^FDFE�I�A�X�_HEV?U`�D/X�=�Z�l~=�Z\`x� � ¾� �DFP�P8DFGJI�K6l~=YZ�`�^/DFEHGc��XHqFK�G�acb>`�Kg�"XVWm=2?RdFK�GUZ\=2I�A�S�AFX�W?�EH_H_NDFG�Z�=2XHq�AmI�A�G-DFP�e�AF?\?6� � ¾ ����¾ � O[q�AFq/A�=2X�?UZ-qFGJA*d[=YZ:^Fa&b>`HK�I�AFG-=2?6� � ¾�e A�LND"dFK4Z�`HK�S2D]I�A�Z�=2DFX�D�P��X�qFK�GiaA[<C»{`VA"Z~K��]_HG\K�?\?U=2DFXnP8DFG�Z�`�K-_HG�Ki?�?�EHG\KBDFP�Z�`�Ks�"X�WQ_H=@?:Z\DFXmAF?>A4P8EHX�I$Z\=YD/XQDFP�Z\`HKM_HG�Ki?�?�EHG\KRDFP�Z\`HK&��?UZ_�=2?UZ�D/X�a

LN<n»{`VA"Z�K��]_HG\K�?\?U=2DFX-P8D/G�Z\`HK�q/A�E�qFK�_HG\K�?\?�EHG�K�D�PHZ\`HK~�"X�W-_�=2?UZ�D/X4AF?�ABP8EHX�I$Z\=YD/XsDFPHZ�`HK�q/AFEHqFK;_HG�Ki?�?�EHG\KDFP�Z\`HK���?UZ~_H=@?:Z\DFX�a

Ii<n»{`VA"Zc=@?�Z�`HK6W]=@A�e&K�Z�K�GBD�P�Z\`HKs�"XVWQ_�=2?UZ�D/X �

¾H� ¶ h/P8EHS2S�¾/¾ ¶ ¾/¾g� ¶ ¾ge&D(WQZ\`H=YX�O[=2XHqVu��cGJIJ`H=Ye&KiW]K�?>_HG\=2X�I�=2_HS2KFo�b�AF?�e�A�XH=@A�XW]K�d(=2S¶ a>»�KF· dFK>A�S2S(`HK�AFG\W-DFPN�BG\IJ`H=2e&K�W]Ki?�AFX�Ws²M=2XHqM£c=2K�G\DFX�· ?�I�G\D"l~X�a���E]Z�e&D(WHK�G\X4?\I�=2K�X[Z�=@?:ZJ?�A�X�W6Z�K�IJ`�XHDFS2DFq/=2?UZAFG�K�?�K�S@W]DFe I�A�S2SYKiW�D/X�Z\Dw`�A�S2SYe�AFG�O�I�G�D"l~XV?�a�¸�K�Z�· ?�A�_H_HS2^z�BG\IJ`�=Ye&K�WHK�?m_HG\=YXVI�=2_HSYK�Z\D{G�KiA�SMl�D/G�S@W?�=�Z\E�A"Z\=YD/X�aA[<)��D/E-l~=2?�`MZ�DRAFI�I�EHGJA"Z�K�SY^�W]K�Z\K�G\e&=YXHK�Z�`HK;WHK�X�?�=�Z:^�D�P]^/DFEHG�b�AF?�e�A�XH=@A�X-W]K�d(=YSN5�¤]AFG\I�DF_H`H=2S2E�?p`�AFG�G\=2?�=2=@<�a��D/E�· dFK�A�S2G�KiAFW]^�WHK�Z�K�G�e&=2XHK�W�`HK�G-e�AF?\?�Z�D�LNK���¾ � ¾jO(q �{LNK�Z:l�K�K�X�e&A/?:Z\K�G6AFX�W�_VK�Z�o�l~`VA"ZsA�G\K&AP8K�lz?\I�GJA"ZJIJ`HK�?>A�XVWnD/XHKRS2=YZUZ�S2K-LH=YZ�K�Z�DgZ\`HKMLVD/XHK�� ��E]ZcX�D"l�^FD/EnXHK�K�WnZ�D�W]K�Z\K�G\e&=YXHKM`HK�G~dFD/SYEHe&K/a»{`VA"ZBW]D&^FD/EWHD �

LN<��G\=@?:T:��G�=@?~W]D(K�?�X�· ZR?�EHLHe&K�G\qFKMP8EHS2S2^FoNLHE]ZR?�`HKsW]D(Ki?UX�· Z~Z�G\^QZ�DC?�l~=Ye�A�X�Wm=@?cI�DFX[Z�K�X/ZBZ�D�A:E�?UZB��D[A"Ziab>`�K-l�A�Z�K�G>S2K�d/K�SpG\=2?�K�?>L(^ ½ � ¾ ����¾ � ��e � a;¤(D�l~`VA"Z~=2?c`HK�GcW]K�X�?�=�Z:^��

Ii<Q£RA*d(=YXHqrW]K�Z�K�G\e&=YX�K�Wt=YX�Z�`HKm_�AFGUZ�58LN<4AFX�?�l�K�GsZ\`�A"Z�^FD/EtI�A�X�· Z&WHK�Z�K�G�e&=2XHK���G�=@?UT!��G\=2?�· ?4W]K�X�?�=�Z:^l~=YZ�`rZ\`HKn=2X]P8D/G�e�A"Z\=YD/Xr^FDFEr`�A*d/KFo�^FDFErXHD"l�W]KiI�=@W]K�Z�D�G�K�SY^xDFXrZ�`�K��U=@I�K�LVK�G�q��Q_�G�=2X�I�=2_HS2KFug?U`HK/· ?�i¾ � E�X�?UE�LHe&K�G\qFK�W�a� cD"l ?�DFS2dFKMP8DFGB`HK�GBWHK�X�?�=�Z:^l~=YZ�`HD/E]ZBE�?�=YX�q�^FDFE�G~K�A�S2=2K�GBW]K�Z�K�G�e&=2XHK�Wme�AF?\?�u=YZ�· ?cA/I�I�E�G\A/I�^CI�AFX�· Z>`�K�S2_^/DFEl~`HK�Xm^/DFEmA�G\KRG\K�S2^(=YXHq&D/XnZ\`HK-=2I�K�LNK�G\q&_HG�=2X�I�=Y_HS2K

WV<Q BD"l�^/DFEm?�A*^��m�cXVWm��G\=@?:T:��G�=@?>?�A*^]?�� � � � b�D��VX�W�DFEHZ4A�LNDFE]Zgb�A/?Ue�A�X�=2AFX�W]K�d(=2S2?s=YX�I�SYEVW]=YX�q�l~`�A"Z4Z�`HK�^xG\K�AFSYS2^r?UD/EHX�WrS2=YO/K�58LHEHZ4XHDFZl~`�A�Z~Z�`HK�=YGcWHK�X�?�=�Z:^Q=2?J<;Z�G\^CZ\`HK6b�A/?Ue�AFXH=2AFXQW]K�d(=YS�_VA�qFK/u

`[Z�Z�_�u yFy"l~l~l-a _�AFG�O]?�a ZJAF?�a q/D"d�a AFENy*l~=2S2WHSY=YP8K*y"e&AFe&e&AFS2?$y"WHK�d(=YS�a `/Z\e&S

¾H� ¶ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(We�A"Z\`�u�I�=YZ:^Cl>A"Z\K�G>Z\AFXHO�Z\D&Z\A�_¹ a ��D/EHGcI�=YZ:^nl>A"Z\K�G�Z\AFXHOn`�A/?~A�XmA*dFK�G\AFqFKBl>A"Z\K�G>S2K�dFK�S�A�LND"dFKM^FD/EHG�Z\AF_�?>D�P>��¾/¾jema

A[<n�R?�?�EHe&=2XHqZ�`HK�G�K/· ?MXHDP8EHX�X[^xLHE�?�=YX�K�?\?�Z�D�AFW A:EV?:Z-Z\`HK�_HG\K�?\?UEHG\KgLVK�Z:l�K�K�XxZ\A�X�O�A�X�W�Z\AF_{58l~`H=@IJ`Z\`HK�G\K�_HG\DFLVA�LHS2^ =@?J<$ol~`�A"Z�=@?�Z�`HK�l>A"Z\K�Gt_HG�Ki?�?�EHG\K�A"Z�^/DFEHG�Z\AF_�?�l~`HK�X�Z�`HK�^ A�G\K�I�S2D/?�K�W �»{`VA"Z4=@?sZ�`HKq/AFEHqFKC_�G�Ki?�?�EHG\K�� �R?�?�EHe&KQAF=YG4_HG\K�?\?UEHG\KC=@?C� � ¾�� ����¾ � 9jA�A�XVW�l�A�Z�K�G4W]K�X�?U=YZ:^r=2?� � ¾ ����¾ � O(q �"e � a

LN< ��D/E�D/_VK�X�^FD/EHGcZJA�_xAFX�W�=YZ\?RZ�`�K4D/XHSY^mD/_VK�X�Z\AF_�=2X�Z�`�KgI�=�Z:^�u~XHDnZ�DF=2S2K�Z\?R��EV?U`H=2XHqQK�=YZ�`HK�G�a ��DFEHGZJA�_�¡R7:�B¯���b~�;¿�=@?-� � ¾�I�e )�Z�`HKsI�=�Z:^nZ\AFXHOQW]=@A�e&K�Z�K�GB=2?���¾jema�»{`�A�Z�· ?~Z\`HKs?�_VK�K�WmD�P�Z�`�K6l�A�Z�K�GP8G\DFe�^/DFEHGBZ\AF_ �{¡R=2Wx^FD/E�G�KiA�S2SY^mXHK�K�W�Z�DO[X�D"l Z�`HK&W]=@A�e&K�Z\K�GJ? �w»{`(^�e&=2qF`[ZBZ\`H=2?-AFX�?�l�K�GBXHDFZLNKMZ�D(D�AFI�I�EHGJA"Z\K��m£B7: BbMu��R?UK ��K�G\XHD/EHSYS2=�· ?>Kih/EVA"Z�=2DFXmA�XVWCZ\`HK6I�D/X/Z\=YX(EH=YZ:^CKih/EVA"Z�=2DFX�a

¾H� ¶ h/P8EHS2S�¾���¾F¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujl>A"Z\K�GcI�S2D]IJO�oHI�S2K�_�?�^]W]G\A

Page 82: Introductory Physics Problems David J. Jeffery Department of

º ¼ v�`�AF_]Z�a~� ¶ |�SYE�=2WH?

º(a~b>`HK&l>A"Z\K�GMI�S2D(IJO�D/G�I�SYK�_�?�^(WHG\Ax58S2=�Z\K�GJA�S2SY^���G\K�K�OmP8DFGMl�A�Z�K�GRZ\`H=2K�P\<�=@?�DFXHKgD�P�Z\`HK&e&D/?UZMAFX�I�=2K�X[ZMZ�=2e&Ke&K�A/?UE�G�=2XHqMW]K�d(=@I�K�?�a�b>`HKc��q/^[_HZ�=@A�X�?�E�?�K�W4Z�`�K�efe&=2SYS2K�X�XH=2A-AFqFDVa�b>`HK�^sl�DFG\O6A"ZjXH=2qF`[Z�EHXHS2=YO/K~?UEHXVW]=2AFS2?AFX�WtZ�`HK�A/W]d"A�X�I�K�W±dFK�G\?�=YD/X�O/K�K�_V?� cK�l>Z\DFXH=@A�X±Z\=Ye&K�58Z�`HK�?UZ�E,��l�K A:E�?UZQI�A�S2SBI�S2D]IJO�Z�=2e&K�E�?UEVA�S2SY^H<$ab>`HK�^�A�G\Ksh[EH=�Z\KsLH=YZRKiAF?�=YK�GcZ\DnLHEH=2S@WmZ�`�AFX�`HD/EHGRq/S2A/?�?�K�?�a~»rA"Z�K�GB_NDFEHGJ?�oN?�Dn^/DFE�W]D/X�· Z�XHK�KiW�A&P8EHX�XHK�SI�DFX�?UZ�G\E�I$Z\=YD/X�ar»�A�Z�K�GgI�A�X�KiAF?�=YS2^rLVKG\K�_HS@AFI�K�W�AFX�W�q/D�Z4G\=@W�DB��o;?�D�^/DFE�W]D/X�· Z&AFL�?UD/SYEHZ�K�S2^rXHK�KiW�Z\D`HK�G�e&K�Z�=@I�A�S2S2^n?UKiA�S�Agl>A"Z�K�GcI�S2D]IJO �{=YZ>e&=2qF`[Z~LVK6A&q/D(D(WQ=@W]K�A4Z�`�DFEHq/`�a��D/E�`�A*d/Kn?U=2e&_HS2KnDFG&��q/^(_]Z�=@A�X�l>A"Z\K�GgI�S2D(IJO�I�DFX�?�=2?UZ�=2XHq�DFPRA�_�G�=2e�A�G\^xd/K�?\?UK�S�5,dFDFS2EHe&K � � o�?UEHG�P,AFI�KAFG�KiA�� � <jl~=YZ�`nA-`�DFS2KRA"Z;Z�`HKRL�AF?�Ks58`�DFS2KRA�G\K�A�� � <�AFX�WCA6I�A"ZJIJ`He&K�X[Z;dFKi?�?�K�SVl~`H=@IJ`CI�A"ZJIJ`HK�?�Z�`HKRl�A�Z�K�GI�DFe&=YX�q�DFE]Z6DFP�Z\`HKC_HG\=2e&AFG�^/aQb>`HK�d/DFS2EHe&K�D�P~l>A"Z�K�G ��AFI�I�EHe4EHS2A�Z�KiWx=2XrZ�`�KnI�A�Z\IJ`He&K�X[Z6e&K�A/?UE�G�Ki?Z\=Ye&KFu � � , � =2?~Z�`HK-d/DFS2EHe&K�DFP�l>A"Z\K�G~G\K�e�A�=2XH=2XHq4=2XZ�`HK-_�G�=2e�A�G\^FaA[<Q¤]`HD"l�Z\`�A"Z~Z\`HK6W]= �NK�G�K�X/Z\=2AFSpLH=YZBD�P�l�A�Z�K�G~d/DFS2EHe&K-?UK�X/Z>Z\D4Z\`HK6I�A�Z\IJ`He&K�X/Zc=@?

� � $ � � � � � � ������� � �BI$Z\E�A�S2S2^Fo]Z\`H=2?c=2?~D/XHKMD�P�Z�`HD[?UK-D/L[d(=2DFE�?�S2^�=�Zi· ? ��� � Z\`H=YX�q/?�a

LN<Q�R?U=2XHqgZ�`�K6I�DFX[Z\=YX(EH=YZ:^nKih/EVA"Z�=2DFX � � $�v�DFX�?UZ\AFX[ZAFX�W'��K�G\XHDFEHS2S2=�· ?�K�h[E�A"Z\=YD/X

� � �� � � � � � � $�v�D/X�?UZ\A�X[Z

?�`HD"l�Z�`�A�Z � � � ��$ � # � � , �

l~`�K�G\K� $ � �

+ � �� � � ,±5%� � ��� � < � �

Ii<¤]DFS2dFK�Z�`HK6WH=���K�G\K�X[Z�=@A�SpKih[E�A"Z\=YD/X

� �� � $ � � � � $ � # � � , �

l~=YZ�`r=2XH=YZ�=@A�S�I�D/X�W]=YZ�=2DFX�? � $ ¾QAFX�W � $ ¾HuM=�a KFa2op��XVW ��K��]_HS2=@I�=YZ�S2^xAF?MAQP8EHX�I�Z�=2DFX�D�P�Z�=2egK/a���Zl~`VA"ZsZ\=Ye&K � ���� W]D(Ki? � G�KiAFIJ`�A�e&A��]=Ye4EHe ��»{`VA"Z&=2? � ���� � ��Zgl~`�A�ZsZ\=Ye&K � � � � � � =2?4Z�`�K_�G�=2e�A�G\^gK�e&_]Z:^��7kP�DFXHKMW]G\DF_�?�Z�`HK6��X�W�DFGJW]K�G;Z\K�G\e =2XCZ\`HK �C5 � <�?�DFS2E]Z�=2DFX�o/l~`�A�Z�l�DFE�S2W �fLNK�A�ZZ\=Ye&K � � � � � � �

WV<n»{`(^Q=2?�Z\`HK6?U=2e&_HS2K-l�A�Z�K�G~I�SYD]IJO�� � Agq/D[D]WQe&K�AF?�EHG\K�G>D�Pj cK�l>Z�D/XH=2AFXnZ\=Ye&K � �K*<Q¡RD(K�?>Z\`HK-l>A"Z�K�G~I�S2D(IJOQW]K�_NK�X�WD/XmAF=YG>_HG\K�?\?�EHG�KMD/G�l>A"Z\K�GcW]K�X�?�=�Z:^��m»{`(^CD/G~l~`[^nXHD�Z �P\<�v�D/X�?UZ�G\E�I$Z;AMl>A"Z\K�G;I�SYD]IJOsAFX�W&e&K�AF?�EHG\K�Z�`HKcG\K�S2K�d"AFX/Zj_�AFG\AFe&K�Z�K�G\?�a�7j?�EHqFq/K�?UZ�A�P8G�EH=YZ�A:EH=@I�KRI�A�X&D/GZ\`HK6S2=YO/KMl~=�Z\`�AgI�A�XmDF_NK�X�K�Gc`HD/SYK-A�Z~Z�`HK6LVAF?�KRP8D/G~Z�`�K-_HG�=2e�A�G\^Fa���e&KiAF?�EHG�=2XHq�I�E�_l�DFE�S2W?UK�G�d/KP8D/G-AQI�A"Z\IJ`�egK�X[Z�uMW]K�_NK�X�WH=YXHqmD/Xx^/DFEHG�_HG\=Ye�A�G\^�· ?�?�=Y��KFo�^/DFE�e�A*^�XHK�K�W�Z�DmK�e&_]Z:^�_NK�G\=2D(WH=2I�A�S2SY^/ab�A�O/K�AnP8K�lfe&K�A/?UE�G�K�egK�X[Z\?MD�P>AFI�I�EHe4EHS2A�Z�KiW�l>A"Z\K�GMdFK�G\?�E�?RZ�=2e&KCA�X�Wx_HS2D�Z-Z�`�K&W�A"Z\A�a�¡BGJA*lf=2XZ\`HKQZ�`HK�DFG\K�Z�=@I�AFS�I�EHG�d/Kn_HG\K�WH=2I�Z�K�W�L[^rD/EHGsZ\`HK�D/G�^�AFX�W�^FD/EHGs_VA�GJA�e&K�Z\K�GJ?�ax7:?6Z\`HK�G\KnG\K�A/?UD/X�A�LHS2KAFqFG\K�K�egK�X[Z� � � � � b>`H=@?c=@? A:EV?:ZMA&P8EHX�K��]_NK�G\=Ye&K�X/Ziu�X�DCqFG\K�A�Zc_�A�=2X�?cG\K�h[EH=2G\K�Wpu A:E�?:ZM?UK�K6`HD"l=YZcl�DFG\O(?�D/E]Z�uj7$· WSY=2OFK�Z�D&O(XHD"l-a

q(<n²�Z\K�?�=YL�=YD[?RDFP��cS2K��HAFX�W]G\=2Ax5,I�=2GJI�A�,B��¾F¾[<~=2X(dFK�X[Z\K�W�AFX�=2e&_HG�D"d/K�W�D/G�²�Z\K�?�=YL�=2AFX�l>A"Z�K�G�I�SYD]IJO�as£BK?�=2eg_�SY^m`�A/W�AnI�DFX[Z�=2X(EHDFE�?R?UD/EHGJI�K-_NDFEHG�=YX[Z\DCZ�`�Ks_HG\=Ye�AFG�^l~=�Z\`�An?�_H=2SYSYTkDB��?U_NDFE]ZMA"ZRZ�`HKsZ�DF_�D�PZ\`HK�_HG\=Ye�AFG�^/agb>`(E�?MZ\`HK�_HG\=Ye�AFG�^�AFSYl>A*^]?R?UZ\A*^/K�WxK��HAFI�Z�S2^�P8EHS2S;A�X�W�Z�`�K&��D"lfLNK�`�A*d(=2DFGMLNK�I�AFe&K?UZ\A�Z�=2DFX�AFG�^�ut=�a KFa2oRE�X�IJ`�A�X�qF=2XHqtl~=YZ�`zZ�=2e&KFa »{`�A"Z�=@? �C5 � <n=2XzZ�`HK�I�A"Z\IJ`�egK�X[ZXHD"l � 7:?Z�`�K²�Z\K�?�=YL�=2AFXQl>A"Z\K�GcI�S2D]IJOnAgqFD(D]Wne&KiAF?�EHG�K�G>D�P� BK�l>Z\DFXH=@A�XZ�=2e&K��

Page 83: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ¶ |�SYEH=@WH? º ½

`N<¤]EHqFq/K�?UZ~?�DFe&KM_HS@A�E�?�=2LHSYKMG\K�A/?UD/X�?�l~`[^nl�A�Z�K�GcI�SYD]IJO]?�P8K�S2S�D/E]Z~D�P�P,A*dFDFGia� � � � 9�G\DFL�AFLHS2^�Z\`HKne&D/?UZ&=Ye&_HG\K�?\?U=2dFKnl�A�Z�K�G&I�S2D]IJOxK�dFK�G4l>AF?sK�XHq/=YXHK�K�G\K�W�L(^�¤(Ew¤(EHXHq�=YXz�F��Z�`I�K�X[Z�EHG\^6v�`H=YXVA65�¤(E�XHqBW]^(X�A/?:Z:^R_VK�G�=2D]W�<$u�Ace&A/?�?�=2dFK�P8DFE�X/ZJA�=2X]Tkl�A�Z�K�G�Tkl~`HK�K�S�W]K�d(=@I�KjZ\`�A"Z�W]G�D"d/KjW]=2?�_HS@A*^]?DFP�S2EHX�AFG;A�XVW&D�Z�`�K�G;I�K�S2K�?UZ�=@A�S�I�^(I�SYKi?�aj�{l�K�L�?�K�AFG\IJ`&DFXC¤(En¤]EHXHq6l~=2SYSVLHG\=YXHqsEH_�SYDFZ\?jDFPp=YX]P8D/G�e�A�Z�=2DFX�u�Al�K�Ln?�K�AFG\IJ`&D/XnA�X(^[Z�`H=2XHq6L�G�=2XHq/?�EH_Ce&D/G�K~Z\`�A�Xn^FDFE�· W�K�dFK�G;l>A�X[Z�Z�D4O(XHD"l-a�¤]E¤(EHX�q�· ?;I�S2D]IJO&l�A/?jZ�`�KK�X�WgD�P�Z\`HK~G\D/AFWsP8DFGjl>A"Z\K�GjI�S2D]IJO-Z�KiIJ`HXHD/SYD/qF^Fo"L�E]Z�XHD�ZjZ\`HK~l>A"Z�K�G�I�S2D]IJON· ?�S2A/?:Zj`(EHG\G\AF` ���MA�S2=YS2K�D�E�?�K�WgA?�=Ye&_HS2KBl>A"Z\K�G;I�SYD]IJOg=YXCZ�`HKcO(=2XHK�e�A�Z�=@IcK��]_NK�G\=Ye&K�X/ZJ?jZ\`�A"Z�K�?UZ\A�L�SY=@?U`�K�WgZ�`�KRI�D/X�?UZ\A�XVI�^sDFP�qFGJA*d(=�ZJA"Z�=2DFXVA�SA/I�I�K�SYK�G\A�Z�=2DFX�aj�MA�S2=2SYK�D&AFS2?�D�?UD/e&K�Z�=2e&K�?>E�?�K�WQ`H=@?~_HEHS@?�K-7;LNK�S2=YK�dFKFa

Page 84: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � � EGHJ*IN-N[&:;<*[?T>�E &A>�, UF*-=!9fN[1�M�&:5 =!?T>�*-H � ?:;<*-?T>

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H� ¹ h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujS2=YX�K�A�G�P8D/G\I�K�S@A*l-oH£cD(D/OFKF· ?>S@A*l�Fa~b>`HKBSY=2XHK�AFGjP8DFGJI�KBS2A*l±DFG;£BD(DFOFK/· ?jP8DFGJI�KcS@A*l±AF_H_HS2=YKi?;AF_H_HG\D*�(=2e�A"Z\K�S2^-Z�DsAMl~=@W]KRd*AFG�=2K�Z:^4D�P�?�^(?UZ�K�e�?�a�7!XP,A/I$Z�oHAFSYe&D[?:Z>A�X(^�?U^]?UZ�K�e�P8G\DFe A�Z�D/eg=@IcLNDFXVWH?�Z�D4LHG�=@W]q/K�?�DFLNK�^]?;Z�`HKMS2=YXHKiA�G�P8DFGJI�KRS2A*l{P8D/G�?�E]�CI�=2K�X[Z\SY^?�e�A�S2Sp_VK�GUZ\EHG�LVA"Z�=2DFXV?~A�G\DFEHX�WnZ�`�K6?U^]?UZ�K�em· ?~K�h[EH=2S2=YLHG\=2EHe}I�DFX]��q/EHGJA"Z�=2DFX�aj¤]^(?UZ�K�e�?>egD"d(=2XHq&EHX�W]K�G~Z�`�KS2=YX�K�A�G;P8DFGJI�KcS@A*lwD�P Z\K�XCD/LVK�^&?�DFe&KB?�DFG�Z;DFP�D/?\I�=2SYS@A"Z\DFG\^6`�A�G\e&DFXH=@I~e&D�Z\=YD/X�ajb>`HKBS@A*lw=YXnDFXHK�TkW]=2e&K�X�?�=2DFXl~=YZ�`Z�`�K6?:ZJA�LHS2KMK�h[EH=2SY=2LHG\=YEHe}_VD/=YX[ZBA�Z�Z\`HK-DFG\=2qF=2XQ=@?>qF=2dFK�XQL(^�uA[< � $�, � � ��� ��aLN< � $�, � ��aIi< � $�, � � � � ��aWV< � $�, � � �FaK*< � $ � ��a

¾H� ¹ h[e4EHS�ZB¾/¾/�F¾F¾ ³ µ��M`�AFG\WW]K�WHE�I$Z\D�TkegK�e&DFG\^Nu�S2=YXHKiA�G\=�Z:^nD�P�¤]£�°�K�h[E�A"Z\=YD/X�]a~b>`HK6WH=���K�G\K�X[Z�=@A�SpKih[E�A"Z\=YD/XnP8D/G>Z�`HK6?�=Ye&_HS2K-`�AFG�e&DFX�=2IRD/?\I�=2SYS@A"Z\DFG

��� �� � � $�, � � ��5 � <

=@?�uA[<CS2=2XHK�AFG�aLN<nX�DFX]TkSY=2XHKiA�GiaIi<nX�K�=YZ�`HK�GcSY=2XHKiA�G~XHD/G�X�DFX]TkSY=2XHKiA�GiaWV<nLND�Z\`mSY=2XHK�AFGcA�X�WQXHD/X]T�S2=2XHK�AFG�aK*<QI�DFS2=YX�K�A�Gia

¾H� ¹ h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj?U=2e&_HS2K-_VK�X�W]EHS2EHe _VK�G�=2D]WCP8D/G�e4EHS2A³ a~b>`HK-_NK�G\=2D(WnP8DFG\esE�S2A4P8DFG>Z\`HK6?�=Ye&_HS2K-_VK�X�W]EHS2EHe}=2?

� $����� 0�

7kP�Z�`HK-S2K�X�q�Z�` 0 =2?>=2X�I�G\K�A/?UKiWnL(^nA4P,A/I$Z�D/G~D�P�µ�o]`HD"l�W]D(K�?�Z\`HK-_VK�G�=2D]WmIJ`�A�XHq/K��A[<C7!XVI�G\K�AF?�K�?�L(^nAgP,A/I$Z�D/G>µ�aLN<Q¡RK�I�G�KiAF?�K�?�L(^QA4P,AFI�Z�D/G~µ�aIi<n7!XVI�G\K�AF?�K�?�L(^nAgP,A/I$Z�D/G>D�P��]aWV<Q¡RK�I�G�KiAF?�K�?�L(^QA4P,AFI�Z�D/G~D�P��HaK*<n7!XVI�G\K�AF?�K�?�L(^nAgP,A/I$Z�D/G>D�P>� ¹ a

¾H� ¹ h[e4EHS�ZB¾/¾�µ[¾F¾C� ³ �4K�A/?U^�e�A�Z�`�uj�NW]E�I�=@A�Sp_NK�XVW]EHS2EHe}_NK�G\=2D(W

Page 85: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~� ¹ °�?\I�=2SYS@A"Z\=YD/X�?>A�X�Wm¤(=2e&_HSYK4£BA�G\e&DFXH=@I�¯�D�Z\=YD/X ¼ �

µ�a~b>`HK-_NK�G\=2D(WQD�PjA&?U=2e&_HS2K-_VK�X�W]EHS2EHe�=@?~q/=Yd/K�XL[^

� $����� 0

l~`HK�G�K 0 =@?QZ�`HKrS2K�XHqFZ�`�D�P6Z\`HKr_VK�X�W]EHS2EHe AFX�W {=@?QZ�`HKrqFGJA*d(=�ZJA"Z\=YD/X�A�S�AFI�I�K�S2K�GJA"Z\=YD/X�a � �NW]E�I�=@A�S_NK�X�WHEHSYE�e _VK�G�=2D]W�5,=�a KFa2o]_VK�G�=2D]W�Z\`�A"ZcI�AFXCLNK�EV?UKiWnAF?>A4?:ZJA�X�WHAFG\W�P8DFG>G�K�P8K�G\K�X�I�KBD/G�h[EH=@IJO�K�?UZ�=2e�A"Z�=2DFXN<=@?�DFL]ZJA�=2XHK�W6P8DFG�AR_VK�X�W]EHS2EHe D�PVS2K�X�q�Z�`gK��HA/I$Z�S2^-DFX�K�e&K�Z\K�G�AFX�W4A/?�?�EHe&=2XHqcZ\`�A"Z $ ½ � ¼ ew? � �;K��]A/I$Z\SY^/a»{`�A�Zc=2?�Z\`H=@?>�VW]E�I�=2AFS�_NK�G\=YD]WnZ�Dn�g?U=2qFX�=��VI�A�X[Z>��qFE�G�Ki? �mb�D&µ&?�=2qFXH=Y�VI�AFX[Z��VqFEHG\K�?�A[<�� � ¾;?�AFX�W�� � ¾H�i¾�?�aLN<� � ¾;?�AFX�W�� � ¾F¾(º�?�aIi<� � ¾;?�AFX�W�� � ¾H��?�aWV<�� � ¾;?�AFX�W�� � ¾H��?�aK*<�� � ¾;?�AFX�W�� � ��?�a

¾H� ¹ h[e4EHS�ZB¾/¾ ¶ ¾F¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�uj_NK�X�WHEHSYE�e}_NK�G\=YD]W?�AFX�?~I�AFS2I�EHS@A"Z�D/G¶ a>»{=YZ�`HD/E]ZcE�?�=YX�q&A&I�A�S@I�EHS@A"Z\DFG-58^/DFE�· G�KMD/XQ^/DFEHG>`HD/XHDFG>`HK�G�K*<$oHl~`�A�Z~=2?~AF_H_HG\D*�(=2e�A"Z\K�S2^&Z�`HK-_NK�G\=YD]WQD�P�A?�=Ye&_HS2K~_NK�X�W]E�SYEHe D�P�SYK�XHq�Z\` ½ e � ������ � �FE�?UZjSYD(D/OsA"Z�l~`�A�Z�Z�`HKc?�=Ye&_HS2K~_NK�X�W]E�SYEHe _NK�G\=YD]WsP8DFG\esEHS@AAFX�WnG\K��VK�I$ZcD/XnZ\`HK6A�XV?Ul�K�G�Z�D&Z\`HKM�VW]EVI�=@A�Sp_NK�X�W]E�SYEHe _NK�G\=YD]Wh/E�K�?UZ�=2DFX�aA[< ½ � ¼ ?�aLN<�� ¹ �j?�aIi<� � ¾;?�aWV<�� � ¾;?�aK*< ¹ � ¾;?�a

¾H� ¹ h[e4EHS�ZB¾/¾ ¹ ¾F¾ ³�¶ µgZ�D/EHqF`QZ�`�=YXHO(=2XHq�uj_NK�XVW]EHS2EHe}_NK�G\=2D(W?\A�X�?>e�AF?\?¹ a~b>=2e&KcP8DFG�W]K�K�_�Z�`�DFEHq/`/Zia�� D��$+,�"�$+�=YP�^FD/ECA�G\KcI�S2K�d/K�G�AFX�W�A-_ND/?UZ�K�G�=2DFG\=�=YP�^FD/ECA�G\X�· Z�58S2=YO/Kc^FD/EHG;_H`(^]?�=2I�?_HG\D�P8Ki?�?�DFG$<�LNK�P8DFG\KBW]D/=YX�q6A�X(^4K�S2AFLVD/G\A�Z�KcW]^(X�AFe&=2I�A�S�AFX�A�S2^]?U=@?�o/l~`(^g?�`HDFE�S2W&^/DFE&O(XHD"l±Z�`�A�Z�Z�`HKR_VK�G�=2D]WDFP�Z\`HK6?U=2e&_HS2K�_NK�XVW]EHS2EHe}=@?~=2X�W]K�_VK�X�W]K�X[ZcDFP�e�AF?\?�A[<n¯�AF?\?6=@?4W]K�X�?�=�Z:^�Z�=2e&K�?4dFD/SYEHe&K/a�´jDFS2EHe&KnXHK�dFK�G4I�D/e&K�?6=2X[Z�D�Z�`HK?U=2e&_HSYKQ_VK�X�W]EHS2EHe _�G�D/LHSYK�ema�;G�q/D4e�A/?�?>XHK�dFK�G>I�DFe&K�?>=2X[Z�D&Z\`HK6?U=2e&_HS2K�_NK�XVW]EHS2EHe}_�G�D/LHSYK�ema

LN<Qb>`�K�G\KgX�D�e&A/?�?M=2X�Z�`HKnO[=2XHK�e&A�Z�=@I&K�h[E�A�Z�=2DFX�?-AFX�W�Z\`(E�?-e�AF?\?6I�AFXxX�K�dFK�G6A ��K�I�Z-Z�`HK�e&D�Z\=YD/XrD�PAFX(^/Z\`H=2XHq�ajb>`HK6?�=Ye&_HS2K-_NK�X�W]E�SYEHe}=2?c=YX�I�SYEVW]K�W=2XQZ\`HK6?�K�Z~D�PjA�X(^[Z�`H=2XHqVa

Ii<Q9;`(^(?�=@I�A�S�=2X[Z�EH=YZ�=2DFX�aWV<Q|�DFGMA�X(^�_�AFGUZ\=2I�SYKgAFI$Z\=YX�qQD/X�DFXHS2^�L(^�qFGJA*d(=�Z:^mA�X�W�l�D/G�O(S2K�?\?~P8DFGJI�Ki?BDFP�I�D/X�?UZ�GJA�=2X/Z&58K/a qVaYopXHD/G�e�AFSP8D/G\I�K�?4?UE�IJ`tAF?-Z\`HD/?�KCDFPBA�P8G\=2I�Z�=2DFXHS2K�?\?s?�SYD/_VKQDFG4D�P>P8G�=@I$Z\=YD/XHS2K�?\?sl~=2G�KCP8DFG4Ax?US2=@W]=YX�q�LNK�AFWV<$o�Z�`�K?�_NK�K�WQP8D/GcA�X(^C_ND/?�=�Z\=YD/XQ=@?~qF=2dFK�XnL(^

� $�� � �� � � p5� � , �H<�l~`�K�G\K � � =@?&=YX�=�Z\=2AFSc?U_NK�KiWpo ��=@?&`HK�=Yq/`/Zio�AFX�W � � =@?g=YX�=�Z\=2AFSc`HK�=2qF`[Ziatb>`HK�G�K=2?&X�D�e�A/?�?g=2X�Z\`H=2?Kih[E�A"Z\=YD/Xm?�=2X�I�K-=YZRI�AFX�I�K�SYKiWDFE]ZcDFP�Z\`HKsI�D/X�?�K�G\d*A�Z�=2DFXD�P�K�XHK�G�q/^nKih/EVA"Z�=2DFX�a ��DFE�I�DFEHS@WXHD"l��VX�WZ\`HKs_ND/?�=YZ�=2DFX�D�P�Z\`HK6_�AFGUZ\=2I�SYKsA�ZRA�X(^nZ�=2egK4=�Pj=YZRl�K�G\K-DFX�ACI�DFX�?UZ�GJA�=2XHKiWQ_VA"Z�`�L(^mA�Xm=2X/Z\K�q/G\A�Z�=2DFX=2Xm=YXH��XH=YZ�K�?�=2e&AFS�?UZ�K�_V?�u

� �[5 � < $ � � � l~`�K�G\K �[5 � <�=2?cWH=2?UZ\AFX�I�K-A�S2DFX�q4Z\`HKM_�A"Z\`�A�X�W

� � $�I�D/? � � �

l~`�K�G\K �6=2?jZ�`HKBAFXHqFS2K~D�P�Z\`HKc_�A�Z�`&P8G\DFe Z�`HKcd/K�G�Z�=@I�AFS�a�|HD/G�e&D�Z�=2DFX�AFSYD/XHq6A-I�D/X�?:Z\G\AF=YX�K�Wg_�A"Z\` �-=2?Ag���(KiW�A�X�W�o�=2X_�G�=2X�I�=2_HS2KFoVO[X�D"l~XQP8E�X�I$Z\=YD/X�D�P�Z�`HKs_�A"Z\`_ND/?�=YZ�=2DFX �/u;K/a qVaYo]Z\`HK6e&D�Z\=YD/XmD�P�A&LVD/L

Page 86: Introductory Physics Problems David J. Jeffery Department of

¼ � v�`�AF_]Z�a~� ¹ °�?\I�=2SYS@A"Z\=YD/X�?~A�X�Wm¤(=2e&_HSYK6£RA�G\e&DFXH=@IM¯�D�Z\=YD/X

DFP�Ag?U=2e&_HSYKM_NK�X�WHEHSYE�e DFG~A4LVKiAFWnI�DFX�?UZ�GJA�=2XHKiW&Z�Dge&D"dFK�DFXQA4l~=2G�K/a�|�DFG>As_�G�D A:K�I$Z\=YS2K�egDFZ�=2DFX ���=@?cA&I�D/X�?UZ\A�X[ZcA�XVW

� � $ # � � , � � AFX�Wm?UD

� � $ � � � � AFX�W � � $ � � � � ��Bq/AF=YXnZ�`HK-K�X/Z\=YG\K�_�A"Z\`I�DFEHS@WnLNK-W]=@?�I�D"dFK�G\K�WCL[^�=2X[Z�K�qFGJA"Z�=2DFXQ=YX=2X]��XH=YZ�Ki?U=2e�A�S�?UZ�K�_V?�a ��D/EQl�DFEHS@W`VA*dFKcZ\DsLNK�I�A�G\K�P8EHSVZ�DgqFK�Z;Z\`HK�WH=YG\K�I�Z�=2DFX�?�D�P�Z\`HK�dFK�S2D]I�=YZ�=2K�?�=YXQLVDFZ�`I�AF?�K�?�o[LHE]Z>=YXQ_HG�=2X�I�=Y_HS2KRZ�`�A�Z=@?cW]K�Z�K�G�e&=2XHK�WQL(^CZ�`�K-=YXH=YZ�=@A�S�I�DFX�WH=�Z\=YD/X�?cA�XVWCP8D/G\I�K�?>D�P�I�D/X�?:Z\G\AF=YX[Zia

b>`HK4_NDF=2X[Z�DFP�Z�`�=2?�S2DFXHq/l~=YX�WHK�W�e4EHSYZ�=2_HSYK�TkIJ`�DF=@I�K4AFX�?�l�K�GB=@?BZ\`�A"ZM^FD/E�I�D/EHS@W���X�W �[5 � <g58=�a K/aYo_VA"Z�`g_ND/?�=�Z\=YD/XgA/?jAcP8EHXVI$Z�=2DFX&DFP�Z�=2e&Ki<�I�DFe&_HS2K�Z�K�SY^-l~=YZ�`�DFE]Z�O(XHD"l~=2XHqRZ�`HK>_�AFGUZ\=2I�SYK/· ?�e�AF?\?�a��cXVW4=YP^/DFE&O(XHD"l �/5 � <jI�D/e&_HSYK�Z�K�SY^sZ�`HK�X�^FDFE&O(XHD"l±A�S2SHZ�`�K~O[=2XHK�e&A�Z�=@I�?�I�DFe&_HS2K�Z\K�S2^s=2X�I�S2E�W]=2XHq6d/K�S2D]I�=YZ�=2K�?�oA/I�I�K�S2K�GJA"Z�=2DFXV?�o]A�XVWn_NK�G\=YD]WH?>=YP�Z�`HK-e&DFZ�=2DFX=2?>_NK�G\=YD]W]=@I�a

7!X6Z�`�K>?�=2eg_�SYK�_VK�X�W]EHS2EHefI�AF?�KFoiZ�`�K�G\K�=@?�DFXHS2^MqFGJA*d[=YZ:^MA�X�Wsl�D/G�O(S2K�?\?�I�D/X�?UZ�GJA�=2X/Z�P8DFGJI�Ki?�a�b>`(E�?AFSYD/XHqgl~=�Z\`mZ�`HK-G\K�?UZ~D�P�Z\`HK-O(=YX�K�e�A"Z\=2I�?�o]Z\`HK-_NK�G\=YD]WQ=2?~=2X�W]K�_VK�X�W]K�X/ZcDFP�e�A/?�?�a

K*<¤]D(I�G\A�Z�Ki?>`�AF?>e�AF?\?�a�BSYS�`[E�e&AFX�?>`�A*d/K�e�A/?�?�a�;G�q/DgAFSYSp`(EHe�AFX�?~A�G\K6¤(D]I�GJA"Z�Ki?�a

¾H� ¹ h[e4EHS�ZB¾/¾[º�¾F¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu�_NK�X�W]E�SYEHe I�S2D]IJOº(a ��D/E�A�G\K-�MAFSY=2S2K�Dn�MA�S2=2SYK�=�5:� ¶�¹ µ�N� ¹ µ(�F<j_�G�DFP8K�?\?UD/GM5,EHX[Z�K�X[E�G�KiW�<>D�Pje�A"Z\`HK�e�A�Z�=@I�?cA�Z~Z�`HKs�BXH=2dFK�GJ?�=�Z:^QD�P9;=2?\AxI�=YGJI�A±� ¶�½ ¾�a*��D/E±AFG�KG�KiW(TkLVKiA�GJW]K�WtA�X�WtP8K�=@?UZ:^�587kZJA�S2=2AFXtl�DFGJW�e&K�AFXH=2XHq�?U`HD/GUZCAFX�WtAFLHE�?�=Yd/Ki<�ab>=2G�KiWrD�P>_VK�DF_HS2KCe�A�O(=2XHq�P8EHX�DFP~^FDFE�G6G�KiW]EHX�W�A�X[Z6X�A�e&K�5,K��HAFI�Z�S2^�?�D�=2X�¸�A"Z\=YX�ug�MA�S2=2SYK�E�?4�MAFSY=2SYK�E�?J<A/?c=YP�^FDFEml�K�G\Ks£cE�esLNK�G�ZR£cEHe4LVK�GUZ�DFG�?UD/egK6?�E�IJ`�AFX�W�LNDFG\K�Wl~=�Z\`�W]G\DF_H_�=YXHqnL�A�S2S2?BDB�xZ�`HKg¸�K�AFXH=2XHqb�D"l�K�Gj=YX&Z\`HK~_H=@A�����AHo/^FD/Eg?�K�K�O4I�AFSYe =YX&Z\`HKBA/W AUAFI�K�X[Z�v�A"Z\`HK�W]GJA�S]DFP�9�=@?�A�a�b>`HK�G�K~^/DFE&XHD�Z\=2I�K>Z�`�A�Z�Z�`�Kv�A�Z�`HKiW]G\AFS(S2AFX/Z\K�G\X�?�D/?\I�=2S2S2A�Z�K�=YX4Z�`HK~l~=2X�Wgl~=YZ�`&A�I�DFX�?UZ\AFX[Z�_NK�G\=2D(W4XHDMe�A"Z�Z�K�Gjl~`VA"Z�Z�`HK~AFeg_�SY=YZ�E�WHK~D�PZ\`HKMD/?\I�=2SYS@A"Z\=YD/X�aj��Z>D/X�I�K�5,^FDFEA�G\K�AFXn=2X�I�D/e&_�A�GJA�LHS2K�qFK�X�=YE�?>A�P Z�K�GcAFSYS <$o]^/DFEQG�KiA�S2=Y��KBZ\`�A"Z~_NK�X�W]E�SYEHe�?l�DFEHS@WQe&AFOFKMqFG\K�A�Z�G\K�q/EHS@A"Z�D/G\?�P8D/GcI�S2D(IJO]?�LNK�I�AFE�?�KFuA[<C=YZc`�A/? � �� � � LNK�K�XZ\`HDFEHq/`[Z>DFP�LNK�P8D/G�K/aLN<n=YZc`�A/? � Z�`HD/EHqF`[Z~D�P�LNK�P8DFG\KFaIi<CZ\`HK�`(^(_HXHD�Z\=2Ig_NK�X�WHEHSYE�e ?�l~=YX�qF=2XHqQe&DFZ�=2DFX�l�D/EHS2Wx=2X�W]E�I�K�K�dFK�X�WHK�K�_NK�G6?�S2EHesLNK�G-=2Xr^FDFE�G�S2K�?\?UTAFesE�?�=2XHq�oHI�SYD]IJO(l�A�Z\IJ`H=2XHq&?:Z\E�W]K�X/ZJ?�a

WV<nK�dFK�XAgL�A/WQ=@W]KiAgI�A�Xe�A�OFKMe&DFX�K�^Fa��BSYS�Z�`�A�Zc=2?>XHK�K�W]KiW=2?~AgqFG\K�A�ZcAFW]d/K�G�Z�=2��=2XHqgI�A�e&_�AF=Yq/X�aK*<QAR_NK�X�W]E�SYEHe W]G�=2d(=YX�qRI�S2D]IJO-`�A�XVWH?�l�D/EHS2W6OFK�K�_4ARdFK�G�^-?UZ�K�A/W]^MG\A�Z�K>W]K�?�_H=YZ�K�Z�`HK>GJA"Z\`HK�G�=YXVI�DFXV?:ZJA�X[ZP8G\=@I$Z�=2DFX I�D/X/Z\=YX(EHD/E�?�SY^ ?UE�LHG\A/I$Z\=YXHq�P8G�D/e Z�`HK±_VK�X�W]EHS2EHe K�XHK�G\qF^�58=�a KFogZ�G\^(=YXHq�Z�D�G�KiW]E�I�K�Z�`�KAFe&_HSY=YZ�EVW]K&D�PjZ�`�Kg_NK�XVW]EHS2EHe e&D�Z\=YD/XV<BAFX�W�Z\`HKgG\A�Z�`HK�GR=2X�I�D/X�?UZ\A�X[Z-W]G\=Yd(=2XHqCP8D/G\I�K4I�D/X[Z�=2X[E�DFE�?�SY^A/WHW]=2XHq4Z�D4Z�`HKM_NK�X�W]E�SYEHe�K�XHK�G�q/^�58=�a K/aYo(Z\G�^(=2XHq6Z\Dg=2X�I�G�KiAF?�KcZ�`�KR_NK�X�WHEHSYE�e}A�e&_HS2=YZ�E�W]K*<$aj7kZi· ?�DFX�KDFP�Z\`HD/?�K-��EHG\K�O"A4e&DFe&K�X[Z\?�a

¾H� ¹ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u;¤]£M°�AFX�WEHXH=YP8DFG\e�I�=2G\I�EHS@A�G>e&D�Z�=2DFX¼ a~b>`HKgI�D/eg_NDFX�K�X[ZBD�P;ACEHXH=YP8DFG\e�I�=YGJI�E�S2AFGce&D�Z�=2DFX�dFK�I�Z�D/GBA�S2DFXHqCAFX(^A��(=@?c=2X�Z\`HKs_HS@A�X�KsD�P�Z\`HKse&D�Z\=YD/XK��(KiI�E]Z\K�?�uA[<n?�=2eg_�SYK-`�AFG�e&D/XH=2IRe&D�Z\=YD/X�aLN<nE�XH=�P8D/G�e I�=2G\I�EHS@A�G>e&D�Z�=2DFX�aIi<n=2G\G�K�qFEHS@A�G�e&D�Z�=2DFX�aWV<Q?UZ\A�Z�=@IMe&D�Z�=2DFX�aK*<nX�Dge&DFZ�=2DFX

¾H� ¹ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujWHA�e&_NK�WD/?\I�=2S2S2A�Z�=2DFX�?½ a �\¸�K�Zi· ?c_HS2A*^��]1\��D3�����"# 1 |�DFG �]��¾F¾�o(Z�`HK4A�X�?�l�K�Gc=@?�ujZ\`HK6e&D�Z\=YD/X�D�PjAC?�^(?UZ�K�e}?�SYD"l~=2XHq�W]D"l~XmZ\D�G�Ki?:ZBA�ZA&?UZ\A�L�SYK-Kih/E�=YS2=YL�G�=2EHe Z\`HG�D/EHqF`mA&?UK�G�=2K�?>DFP�W]KiI�A*^(=2XHq&D/?\I�=2SYS@A"Z\=YD/X�?>A�LNDFE]Z~Z\`HKMK�h[EH=2SY=2LHG\=YEHe}_VD/=YX[Zia �

Page 87: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~� ¹ °�?\I�=2SYS@A"Z\=YD/X�?>A�X�Wm¤(=2e&_HSYK4£BA�G\e&DFXH=@I�¯�D�Z\=YD/X ¼/³

A[<C»{`VA"Zc=@?~I�G\=�Z\=2I�A�S2SY^nW�A�e&_VKiWegDFZ�=2DFX�oV�cS2K�� �LN<n»{`VA"Zc=@?>EHX�W]K�G\WHAFe&_VKiWQe&DFZ�=2DFX�o��BSYK�� �Ii<n»{`VA"Zc=@?>D"dFK�GJWHAFeg_NK�WQe&D�Z\=YD/X�oH�cS2K�� �WV<n»{`VA"Zc=@?>EHXH=YP8DFG\e}I�=2GJI�EHS@A�G>e&D�Z\=YD/X�o��cS2K�� �K*<n»{`VA"Zc=@?~A�S2S�l�K�Z~egDFZ�=2DFX�oV�cS2K�� �

¾H� ¹ h[e4EHS�ZB¾���¾/¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�D/?\I�=2SYS@A"Z\DFG\^�G�Ki?UD/X�A�XVI�K��¾Ha �\¸�K�Zi· ?B_HS@A*^��]1J� D+�"����# 1 |�DFG��(��¾/¾Ho�Z�`HKgA�X�?�l�K�Gc=@?�u�Z�`�KsLNK�`�A*d(=2DFGBDFP�A�X�D[?�I�=YS2S2A�Z�D/G�^?U^]?UZ�K�e�W]G\=Yd/K�X�A�Z

=YZ\?~XVA"Z�E�G\AFSpDFG>G�Ki?UD/X�A�XVI�KRP8G�Kih/E�K�X�I�^Fa �A[<C»{`VA"Zc=@?>EHX�W]K�G\WHAFe&_VKiWQD[?�I�=YS2S@A"Z�=2DFX�oH�cS2K�� �LN<n»{`VA"Zc=@?~?U=2e&_HSYK-`VA�G\egD/XH=@IRe&DFZ�=2DFX�oH�BSYK����Ii<n»{`VA"Zc=@?>EHXH=YP8DFG\e}I�=2GJI�EHS@A�G>e&D�Z\=YD/X�o��cS2K�� �WV<n»{`VA"Zc=@?>G�Ki?UD/X�A�X�I�KFo]�cS2K�� �K*<n»{`VA"Zc=@?>SYD]I�DVo��cS2K�� �

¾H� ¹ h[e4EHS�ZB¾��F�i¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj?Ul~=2XHq&G\K�?�DFX�AFX�I�K�D�PjIJ`H=2S2W�F�Fa~�BX�D/?\I�=2SYS@A"Z\DFG\^�?U^]?UZ�K�e W]G\=2dFK�X�A�Zs=�ZJ?6G\K�?�DFX�AFX�I�K&P8G\K�h[EHK�X�I�^xl~=YS2S;K��]`H=YL�=�ZgS2AFG�q/KgD[?�I�=YS2S@A"Z�=2DFXV?�am��d/K�G\^

IJ`H=2S@W �wLNK�P8D/G�K�Z\`HK�^QO[X�K�lzZ�`HK-X�AFe&K�DFP�Z\DFGJh[EHK �{EHX�W]K�G\?UZ�D(D]W�Z\`H=@?~l~`HK�Xm_HS@A*^(=YX�q�uA[<CD/XA�?�l~=2XHq�aLN<nD/XA&S@AFW�W]K�GiaIi<Q?�D]I�I�K�GiaWV<n`�DF_�?\I�DFZ\IJ`�aK*<nl~=YZ�`me�A"ZJIJ`HK�?�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H� ¹ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj_NK�G\=YD]Wpo(P8G\K�h[EHK�X�I�^/o ��Fa~b>`HK�G�K4=2?�An?�=2eg_�SYKg`�A�G\e&DFXH=@I-D[?�I�=YS2S2A�Z�D/G45�¤H£�°M<cZ�`�A�ZRZJA�OFKi?BACZ�=2egK � � $ ¾ � º ¶ ?BLVK�P8DFG\Ks=YZ�LNK�q/=YXV?cZ\DG\K�_NK�A�Z�a�»{`�A�ZRA�G\KM=�ZJ?65,A[<>_NK�G\=YD]W �&o�58LN<�P8G�Kih[EHK�X�I�^�#�58=2X�`HK�G�Z��*<$oVAFX�Wr5,Ii<>A�XHq/EHS2AFG>P8G�Kih[EHK�X�I�^ ��58=2XGJAFW]=@A�XV?�_NK�GR?UKiI�DFXVW�<��

¾H� ¹ h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuje&A��]=Ye4EHe P8D/G\I�KRDFP�A�¤]£M°4oHK�ZJI�]a~��LND]W]^MD�P]e�AF?\? � $�¾ � �i��O(q�=2?�Ac?�=Ye&_HS2K�`�AFG�e&DFX�=2I�D[?�I�=YS2S2A�Z�D/G;5�¤]£M°M<�l~=YZ�`sAFeg_�SY=YZ�E�WHK � �����$ ¼ � ¶ I�eAFX�Wn_NK�G\=2D(W � $�¾ � �F¾�?�aA[<C»{`VA"Zc=@?�Z�`HKMP8D/G\I�KMI�DFX�?UZ\AFX[Z>DFP�Z\`HK-S2=YXHKiA�G65,DFGc£cD(D/OFKF· ?�S2A*lB<;P8D/G\I�K��LN<n»{`VA"Zc=@?�Z�`HK-e�A"�]=2esEHe A�L�?�DFS2E]Z\K�d"AFSYEHKMDFP�Z\`HKMP8DFGJI�K-AFI�Z�=2XHq&DFXQZ�`HK-LND]W]^��Ii<n»{`VA"Zc=@?�Z�`HK-e�A"�]=2esEHe A�L�?�DFS2E]Z\K�d"AFSYEHKMDFP�Z\`HK6AFI�I�K�S2K�GJA"Z\=YD/XnDFP�Z�`�K-LVD]W]^��

¾H� ¹ h/P8EHS2S�¾/¾/�]�i¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�ujqFK�X�K�GJA�S�¤]£M°�?�DFS2E]Z�=2DFXG�Ki?UE�S�ZJ?³ a~b>`HK-q/K�XHK�G\AFSp?UD/SYE]Z\=YD/XQDFP�Z\`HK���T!W]=2e&K�X�?�=YD/XQ?�=Ye&_HS2K-`�AFG�e&DFX�=2I�D/?\I�=2S2S2A�Z�DFG�_HG\DFLHS2K�emo

�� � �� � � $ , � �

=@?��5 � < $ ��I�D[?�5 � � < � ��?U=2X�5 � � <�

l~`HK�G�K �zA�X�W��fA�G\KcW]K�Z\K�G\eg=2XHKiW&L[^sZ�`HKR=YX�=�Z\=2AFSVI�D/X�W]=YZ�=2DFX�?;A�X�W�I�A�X�`�A*d/K>AFX(^4d"A�S2EHKi?j=YX�q/K�XHK�G\AFS�a�»�Kl~=2SYS�XHD�Zc_HG\D"dFKRZ�`VA"Z~=2?~Z�`HK-e&D/?UZcqFK�XHK�GJA�Sp?�DFS2E]Z�=2DFX�u�Z\`�A"Zc=@?c?�DFe&K�Z\`H=2XHqgP8DFGcAge�A"Z�`�I�DFEHGJ?UK/a � � � �b>`H=@?ch[EHKi?:Z\=YD/XI�DFEHS@WnLNK6AgesEHSYZ�=YTk_�A�q/K�G~=2XmA4Z\K�?UZceg=@?�K�K�X�?�I�(K�XHK/a

Page 88: Introductory Physics Problems David J. Jeffery Department of

¼ µ v�`�AF_]Z�a~� ¹ °�?\I�=2SYS@A"Z\=YD/X�?~A�X�Wm¤(=2e&_HSYK6£RA�G\e&DFXH=@IM¯�D�Z\=YD/X

A[<C´jK�G�=YP8^tZ�`�A�Z�Z�`HK�q/K�XHK�G\AFSc?UD/SYEHZ�=2DFXw=2?QA�?UD/SYEHZ�=2DFX{A�X�WwW]K�Z�K�G�e&=2XHK�Z�`�K�K��]_HG\K�?\?U=2DFXtP8DFGQA�XHq/EHS2AFGP8G\K�h[EHK�X�I�^ �ca

LN<Q�R?6=2XH=YZ�=@A�S;I�DFX�W]=YZ�=2DFXV?sA"Z � $ ¾�o���$ � � A�X�W � $ � � a¡BK�Z�K�G�e&=2XHK'� AFX�W���=YXrZ\K�G\e�?-D�P>Z�`�K=2XH=YZ�=@A�S�I�DFX�WH=�Z\=YD/X�?�a

Ii<Q�R?�?�EHe&KM��GJ?:Z~Z\`�A"Z�� $z¾&A�XVWnZ\`HK�XZ\`�A"Z�� $�¾Haj7!XmLND�Z\`�I�AF?�K�?~WHK�Z�K�G�e&=2XHK�Z�`HK � � d"A�S2EHK�?~Z�`�A�Zq/=Yd/K ��e&A��]=Ye4EHe�A�XVWne&=2XH=YX(EHe�A�XVWnl~`�A�Z~Z�`HKMd"A�S2EHKi?~D�P�Z�`HK-e�A"�]=2esEHe}A�X�We&=YX�=Ye4EHe ��AFG�K/a

WV<Q�R?�?�EHe&=2XHq�XHK�=YZ�`�K�G���XHD/G���=2?-��K�G\D�o�WHK�Z�K�G�e&=2XHKgP8DFGMZ\`HKCqFK�XHK�GJA�Sj?�DFS2E]Z�=2DFXxZ�`�K � � d"A�S2EHK�?-Z�`�A�Zq/=Yd/K�Z�`HK-e�A"�]=2esEHe A�X�We&=2XH=Ye4EHe d*AFSYE�K�?>D�P ��AFX�WqF=2dFK�Z�`HK-K��]_HG�Ki?�?�=2DFX�?�P8DFGcZ�`HD[?UKMe�A"�]=2esEHeAFX�WCe&=2XH=2esEHe �md"A�S2EHKi?�ajb>`HKRZ�G\=2IJO(^�_�AFGUZ�=2?���q/EHG\=YXHqgDFEHZ�l~`H=@IJ`nDFP�Z�`�K � � d*AFSYE�K�?�Z�`�A�Z�e�AFOFK��?UZ\A�Z�=2DFX�AFG�^nqF=2dFK�?�Z\`HK6e�A"�]=2esEHe A�X�Wl~`H=@IJ`Z�`HKseg=2XH=2esEHema ������ � 7kP ���w¾HoV=YXml~`�A�ZcG�K�qF=2DFXe4E�?UZ�� � LNK6I�DFXH��XHK�WQP8D/GcA4e�A��(=2esE�e �

K*<n´jK�G�=YP8^CZ\`�A"Z��5 � < $ � I�D/?�5 � � ��� <

=@?cAFXKih[EH=Yd"AFSYK�X/ZcK��]_HG�Ki?�?�=2DFXQP8DFG~Z\`HK6qFK�XHK�GJA�Sp?�DFS2E]Z�=2DFXmDFP�Z\`HKs¤]£M° _�G�D/LHSYK�emu�Z�`HKsAFe&_HSY=YZ�EVW]K �AFX�W�_H`VAF?�K~P,AFI�Z�DFG � A�G\KB?�K�Z�L(^g=YX�=�Z\=2AFSNI�DFX�W]=YZ�=2DFXV?�AFX�WCI�AFX&Z\AFOFKcD/XnA�X(^gd*AFSYE�KFo(K��HI�K�_]Z;DFP�I�DFE�G\?�KZ\`�A"Z � � � , � �� !ka67!X�Z�`HKgdFK�G�=Y�VI�A�Z�=2DFX�_�G�D]I�Ki?�?�oV��X�W � AFX�W � AF?BP8EHX�I�Z�=2DFX�?MDFP � A�XVW � ucZ\`H=2??�`HD"lc?6Z�`�A�ZgA�G\LH=YZ�GJA�G\^ � AFX�W � I�AFX�LVKQG�K�_HS@AFI�KiWrL(^��}A�X�W �Ca�7kP~Z\`HKn_�G�D/_VD[?UKiWrK�h[EH=2d*AFSYK�X[Z?�DFS2E]Z\=YD/X�=2?6Z�DxLVKG�KiA�S2SY^�K�h[EH=2d"A�S2K�X[Z�ojAFG�LH=YZ�GJA�G\^ � A�XVW � e4E�?:ZgLVKQG�K�_HS@AFI�KiA�LHS2KCL(^ � A�X�W � a¤]`HD"l�Z\`�A"Z~Z\`HK�^A�G\KRL(^C�VX�W]=2XHq � AFX�W � AF?�P8E�X�I$Z\=YD/X�? ��A�XVW��na

¾H� ¹ h/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�?�_HG\=YXHq[?>=YXm_�AFG\AFSYS2K�S�o(D/?\I�=2SYS@A"Z\=YD/X�?µ�a ��D/E�`�A*dFKCA�LHS2D(IJO�D�P~e�AF?\?�� ?\A�X�W]l~=@IJ`HKiWrLVK�Z:l�K�K�X�A�L�EHX�IJ`�DFP~?�_HG\=YX�q/?6=2X�_�AFG\AFSYS2K�S�a�b>`HKCl~`�DFS2K?�^]?:Z\K�e =@?-A���T!W]=Ye&K�X�?U=2DFXVA�S�?U^]?UZ�K�ema�b>`HK�?�_HG�=2XHq[?�AFG�K&A"Z�Z\A/IJ`HK�W�Z�DmDF_H_ND/?�=2XHqml�AFSYS@?�a&¤(DFe&K�?�_HG�=2XHq[?AFG�KsP8G�D/e�Z�`HKgSYK�P Z6A�X�Wx?UD/egK&A�G\K6P8G\DFe Z\`HK&G�=2qF`[Z�b>`�K4LHS2D]IJO�?U=YZ\?�D/XxAQSYK�dFK�S�P8G\=2I�Z�=2DFXHS2K�?\?R��D(DFGiaMb>`�K?�_HG\=YXHq[?-A�G\K�W]=2?\?�=Y_�A�Z�=2DFXHS2K�?\?�a&��AFIJ`r?U_�G�=2XHqm`�AF?-AP8D/G\I�K�I�DFXV?:ZJA�X[Z � � AFX�WrA�X�WxK�h[EH=2S2=YLHG\=2EHe _ND/?�=�Z\=YD/X� � P8DFG~Z\`HK6I�K�X[Z�K�GBD�P�Z�`HK-LHS2D]IJO�u�=�a KFa2o�� � =2?cl~`HK�G\KMZ�`HK-L�SYD]IJOQI�K�X[Z�K�G~l�D/EHS@WQLNK-=2X�K�h[EH=2SY=2LHG\=YEHe}=�P�DFX�SY^?�_HG\=YXHq���l�K�G\K-A"Z�Z\AFIJ`�K�WnZ�DgZ�`HK-L�SYD]IJO�aA[<C»{`VA"Zc=@?�Z�`HK-K��(_�G�Ki?�?�=YD/XnP8D/G>Z�`HK-X�K�Z~P8DFGJI�KMD/XnZ\`HK-e�AF?\?�aLN<Q|�=2X�W�Z\`HK AF_H_HG\DF_HG\=@A"Z�K ?�=2XHqFS2K�T!?U_�G�=2XHq K�h[EH=2d"A�S2K�X[Z � 58=�a K/aYorP8D/G\I�KfI�D/X�?:ZJA�X[ZJ<�A�X�W � ��� 58=�a K/aYo

Kih[EH=YS2=2LHG�=2EHe}_VD[?U=YZ�=2DFXV<�K��(_�G�Ki?�?�=YD/X�?>?UEVIJ`QZ\`�A"Z~Z\`HKMXHK�Z~P8D/G\I�KMK��]_HG\K�?\?U=2DFXIJ`�A�XHq/K�?�Z\D

� $�, �p5� , � ��� < �»{`VA"Zc=@?�Z�`HK-Kih/E�=YS2=YL�G�=2EHe�_ND/?�=YZ�=2DFXmD�P�Z�`HKMZ\D�Z\AFS�?U^]?UZ�K�e ��»{`[^��

Ii<Q|�=2X�WK��]_HG\K�?\?U=2DFXQP8DFG>Z\`HKMZ�DFZ\AFS�?U^]?UZ�K�e �t=2XZ�K�G\e�?>D�P�Z�`HK-=2X�W]=2d(=2WHE�A�S�?�_HG\=YX�q�� � · ?cA�XVWCZ\`HKMZ�DFZ\A�S?�^]?:Z\K�e _NK�G\=2D(W �m=2XQZ\K�G\e�?~D�P�Z�`HK-=2X�W]=2d(=2W]EVA�S�?�_HG\=YXHq&_NK�G\=YD]WH? � � a

¾H� ¹ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�Z:l�D�Tk_H`�A/?UK�e&D�Z�=2DFX�o�I�D/SYS2=2?�=2DFXQAFX�W�¤]£B¯� ª�¬"¨ �V«������V¬ ��­�� I�DFXV?UK�G�d"A"Z\=YD/XnDFP�e&DFe&K�X/Z\EHemo�I�D/X�?�K�G\d*A�Z�=2DFXQD�P�K�XHK�G\qF^

¶ a~b>`HK�G�Ks=2?RA�`(EHXHOD�P�e�AF?\? ¶ O(qCD/X�A&P8G�=@I$Z\=YD/XHS2K�?\?~`HDFG\=2��DFX[ZJA�S�?�EHG�P,AFI�K4A"ZUZJAFIJ`HKiWQZ�DQAC`HDFG\=Y��DFX[Z\AFSp=2WHK�A�S?�_HG\=YXHqVaRb>`HKg`(EHXHOm=@?B=2XH=YZ�=@A�S2SY^�=2X�Z�`�K4Kih/E�=YS2=YL�G�=2EHe�_VD[?U=YZ�=2DFX�A"Z�G�Ki?:Z�l~=�Z\`���K�G�DQK�XHK�G�q/^FaR�fLHEHS2SYK�Z�D/XZ\`HKRD/_H_ND/?�=�Z\KR?�=2W]KBP8G�D/e Z�`HKM?U_�G�=2XHq�o[LHE]Z�Z�GJA*dFK�SY=2XHq6D/X�Z�`�KR?�_HG�=2XHqV· ?�A"�]=@?�o[`H=YZ\?�Z�`HKR`(EHXHOCA�XVW�K�e4LVKiWH?�ab>`HK-L�EHSYS2K�Zce�A/?�?>=@?~¾ � ¾ ¶ ¾jO(q4A�XVWQ=YZ\?~?�_NK�K�W=@? ¶ ¾/¾je��"?�58l~`H=@IJ`m=2?~?�EH_NK�GJ?UD/XH=@IRX�D�Z~Z�`VA"Zc=YZce&A�ZUZ\K�GJ?\<�aA[<C»{`VA"Zc=@?�Z�`HK-=2XH=YZ�=@A�S�?�_VK�K�WD�P�Z�`�K-`[E�XHO A:E�?UZBA"P Z\K�G~Z\`HK-LHEHS2SYK�Zc`H=YZ\?�LN<Qb>`�K6?U_HG\=2XHq&=2?~I�DFe&_HG\K�?\?UKiW�P8DFGB�ge&K�Z�K�GJ?>LNK�P8DFG\KMG�K�LVD/EHX�W]=2XHqVa�»{`VA"Zc=@?~=�ZJ?c?�_HG�=2XHq&I�D/X�?:ZJA�X[Z�Ii<n»{`VA"ZB=@?~Z\`HK6A�XHq/EHS@A�G~P8G\K�h[EHK�X�I�^A�X�We�A"�]=2esEHe�AFI�I�K�S2K�GJA"Z\=YD/XnDFP�Z\`HKs?�=Ye&_HS2K6`�AFG�e&D/XH=2I�e&D�Z\=YD/XZ\`�A"ZcG\K�?�EHSYZ\?�P8G\DFe Z\`HK-LHEHS2S2K�Zc=2eg_VAFI$Z �

Page 89: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a~� ¹ °�?\I�=2SYS@A"Z\=YD/X�?>A�X�Wm¤(=2e&_HSYK4£BA�G\e&DFXH=@I�¯�D�Z\=YD/X ¼[¶

¾H� ¹ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj_H`(^]?�=2I�A�Sp_NK�X�W]E�SYEHe¹ aBv�D/X�?U=@W]K�G�Aw_H`(^(?�=@I�A�Ss_VK�X�W]EHS2EHe =YX�Z�`�K�?Ue�AFSYSsAFe&_HSY=YZ�EVW]K�A�_�_HG�D*�]=2e�A"Z�=2DFX�a b>`HK�_H=2dFD�Z�_NDF=2X[Z�=2?P8G\=2I�Z�=2DFXHS2K�?\?�aA[<C»{`VA"Zc=@?�Z�`HK-q/K�XHK�G\AFSp_VK�G�=2D]WCP8D/G�e4EHS2A �LN<Q¿cK�l~G\=�Z\K4Z\`HK&P8DFG\esE�S2Am?�EHL�?UZ�=YZ�E]Z\=YXHqmZ\`HK�_�AFG\AFSYS2K�S�A��(=@?RZ�`HK�DFG\K�e K��]_HG�Ki?�?�=2DFXxP8DFGMZ�`�K�egD/e&K�X[Z-D�P

=2XHK�GUZ\=2A�u� $ � 0 � � � � �

l~`�K�G\K 0 =2?;Z�`�KRW]=@?:ZJA�X�I�KcP8G\DFe�_H=2dFDFZ;_VD/=YX[Z�Z�D4I�K�X[Z�K�G�DFP�e�AF?\?;A�XVW � � � =2?;Z�`HK�e&DFe&K�X[Z�D�P�=2XHK�G�Z�=@AAFLVD/E]Z~Z�`�K6I�K�X[Z\K�G~D�P�e�AF?\?�a

Ii<n»{`VA"Z�=2?�Z�`�K�S2=Ye&=YZ�=2XHq�LVK�`�A*d(=YD/G�l~`HK�X � � � � � qFD(Ki?�Z\DR��K�G\DBl~=YZ�` 0 ���(KiW �Q»{`�A"Z�=@?�Z\`HK�_VK�X�W]EHS2EHe=2XZ�`H=@?~S2=Ye&=YZBI�AFSYS2K�W �

WV<n»{`VA"Zc=@?�Z�`HK-S2=Ye&=YZ�=2XHqCLNK�`�A*d(=2DFG~AF? � � � � ��qFD(K�?�Z\D�=YX]�VXH=�Z:^Ql~=�Z\` 0 �H�]K�W �K*<Q BD"l±I�DFX�?�=@W]K�G � � � � � �H�]K�Wpaj��=Yd/Kc?Ue�AFSYS 0 A�XVW4S@A�G\qFK 0 A�_H_HG\D*�]=Ye�A�Z�=2DFX�?�P8DFG�Z\`HKc_NK�G\=YD]W4P8DFG\esE�S2A�a»{`VA"Z~=2?�Z\`HKMS2AFG�q/K 0 P8D/G�e4EHS2A �»{`�A"Z>=@?�Z�`HK�SY=2e&=�Z\=YX�qgLNK�`VA*d[=2DFG>AF? 0 q/D(K�?;Z�D&��K�G�DgA�X�WQAF? 0 qFD(Ki?Z\D�=YXH��XH=YZ:^ ���j�]_HS@A�=2XnZ\`HK-G�Ki?UE�S�Zia

P\<m|�DFG>�H�]KiW � � � � �xo]�VX�WQZ�`HK-e&=2XH=Ye4EHe�_NK�G\=2D(WA�XVWnZ\`HK-S2K�XHqFZ�`QZ�`�A�ZcqF=2dFK�?>=YZ�aq(<Q¤]OFK�ZJIJ`-Z�`�K�_HS2D�Z�D�PHZ\`HK;_�`[^]?�=2I�A�S(A�X�Ws?U=2e&_HSYK�_NK�X�W]E�SYEHe�_NK�G\=2D(W�?�A/?�AcP8EHX�I$Z\=YD/XsDFP 0 P8DFG 0 ��� ¾ !�a7:?�Z\`HK6?�=Ye&_HS2K-_VK�X�W]EHS2EHe _VK�G�=2D]WnK�dFK�G~qFG\K�A"Z\K�G>DFG~Kih[E�A�S�Z\D4Z\`HK-_H`(^]?U=@I�AFSp_VK�X�W]EHS2EHe _VK�G�=2D]W �

Page 90: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � � &)(A1_E�Q�� �'1_>a145\&AN � &)(A1_E�&A>�,�� &)(A1_E�?T> & UW;75 *->ac

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H�"º6h[e4EHS�ZB¾/¾F¾/¾ ¶ �Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l�A*d/K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º ¹

�Fa �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�uj7kZc=@?~Ag_VK�G�=2D]W]=2IMD[?�I�=YS2S@A"Z�=2DFXQD�Pj?UD/e&K�Z�`�=YXHqVa �»{`�A�Zc=2? oH�BSYK����

A[<�e�AF?\? LV<>K�X�K�G\qF^ Ii<�_HG�Ki?�?�EHG\K W�<�Z�K�eg_NK�GJA"Z\EHG\K K*<�l�A*d/KR_H`�K�XHD/egK�XHDFX

¾H�"º6h[e4EHS�ZB¾/¾F¾���¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u ³ O[=2X�WH?cD�P�l>A*dFKi?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�]a>7!XmDFX�K�e&K�Z�`HD]WD�P�_H`(^]?U=@I�AFSYS2^CI�S@AF?\?U=YP8^(=YX�qgl>A*dFKi?�o(D/XHKM`�AF?�uA[<Ce&KiIJ`�A�XH=@I�AFS�o]K�SYKiI$Z\G�D/e&AFqFXHK�Z�=@I�o]A�XVWh[E�AFX[Z�EHe e&KiIJ`�A�XH=@I�AFSpl�A*d/K�?�aLN<nS2K�P ZioHG\=Yq/`/ZioHA�X�We&=@WHW]S2K-l�A*d/K�?�aIi<¤po�9�oHA�X�Wm¯�=@WHW]S2K6�;AFGUZ\`nl>A*dFKi?�aWV<Q�Be&K�G\=2I�A�Xl�A*d/K�?�o���G\=�Z\=2?�`l�A*d/K�?�o(AFX�W�cE�?UZ�GJA�S2=2AFXQl~=2dFKi?�aK*<ne&KiIJ`�A�XH=@I�AFS�o(�VX�A�X�I�=2AFS�oHAFX�WQK�e&D�Z\=YD/X�A�Spl>A*dFKi?�a

¾H�"º6h[e4EHS�ZB¾/¾F¾[��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�Z�GJA�X�?�dFK�G\?�KMA�X�WQSYD/XHqF=YZ�EVW]=YXVA�Spl>A*dFK�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

³ a>7!X�A�X�D�Z�`�K�G>e&K�Z�`�D(WmDFP�_H`(^]?�=2I�A�S2SY^nI�S2A/?�?�=YP8^[=2XHqgl�A*d/K�?�o(DFXHKM`�A/? l�A*d/K�?�uA[<~Z\G\AF_VK���K&A�X�W�SYK�D�Z\AFG\W LV<BZ�K�G�G\=��NIsA�XVW�S2K�lcW I�<BZ�D/G�X�A/W]DnAFX�W�S2DFEHX�qFK W�<cZ�D/A/?:Z:^AFX�WSYK�e&DFX(^ K*<�Z\G\AFX�?�dFK�GJ?�K�AFX�WnS2DFX�qF=YZ�E�W]=2X�AFS

¾H�"º6h[e4EHS�ZB¾/¾H�i¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l�A*d/KRd/K�S2D]I�=YZ:^CK��]_HG\K�?\?U=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a>»{`�A�Zt=@?�Z\`HK�G�K�S2A�Z�=2DFX LNK�Z:l�K�K�X�l�A*d/K{dFK�S2D]I�=YZ:^FoQP8G�Kih[EHK�X�I�^FomA�X�W l�A*d/K�S2K�XHqFZ�` P8DFGw?U=2e&_HS2K�l>A*dFK_H`�K�XHD/egK�X�A�� ������ � b>`HK-EHXH=YZ\?B?U`HD/EHS@Wnl�DFG\O�DFE]ZBI�DFG\G�KiI$Z\SY^/a

A[< # $ � � LV< � $ # � a I�< � $ � #�a W�< � � $ # � a Ki< � ��$ � #�a¾H�"º6h[e4EHS�ZB¾/¾H�/��¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujl>A*dFK�SYK�XHq�Z\`QW]K���XHK�W

� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]�*�*TJ�¶ a~b>`HK6WH=2?UZ\AFX�I�K-A�S2DFX�qgA&l>A*dFK�_�A"Z�Z�K�G�XLVK�P8DFG\K�Z�`HK6?�`�A�_NK-LNK�qF=2X�?�Z\D�G�K�_VKiA"Z~=2?~I�A�S2SYKiWCZ\`HKFu

A[<jP8G\K�h[EHK�X�I�^/a LV<�A�e&_HS2=YZ�E�W]K/a I�<�l>A*dFK�SYK�XHq�Z\`�a WV<;_NK�G\=2D(W�a Ki<�_H`�A/?UK�dFK�SYD]I�=�Z:^/a

¾H�"º6h[e4EHS�ZB¾/¾H�/�i���&�-µ&K�A/?U^�e&K�egD/G�^�ujl>A*dFK�SYK�XHq�Z\`CP8G\K�h[EHK�XVI�^CG\K�S@A"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]�*�*T ½

¹ a~b>`HK-`�=Yq/`HK�G>Z\`HKMP8G�Kih[EHK�X�I�^CD�P�Agl�A*d/KFo[Z�`HK/uA[<RG�K�egDFZ�K�GR=YZ\?-?�DFEHGJI�K LV<Rq/G\AFX�W]K�G�=YZ\?�LVKiA�G\=YX�q Ii<RSYD"l�K�G�=�ZJ?M_H=YZ\IJ`�a W�<M?�`HDFG�Z�K�GR=YZ\?l>A*dFK�SYK�XHq�Z\`�a K*<>I�S2D/?�K�G~=YZ\?>G\K�I�K�=2dFK�Gia

Page 91: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~�*º�»rA*dFKi?�7$uV��K�XHK�G\AFSp»�A*d/K�?>A�XVWn»rA*dFKi?>DFXmA&¤(Z�G\=YXHq ¼ º

¾H�"º6h[e4EHS�ZB¾/¾H�*��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l�A*d/K�?�Z�GJA�XV?U_NDFG�Z�K�XHK�G\qF^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]�*�*T ³

º(a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�u��;XHK�G\qF^/a �»{`�A�Z oV�cS2K�� �

A[<�=2?�d[=@?jd(=2d*A LV<�=2?;A�XHq/EHS2AFGje&DFe&K�X[Z�E�e Ii<�=2?�egD/e&K�X[Z�EHe WV<�=2?;ARd/K�I�Z�DFG Ki<�WHDl>A*dFKi?�Z�GJA�X�?�_VD/GUZ

¾H�"º6h[e4EHS�ZB¾/¾/�F¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�D�e&K�e&D/G�^�uj?U=2X(E�?�DF=@WHA�Sp_NK�G\=YD]W]=@I�l�A*d/K¼ a~��?�=YX(E�?�DF=@WHAFSNl>A*dFK�=@?cA�XK��HA�e&_HS2KMD�P:u

A[<nAFXAF_VK�G�=2D]W]=@IRl>A*dFK/aLN<QAg_NK�G\=YD]W]=@IMl>A*dFKFaIi<QA4Z\G\AFX�?Ud/K�GJ?UK�l>A*dFKFaWV<QAgS2DFXHq/=�Z\E�W]=2X�A�S�l�A*d/KFaK*<QA4Z\G\AF_VK���KMl�A*d/KFa

¾H�"º6h[e4EHS�ZB¾/¾/�H��¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�SY=2XHKiA�G\=�Z:^CDFP�Z\`HK-l�A*d/KRKih[E�A"Z\=YD/X½ a>»{`�A�ZBW]D(K�?�Z\`HK-SY=2XHKiA�G\=�Z:^CDFP�Z\`HK-l�A*d/KRKih[E�A"Z\=YD/X�5�W]=���K�G\K�X[Z\=2AFS�l�A*d/KRKih[E�A"Z\=YD/XV<�=Ye&_HS2^��

A[<n� S2=2XHK�AFGcI�DFe4LH=2X�A"Z\=YD/XQDFP�?�DFS2E]Z�=2DFX�?>=@?>Z\`HK6?�h[E�AFG�K�D�P�A�?UD/SYEHZ�=2DFX�aLN<Q� S2=2XHK�AFGcI�DFe4LH=2X�A"Z\=YD/XQDFP�?�DFS2E]Z�=2DFX�?>=@?>Z\`HK-=YX(d/K�GJ?UK�D�P�Ag?�DFS2E]Z\=YD/X�aIi<Qb>`VA"Z~Z�`�K�G\KMAFG�KMXHD�?�DFS2E]Z�=2DFXV?�aWV<Q� S2=2XHK�AFGcI�DFe4LH=2X�A"Z\=YD/XQDFP�?�DFS2E]Z�=2DFX�?>=@?cA&?�DFS2E]Z�=2DFX�aK*<Qb>`VA"Z~Z�`�K�G\K�=@?~D/XHSY^nDFXHK-?�DFS2E]Z�=2DFX�a

¾H�"º6h[e4EHS�ZB¾/¾ ³ ¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u�S2=2XHK�AFG>WHK�X�?�=�Z:^��¾Ha~��?UZ�G\=YX�qg=@? ¼ e}SYD/XHqgAFX�W`�AF?>e�A/?�?~¾ � ¾[��O(q�a�»{`�A"Z~=@?~=�ZJ?~S2=YXHKiA�GcW]K�X�?�=�Z:^ � �

A[<Cµ[¾F¾jO(qje � �"aLN<� ¶ ¾jO(qje � �"aIi<nµ[¾F¾je±O(q � ��aWV<� � ¶ ����¾ � � O(q�e � �"aK*<� � ¶ ����¾ ��� O(q�e � �"a

¾H�"º6h[e4EHS�ZB¾/¾�µ[¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u�l>A*dFK�SYK�XHq�Z\`CDFX�A&?UZ�G\=YXHq�F�Fa~b>`HK-l>A*dFKM?�_VK�K�WnP8DFGcA�?UZ�G\=YXHq&=@?

� $� � �

l~`HK�G�K � � =2?�Z\`HK6?:Z\G�=2XHqgZ�K�X�?�=YD/XAFX�W � =@?�Z�`HK-S2=YX�K�A�G~W]K�X�?�=�Z:^/aj»{`�A"Zc=@?>l�A*d/K�S2K�XHqFZ�`AF?>A4P8EHX�I$Z\=YD/XmD�P� � �

A[< � $ # + � � � aLN< � $ # # � � � � aIi< � $ # � � + � � � aWV< � $ # � �3# � � � � aK*< � $ # ��� � a

¾H�"º6h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l~`�A"Zi· ?BA�XmA�X[Z�=2XHD]W]K���i�]a>»{`�A�Zc=2?~AFX�A�X[Z�=2XHD]W]K��

A[<n� _NDF=2X[ZcD�P�XHD�e&D�Z�=2DFX=2Xm?UZ\AFX�W]=2XHq&l�A*d/K�?�aLN<Q� _NDF=2X[ZcD�P�eg=2XH=2esEHe�A�e&_HS2=YZ�E�W]K-=2X�?:ZJA�X�WH=YXHq&l>A*dFKi?�a

Page 92: Introductory Physics Problems David J. Jeffery Department of

¼F¼ v�`�AF_]Z�a~�"º »rA*dFK�?>7$uN��K�XHK�G\AFSN»rA*dFKi?~A�X�WQ»rA*dFK�?>D/XA�¤[Z\G�=2XHq

Ii<Q� _NDF=2X[ZcD�P�e&A��]=Ye4EHe}AFeg_�SY=YZ�E�WHK-=YX�?UZ\A�XVW]=YX�qgl>A*dFKi?�aWV<Qb>`VA"Zcl~`H=@IJ`Q_�G�D]I�K�K�WH?~AgXHD]W]K/aK*<Qb>`VA"Zcl~`H=@IJ`nP8D/SYS2D"lc?~AgXHD]W]KFa

¾H�"º6h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�X[Z�=2XHD]W]Ki?~A�X�W`(EHe&_�?� ³ a>7!XQZ�`HK ³ G\Wn`�A�G\e&DFXH=@IRD�P�?UZ\AFX�W]=2XHq&l�A*d/K�?�DFXmA&?:Z\G�=2XHq4�H�]K�WmA"Z~LND�Z�`K�XVWH?�o]`�D"l�e�A�X(^CA�X[Z\=YXHD]W]Ki?~A�G\K

Z\`HK�G\KFuA[<Q¤]=��pu;�sP8DFG~KiAFIJ`D�P�Z�`HK ³ P8EHS2S�l>A*dFK�S2K�X�q�Z�`V?�e�AFO[=2XHq&EH_Z�`�K-_�A"Z�Z�K�G\X�aLN<Q|�DFEHGiu�Z�`HK-K�X�W_VD/=YX[ZJ?cA�X�WnZ�`�Ks�s=2XHXHK�Gc_NDF=2X/ZJ?>D�P�XHD&e&D�Z�=2DFX�aIi<Qb>`�G�K�KFaWV<Qb>l�D&SY=2OFK�Z\`HK �>AFI$Z\G�=@A�XI�AFegK�S�aK*<m°RX�K�S2=2OFKMZ�`�K6�cGJA�LH=@A�XI�A�e&K�S�a

¾H�"º6h[e4EHS�ZB¾/¾[º�¾F¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�u�?UZ\AFX�W]=2XHq&l�A*d/KRl>A*dFK�SYK�XHq�Z\`nDFXmA&?:Z\G�=2XHq��µ�a ��D/E�`�A*d/K4A?:Z\G�=2XHqnDFP;S2K�XHqFZ�` �zl~=YZ�`����(KiW�K�X�W�_NDF=2X[Z\?�a6b>`HK�G\KgAFG�Kg?:ZJA�X�WH=YXHqQl�A*d/K�?RDFX�Z\`HK�?:Z\G�=2XHqVa

��D/EmI�DFEHX[Z �rA�X[Z�=2XHD]W]K�?�a�»{`�A"Zc=@?�Z�`�K-l�A*d/K�S2K�XHqFZ�`nDFP�Z\`HK-l>A*dFK�?�A[< � $ � �jaLN< � $ � � �jaIi< � $ � ��� �jaWV< � $ �BaK*< � $�� � � �ja

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H�"º6h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�A&?�=YX(E�?�DF=@WHA�SNZ\G\A*d/K�S2=YXHqgl>A*dFK�Fa~b>`HKnK�h[E�A"Z\=YD/X�D�PcAmZ\G\AFX�?Ud/K�GJ?UKgl>A*dFK�DFX�A�?UZ�G\=2XHq�=@? �p5 � <�$ ½ � ¾�?�=2X�5�¾ � ¾H� � � � µ � ¾�� � <-l~`HK�G\K ��AFX�W��AFG�K4=YX�I�K�X[Z\=Ye&K�Z\K�GJ?�o � =@?�=YX�?UKiI�D/X�WH?�o�AFX�W�Z\`HK&A�G\qFEHe&K�X[Z�D�P�Z\`HKg?�=2XHK4=@?�=YXxG\A/W]=@A�X�?�a�|�=2X�W±5,A/<cZ�`�KAFeg_�SY=YZ�E�WHKFo658LN<&Z�`�K�l>A*dFK�S2K�X�q�Z�`�o�5�I�<&Z\`HK�P8G\K�h[EHK�X�I�^/o65,W�<gZ\`HK�_�`�AF?�K�?U_NK�KiWpos5,Ki<gZ\`HKxW]=2G\K�I$Z\=YD/XwD�P_HG\DF_VA�q/A�Z�=2DFX�oNA�X�W�5 P\<BZ�`�K4e�A"�]=2esEHe�Z\G\AFX�?�dFK�GJ?�K6?U_NK�KiW�D�PjZ\`HK&?:Z\G�=2XHq�a&58q(<~»{`�A�Z�=@?BZ�`HK4Z�GJA�X�?�dFK�G\?�KW]=@?�_HS2A/I�K�egK�X[Z~A�Z�� $ ³ � ¶ I�e�AFX�WCZ\=Ye&K � $�¾ � � ¹ ?�

¾H�"º6h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�Z�GJA�XV?Ud/K�GJ?UK�l�A*d/KR?�_VK�K�W=2Xm?UZ�K�K�S�]a~b�K�X�?�=2SYK6?UZ�G\K�?\? �=@?�P8DFGJI�KM_NK�G~EHX�=�ZRAFG�KiA4AFX�WQ=2?~e&KiAF?�EHG�KiWC=2XmEHXH=YZ\?~DFP�  �*e ��a

A[<Q��=2dFK�XZ�`HK-?UZ�G\=YXHq&l>A*dFKM?U_NK�KiWQP8DFG\esEHS@A

� $� �

�VX�W&Z�`�KBK�h[EH=2d"A�S2K�X[Z�P8D/G�e4EHS2AM=2XC=2X&Z�K�G�e�?�DFP �CA�X�W&d/DFS2EHe&KBW]K�X�?U=YZ:^ �4AF?\?�EHe&=YXHq6Z�`�A�Z�Z�`HKBZ�K�X�?U=2S2K?UZ�G\K�?\?>=@?~I�DFXV?:ZJA�X[ZcAFI�G\D/?\?�Z�`HK6I�G�D[?�?UT!?UKiI$Z�=2DFXVA�S�A�G\K�A4D�P�Z\`HK6?UZ�G\=YXHqVa

LN<Q|�DFGw?�A�P8K�Z:^/oQZ\`HK�e�A��(=2esE�e Z�K�XV?U=2SYK�?:Z\G�Ki?�?�Z�D l~`H=@IJ`�?:Z\K�K�Sl~=2G\K�?±?U`HD/EHS@W LVK ?�EHL,A:K�I�Z�KiW =2?º � ¾ ���i¾p  �*e ��aBb>`�K4W]K�X�?U=YZ:^D�P�?:Z\K�K�S�=@?�º ¼ ¾F¾�O[q��*e � ac»{`�A�ZR=@?~Z\`HK6P,A/?:Z\K�?UZ�o�?Ue�A�S2SYT�D[?�I�=YS2S2A�Z�=2DFXZ\G\AFX�?�dFK�GJ?�KB?:Z\G�=2XHq4l�A*d/KcZ�`VA"Z~I�A�XQLVKM?\A"P8K�S2^�?UK�X[Z>AFSYD/XHq4Ag?:Z\K�K�SNl~=2G\KBD�P�A�X(^�I�G\D/?\?:T!?UKiI$Z\=YD/X�A�SNA�G\K�AA/I�I�DFGJW]=YX�qMZ�DsD/EHG>?U=2e&_HSYKBZ�`HK�DFG\^&D�P�?UZ�G\=YXHqsl�A*d/K�?�n£BD"l�W]D(K�?;Z�`H=@?�P,A/?:Z\K�?UZ�?UZ�G\=YX�qsl>A*dFKcI�D/e&_�A�G\KZ\D&Z�`HK6?�DFE�X�WQ?�_NK�K�W=2X?UZ�K�K�S�u � � � � � � � � � � � � � � ¹ ¾/¾F¾je��"?�a

¾H�"º6h/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�?UZ�G\=YX�qgl>A*dFKi?�EHX�I�D/X�?UZ\A�X[Z �³ a~� EHX�=�P8D/G�e}G�D/_VKM`�AFXHq/?�P8G\DFe}A&I�K�=2SY=2XHq�a�7kZc`�A/?>SYK�XHq�Z\` �±AFX�WQZ�DFZ\A�Spe�A/?�? ��a

Page 93: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia~�*º�»rA*dFKi?�7$uV��K�XHK�G\AFSp»�A*d/K�?>A�XVWn»rA*dFKi?>DFXmA&¤(Z�G\=YXHq ¼/½

A[<Q¤]`HD"lwZ�`�A�Z�Z\`HKM?:Z\G�=2XHq4?�_NK�K�WCDFXCZ\`HKBG\DF_NKRA/?�A6P8EHX�I�Z�=2DFXnDFP ��58e&K�A/?UE�G�KiW�G�K�S2A�Z�=2dFK~Z\D4��K�G\DsA"Z�Z�`�KLND�Z�Z�D/e�K�XVWQDFP�Z\`HK-G�D/_VKM=@? � $ + � Na

LN<¤]`HD"l{Z�`VA"Z�Z�`HK�Z�GJA*dFK�S�Z\=Ye&KRP8DFG~A4l�A*d/KBAFI�G�D[?�?�Z�`HKMl~`HD/SYK�G�D/_VKR=2? � $��)# � � �a �������� � »{`�A�Z=@?�Z�`HKRZ�GJA*dFK�SHZ\=Ye&KRP8DFG�Z�`HK�l�A*d/KBAFI�G�D[?�?;A4W]= ��K�G\K�X[Z�=@A�SNLH=YZ�DFP�G�D/_VK � � A"Z�q/K�XHK�G\AFS ���m£cD"lzW]Ds^/DFEq/DgP8G�D/e�A&W]=���K�G\K�X[Z\=2AFS�A�X�?�l�K�G�Z�D�AgqFS2DFL�AFS�A�X�?�l�K�G �

¾H�"º6h/P8EHS2S�¾/¾�µ/¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVuj`�A�G\e&DFXH=@IBP8G�KihVa~�i?:Z~D/G\W]K�G~A�_H_HG\D*�]=Ye�A�Z�=2DFXµ�a~b>`HKMP8D/G�e4EHS@A6P8D/G>Z�`HK-`�AFG�e&D/XH=2I�G\K�?�DFX�AFX�I�KRP8G\K�h[EHK�XVI�=2K�?>D�P�?:Z\G�=2XHq&l~=YZ�`m�H�]K�WQK�XVWH?~=@?�u

# $ ��

� �

l~`HK�G�K �=@?�Z\`HKB`�AFG�e&D/XH=2I>X(EHe4LVK�G�o � =@?jZ\`HKB?UZ�G\=YX�q6l�A*d/K~?U_NK�KiWpo[AFX�W ��=@?jZ\`HKB?UZ�G\=YXHq-S2K�X�q�Z�`�aj¤HA*^sDFX�KIJ`�AFXHqFKiW �zL[^ � �Ba-»{`�A"ZM=2?RZ\`HK&K��]_HG\K�?\?U=2DFXmP8D/G � #{58Z�`HK&I�D/G�G\K�?�_NDFX�W]=2XHqIJ`�A�XHq/K6=2X�#p<RAFI�I�DFGJW]=2XHqZ\D&Z�`HK&��?UZcDFGJW]K�G>AF_H_HG\D*�]=Ye�A"Z\=YD/XnDFP�I�AFS2I�EHS2E�?�uj=�a KFa2o � # � � � � �4# � ���ca

Page 94: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � � &)(A1_E�Q7Q � U+?Td�>�,�� &)(A1_E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H� ¼ h[e4EHS�ZB¾/¾F¾���¾C�&���MK�A/?U^�e&K�egD/G�^�u�?�DFEHXVWnl>A*dFK�SYD/XHqF=YZ�EVW]=YXVA�S�Fac¤(D/EHX�Wl>A*dFK�?�=2XQ�VEH=2W�?cA�G\K-A�S2l�A*^]?�u

A[<�SYD/XHqF=YZ�EVW]=YXVA�S�a LV<�S2A�Z�=YZ�E�WH=YX�AFS�a Ii<;Z�GJA�X�?�dFK�G\?�KFa W�<�G�K�dFK�G\?�KFa Ki<>I�EHGJ?UK/a

¾H� ¼ h[e4EHS�ZB¾/¾F¾��i���&���MK�A/?U^�e&K�egD/G�^�u�?�DFEHXVWnl>A*dFKi?�S2DFX�qF=YZ�E�W]=2X�AFS� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]�*�*T ¶

�]ac¤(D/EHX�Wl>A*dFK�?�=2XQ�VEH=2W�?cA�G\K-A�S2l�A*^]? l�A*d/K�?�aA[<gSYD/XHqF=YZ�EVW]=YXVA�S LV<gZ\G\AFX�?Ud/K�GJ?UK Ii<&e&=��]K�WwS2DFX�qF=YZ�E�W]=2X�AFS�T�Z�GJA�X�?�K�G\dFK W�<CA"ZUZ\=�Z\E�W]=2X�A�SK*<�_VK�G�d/K�GJ?UK

¾H� ¼ h[e4EHS�ZB¾/¾F¾[��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj_HG\K�?\?�EHG�K�D/?\I�=2S2S2A�Z�K�?�=2X�?UD/EHX�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

³ aB°RXHKMD/L[d(=2DFE�?~h[E�AFX[Z�=YZ:^�Z�`�A�ZcD/?\I�=2SYS@A"Z\K�?�=2Xm?�DFE�X�Wnl>A*dFKi?�=2?�uA[<�SY=2qF`[Zia LV<>WHA�G\O�a I�<�P8G\K�h[EHK�X�I�^/a W�<�_HG\K�?\?UE�G�K/a K*<�qFGJA*d(=�Z:^/a

¾H� ¼ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ��Me&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�?UD/EHX�Wm?U_NK�KiWQP8DFG\esEHS@Aµ�a~b>`HK-EV?UE�AFS�?U_NK�KiWD�P�?�DFE�X�WQP8DFG\esEHS@As=@?�u

A[< � $�# 5�� � ��� �]<�l~`HK�G\K�Z�`HK6W]K�G�=2d"A"Z\=Yd/K�=@?>ZJA�OFK�XnP8D/G>Z�`HK6A/W]=@A�L�A�Z�=@IRI�DFX�W]=YZ�=2DFX�aLN< � $�# � � � oHl~`HK�G\K � =@?�Z�K�X�?�=YD/XmAFX�W � =@?>SY=2XHKiA�G~e�AF?\?~W]K�XV?U=YZ:^Ii< � $�# 5�� � ��� �]<�l~`HK�G\K�Z�`HK6W]K�G�=2d"A"Z\=Yd/K�=@?>ZJA�OFK�XnP8D/G>Z�`HK-=@?�D�Z�`�K�G\e&AFSpI�DFXVW]=�Z\=YD/X�aWV< � $�# � � � oHl~`HK�G\K � =@?�Z�K�X�?�=YD/XmAFX�W � =@?>SY=2XHKiA�G~e�AF?\?~W]K�XV?U=YZ:^K*< � $�# 5�� � ��� �(<�l~`HK�G�K�Z\`HK6W]K�G\=2d*A�Z�=2dFKM=@?>Z\AFOFK�XQP8DFG>Z\`HK6AFWH=2AFL�A"Z\=2I�I�D/X�W]=YZ�=2DFX�a

¾H� ¼ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¡BD/_H_HS2K�GcK.�NKiI$Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

¶ a~b>`HK6¡RDF_�_HSYK�G~K ��K�I�Zc=2?cA(y"AFX�uA[<CK.�NKiI$ZcDFP�Z\`HK-G�K�S2A�Z�=2dFK�SY=2XHK�T�DFP Tk?�=Yq/`[Z>e&DFZ�=2DFXD�Pj?UD/EHG\I�K�?>A�XVWnG\K�I�K�=2dFK�GJ?�DFXl�A*d/KBP8G\K�h[EHK�X�I�^/aLN<nK.�NKiI$ZcDFP�l>A*dFKRP8G�Kih[EHK�X�I�^CDFXQZ�`�K-egDFZ�=2DFXD�Pj?UD/EHGJI�K�?>AFX�WG�KiI�K�=2dFK�G\?�aIi<QWHK�I�G\K�A/?UK~DFPp=YX[Z�K�X�?�=�Z:^&AF?�Z�`HKc=2X(dFK�G\?�Kc?�h[E�AFG�K~DFP�W]=2?UZ\AFX�I�KcP8G�D/e A-_NDF=2X[Z�?�DFEHGJI�K~DFP�?UD/EHX�W&DFG;SY=2qF`[Z�aWV<QI�A�E�?�KMD�P�K�X[Z�G\DF_(^FaK*<QI�A�E�?�KMD�P�`HK�A�ZBI�A�_VAFI�=YZ:^Fa

¾H� ¼ h[e4EHS�ZB¾/¾/�/��¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�¡RDF_H_�SYK�G~K ��K�I$Zcq/K�XHK�G\AFSY=YZ:^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]�*�*TJ�F�

¹ a~b>`HK6¡RDF_�_HSYK�G~K ��K�I�ZcD(I�I�EHGJ? l>A*dFKi?�uA[<jD/XHSY^&P8D/G�?�DFE�X�W LV<�P8DFG�e�A�X(^&O(=YX�W�?;DFP I�<;DFX�SY^gP8DFG�S2=Yq/`/Z W�<;DFXHS2^gP8DFG�Z�GJA�X�?�dFK�G\?�KK*<�XHD&O(=YX�W�?~D�P

Page 95: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia~� ¼ »rA*dFKi?>7U7$uV¤]DFEHX�WQ»rA*dFK�? ½ �

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H� ¼ h/P8EHS2S�¾/¾H��¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVu�?UD/EHX�WA�X�WS2=Yq/`[Z~?�_NK�K�W�?�Fa>7kZi· ?RZ�`�K4µFZ�`�DFP��FE�SY^mXH=2qF`[Z-A�X�W�A/?BEV?UE�AFS�Z\`HK�G\KF· ?�`�A�SYP;A�Xx`HDFE�GRDFPj��G�KiI�GJAFIJO/K�GJ?�aB�cP Z�K�G�l>A"ZJIJ`H=2XHqCP8D/G�F¾Be&=2X[EHZ�K�? �{^FDFE&A�G\K>?Ul~=YP Z �{^FD/EsG\K�A�S2=2��K>?UD/egK�Z�`H=2XHqM=@?�l~G�D/XHq�a ��DFEg`HK�AFG�Z\`HK>K��]_HS2D/?�=YD/X4AFSYl>A*^]?�A�P Z�K�G^/DFE�?�K�K6=YZ�ac7!X�P,AFI$Zio�Z\`HK6Z\=Ye&KgW]=���K�G\K�XVI�K6=@?BAFLVD/E]Z4�/a ¶ ?�K�I�DFX�W�?�a~�j�]_HS@A�=2XmZ�`�=2?�A�X�WZ\K�S2S�`�D"lzP,AFGB^/DFEAFG�K�P8G\DFe Z\`HK-G�D]IJO/K�Z�· ?�G�KiWnq/S2AFG�K/a

¾H� ¼ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujS2=YXHKi?~D�P�W]K�?UZ�G\E�I�Z�=2dFKM=YX[Z\K�G�P8K�G\K�X�I�K�]a~b>`HK�G�KA�G\K�Z:l�D�=@W]K�X[Z�=@I�AFS�I�DF`HK�G�K�X[Z�oj=2X]T�_�`�AF?�KQ?�DFEHGJI�Ki?-D�P�?UD/EHX�W�?�K�_�AFG\A�Z�KiWrL[^�� � ¶ emaw5�v�D/`HK�G\K�X�I�Ke&K�AFX�?�`�A*d(=2XHq�A�W]K��VXH=�Z\K � E�?UEVA�S2SY^±I�DFXV?:ZJA�X[Z !c_H`VAF?�K�G�K�S2A�Z�=2DFX�a�7!XHT�_H`VAF?�KFo>e&K�A�XV?&Z�`�A�Z�Z�`HKxI�G\K�?UZ\?�oZ\G�D/EHqF`�?�o(A�X�WnXHD]W]K�?>A�G\KMA�S2S�AFSY=2qFX�K�WCA�Z�Z\`HK-?�AFegKBZ�=2e&KFa <&b>`HK�?�DFE�X�WCl>A*dFK�SYK�XHq�Z\`�=2?�� � ¾jemaj|�AFG;P8G\DFeZ\`HK�?UD/EHG\I�K�?�oVl~`VA"ZM=2?RZ�`�K&AFXHqFS2KsDFP�Z�`�Ks��GJ?UZ�S2=YX�K&WHK�?UZ�G\E�I$Z\=Yd/Ks=2X/Z\K�G�P8K�G\K�X�I�Kse&K�A/?UE�G�KiW�P8G\DFe Z�`HK&S2=YX�KLH=@?�K�I$Z\=YX�q4Z\`HK6?�DFEHGJI�Ki?�a

¾H� ¼ h/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�?�DFEHXVWn=2X(dFK�GJ?�K�T!?�h[E�AFG�KRS2A*l³ a~b>`HK-=2X[Z�K�X�?U=YZ:^CDFP�?�DFEHXVWQA�ZM�i¾je P8G\DFe�A&_NDF=2X[Zc?UD/EHG\I�KM=2?M�i¾F¾j» �"e �"aj»{`�A"Zc=@?>=YZBA"Z6��¾/¾je �

¾H� ¼ h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�W]KiI�=2LVK�S�?\I�A�S2Kµ�a~b>`HK�?�DFEHXVW�S2K�dFK�SjA"Z-b>`HKQ· ��DFG\Dx58Z�`HK�?UZ�E�W]K�X[Z-WH=Yd/K4=2X�¯�EHGUP8G\K�Ki?ULNDFG\D�opb�K�XHX�K�?\?UK�Ki<B`�AF?�A:E�?UZ<A:EHe&_VKiWµ ³ W3��a3��^Cl~`�A"Z>P,A/I$Z�D/G~`�AF?�Z\`HK6?�DFEHX�W=2X[Z�K�XV?U=YZ:^C=2X�I�G\K�A/?UKiW �

¾H� ¼ h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujDF_NK�Xm_H=2_NK-`�A�G\e&DFXH=@I�?¶ a~b>`HKC�"T�D/_VK�X]T�K�X�W�_�=Y_NKC� =2?&� � ¶ e�S2DFX�qmAFX�Wx=2?MD[?�I�=YS2S2A�Z�=2XHq=YX�=�ZJ? ³ GJW�`�AFG�e&D/XH=2IFagb>`�K��TkI�SYD[?UKiW(TkK�X�W_H=2_NK �w=2?>D[?�I�=YS2S2A�Z�=2XHqg=YXm=YZ\?~?�K�I�D/X�WCS2D"l�K�?UZ�`�AFG�e&D/XH=2IFajb>`HK�P8G�Kih/E�K�X�I�=YKi?�DFP�Z\`HK�Z:l�D&_H=2_VKi?>`�A�_�_VK�XnZ\De�A"ZJIJ`�a�b>`HK-A�=2Gc?�_VK�K�W=2? ³ µ ³ e���?�5�A�_H_�G�D/_HG�=@A"Z\KBP8D/GcA�=2GcA"ZB��¾ � v�A�X�Wx��A"Z\eC<$aA[<C»{`VA"ZR=@?BZ�`HKsP8EHX�WHAFegK�X[Z\A�S�P8G\K�h[EHK�XVI�^mD�P�_H=2_NK4��5,l~`H=@IJ`�=@?cXHDFZBZ�`�KsP8G\K�h[EHK�X�I�^=�Z�=2?RD/?\I�=2S2S2A�Z�=2XHqA�Zc=YXQZ�`�=2?~_�G�D/LHSYK�eC<$a

LN<Q£BD"l�S2DFXHq&=@?~_H=2_VK � �Ii<n7kPBAFX �HT!A"�]=@?-K��(Z�K�X�WH?gA�S2DFXHq�_�=Y_NKQ� l~=YZ�`tA���K�G�D�A�ZsDFXHKnK�X�Wpo�l~`HK�G�KQA�S2DFXHqmZ\`HKn_H=2_NKnA�G\K�Z�`�KWH=2?�_HS@AFI�K�e&K�X[Z~XHD]W]K�?�

¾H� ¼ h/P8EHS2S�¾/¾ ¹ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�?UEHL�e&AFG�=2XHK-¡RDF_H_HS2K�GBK ��K�I$Z¹ a~b>l�Dc?UE�LHe�A�G\=YXHKi?�I�G�EH=@?�=YXHq>Z\`HK;�BG\I�Z�=@I�°�I�KiA�X6A�_�_HG�D[AFIJ`�K�A/IJ`�DFZ�`HK�G�l~=YZ�`�� ������� ¶ ¾jO(e �"`HG�5,?�EHL��*<AFX�W���¾/¾jO(e��*`HGB5�?UE�LQ�F<�aj¤]EHL��RK�e&=�ZJ?�A4?UD/X�A�G�?U=2qFXVA�S�DFPpP8G�Kih[EHK�X�I�^�# � $ �i¾F¾F¾;£c�Fa�b>`HKM?UD/X�A�G;?�DFE�X�W?�_VK�K�W=2Xm?�K�Agl>A"Z\K�G>=2? ¶ µ(º�¾jO(e��*`HG$aA[<C»{`VA"Zc=@?�Z�`HK6?�=Yq/X�A�S�P8G\K�h[EHK�X�I�^�# � W]K�Z\K�I�Z�K�WL(^n?�EHL����LN<n»{`VA"Zc=@?�Z�`HK-G\K���KiI$Z\K�Wm?U=2qFXVA�SNP8G�Kih[EHK�X�I�^�#��� W]K�Z�KiI$Z�KiWL[^?UE�Lx� �

¾H� ¼ h/P8EHS2S�¾/¾[º"¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�bc��´ Z�GJA�=2X�?�o]`(EHG\G\=2I�A�XHKMl~=2X�Wpo�¡RDF_H_�SYK�Gc?U`H=YP Zº(a~b>l�D�Z�GJA�=2X�?CAFG�K�Z�GJA*dFK�S2=2XHq�Z�D"l>A�GJWtKiAFIJ`wD�Z\`HK�G�58D/X�W]= �NK�G�K�X/ZnZ�GJAFIJO]?&Z�D�LVK�?UEHG\Ki<�K�AFIJ`{A�Z ¹ ¾�e ��?

� � � � � Z\DnZ\`HK&qFG\DFEHX�W�58=�a K/aYo��H� ¹ O(e��*`�uBZ�`HK�^�A�G\Kgbc��´�?\<�asb>`HK&?U_NK�KiW�DFP�?UD/EHX�W�=YX�A�=2G&5,=�a KFoG\K�S@A"Z\=Yd/KBZ\DCA�=2GJ<�=@? ³ µ ³ e ��?$a�b�G\AF=YXm� LHS2D"lc?>=�ZJ?~l~`H=@?:Z\SYK-A"Z ¶ ¾F¾�£B�g5,=YXm=YZ\?~D"l~XQP8GJA�e&Ki<�aA[<C»{`VA"Zc=@?�Z�`HKMP8G\K�h[EHK�X�I�^Q`HK�AFG\WnDFXZ�GJA�=2X!��=�P�Z�`�K6A�=2G�=@?c?UZ�=2SYS �LN<n»{`VA"Z;P8G\K�h[EHK�X�I�^g=@?;`HKiA�GJWgDFX�Z\G\AF=YX �t=�PpZ\`HKRAF=YG�=2?�LHS2D"l~=YX�q6A"Z ¹ ¾je��"?c5,=�Zi· ?�`(EHG\G�=@I�AFXHK>P8DFGJI�K/oFLHE]Z

d/K�G\^n?UZ�K�A/W]^nAFX�WnX�DFX[Z�EHG\LHEHS2K�X[Z$<�=YXZ�`�KMWH=YG\K�I�Z�=2DFXP8G�D/e Z�GJA�=2Xm��Z�DgZ�GJA�=2X � �Ii<n»{`VA"Z~P8G\K�h[EHK�XVI�^C=@?~`HKiA�GJWCDFXZ\G\AF=YX'�{=YP�Z\`HK-l~=2X�WQWH=YG\K�I�Z�=2DFXm=2?>G\K�d/K�GJ?UKiW �

Page 96: Introductory Physics Problems David J. Jeffery Department of

½ � v�`�AF_]Z�a~� ¼ »rA*dFK�?>7�7$uV¤(D/EHX�W»�A*d/K�?

¾H� ¼ h/P8EHS2S�¾/¾ ¼ ¾/¾g� ¶ ¾g`�A�GJWnZ�`H=2XHO(=YX�q�u�?�l�K�K�Zc9�DFS2SY^Q9�EHG\K�LHG\K�W¼ a~b>`HK�P8D/EHS �>A"Z\LH=YGJWQ`�AF?>O(=@W]X�A�_NK�W?�l�K�K�Zc9�DFS2SY^C9;EHG\K�LHG\K�WQA�X�W?UKiI�G\K�Z\K�WQ`HK�G~=2XQ`�=2?~S@A�=2G>=YX�AFXQEHX�OFD"l~XG\K�A/IJ`sD�P�Z�`HKRv�AFG�S@?ULVAFW4v�A*d/K�G\X�? �wZ�`�K;K�X�DFG\egD/E�? �>A"Z�L�=YGJWgv�A*d/K 1 b>`�=2?�S2D(DFO]?�SY=2OFK>A�A:DFL4P8DFGj�cX�WHK�GJW]DFqVa� � � � b>`H=@?~h[EHK�?UZ�=2DFX�I�DFEHS@WnLNK6AgesEHSYZ�=YTk_�A�q/K�G~=2XAgZ\K�?UZ>e&=@?UK-K�X�?�I�(K�XHK/aA[<n£RA*d(=YXHqg_NK�XHK�Z�GJA"Z�KiWQZ�`HKM_H=YZ\IJ`]T!WHAFG�Ov�A*d/KFo[Z�`�K-¤]DFLNK�GB¤(KiA�S2^[`VA�e q/=Yd/K�?�qF=2dFKi?�Age&=2qF`[Z:^C»�D[DFP�Z\Dl~`�=2IJ`�Z�`�Kn¤(EHSYZ�G\^x¤]A�S2EHO(=jEH_NDFXr`HKiA�G\=YXHqm=YZ6=YXV?:ZJA�X[Z�S2^�G\K�_HS2=YKi?Ml~=�Z\`�AQ_�S2AF=YX[Z�=2dFK&l~`H=2e&_VK�G�aCb>`�KZ\=Ye&KLVK�Z:l�K�K�X�»�D(D�PRAFX�WrZ\`HKQG\K�_�SY^r=@?g� � �F¾�?6A�XVW�Z�`�KQ?�_VK�K�W�DFPB?UD/EHX�W�=@? ³ µ/¾�e ��?$ar»{`�A"Zg=2?WH=2?UZ\AFX�I�K�P8G\DFe}�BX�W]K�G\W]D/qsZ\DC9�DFS2SY^��

LN<#�/E�?UZ�Z�`HK�XwZ�`HK�L�A"Z\`HDFS2=�Z\`H=@I ��A�Z�LH=2GJW±?�l�D[D/_�?�A"Z�cX�W]K�G\WHDFqr`�A*d(=YX�qrWHK�Z�KiI$Z\K�Ww`H=@?CS2D]I�A"Z\=YD/XtL(^LVA"Zs?�DFX�AFG�a���E]Z-Z:l�D�I�A�Xr_HS@A*^�Z�`�A�Z6q/AFegK/u�Z�`HKC¯�EV?U=@I�AFS�¯�E]ZUZio�?UZ�=2S2S;A"Z6G\K�?UZ-`H=Ye�?�K�SYP:o�K�e&=�ZJ?-AI�DFX�I�K�G�ZR� q/G�D"l~S�5,µFµ[¾�£c�*<~A�X�W�WHK�Z�KiI$ZJ?cZ\`HKsKiIJ`HD�K��HAFI�Z�S2^x� � ¾/¾�?~S@A"Z\K�GRA�ZcP8G\K�h[EHK�XVI�^D�P ¹F¹ ¾�£c�/a£BD"l P,A�G�=2?��>A"Z\LH=2G\W�A�ZBZ\`HKsZ\=Ye&K4Z�`HK&?�DFEHX�W�K�IJ`HD(K�?RDB�rD�P�`H=Ye �±»{`�A�Z�=@?R`H=2?�d/K�S2D(I�=�Z:^Z\D"l�AFG\W�BX�W]K�G\W]D/qnZ\`HK�X � »{`�A"Z6=@? �>A"Z\LH=YGJWp· ?MW]=2?UZ\AFX�I�K�A�Z�Z\`HK&Z�=2e&KC�cX�WHK�GJW]DFq`HK�AFG\?RZ\`HK�K�IJ`HDD�P�Z�`�Kq/G�D"l~SpA/?�?�EHe&=YX�q��>A�Z�LH=2G\W�· ?>d/K�S2D(I�=�Z:^�=@?cI�DFX�?UZ\AFX/Z �

Ii<Qb>`�Kx¤(DFS@W]=2K�GQ¤]K�ZUZ\K�GCS@A�E�X�IJ`HK�?C`H=Ye�?�K�SYP6?:Z\G\AF=Yq/`/ZnA�Z �>A"Z�L�=YGJW±l~=�Z\`�?UE]�CI�=YK�X/ZQdFK�S2D]I�=YZ:^�Z\D�?UK�X�W�>A�Z�LH=2G\W6G�K�K�S2=YXHq�?:Z\G\AF=Yq/`[Z�L�AFIJOMA"Z�Z:l~=@I�K;`�=2?�=YX�=�Z\=2AFS(?�_NK�K�W6P8DFS2SYD"l~=2XHqBAs��T!W]=2egK�X�?�=YD/X�A�S� � � � � ¦I�DFS2SY=@?�=YD/X�a;�cXVW]K�GJW]DFq�`VAF?>e�AF?\?Rº"¾�O[q�AFX�W'��A�Z�LH=2GJWpo ³ ¾/¾jO(q�aj»{`�A�Zc=2?B�cX�W]K�G\WHDFq�· ?~_HG\K�T!I�D/SYS2=@?U=2DFX?�_NK�K�W ��5, BD�Z�K/ugb>`�KnA�X�AFSY^[Z\=2I�?�DFS2E]Z�=2DFXrl~G\=�Z�Z�K�X�qF=2dFK�XrA/?-K��]_HS2=@I�=YZ�S2^�A/?6_ND/?\?U=2LHS2K�=2?sl�D/GUZ\`xP8E�SYSe�AFG�O]?>K�d/K�X=�P�^FD/EQl�K�G\K�X�· ZBAFLHSYK�Z\DCA�X�?�l�K�G>_�A�G�Z658LV<�a���^QA�XVA�S2^/Z\=2I�7�e&K�A�XmW]D/X�· ZB?�EHL�?UZ�=YZ�EHZ�K6=2XAFX(^X(EHe4LVK�G\?�a ��^�K��]_HS2=2I�=�ZM7ce&K�AFXx�cXVW]K�GJW]DFqV· ?BdFK�SYD]I�=YZ:^�?U`�DFEHS@W�AF_H_VKiA�G�=2?�DFS@A"Z\K�W�D/X�D/XHK4?�=2WHKDFP�Z\`HK-K�h[E�A�Z�=2DFXmA�X�WA�X(^nAFX�A�S2^[Z�=@IM?U=2e&_HSY=Y�VI�A"Z�=2DFXV?�Z�`�A�ZBI�A�XLNK-e&A/W]K-?U`�DFEHS@WLVK-e�AFWHKFa <

¡BK�XHDFEHK�e&K�X[Z�uc¸�K�A*d(=YX�q&Z�`HKg=Ye&_HG\K�I�A"Z\=YXHq#��A�Z�LH=2GJWmLVK�`H=YXVWpoNZ�E�IJO(=2XHqCZ\`HK4|VA�=2GR|HD*��EHXVW]K�G�AP8D/G�K�SYK�q�o(Z\`HK6¡BD/qFq/K�Wn¡RDFq�I�A�G\K�K�XV?>DFE]Z~D�P�Z�`�K ��A�Z�LH=2GJWmv�A*d/KR=2X[Z�DgZ�`HK6?UZ\AFGUT!I�G\D/?\?�K�W�XH=2qF`[Zia

Page 97: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 p � � Da145 =!?+,F6F>a&A= *IHJE�Q�� � 1_=!9�1)5<&X;<da5\1T`fM�1)&X;J` ��*[5 E�; ��& �

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾H� ½ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u���K�G�DFZ�`S2A*l�A�X�WnZ�K�eg_NK�G�Z�E�G�K�Fa~b>`HK���K�G�DFZ�`CS@A*l{D�P�Z�`HK�G�e&D]W]^(X�A�e&=@I�?�A�S2SYD"lc?;E�?�Z�D&W]K��VXHKBZ\`HKRP8EHX�I$Z\=YD/XnDFP�?:ZJA"Z\K458D/G;Z\`HK�G\e&D]W]^(X�A�e&=@I?UZ\A�Z�KMd"A�G\=2AFLHSYK*<$u

A[<�_HG\K�?\?UEHG\KFa LV<�G\K�?�_H=2G\A�Z�=2DFX�a Ii<�K��]_H=2G\A�Z�=2DFX�a W�<�Z\K�e&_NK�GJA"Z�E�G�K/a K*<�K�X[Z�G\DF_(^/a

¾H� ½ h[e4EHS�ZB¾/¾H�/��¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�L�?�DFS2E]Z\K���K�G\D�W]K���X�K�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ T ½

�]a �\¸�K�Zi· ?4_HS@A*^ �]1J� D+�"�\�"# 1 |HDFG��(�i¾F¾�o�Z\`HKQAFX�?Ul�K�G4=2?�uC��ZsZ\`H=@?6Z\K�e&_VK�G\A�Z�EHG\KFo�Z\`HKne&=@I�G\D/?\I�D/_H=2ICO[=2XHK�Z�=@IK�XHK�G\qF^�DFP�A&?�EHL�?UZ\A�XVI�KM=2?BAF?>S2D"lzAF?~h[E�AFX[Z�EHe e&KiIJ`�A�XH=@I�?~AFSYS2D"lc?�a �»{`�A�Zc=2? oH�BSYK����

A[<c��K�G\DI�K�S@?U=2E�? LV<cZ�`�KgLNDF=2S2=YXHq_NDF=2X/Z-DFP;l�A�Z�K�G Ii<~Z\`HKgP8G�K�K���=2XHqQZ�K�eg_NK�GJA"Z\EHG\K4DFP;l�A�Z�K�GWV<>A�L�?�DFS2E]Z�KM��K�G\D Ki<�G\K�S@A"Z\=Yd/KR��K�G\D

¾H� ½ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�Z�G\=Y_�SYK-_NDF=2X[ZcD�P�l>A"Z\K�G³ a �\¸�K�Zi· ?c_HS2A*^��]1\��D3�����"# 1 |�DFG �]��¾/¾Ho]Z\`HKsA�XV?Ul�K�G~=@?�u�b>`HK6X�AFe&K-P8DFG~Z\`HKs?UZ\A�Z�K6=2X�l~`H=@IJ`�l�A�Z�K�GRI�D(K��]=@?:ZJ?=2X�=YZ\?~Z\`HG\K�K6_H`VAF?�K�?s5,d"A�_NDFGio�S2=2h[EH=@Wpo�A�X�W�=@I�K*<~A"Z�²MK�S2d[=2XmZ�K�e&_VK�G\A�Z�EHG\K4�/º ³ � � ¹ ²}58L(^mW]K���X�=�Z\=YD/XV<cAFX�W_HG\K�?\?�EHG�K ¹ �i¾�9jAHa �A[<C»{`VA"Zc=@?�Z�`HK-EHX�=2h[EHK-_NDF=2X[ZcD�P�l�A�Z�K�Gio]�cS2K�� �LN<n»{`VA"Zc=@?�Z�`HK-l>A"Z\K�G~_HS@AF?�e�A4_�`�AF?�KFoH�BSYK����Ii<n»{`VA"Zc=@?�Z�`HKMZ\G�=2_HS2K-_VD/=YX[ZcD�P�l�A�Z�K�G�oH�BSYK����WV<n»{`VA"Zc=@?�Z�`HK6?UZ\A�Z�K-l~`HK�G�K�Z�`�K4v�K�S@?U=2E�?~A�XVW|VA�`HG\K�X�`HK�=YZ>Z�K�e&_NK�GJA"Z\EHG�K-?\I�AFSYKi?~A�qFG\K�K/o]�cS2K�� �K*<n»{`VA"Zc=@?>`HD]IJOFK�^nl�KiA"Z�`�K�GioH�cS2K�� �

¾H� ½ h[e4EHS�ZB¾/¾/�H��¾C�&���MK�A/?U^�e&K�egD/G�^�u ³ Z�K�e&_VK�G\A�Z�EHG\K-?�I�A�S2K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a~b>`HKMZ\`HG\K�K-I�D/ege&D/XnZ\K�e&_VK�G\A�Z�EHG\K-?�I�A�S2K�?~AFG�K/uA[<j|�AF`HG\K�XH`HK�=�Zio]v�K�S2?�=2E�?�o(A�XVWC²MK�S2d(=YX�a LV<;|�A�`�G�K�XH`HK�=YZ�oHv�K�S@?�=YE�?�o(A�X�W� BK�l>Z�D/X�ajI�<;|�A�`�G�K�XH`HK�=YZ�o´jKi?UE�d[=2E�?�o�A�XVWx²MK�SYd(=2X�agWV<R|VA�`HG\K�X�`HK�=YZ�o�v�K�S2?�=2E�?�o�A�X�W�v�A�S2d(=YX�a4Ki<M��K�?�EHX�WH`HK�=YZ�o�´jK�?�EHd(=YE�?�o�AFX�Wv�AFSYd(=2X�a

¾H� ½ h[e4EHS�ZB¾/¾ ³ ¾F¾C� ³ �4K�A/?U^�e�A�Z�`�ujZ\K�e&_NK�GJA"Z�E�G�K-I�D/X(dFK�GJ?�=YD/X¶ a>»{`�A�ZwAFG�Kf��¾ ��vRo&�F¾ ��vRo�A�XVW ³ ¾���v�=YX}|�A�`�G�K�XH`HK�=YZ� ������ � 7�AFSYl>A*^]?�esEHSYZ�=2_HS2^ A v�K�S@?�=YE�?Z\K�e&_VK�G\A�Z�EHG\KmL(^��Fa ¼ A�X�W±AFWHW ³ � �QZ�DrqFK�Zn|�AF`HG�K�XH`HK�=�Zia{��D/=YX�qxZ\`HK�D�Z\`HK�G&l>A*^�?�EHL]Z�GJAFI�Z ³ � �AFX�WW]=2d(=2WHK-L[^��Fa ¼ aA[< ,B�[º ³ � � ¶ �N|�oV�/º ³ � � ¶ ��|�o ³ º ³ � � ¶ �N|�aLN< ¶ ¾ �p|�o ¹/¼ �p|�o ¼/¹ �p|�aIi<nµ[¾ �p|�oHµ ¼ �p|�o ¶F¹ �p|�aWV<nµ ¼ �p|�o ¹/¼ �p|�o ½ ¾ �p|�a

Page 98: Introductory Physics Problems David J. Jeffery Department of

½ µ v�`�AF_]Z�a~� ½ b>`HK�G�e&D]W]^(X�A�e&=@I�?>7$u�b�K�e&_NK�GJA"Z\EHG�K/oH£cKiA"Z�oH|�=2G\?UZB¸�A*l

K*<Q¾���|�o��i¾F¾ ��|�oV�H�i� �p|�a

¾H� ½ h[e4EHS�ZB¾/¾ ³ ��¾C� ³ �MK�A/?U^�e&K�egD/G�^�ujLNDF=2SY=2XHq&K�Z\`(^[S�A�S@I�DF`�DFS� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ¾"T:� ³

¹ a~��Z�`(^(S;A�S@I�D/`HDFS�LNDF=2S@?6A"Z4AFLVD/E]ZC�*ºF� ��| 5�A"Zn�CA�Z�e&D/?�_H`HK�G�K�_HG\K�?\?�EHG�K&D/XHKCAF?\?UE�egKi?\<�ab>`�KCI�DFX(d/K�GJ?U=2DFXP8D/G�e4EHS2A4P8G\DFe�|VA�`HG\K�X�`HK�=YZ>Z�DQv�K�S@?�=YE�?>=@?

� � $��� , ³ �½ � ¶ �

b>`HK-LNDF=2S2=YXHq&_NDF=2X[ZcDFXQZ�`HK4v�K�S2?�=YEV?~?�I�A�S2K�=@?�uA[<cº ¼ � ³ ��vRa LV< ³ � �ivRa I�<>¾��ivRa W�<���¾/¾ ��vRa Ki<��"º�� ��vRa

¾H� ½ h[e4EHS�ZB¾/¾ ³/½ ¾ ³&³�³ `�AFG\WQe�A"Z�`�uj`H=Yq/`HK�G�y*S2D"l�K�G>b�P,A�`HG\K�Xmb~I�K�S2?�=YEV?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ TJ�

º(a~|�DFGgZ�`HKm?\A�e&KQ_�`[^]?�=2I�A�S�Z�K�eg_NK�GJA�G�Z�E�G�KAx|VA�`HG\K�XH`�K�=YZgX(EHe&K�G\=@I�A�S>G\K�A/W]=YX�q�=@? Z\`�A�X±Av�K�S2?�=YEV?�X[E�egK�G�=@I�AFS(G�KiAFW]=2XHq�a ������ � ¿~KiI�A�S2S(Z�`�K�G\K>AFG�K>XHK�q/A�Z�=2dFK�Z�K�e&_NK�GJA"Z\EHG�Ki?�P8DFGjLND�Z�`gZ\`HK�?�K~?�I�A�S2K�?�a

A[<�A�S2l>A*^(?&`�=Yq/`HK�G LV<CAFSYl>A*^]?&SYD"l�K�G I�<&`H=2qF`�K�GCD/GCSYD"l�K�GQW]K�_NK�X�WH=YXHq�DFXwZ�`�K�_H`(^]?U=@I�AFSZ\K�e&_NK�GJA"Z�E�G�K/o WV<�LVDFZ�`m`H=2qF`HK�GcA�X�WQSYD"l�K�G K*<�XHK�=YZ�`�K�Gc`H=2qF`�K�G~DFG>S2D"l�K�G

¾H� ½ h[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj?:ZJA"Z\K-d*AFG�=@A�L�SYK¼ a �\¸�K�Zi· ?�_HS@A*^ �]1J� D+�"����# 1 |HD/G��(�i¾F¾�oMZ�`HK±A�X�?�l�K�G�=2?�u�� Z�`�K�G\egD]W]^(X�AFe&=2I�h[E�AFX[Z�=YZ:^�P8D/GxA{?\A�e&_HS2KDFP�e�A"Z\K�G\=2AFS�58l~`H=@IJ`�=2?{=2X Z�`HK�G�e&D]W]^(X�AFeg=@I�K�h[EH=2SY=2LHG\=YE�e�<tZ\`�A"Z�=@?{K�X/Z\=YG\K�S2^�A P8EHX�I�Z�=2DFX�D�P�Z�`�KZ\`HK�G\e&D(WH^[XVA�e&=2IM?UZ\A�Z�K �{XHDFZ~AgP8E�X�I$Z\=YD/XDFP�_�A/?:Z~`H=@?UZ�DFG\^ �wX�DFG�P8E]Z�E�G�K-`H=@?UZ�DFG\^�P8D/G>Z�`�A�Z>e�A�ZUZ�K�G�a�b>`�KZ\`HK�G\e&D(WH^[XVA�e&=2Ig?UZ\A"Z\KsP8D/G-AC�H�]KiW�e�AF?\?BDFP�e�A"Z\K�G\=2AFS�=@?MI�D/eg_�SYK�Z�K�S2^�W]K�Z�K�G\e&=YX�K�WxL[^�?�_NK�I�=YP8^(=YX�qAFX[^Z:l�D�?UE�IJ`mh[E�A�X[Z\=�Z\=YKi?�ujK/a qVaYo(Z\K�e&_VK�G\A�Z�EHG\K-A�X�W_HG\K�?\?�EHG�K�DFG>Z\K�e&_NK�GJA"Z�E�G�K-A�XVWnd/DFS2EHe&KFa �A[<C»{`VA"Zc=@?~A�?:ZJA"Z�KMd"A�G\=@A�LHS2KMDFG�P8EHX�I�Z�=2DFX�D�P�?:ZJA"Z\KFo��BSYK����LN<n»{`VA"Zc=@?�Z�K�e&_NK�GJA"Z\EHG�K/o��cS2K�� �Ii<n»{`VA"Zc=@?>_HG�Ki?�?�EHG\KFoH�BSYK����WV<n»{`VA"Zc=@?~I�A�S2DFG\=@I�oH�cS2K�� �K*<n»{`VA"Zc=@?>XHDC?UEVIJ`nZ\`H=YX�q�o��BSYK����

¾H� ½ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&���MK�A/?U^&Z\`H=2XHO(=YXHqVu�S2=YXHKiA�G>K��]_�AFX�?�=YD/XQ=2X��EH=@WH?� ª�¬"¨ �V«������V¬ ��­�� b>`H=2?Bh/E�K�?UZ�=2DFX=2?�Z\D[D�l�DFGJW]^/a

½ a>´jD/SYEHe&K~K��(_VA�X�?�=YD/X4I�D[K��CI�=2K�X[Z\?jAFG�K�E�?�E�A�S2SY^sqF=2dFK�XsP8DFGjS2=2h[EH=@WH?~5,l~`H=2IJ`gZ\DFqFK�Z�`HK�G�l~=�Z\`gq[AF?�K�?�I�D/X�?UZ�=YZ�E]Z\K��E�=2WH?J<;=YX�?UZ�KiAFW�DFP�SY=2XHKiA�G;K��]_�A�X�?�=2DFXCI�D(K���I�=YK�X[Z\?�a�¸�=YX�K�A�G�K��]_�AFX�?U=2DFXQI�D(K��CI�=2K�X[ZJ?B5,AFS�Z\`HDFE�qF`�Z\`HK�^�I�AFXLNK6?U_NK�I�=��VK�W�<>AFG�X�· Z~dFK�G�^Ce&KiA�XH=2XHq�P8E�S�Z�`HK�DFG\K�Z�=@I�AFSYS2^CD/G~_HG\A/I$Z\=2I�A�S2SY^/a�b>`�=2?>=@?~LNK�I�AFE�?�KFuA[<��VEH=2W�?x5�?U=2e&_HSYKx��EH=@WH?A"ZSYKiAF?UZJ< ¦&� ��� � l~=YZ�`�?UZ\AFX�W{Z\`HK�Z\K�X�WHK�X�I�^±DFPsA�X(^{A�_H_�SY=2K�WwP8D/G\I�KZ\D W]K�P8D/G�e Z�`HK�e =2X A l�A*^ Z\`�A"Z�S2K�A*d/K�?�dFD/SYE�egKwEHXVIJ`�A�XHq/K�Wpa b>`(E�?�oC=YP�A��VEH=2W�K��]_�A�X�W�?Z\`HK�G\e�A�S2SY^/oV=YZ�· ?B?�`�AF_VK4l~=YS2S�E�?�E�AFSYS2^IJ`VA�XHq/K6EHXHS2K�?\?�oVP8DFGRK��HA�e&_HS2KFo�Z�`HKs��EH=@W�I�D/X[Z\A�=2XHK�GB?�I�A�S2K�?BEH_� ��� � � ��� ¦&� ��� � l~=YZ�`CZ�`HK�?�AFegKBdFDFS2EHe&KBK��]_�A�X�?�=2DFX�I�D(K��CI�=YK�X/Z>AF?�Z�`HKRl�A�Z�K�Gia�b>`HK�G\K�P8D/G�K/o_NDF=2X[ZUT�Z�DFT�_NDF=2X[ZRW]=@?:ZJA�X�I�K�?RLVK�Z:l�K�K�X�?�_VKiI�=Y��K�Wm�VEH=2W�K�S2K�e&K�X[ZJ?cl~=2SYS�E�?�E�A�S2SY^ � � � ¦&� � � �

E�XH=�P8D/G�e&S2^FaLN<C�VEH=2W�?-5,?�=Ye&_HS2KB�VEH=2W�?~A"Z>SYKiAF?UZJ< ¦ � � l~=YZ�`�?UZ\AFX�W�Z\`HK�Z�K�X�W]K�XVI�^CDFP�A�X(^�A�_H_�SY=2K�WnP8DFGJI�KBZ�D&W]K�P8D/G�e

Z\`HK�e =2XCA-l�A*^6Z�`�A�Z;SYKiA*dFKi?jdFD/SYEHe&K~EHXVIJ`�A�XHq/K�Wpa�b>`(E�?�oF=YPpA-��EH=@W&K��]_�A�XVWH?�Z�`�K�G\e&AFSYS2^Fo/=�Zi· ?�?U`VA�_NKl~=2S2SVE�?�E�AFSYS2^�IJ`�A�XHq/KcEHXHS2K�?\?�oFP8D/G�K��]AFe&_HSYK/oFZ\`HKR��EH=@WCI�D/X/ZJA�=2XHK�G�?�I�A�S2K�?;EH_�� � � � � ��� ¦&� � � �l~=YZ�`�Z\`HK�?\A�e&K{dFD/SYE�egK{K��]_�A�X�?�=2DFX�I�D(K��CI�=2K�X[ZtA/?rZ�`�K{l�A�Z�K�Gia b>`�K�G\K�P8DFG\KFon_VD/=YX[ZUT�Z�DFT�_NDF=2X[ZWH=2?UZ\AFX�I�Ki?>LVK�Z:l�K�K�X�?U_NK�I�=��VK�WQ��EH=@WK�S2K�e&K�X[Z\?>l~=2S2S�E�?�E�A�S2SY^ � � � ¦&� � � � EHXH=YP8DFG\e&SY^/a

Ii<C�VEH=2W�?x5�?U=2e&_HSYKx��EH=@WH?A"ZSYKiAF?UZJ< ¦&� ��� � l~=YZ�`�?UZ\AFX�W{Z\`HK�Z\K�X�WHK�X�I�^±DFPsA�X(^{A�_H_�SY=2K�WwP8D/G\I�KZ\D W]K�P8D/G�e Z�`HK�e =2X A l�A*^ Z\`�A"Z�S2K�A*d/K�?�dFD/SYE�egKwEHXVIJ`�A�XHq/K�Wpa b>`(E�?�oC=YP�A��VEH=2W�K��]_�A�X�W�?Z\`HK�G\e�A�S2SY^/o~=�Zi· ?Q?U`VA�_NK�l~=YS2SBEV?UE�AFSYS2^wIJ`�A�XHq/K�EHXHS2K�?\?�o�P8D/GnK��HAFeg_�SYK/o�Z\`HK��VEH=2W{I�DFX[Z\AF=YX�K�Gn?\I�AFSYKi?

Page 99: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ½ b>`HK�G\e&D(WH^[XVA�e&=2I�?>7$u�b�K�e&_VK�G\A�Z�EHG\KFoH£BK�A�Z�oH|�=YGJ?UZB¸�A*l ½[¶

E�_ � ��� � � ��� ¦&� � � � l~=YZ�`�Z\`HK ?\A�e&K�d/DFS2EHe&K�K��]_�A�XV?U=2DFX�I�D(K���I�=YK�X[ZzAF?wZ\`HK l>A"Z\K�Giab>`�K�G\K�P8DFG\KFop_NDF=2X[ZUT�Z�DFT�_NDF=2X[ZMW]=@?UZ\A�XVI�K�?�LNK�Z:l�K�K�X�?�_VKiI�=Y��K�W���EH=@WxK�S2K�e&K�X[Z\?�l~=2SYSjEV?UE�AFSYS2^ � ¦&� � � � EHXH=YP8DFG\egS2^Fa

WV<n^/DFEmI�AFXHXHD�ZcW]GJA*lzAgS2=YX�K-=YXmAg��EH=@WpaK*<C�VEH=2W�?~XHK�d/K�G~K��(_VA�X�WnZ�`HK�G�e�AFSYS2^Fa

¾H� ½ h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu�S2=YXHKiA�G>K��]_�AFX�?�=YD/XQDFP�=2X(d*AFG��¾Ha~b�^(_H=2I�A�SjI�D/e&egD/X�e&K�ZJA�S@?&5,?UZ�K�K�S�o�A�S2EHe&=YX(EHemo�I�D/_H_NK�GiopLHG\A/?�?J<~`VA*dFKgSY=2XHK�AFGRK��]_�A�X�?�=2DFXxI�D(K��CI�=2K�X[Z\?�=2X

Z\`HK�GJA�XHq/K � ��¾�]� ¶ =2X{EHXH=YZ\?nD�P���¾ � !p² � �A�ZQA�LNDFEHZnG�D(D/e Z�K�e&_VK�G\A�Z�EHG\KFa�5 � � � � ���]_�A�X�?�=2DFXI�D[K��CI�=2K�X[Z\?6AFG�KgZ\`HK�e�?�K�S2dFK�?-Z�K�e&_NK�GJA"Z\EHG�K�W]K�_VK�X�W]K�X/Z4=YX�q/K�XHK�G\AFS�o�L�E]Z6Z�`VA"Z6K��(Z\G\AmK.�NKiI$Z6=@?-LVK�^FD/X�WZ\`HKR?\I�D/_VKcDFP�Z�`H=@?�I�S2A/?�?�a <s��S@AF?\?�=@?�e&DFG\KcG\=Yq/=2W&l~=YZ�`nAsI�D(K��CI�=2K�X[Z;DFP � ³ �n�i¾ � !p² � �iaj��?�_NK�I�=@A�SNA�S2SYD"^+ � � ���R58_�G�D/L�A�LHS2^&e&K�A�X�=YXHq4=YX(d"A�G\=@A�LHS2Ki<�e&A/W]KBDFP ¹ µ � =2G\DFXnAFX�W ³/¹ � X�=2IJO/K�S�`�AF?�AsI�D(K��CI�=2K�X[Z>D�P�DFX�SY^¾ � ½ ����¾ � ! ² � � a�»{`�A�ZB=2?~Z�`HKMP8GJAFI�Z�=2DFX�AFSpSY=2XHK�AFG~K��]_�AFX�?U=2DFXmDFP�=2X(d*AFG � 0 �

����� l~`HK�XZ\`HKMZ�K�eg_NK�GJA"Z\EHG\KG\=2?�K�?M� ��vf58DFG-��²6<�������� � ¿~K�e&K�e4LVK�G

� 0 $ 0 � � �

l~`HK�G�K 0 =@?�AFX[^&S2K�XHqFZ�`Q=YXnZ�`HK�e�A"Z�K�G�=@A�S�o � 0 =2?;Z�`HKMIJ`�AFXHqFKR=YXnZ�`�A�Z�S2K�XHqFZ�`�o ��=@?;Z\`HK�SY=2XHK�AFG�K��]_�A�X�?�=2DFXI�D[K��CI�=2K�X[Z�o�AFX�W � � Z�`�K6IJ`�A�XHq/KR=2XZ�K�eg_NK�GJA"Z\EHG\KFa

A[<>¾ � ½ �x�i¾�� ! a LV<>¾ � ½ ����¾�� �"a Ii< ³ �x�i¾�� ��a W�<~� ¶ ����¾ � �"a K*< ½ �x�i¾�� ��a

¾H� ½ h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_H`�A/?UK-IJ`�AFXHqFK�F�Fa~¡REHG\=YXHq&A4_H`�AF?�KMIJ`�A�XHq/KRDFP�Z�`�KMI�DFe&e&DFXQO[=2X�Wpo(Z\`HK�Z�K�eg_NK�GJA"Z\EHG\KRDFP�A4?�EHL�?UZ\AFX�I�K�=2X?�K�SYP T�Kih[EH=YS2=2LHG�=2EHe

5�?UD�A�S2SpZ\`HK-e�A"Z�K�G�=@A�S�`�A/?�Z�`HK6?\A�e&K�Z�K�e&_VK�G\A�Z�EHG\Ki<�=@?�uA[<��/º ³ � � ¶ ²&a LN< ³ � ��|�a I�<jIJ`�AFXHqFKiWgL[^Q��¾ � DFG�e&D/G�K/a W�<�I�DFXV?:ZJA�X[Z�a Ki<j=YX]�VXH=�Z\KFa

¾H� ½ h[e4EHS�ZB¾/¾ ¼ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu;?�_VD/X/ZJA�XHK�DFE�?�`HKiA"Z>��D"l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�i�]a>7!XZ�`�K-e&A/I�G\D/?\I�D/_H=2IBl�D/G�S@Wpo]`HKiA"Zc?�_VD/X/ZJA�XHK�DFE�?�S2^nA�S2l�A*^]?;��D"lc?�P8G\DFemuA[<�`�D�Z�Z�D I�DFS@Wpa LN<xI�DFS@W�Z\Dz`HDFZ�a Ii<x`HD�Z�Z�D�`HD�Z�Z�K�G�a WV<�`�D�Z�Z�D�`HD�Z�Z�K�?UZ�aK*<�DFL,A:KiI$ZJ?~A"ZB¾�²&a

¾H� ½ h[e4EHS�ZB¾/¾ ½ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�h[E�A/?U=@?:ZJA"Z\=2IR_HG\D(I�K�?\?� ³ a~��h[E�A/?U=@?:ZJA"Z\=2IRZ�`�K�G\egD]W]^(X�AFe&=2I�_HG\D]I�K�?\?�=2?cDFXHKM=2Xl~`�=2IJ`QZ�`HK6?�^]?:Z\K�e}=2?~IJ`�AFXHqFKiWQ?�D�u

A[< � � � ¦ � � ��Z�`�A�Z4Z\`HK�G\e&D]W]^(X�A�e&=@I �� � ��� � ��� �'� =2?4d(=YG�Z�EVA�S2SY^re�A�=2X[Z\A�=2XHKiWrZ�`HG\DFE�qF`HD/E]ZZ\`HK-_HG\D]I�K�?\?�a

LN< �� � � � � Z\`�A"Z�Z�`HK�G�e&D]W]^(X�AFeg=@I � � ��� �� � ��� � ��� �'� =@? d(=2GUZ\E�A�S2S2^ e�A�=2X[Z\AF=YXHKiWZ\`HG\DFEHq/`HDFE]Z>Z\`HK-_HG\D(I�K�?\?�a

Ii< �� � � � � Z�`VA"Z�Z�`HK�G�e&D]W]^(X�AFeg=@I � � � � � �����4� =@?�d[=2G�Z�E�AFSYS2^6e�A�=2X[Z\A�=2XHKiW6Z\`HG�D/EHqF`�DFE]Z�Z�`�K_�G�D]I�Ki?�?�a

WV< � � � ¦ � � � Z\`�A"Z�Z�`�K�G\egD]W]^(X�AFe&=2I � � ��� � � � � � �����4� =@?�d(=YG�Z�EVA�S2SY^ e�A�=2X[Z\AF=YXHKiWZ\`HG\DFEHq/`HDFE]Z>Z\`HK-_HG\D(I�K�?\?�a

K*< �� � � � ��Z\`�A"Z;Z�`HK�G�e&D]W]^(X�A�e&=@I �� � ��� � ��� �'� I�A�X�XHD�Z;LNKBG\K�A/IJ`HK�WgL(^4Z�`HK ����D�PpZ�`�K_�G�D]I�Ki?�?�a

¾H� ½ h[e4EHS�ZB¾���¾/¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u~�i?:Z~S@A*l�D�P�Z�`HK�G�e&D]W]^(X�AFeg=@I�?��µ�a~b>`HK�?UZ\AFX�WHA�GJW�P8D/G�e P8DFGMZ�`�K�i?:Z-S@A*lfDFP;Z�`�K�G\egD]W]^(X�AFe&=2I�?g5,_HG\=YD/GRZ\Dm=YX[Z�G\D]W]E�I�=YXHqmK�X/Z\G�D/_(^�A�X(^(l�A*^H<

P8D/Gch/EVAF?�=2?UZ\A�Z�=@IR_�G�D]I�Ki?�?�K�?�=@?A[< � $ ��� � � � ��a LV< � $ ��� , � � �Ca I�< � $ , ��� � � � ��a WV<� $ ��� � � � ��a Ki< � $ , ���&, � � ��a

Page 100: Introductory Physics Problems David J. Jeffery Department of

½F¹ v�`�AF_]Z�a~� ½ b>`HK�G�e&D]W]^(X�A�e&=@I�?>7$u�b�K�e&_NK�GJA"Z\EHG�K/oH£cKiA"Z�oH|�=2G\?UZB¸�A*l

¾H� ½ h[e4EHS�ZB¾��F�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�?�_VKiI�=Y�VI�`HK�A�Z� ¶ ac¤(_NK�I�=��NIM`HK�A�ZcD�P�Age�A"Z\K�G\=2AFSp=2?c=�ZJ?�u

A[<CGJA"Z\K�D�PcIJ`�AFXHqFK�DFP>`�K�A"Z4K�XHK�G�q/^xI�D/X[Z�K�X[Zn5,E�?UEVA�S2SY^rI�AFSYS2K�Wr=2X[Z�K�G\X�AFS�K�XHK�G�q/^H<�_VK�GsEHXH=YZ4e�A/?�?-_NK�GE�XH=�Z~Z\K�e&_NK�GJA"Z�E�G�K/a

LN<nGJA"Z\KsDFP�IJ`�A�X�qFKsDFP�Z�K�e&_VK�G\A�Z�EHG\Ks_NK�GMEHXH=YZMe&A/?�?�_NK�G�EHXH=YZ-`HK�A�Z�K�XHK�G\qF^mI�D/X/Z\K�X[Z�58E�?�E�A�S2S2^mI�A�S2SYKiW=2X[Z�K�G�X�AFSpK�XHK�G�q/^H<$a

Ii<CZ\K�e&_NK�G�Z�EHG\K-=YX�Ag_HG\K�?\?UE�G�K�D�P>�-A"Z�e&D[?U_H`�K�G\KFaWV<CZ\K�e&_NK�G�Z�EHG\K6A"Z~=YZ\?~e&K�SYZ�=2XHq�_NDF=2X[Z�aK*<n`�K�A"ZcK�XHK�G\qF^CI�DFX[Z�K�X[Z-5,E�?�E�A�S2SY^I�AFSYS2K�WQ=YX[Z\K�G\X�A�SpK�XHK�G\qF^H<�A"Z~=YZ\?~e&K�SYZ�=2XHq�_NDF=2X[Z�a

¾H� ½ h[e4EHS�ZB¾��i�F¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=2WHK�A�S�Z�`HK�G�e�A�Sp_�G�D]I�Ki?�?�K�?� ¹ a>7:?�D�Z\`HK�G\e�A�S�o�AFW]=@A�L�A�Z�=@I�ojK�XHqF=2XHKmI�^]I�S2KFo�AFX�W�P8G\K�KK��]_�AFX�?U=2DFX�_�G�D]I�Ki?�?�K�?�u�LHG\=YK���^�A�XVW�=YX±DFGJW]K�G6Z�`�K�?�K

_HG\D]I�Ki?�?�K�?>I�AFXQLNK6IJ`�AFG\A/I$Z�K�G�=2��KiWCL(^�Z\`HK-_H`HGJAF?�K�?�uA[<�5,=@<�I�DFX�?UZ\AFX/Z�Z�K�e&_VK�G\A�Z�EHG\KFoH5,=Y= <�XHDM`HK�A�Z���D"lc?�58X�D�K�X[Z�G\DF_(^-IJ`�A�XHq/Ki<�oH58=2=Y= <���X�A�S]?UZ\A�Z�K>=2?�Z\`HK>=YXH=YZ�=@A�S?UZ\A�Z�KBAFX�W � `�K�A"Z;AFX�W&l�DFG\O-��D"l-o/AFX�W�58=2dH<�XHD6`�K�A"Zj�VD"l±AFX�W&XHD-l�DFG\O4A�XVW4X�D�Z�h[E�A/?U=@?:ZJA"Z\=2IFa

LN<x5,=@<�I�DFX�?UZ\AFX[Z�Z\K�e&_VK�G\A�Z�EHG\KFoV58=2=@<���XVA�SH?UZ\A"Z\K>=2?�Z\`HK>=YXH=YZ�=@A�SV?:ZJA"Z�K>A�XVW � � � � z`HKiA"Z�A�X�W4l�DFG\O�VD"l-o�58=2=Y= <�XHD`HK�A�Z��VD"lc?45,XHDmK�X[Z�G\DF_(^�IJ`�A�X�qFKi<�o�A�X�W±58=2dH<RXHDQ`�K�A"ZM��D"l A�X�W�XHDQl�DFG\O�A�XVW�XHDFZh[E�A/?U=@?UZ\A"Z\=2IFa

Ii<x5,=@<�I�D/X�?UZ\A�X[Z�Z\K�e&_NK�GJA"Z�E�G�K/oN5,=Y= <�X�Ds`HKiA"Z;�VD"lwAFX�W�XHD4l�D/G�O&A�XVW�XHD�Z>h[E�AF?�=2?UZ\A�Z�=@I�oN58=2=Y= <j�VX�A�S�?:ZJA"Z\K=@?�Z\`HK~=YX�=�Z\=2AFS�?:ZJA"Z\K>AFX�W � �� � � �`HK�A�Z;A�X�W4l�DFG\OM��D"l-o/AFX�WQ5,=YdH<�X�D�`�K�A"Zj�VD"lc?~58XHDMK�X[Z\G�D/_[^IJ`VA�XHq/Ki<$a

WV<x5,=@<sI�D/X�?:ZJA�X[Zs_HG\K�?\?�EHG�K/o�5,=Y= <6I�DFX�?UZ\AFX[Z6dFDFS2EHe&KFo~5,=Y=2=@<sI�D/X�?:ZJA�X[ZsK�X/Z\G�D/_(^Fo�A�X�W{5,=YdH<6I�DFX�?UZ\AFX[Z-P8G�K�KK�XHK�G\qF^/a

K*<x5,=@<�G\K�?�DFXVA�X�I�KBP8G\K�h[EHK�X�I�^/o�58=2=@<��VG\?UZ~`�A�G\e&DFXH=@I�o�5,=Y=2=@<>¡RDF_�_HSYK�GcK ��K�I�Z�o�AFX�W�58=2d]<>¯�A�XH=YP8K�?UZB¡BKi?:Z\=YX(^/a

¾H� ½ h[e4EHS�ZB¾�� ³ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�Z�`HG\K�K-e&D]W]Ki?>D�P�`HK�A�Z�Z\G\AFX�?UP8K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�*º(a~b>`HKMZ\`HG\K�K-I�D/ege&D/XQ`HKiA"Z~Z\G\AFX�?:P8K�G>_HG�D]I�K�?\?UKi?�AFG�K/uA[<nI�DFX�WHE�I$Z\=YD/X�o]=YX(d/K�I$Z\=YD/X�oHA�XVWQGJAFWH=2A�Z�=2dFKRZ�GJA�X�?UP8K�GiaLN<n=2X�W]EVI$Z�=2DFX�o�I�D/X[d/K�I�Z�=2DFX�o]A�XVWQGJAFWH=2A�Z�=2dFK�K�h[EH=2SY=2LHG\=YEHemaIi<QI�DFX�WHE�I$Z\=YD/X�oHI�D/X[d/K�I�Z�=2DFX�oHAFX�WnGJAFWH=2A�Z�=2dFKRZ�GJA�X�?UP8K�GiaWV<QI�DFX�WHE�I$Z\=YD/X�o]=YX(d/K�I$Z\=YD/X�oHA�XVWQGJAFWH=2A�Z�=2dFK�K�h[EH=2SY=2LHG\=YEHemaK*<n=2X[Z�G\D]W]E�I$Z\=YD/X�o]=2X�?UE�G�G\K�I�Z�=2DFX�oHAFX�WnGJAFWH=2A�Z�=2dFKM`H=2LVK�G�X�A�Z�=2DFX�a

¾H� ½ h[e4EHS�ZB¾���µ[¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�SYZ�K�G�X�A�Z�K ³ e&D(WHK�?~DFP�`HKiA"Z~Z�GJA�XV?:P8K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ¼ a~b>`HKMZ\`HG\K�K-I�D/ege&D/XHSY^nO[X�D"l~XQe&K�AFX�?>D�P�`HKiA"Z>Z�GJA�X]P8K�GcA�G\KFuA[<nI�DFX�WHE�I$Z\=YD/X�oHI�D/X[d/K�I�Z�=2DFX�oHAFX�Wn`(^(_NK�G\dFK�X[Z\=YS@A"Z\=YD/X�aLN<QI�DFX�WHE�I$Z\=YD/X�oHI�D/X/Z\G�=YZ�=2DFX�oHA�X�WmI�D/X[Z�K�e&_HS@A"Z\=YD/X�aIi<QI�DFX�WHE�I$Z\=YD/X�o]XHK�EHZ�G\=YXHD[?�oVA�X�WQqFGJA*d(=�ZJA"Z�=2DFXVA�SNG\A/W]=2A�Z�=2DFX�aWV<QI�G�K�XHK�S@A"Z\=YD/X�o]X�A*d(=2q/A"Z\=YD/X�o]A�X�WQesEHZ\A"Z\=YD/X�aK*<QI�DFX�WHE�I$Z\=YD/X�oHI�D/X[d/K�I�Z�=2DFX�oHAFX�WnGJAFWH=2A�Z�=2dFKRZ�GJA�X�?UP8K�Gia

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾H� ½ h/P8EHS2S�¾/¾H��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�Z�`HK�G�e�A�SpS2=2XHK�AFG~K��]_�A�XV?U=2DFX�o]=2X(d"A�G� ª�¬"¨ �V«������V¬ ��­�� ?UK�K�»�9�o�_�aHµFµ]ºMP8D/G>Z�`HK-K��]_�A�X�?�=2DFXmI�D(K��CI�=2K�X[ZJ?

Page 101: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a~� ½ b>`HK�G\e&D(WH^[XVA�e&=2I�?>7$u�b�K�e&_VK�G\A�Z�EHG\KFoH£BK�A�Z�oH|�=YGJ?UZB¸�A*l ½ º

�Fa ��D/E�A�G\K6Z\G�^(=2XHqCZ\DC�HZ-A�X�=2X(d"A�GBLNDFSYZMD�P;W]=@A�e&K�Z\K�Gg� � ¾F¾���I�e =YX[Z\DQAn?UZ�K�K�S�X(E]Z�DFP;W]=@A�e&K�Z\K�Gg� � ¾F¾F¾;I�emab>`HKCZ�K�e&_NK�GJA"Z\EHG�Kn=2?s�F¾ �ivRa�b>`HKCS2=2XHK�AFGsK��]_�AFX�?�=YD/X�I�D[K��CI�=2K�X[Z\?sD�P~=YX(d"A�G4A�X�W�?UZ�K�K�S;A�Z4A�LNDFE]Z4G�D(DFeZ\K�e&_VK�G\A�Z�EHG\KMA�G\K � � � �� � $�¾ � ½ ����¾ � !�A�X�W � � � � � � $ �*�����i¾ � !"o]G�Ki?U_NK�I�Z�=2dFK�SY^/a�b�Dgl~`�A"Z�Z�K�eg_NK�GJA"Z\EHG\Ke4E�?:Z>GJA�=@?UKRZ�`HK�DFL3A:K�I$ZJ?>?UD4Z�`�A�Z�Z\`HKMLVD/S�Z>�HZJ?�=YXQZ�`HKMX(E]Z �m»{`(^CI�DFE�S2WCZ�`H=@?~I�AFS2I�EHS2A�Z�=2DFXCLNK-As_ND(DFG\=2?�`_HG\K�WH=2I�Z�=2DFX �

¾H� ½ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK�h[EH=2S2=YLHGJA"Z\=YD/XI�A�S@I�EHS@A"Z\=YD/X�]a ��D/E�`VA*dFKgDFL,A:KiI$Z\?MDFP�I�DF_H_NK�GC5 � � $�¾ � ³ ¾�O[q�o �

� � � $���¾��ivRo�AFX�W * � $ ³F¼F¹ e&O]?-EHXH=YZ\?J<$o�A�S2EHe&=YX(EHe5 � � $�¾ � ¹ ¾jO(qHo �

� � � $���¾F¾���vRo�AFX�W * � $ ½ ¾F¾e&O]?MEHXH=YZ\?J<$o�A�X�W�?�=YS2dFK�GC5 � � $ �/o �� � � $ ¶ ¾���vRo�AFX�W

* � $�� ³F¹ e&O(?>E�XH=�ZJ?\<�a�b>`HK ���(· ?~A�G\KMe&A/?�?�K�?�o(Z�`�K�� ��[· ?cA�G\KM=YX�=�Z\=2AFSpZ�K�eg_NK�GJA"Z\EHG\K�?�oHA�X�WQZ�`�K *��(· ?cA�G\K

?�_VKiI�=Y�VIg`HK�A�Z\?�a ��DFE�_HE]Z-Z�`�K�DFL,A:KiI$Z\?M=2XxZ�`HK�G�e�A�S�I�DFX[Z\A/I$Z-l~=YZ�`�K�AFIJ`�D�Z\`HK�Gio�LHEHZ6=YX�=2?�DFS@A"Z\=YD/X�P8G\DFeZ\`HK-G�Ki?:Z~DFP�Z�`�K-l�D/G�S@Wpa�b>`HK-K�h[EH=2SY=2LHG\=YE�e Z�K�eg_NK�GJA"Z\EHG\K�=@?�P8DFE�X�WQZ�D&LVK �

� $ ¼ ¾��"aj»{`�A�Zc=2?�Z\`HK-e�AF?\?DFP�?�=YS2dFK�G�

¾H� ½ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujl�DFG\OCW]DFXHK-D/XA&?UZ�GJA�=2qF`[Z>SY=2XHK69�´ WH=2AFqFGJA�e³ a>7!X�ACh[E�A/?U=@?UZ\A"Z\=2IM_�G�D]I�Ki?�?�oH^/DFEmZ\AFOFK6AC?�^]?:Z\K�e}P8G�D/e}AC?UZ\A�Z�Ks?�_NK�I�=Y��KiWmL[^QZ�`�K-P8EHX�I�Z�=2DFX�DFPj?UZ\A�Z�K6_VA�=2G5 � � � � <�Z\DnAC?UZ\A"Z\K6?U_NK�I�=��VK�W�L(^CZ\`HKs_VA�=2Gs5 � � � � <$a~b>`HK6_�A�Z�`�D/X�A �HT���W]=@A�qFGJA�e}=2?BAC?:Z\G\AF=Yq/`[ZcSY=2XHKFa°RL]ZJA�=2XsA�X4K��]_HS2=2I�=�Z�P8DFG\esEHS@As5,=�a KFa2o"XHDFZ A:E�?UZjA�X6=2X[Z�K�q/G\AFS/K��]_HG�Ki?�?�=2DFXV<NP8D/G�Z\`HK�l�D/G�OMW]DFX�K;L(^�Z�`HK>?U^]?UZ�K�ea������ � ¡RGJA*lzA&W]=@A�qFGJA�ema

¾H� ½ h/P8EHS2S�¾/¾�µ/¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�?UD/S2AFG�S2EHe&=2XHD/?�=�Z:^/o�?�DFS@A�G~I�D/X�?:ZJA�X[Zµ�a~b>`HK&Z\K�e&_NK�GJA"Z�E�G�K�DFP�Z\`HKn¤(EHX�· ?6_�`HD�Z\D/?�_H`HK�G\K�5 Z\`HKCS@A*^FK�G�P8G\DFe l~`H=2IJ`�I�DFe&K�?Me&D/?UZ6D�P�Z�`�KCSY=2qF`[Z-l�K?�K�K*<�=2?~AFLVD/E]Z ¶�¼ ¾F¾�²�AFX�Wn`VAF?~AgG\A/W]=2E�?>D�PjA�LNDFE]Z ¹ � ½/¹ ����¾ �emaA[<n�R?�?�EHe&=2XHqBZ\`HK>_H`HDFZ�D/?�_H`HK�G�K�GJAFW]=@A"Z\K�?�SY=2OFK>ABL�S2A/IJO[LND]W]^C58l~`�=2IJ`g=2?�X�· Z�?UD�L�AFW4A�X&A�_H_�G�D*�]=2e&A�Z�=2DFXV<�ol~`VA"Z�=2?4Z\`HKZ�D�ZJA�S>S2EHe&=YXHD[?U=YZ:^�D�PRZ�`HKm?�EHX�5,=�a KFa2o;=YZ�· ?gZ�DFZ\AFS�_ND"l�K�G$<�� 5�b>`HK�¤[Z�K�P,A�X]T ��DFSYZ���e&AFXHXI�DFX�?UZ\AFX[Z�� $ ¶�� ¹ º��x�i¾�� =2Xme&O(?>E�XH=�ZJ?�a <

LN<n»{`VA"Zx=@?�Z\`HK�K�XHK�G\qF^z��E]� 5,=�a KFa2os_ND"l�K�G�_NK�Gr?�h[E�AFG�K�e&K�Z\K�G$<�A�Z�Z�`HK±W]=@?:ZJA�X�I�K�D�P&Z\`HKt��A�G�Z�`5U� � µ ½/¹ �w�i¾ � � e�< ��b>`H=@?6�VE]��=2?gDFP Z�K�X±I�AFSYS2K�WrZ\`HK�¤(DFS@A�G�v�DFX�?UZ\AFX/Z&A�X�W�=�Z&LNK�ZUZ\K�G&`�A/W�LNKnP8D/GS2=YP8K-DFXm�;A�G�Z�`�a ������ � ¿~K�e&K�esLNK�G>Z�`�K-=YX(dFK�G\?�K�T!?\h/EVA�G\KBS@A*l-a

Ii<n»{`VA"Z4=@?sZ�D�ZJA�S�_VD"l�K�G4G�KiI�K�=2dFKiW�L[^�Z\`HKQ��A�G�Z�`rP8G\DFe Z�`HKm¤(EHX � 5,b>`HK�;AFGUZ\`�· ?se&K�A�X�GJAFWH=YE�?s=2?¹/³ º ¼ O(ea <

WV<Qb>`�Kg��A�G�Z�`�I�DFS2SYKiI$Z\?�?�EHXHS2=Yq/`/ZMA"ZMDFXHKsZ�=2e&K4D/XHSY^mD/X�DFX�K4?�=2W]K&A�XVW�LVKiI�AFE�?UKgD�PjZ\`HK&I�EHG\d"A"Z�E�G�K4D�PZ\`HKs��A�G�Z�`�· ?c?�EHGUP,A/I�KMZ\`HKs_ND"l�K�GcA�L�?�DFG\LNK�Wd"A�G\=YKi?~l~=�Z\`�Z�`�K-Z�=2S�Z�D�P�Z�`�Ks?UE�GUP,A/I�KMZ�DCZ�`HK4=YX�I�DFe&=2XHqLNK�AFe�?�a�£cD"l�K�d/K�Gio"G�DFZ\A"Z\=YD/X4AFX�W&A�=2G�I�=YGJI�E�S2A�Z�=2DFXgdFK�G\^6I�G\E�W]K�SY^gI�AFX4LNKcAF?\?UE�egKiW6Z\DMK�dFK�XHS2^s?U_�G�KiAFWZ\`HKg_VD"l�K�GRD"dFK�GcZ�`HKgl~`HDFS2Ks��A�G�Z�`�a-°RL[d(=2DFE�?�S2^nZ\`H=2?R=@?BXHDFZ�K��HAFI$Z\SY^QZ�G\EHK/u>Z�`HK4P8EHG�Z�`HK�GBP8G\DFe Z�`�KKih[E�A"Z\DFGjZ\`HKcS2K�?\?�_ND"l�K�Gj=2?;G�KiI�K�=2dFKiWgDFX�A*dFK�G\AFqFKFa�¸�K�Zi· ?�AF?\?UE�egK>Z\`HDFE�qF`&Z�`VA"Z�Z\`HKc_ND"l�K�G�G�KiI�=2K�d/K�WP8G\DFe}Z�`�K4¤(EHX�=@?B?�_HG\K�AFWEHX�=�P8D/G�e&S2^QD"d/K�G>Z�`�K4�;AFGUZ\`�· ?~?UEHG�P,AFI�KFa~ cD"lzZ�`�Ks�;AFGUZ\`=@?ce&D/G�K-D/GBS2K�?\?=2XxAFX�K�XHK�G\qF^�?UZ�K�A/W]^�?:ZJA"Z\KFa-7kZ-G�K�T�GJAFWH=2A�Z�K�?BL�AFIJOZ\D?�_�AFI�Ks=2X�Z\`HK4=2X]P8GJA�G\K�W�d[=2G�Z�E�AFSYS2^�A�S2S�DFP�Z�`�KK�XHK�G\qF^m=YZ�q/K�ZJ?BP8G\DFe Z\`HKC¤(EHX�l~`�=2IJ`xegD[?:Z\SY^�I�DFe&K�?�=2X�Z�`�K4D/_]Z�=@I�AFS�a6�R?�?�EHe&=YX�qCZ�`�K&��A�G�Z�`�=@?�A?�_H`HK�G�=@I�AFSVL�S2A/IJO/TkLND(WH^gAFL�?UD/G�LNK�G�y*GJAFWH=2A�Z�DFGj=2XQAFXCK��HA/I$Z�K�XHK�G\qF^[T!?:Z\K�A/W]^g?UZ\A�Z�K/o[l~`VA"Z>=2?�=�ZJ?>?UEHG�P,AFI�KZ\K�e&_NK�GJA"Z�E�G�K ��v�A�XQZ�`HK6��A�G�Z�`LVK-K��HAFI$Z\SY^QA4L�S2A/IJO/TkLND(WH^CA�L�?�DFG\LVK�G$y"G\A/W]=@A"Z�D/G�

Page 102: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n_o � Da145 =!?+,F6F>a&A= *IHJE�Q7Q�� � *IH^5<? EGH^?A9f*IH �*[1 �

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/�F¾4h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uje&DFS2K�?�Fa ��D/E�`�A*dFK ³ �&q/G\AFe&?BD�P�e&DFS2K�I�EHS@A�GBD*�]^(qFK�X�o�° � 58KiAFIJ`�e&DFS2K�I�EHSYK4`�A*d(=YX�qnI�D/X/ZJA�=2XH=2XHq�� ¹ _HG�DFZ�D/X�?BAFX�W� ¹ X�K�E]Z\G�D/X�?~A�SYZ�D/q�Z�`�K�G$<$aj£cD"lze&AFX(^Ce&DFS2K�?>D�P�° � W]D&^FD/EQ`�A*d/K��

A[< ³ �se&DFS2K�?�a LV<~�4e&DFS2K�?�a I�<�� ¹ e&DFS2K�?�a W�<��-e&DFS2KFa Ki<> BDFXHK/a

¾/�F¾4h[e4EHS�ZB¾/¾/�F¾F¾C� ³ µ&K�A/?U^�e�A�Z�`�u�=@W]KiA�Spq/A/?�S2A*l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=p=YP�egD/SYKi?~A�G\KM=YX[Z�G\D]W]E�I�K�W

�]a~b>`HK-=@W]KiA�Spq/A/?�S2A*lz=2?~D/LVK�^FKiWnL(^Ce&D/?UZcq/A/?UKi?�Z�D�?UD/e&KMWHK�qFG\K�K/u

��� $ � � �

l~`HK�G�K �}=2?M_�G�Ki?�?�EHG\KFo �}=@?-dFD/SYEHe&K/o ��=@?MZ�`�K�X[E�esLNK�G-D�P�e&DFS2K�?�o � =@?MZ�`�K�q/AF?MI�DFX�?UZ\AFX/Zio�A�XVW � =2?Z\K�e&_VK�G\A�Z�EHG\KsD/XmZ�`HKg²MK�S2d(=YX�?\I�AFSYK/aB¤]A*^ml�KsOFK�K�_�?UD/e&Ksq/A/?cA"ZMI�D/X�?:ZJA�X[ZcZ\K�e&_VK�G\A�Z�EHG\KQ5,=2?�D�Z\`HK�G\e�A�S <AFX�WQI�DFX�?UZ\AFX[Z>X(EHe4LVK�GcD�P�e&DFS2K�?-58=@?�D�T!?UD/egK�Z�`H=2XHq(<�AFX�WW]DFEHL�SYK-=YZ\?~d/DFS2EHe&KFajb>`HK-_HG\K�?\?�EHG�K/u

A[<>W]DFE�LHSYKi?�a LV<�q/D[Ki?�Z�D&��K�G�DVa Ii<�=YXVI�G\K�AF?�K�?�a W�<�`�A�S2dFKi?�a Ki<�q/D(K�?�Z�D�=2X]��XH=YZ:^Fa

¾/�F¾4h[e4EHS�ZB¾/¾/�H��¾4� ³C¶ e&D]W]K�GJA"Z\K�e�A�Z�`�uj=@W]K�AFSpq/A/?~A�X�WQ_HG\K�?\?UEHG\K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ T ¹

³ a~b>`HK-=@W]KiA�Spq/A/?�S2A*lzDFLNK�^FKiWnL(^A�S2S�?UE]�CI�=YK�X/Z\SY^W]=2SYE]Z\K-q/A/?UKi?�=@?

��� $�� � �

l~`HK�G�K � =2?;_HG�Ki?�?�EHG\KFo � =2?�dFD/SYE�egK/o ��=@?jZ\`HKBX(EHe4LVK�G�DFPpegD/SYKiI�EHS2K�?�o �g=2?;Z�`HK ��DFSYZ���e�AFXHX�· ?;I�D/X�?UZ\A�X[ZioAFX�W � =@?6Z\K�e&_NK�GJA"Z�E�G�KQDFX�Z\`HK²MK�SYd(=2X�?\I�A�S2KFa�¤]A*^�l�KQOFK�K�_�?�DFe&Knq[AF?4A"Z�I�DFXV?:ZJA�X[ZsdFD/SYE�egK/a�b>`�K_HG\K�?\?�EHG�K�=@?>Z�`HK�X u

A[< ��¾F¾;9jAHa LV<�=2X]��X�=�Z\KFa I�<z_HG\DF_NDFG�Z�=2DFXVA�SxZ�D�e&DFS2K�I�E�SYK ?�=Y��KFa W�<z��K�G�DVaK*<�_HG\DF_NDFG�Z�=2DFX�AFSVZ\DgZ�K�e&_NK�GJA"Z\EHG�K/a

¾/�F¾4h[e4EHS�ZB¾/¾/�/��¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujG\K�AFSNq[AF?�K�?>I�D/X�W]K�X�?UK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ��TJ�*º

µ�a~��ZcA�LV?UD/SYE]Z\KR��K�G\D�o(A4Z�G\EHKR=@W]KiA�S�q/A/?�l�DFE�S2Wn`�A*dFKR��K�G\Ds_�G�Ki?�?�EHG\KRD/G���K�G\D4d/DFS2EHe&KRD/G�LND�Z\`�a�b>`H=@?>=2?�XHDFZZ\G�EHKMP8D/GcAgG�KiA�S�q/A/?~?U=2X�I�K-AFX[^nG�KiA�Spq/A/?�l�D/EHS2W l~`HK�XZ�K�e&_NK�GJA"Z\EHG�KMl�K�X[Z~Z�D(D&S2D"l-a

A[<�LVD/=YS LV<�K�d"A�_NDFGJA"Z\K I�<>I�DFX�W]K�X�?�K W�<>W]EH_HS2=@I�A"Z\K Ki<>?�=2qF`

¾/�F¾4h[e4EHS�ZB¾/¾ ³ ¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u;�BdFD/q/AFWHG�DV· ?;X[E�esLNK�G¶ ac¤]A*^4^FD/E�`�A*dFK �{q/G\AFe�?jD�P�?�DFe&KcK�S2K�e&K�X/Z�l~`HD/?�KcK�S2K�e&K�X/ZJA�SNA"Z�D/e&=2I>e�AF?\?�=@? �su�e�A/?�?;=YX�e�AFI�G�D[?�I�DF_H=@IEHX�=�ZJ?c=@? � ���(oHl~`HK�G�K ����$f� � ¹F¹ ¾ ¶ ���i¾ � ���pq�=@?~Z\`HK6A"Z\DFe&=2IMe�A/?�?~E�XH=�Zia�£BD"lze�AFX[^A"Z\DFe�?cW]D�^/DFE`�A*d/K��

A[< ¹ � ¾/������¾�� � DFGc�6e&D/SYKi?�a LV<R� � ¹/¹ ¾ ¶ ����¾ � � �RD/G>�4e&DFS2K�?�a I�< ¹ � ¾/������¾�� � DFG ³ e&DFS2K�?�aWV<�� � ¹F¹ ¾ ¶ ����¾ � � �MDFG-�Me&DFS2KFa K*< ¹ � ¾/� �x�i¾�� � DFGM�-e&DFS2KFa

Page 103: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a;��¾�b>`HK�G\e&D(WH^[XVA�e&=2I�?>7U7$u�¯�=2I�G�D[?�I�DF_H=@IB´R=YK�l ½/½

¾/�F¾4h[e4EHS�ZB¾/¾ ³ ��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�e&DFS2K�?>OFK�^(l�D/G\W¹ a �\¸�K�Zi· ?B_HS@A*^��]1J� D+�"����# 1 |�DFG��(��¾/¾Ho]Z\`HK4AFX�?�l�K�GB=@?�uM��¾�q�D�P�£B|�o�l~`HK�G\K6`(^]W]G\DFqFK�Xm`�AF?RA"Z�D/e&=2I-e�A/?�?s�AFX�WQAFX�WQ��EHD/G�=2XHKM`�AF?~A�Z�D/eg=@I�e�AF?\?M� ½ a �A[<C»{`VA"Zc=@?>`[^]W]G\D]IJ`HS2DFG\=2I�AFI�=2WpoH�BSYK�� �LN<n»{`VA"Zc=@?>DFXHK-e&DFS2KMD�Pj£B|�egD/SYKiI�EHS2K�?�oH�cS2K�� �Ii<n»{`VA"Zc=@?~A�?Ue�A�S2SpLHEHG\G\D"l~=YXHqge�A�e&e�A�Spl~=YZ�`�?�`HD"dFK�S�TkSY=2OFKRP8G\DFX[Z~_�A*lc?�oH�BSYK�� �WV<n»{`VA"Zc=@?>`�A�SYP�A&?�e�A�S2S�LHEHG\G�D"l~=2XHq4e&AFe&e&AFS�l~=YZ�`�?U`�D"dFK�SYTkSY=2OFKBP8G�D/X/Z~_�A*lc?�oH�cS2K�� �K*<n»{`VA"Zc=@?>`�A�SYP�Age&DFS2K-D�P�£B|�egD/SYKiI�EHS2K�?�o��BSYK����

¾/�F¾4h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]K�qFG\K�Ki?�DFP�P8G\K�KiW]DFe}D�P�q[AF?º(a~£BD"l e�AFX[^�W]K�q/G�K�K�?�DFP&P8G�K�K�W]D/e A"ZxG�D(DFe Z�K�e&_VK�G\A�Z�EHG\K�W]D(K�?xAwZ:^(_H=2I�A�S6e&D/SYKiI�EHS2K�`�A*d/KrZ�`�A�Z�=2?e&DFXVA"Z�D/e&=2IFoHW]=2A�Z�D/eg=@I�oHAFX�W_VD/SY^[A"Z\DFe&=2IFo]G�Ki?U_NK�I�Z�=2dFK�SY^��

A[< ³ o ¶ oHA�XVW ¹ a LN< ³ ���]o ¶ ���]o(A�XVW ³ a Ii<c�/o��]o]A�XVW ³ a WV<B�/oH�]o]A�X�Wn=YXVW]K�Z\K�G\eg=2X�A�Z�KFaK*<>¾Ho��HoHA�X�W_NDFS2^Fa

¾/�F¾4h[e4EHS�ZB¾/¾ ¶ ¾F¾4�Q�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�q/A/?�egD/SYKiI�EHS2K6²-�� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�i� ½ TJ�F�

¼ a~��Z�A~qF=2dFK�XMZ�K�e&_NK�GJA"Z\EHG�K/oiZ�`HK�W]=���K�G\K�X[Z�egD/SYKiI�EHS2KjZ:^(_NK�?�D�P�A~e&=Y�(KiW-q/A/?p`�A*d/KjZ�`HK�?�AFe&K aA[<�O[=2XHK�Z�=@I�K�XHK�G\qF^/a LN<�A*d/K�GJA�q/K�O(=YXHK�Z�=@I;K�XHK�G\qF^/a Ii<�e&A/?�?�a W�<�A*dFK�G\AFqFK;?�_VK�K�Wpa K*<P,A�Z�K/a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/�F¾4h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj=@W]K�AFSpq/AF?~AFX�WQl�D/G�O�Fa ��D/E`VA*dFK6º6e&D/SYKi?>D�P�=2W]KiA�Spq[AF?~A"Z ³ ¾F¾�² A�ZcA4_�G�Ki?�?�EHG\K�DFP ¶ ¾Ho ¾F¾F¾;9jAHa

A[<C»{`VA"Zc=@?�Z�`HK-d/DFS2EHe&K��LN<n7kP~^/DFE�I�D/eg_�G�Ki?�?MZ\`HKCd/DFS2EHe&KCh/EVAF?�=2?UZ\A�Z�=@I�A�S2S2^�A�X�Wr=@?�D�Z�`�K�G\e&AFSYS2^�L(^rAP,AFI$Z\DFG6DFP ³ o�`�D"l e4E�IJ`

l�DFG\O�`�A*d/K�^/DFEW]DFXHK6AFX�WQ`HD"l�e4E�IJ`ml�D/G�O�`�A/?�Z�`HK-q[AF?>W]D/XHK��Ii<Q£BD"lzI�A�XQZ�`HK-q[AF?�· ?>=2X[Z�K�G\X�AFSpK�XHK�G�q/^�XHD�ZBIJ`�AFXHqFK �

¾/�F¾4h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�AFW]=@A�L�A�Z�=@I�=2W]KiA�Spq[AF?~?UZ�= �NXHKi?�?�]a~b>`HK}P8DFG\esE�S2A G�K�S2A�Z�=2XHq _HG\K�?\?�EHG�K A�X�W dFDFS2EHe&K}P8DFG�A�X =@W]KiA�Swq/A/? =2X AFX AFW]=@A�LVA"Z�=@I�?UZ\A�Z�K =2?����� $-v�DFX�?UZ\AFX/ZiaA[<C»{`�=2IJ`mq/A/?�=2? �\?:Z\=���K�G �m58=�a K/aYo�G�Ki?U=@?:ZJ?>I�DFe&_HG\K�?\?�=YD/Xne&DFG\Ki<�u�A4e&D/X�A"Z\DFe&=2I�q[AF?�DFGcW]=@A"Z\DFe&=@IRq[AF?�LN<Q|�G�D/e�Age&=2I�G�D[?�I�DF_H=@I�_VD/=YX[Z~D�P�d(=YK�l-o]l~`[^Q=2?�Z\`HK-S2K�?\?~?:Z\=���q[AF?>S2K�?\?~?:Z\=�� �

Page 104: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n p � Da145 =!?+,F6F>a&A= *IHJE�Q7Q7Q � U+1)HJ?T>�, ��& � &T>a, � >2;75<?T9W6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/�H��h[e4EHS�ZB¾/¾F¾ ½ ¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�`HK�A�ZcK�XHq/=YX�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�Fa �\¸�K�Zi· ?M_�S2A*^ �]1J� D+�"����# 1 |HD/G �(��¾/¾Ho�Z\`HKCA�X�?�l�K�GM=2?�u-��W]K�d(=@I�KgZ�`�A�Z6DF_NK�GJA"Z\K�?�=YX�AmI�^]I�SYK/a47kZ6K��[Z\G\A/I$ZJ?`HKiA"Z-P8G\DFe Am`HD�Z6G\K�?�K�G\dFD/=YGMA�X�WrI�DFX(dFK�GUZJ?-?UD/egKgP8GJAFI�Z�=2DFXrD�P�Z�`H=@?-`HKiA"Z6=2X[Z�D�e�AFI�G�D[?�I�DF_H=@Isl�DFG\O�AFX�WG\K"A:KiI$Z\?�Z\`HK-G\K�?UZ>DFP�Z\`HK-`HKiA"Z>Z�DCA&I�D/S2WQG\K�?�K�G\dFDF=2Gia �»{`�A�Zc=2?~A o��BSYK����

A[<�l�D/G�O(=2XHq6�VEH=2W LV<�_H=@?:Z\DFX I�<>I�^[S2=2X�W]K�G W�<�G�K�P8G�=2qFK�G\A�Z�D/G K*<�`HK�A�ZcK�XHq/=YX�K

¾/�H��h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujG\K�d/K�GJ?U=2LHS2KBK�X�qF=2XHK-K��CI�=2K�XVI�^�]a>»{`�A�Z�WHDcZ�`�K;Z:l�DRI�S2A/?�?�=2I�A�S[?:ZJA"Z�K�e&K�X[Z\?�D�P]Z\`HK~�"X�WsS2A*l�DFP]Z�`HK�G�e&D]W]^(X�A�e&=@I�?�=Ye&_HS2^6A�LNDFEHZ�ABG�K�dFK�GJ?�=YLHS2KK�XHqF=2XHK��

A[<C7kZc=@?>Z\`HKMSYKiAF?UZcK��CI�=2K�X[Z~K�XHq/=YX�K-_VD[?�?�=YL�SYK/aLN<n7kZc=@?>Z\`HKMegD[?:ZcK��CI�=2K�X[ZcK�XHq/=YX�K�_ND/?\?�=YLHS2KFaIi<n7kZc=@?cA4P,A�=2G\SY^CK��CI�=2K�X[Z~K�XHq/=YXHK/aWV<n7kZBI�A�XLVK-EV?UKiWA/?>G�K�P8G�=2qFK�G\A�Z�D/G�aK*<n7kZBI�A�XLVK-EV?UKiWA/?~Agd*A/I�EHE�e}I�S2K�AFXHK�Gia

¾/�H��h[e4EHS�ZB¾/¾/�F¾F¾4�4µn�4e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=�P�v�A�G\XHDFZ�K�XHqF=2XHKMl~G�D/XHq³ a>7kP~^FD/E�I�DFE�S2WrLHE�=YS@W�A�X�K�XHqF=2XHK*y"G�K�P8G�=2qFK�G\A�Z�D/GRe&DFG\K�K��CI�=YK�X/ZsZ�`�AFX�A�X�v�A�G\XHD�Z6K�XHqF=2XHK/o�l~`�A�Z4A�G\K&Z�`�K=2e&egKiW]=@A"Z�K6I�DFX[Z�GJA"P,A/I$Z\E�A�S�=2eg_�SY=@I�A�Z�=2DFX�?�aA[<)��D/E�I�DFE�S2WsZ�`HK�X&LHEH=2S2W&A�e�AFIJ`H=2XHK�Z�`�A�Z�l�D/EHS@W6Z\EHG�X � �1� � K�X[Z�=2G�K�SY^6=2X[Z�DM`HKiA"Z�A�X�W4Z\`�A"Z�l�DFEHS@WZ\G\AFX�?UP8K�G~`HKiA"Z>P8G�D/e�A � � � � Z�DCA&I�DFS@WnL�A�Z�`ml~=YZ�`HD/E]Zcl�D/G�O�LNK�=2XHqCW]D/XHKFa

LN< ��D/E�I�DFEHS@W�Z\`HK�X�LHEH=2S@WxAQe�AFIJ`H=2XHK4Z�`�A�ZMl�DFE�S2W�Z�EHG\X � � �K�X/Z\=YG\K�S2^�=2X/Z\D � � � � A�X�W�Z�`�A�Zl�DFE�S2WnZ�GJA�X�?UP8K�G~`�K�A"Z>P8G\DFe A ¦ ����� � � Z\D&A&`�D�Z~L�A"Z\`ml~=�Z\`HDFE]Zcl�DFG\O�LNK�=2XHqCW]DFX�KFa

Ii< ��D/ECI�D/EHS2WgZ\`HK�XnLHEH=2S2W�A-e�A/IJ`H=YX�K~Z�`�A�Z;l�DFEHS@WgZ�EHG\X � � K�X[Z�=2G�K�SY^g=YX[Z\D � � � � � ��A�XVWgZ�`�A�Zl�DFE�S2WQqF=2dFKM^FD/EA � � � �ra

WV<Q�;X[Z�G\DF_(^�l�D/EHS@WQAFSYl>A*^]?�=2X�I�G�KiAF?�KBZ\DCA4e�A��(=2esE�e =YX�A&I�S2D/?�K�W?�^(?UZ�K�emaK*<Q�;X[Z�G\DF_(^�l�D/EHS@WQAFSYl>A*^]?�=2X�I�G�KiAF?�KBZ\DCA4e�A��(=2esE�e =YX�AFXQD/_VK�Xm?�^]?:Z\K�ema

¾/�H��h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u;v�A�G\XHD�Z~`HKiA"Z>��D"lc?µ�a>»{`�A�Zc=2?~A&O/K�^CG\K�A/?UD/Xnl~`(^�Z\`HK-=2WHK�A�S�v�AFG�X�D�Z~K�XHq/=YX�K�=@?~A&G\K�dFK�G\?�=2LHSYK�K�X�qF=2XHK��

A[<n£BK�A�Z~��D"lc?�D(I�I�EHGcA/I�G\D/?\?�XHDFX]Tk��K�G�D4Z�K�e&_VK�G\A�Z�EHG\KMqFGJAFW]=2K�X[Z\?�aLN<Q£BK�A�Z~��D"lc?�D(I�I�EHGcA/I�G\D/?\?�S2AFG�q/KBZ\K�e&_VK�G\A�Z�EHG\KMqFGJAFW]=2K�X[ZJ?�aIi<Q£BK�A�Z~��D"lc?�D(I�I�EHGcA/I�G\D/?\?���K�G\D4Z�K�e&_NK�GJA"Z\EHG�K-q/G\A/W]=2K�X[Z\?�aWV<Q£BK�A�Z~��D"lc?�D(I�I�EHG>P8G\DFe I�D/S2WnZ�D&`HDFZcL�A"Z\`�?�aK*<Qb>`�K�G\KMAFG�KMXHD&`HKiA"Z~��D"lc?>A�ZBA�S2S�a

¾/�H��h[e4EHS�ZB¾/¾�µ[¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�v�AFG�XHDFZ�K��CI�=2K�X�I�^

Page 105: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;�H� b>`HK�G�e&D]W]^(X�AFeg=@I�?�7�7U7$uN¤]K�I�D/X�W¸�A*lzAFX�W��X[Z�G\DF_(^ ��¾��

¶ a~b>`HK-K��CI�=2K�X�I�^CD�P�Z�`HK-=@W]K�AFS�v�A�G\XHD�Z~K�XHqF=2XHKMl�D/G�O(=2XHqsLNK�Z:l�K�K�X�A4`�D�Z~L�A"Z\`mD�P�Z\K�e&_NK�GJA"Z�E�G�K �� AFX�WA

I�DFS@WnL�A�Z�`mD�P�Z�K�e&_VK�G\A�Z�EHG\K � �B=2?�u

A[<���$ � � � ��]a

LN<���$ �� � � � a

Ii<���$���, � � � ��]a

WV<���$ � � � ���,t�/a

K*<���$ � , � ��� �� a

¾/�H��h[e4EHS�ZB¾/¾�µV��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujS2=Ye&=YZcDFXK�XHq/=YX�K�K��CI�=2K�X�I�^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ ¾"TJ�*º

¹ a~b>`HK;EH_H_NK�G�S2=2eg=YZ�D/XMZ�`HK;AFe&DFEHX[Z�D�P]`HKiA"Z�K�XHK�G\qF^BZ�`�A�Z�I�AFX�LNK�I�DFX(dFK�GUZ\K�WR=YX[Z\D~e&A/I�G\D/?\I�D/_H=2I�e&K�IJ`VA�XH=@I�AFSK�XHK�G\qF^�L(^QAg`HKiA"Z~K�X�qF=2XHKFuA[<nWHK�_NK�X�WH?cDFXQZ�`HK6AFegD/EHX[ZcD�P�P8G�=@I$Z\=YD/X_�G�Ki?UK�X/ZiaLN<n=@?-�i¾F¾ � aIi<n=@?-�i¾ � A�S2l�A*^]?�aWV<QWHK�_NK�X�WH?MD/X�Z\`HK&=YX[Z\AFOFK&A�X�W�K��]`�AFE�?:Z�Z�K�e&_VK�G\A�Z�EHG\K�?&58D/GM`HD�Z-A�X�WxI�D/S2W�L�A"Z\`�Z\K�e&_VK�G\A�Z�EHG\K�?J<BD�PZ\`HK-K�X�qF=2XHKFa

K*<n=@?~��K�G\D�a

¾/�H��h[e4EHS�ZB¾/¾�µ(��¾C� ³ �4K�A/?U^�e�A�Z�`�u�e�A��(=2esE�e K��CI�=2K�XVI�^nI�A�S@I�EHS@A"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³/³ T ³F³

º(a~�BX�K�X�qF=2XHK4D/_VK�G\A�Z�Ki?cLNK�Z:l�K�K�XxL�A"Z\`�?RD�P��F¾F¾F¾;² AFX�W�º�¾F¾�²&aV7kZ\?�AFI$Z\E�A�S�K���I�=YK�X�I�^m=@?�µ/¾ � a�»{`�A"ZM=2?=YZ\?~=@W]KiA�Spe�A"�]=2esEHe}K��CI�=2K�X�I�^��

A[< ³/¶�� a LV< ¹[¶�� a I�<��i¾F¾ � a W�<�µ/¾ � a K*<>¾ � a

¾/�H��h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�?UZ\A�Z�K�P8EHX�I�Z�=2DFX¼ a>7kPp^FD/E4=2X[Z�K�qFGJA"Z�KcAMIJ`�AFXHqFK~=2X�A-h[E�A�X[Z�=YZ:^4AFG�D/EHX�WgA�X(^4I�SYD[?UKiWg_�A"Z\`gD/X�A �HT�� W]=2AFqFGJA�emo�A�XVWgZ�`HK~G\K�?�EHSYZ=@?cA�S2l>A*^(?���K�G�DVo(Z�`H=@?c?�EHqFq/K�?UZ\?�Z�`VA"Z~Z�`�K6h/EVA�X[Z�=YZ:^C=@?�u

A[<�`HK�A�Z�a LV<>l�DFG\O�a Ii<>A&?:ZJA"Z�KMP,AF=YGia W�<>A&?UZ\A"Z\KMP8EHX�I�Z�=2DFX�a K*<>Age&AFG�K/· ?UTkXHK�?UZ�a

¾/�H��h[e4EHS�ZB¾/¾ ¶ ��¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�X/Z\G�D/_(^CW]K���X�K�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

½ a~b>`HKMZ\`HK�G\e&D]W]^(X�A�e&=@I�h[E�AFX[Z�=YZ:^�Z�`�A�Zc=2?~A&e&KiAF?�EHG�K�D�P�e&=2I�G�D[?�I�DF_H=@I�W]=2?�DFGJW]K�G�=@?�uA[<�K�X[Z�G\DF_(^/a LN<�Z�K�e&_NK�GJA"Z\EHG�K/a I�<�_�G�Ki?�?�EHG\KFa W�<>W]K�X�?U=YZ:^Fa Ki<�dFD/SYE�egK/a

¾/�H��h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu�K�X[Z\G�D/_[^CAFX�W?U_NDFX[Z\AFXHK�D/E�?>`HKiA"Z>��D"l��¾Ha>7!X�Z\`HK e�AFI�G�D[?�I�DF_H=@I�l�DFG\S@W 5,=�a KFa2o�DFX�?�I�A�S2K�?{e4E�IJ`�S2AFG�q/K�GwZ\`�A�X�A"Z\DFe&=@I�<$o�`HKiA"Z�K�XHK�G\qF^ �VD"lc?

?�_VD/X[Z\A�X�K�DFEV?US2^�58=�a K/aYo�l~=�Z\`HDFE]ZBAFX(^CDFE]ZJ?U=@W]K6I�A�E�?�Ki<;P8G\DFe ¦ ���(��LND(WH=YKi?>Z�D � � LND]W]=YKi?�u

A[<CX�K�dFK�G�aLN<nl~`�K�XHK�dFK�G>Z\`HKMZ�K�e&_VK�G\A�Z�EHG\KM=2?>q/G�KiA"Z�K�G�Z�`�AFX ³ ¾F¾�²&aIi<nl~`�K�XHK�dFK�G>Z\`HKMZ�K�e&_VK�G\A�Z�EHG\KM=2?>q/G�KiA"Z�K�G�Z�`�AFX��[º �ivRaWV<QAFSYl>A*^]?�aK*<nl~`�K�XHK�dFK�G>Z\`HKMZ:l�D4LND]W]=YKi?cA�G\KMLVDFZ�`m=2XQZ\`HK-q/A/?>?:ZJA"Z�K/a

¾/�H��h[e4EHS�ZB¾/¾[º�¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u;¤]AFX[Z\A�v�S2AFE�?>Z�`�KMP,A"Z�KMDFP�Z\`HK-EHXH=2dFK�G\?�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�F�Fac¤]AFX[Z\AQv�S@A�E�?BesE�?�=2XHqnI�D/G�G\K�I�Z�S2^QD/XmZ�`HK4_H`(^]?U=@I�?BD�PjZ�`�KsEHXH=2dFK�G\?�Ks?\A*^]?>Z�DC`�=Ye�?�K�SYP��U=YP�Z�`HKgEHXH=2dFK�G\?�K-=2?ACI�SYD[?UKiW�?U^]?UZ�K�e AFX�WZ�`HK&�"X�W�S2A*l�D�PjZ\`HK�G\e&D(WH^/A�e&=@I�?~=@?cE�XH=Yd/K�GJ?�AFSYS2^nd"AFSY=@WpoVZ�`HK�X�Z�`HK4EHXH=2dFK�G\?�KsAF?BAl~`HD/SYKMl~=2SYS�EHS�Z\=Ye�A�Z�K�S2^QAF_H_HG\D/A/IJ`QA&?:ZJA"Z\K�DFP:u

Page 106: Introductory Physics Problems David J. Jeffery Department of

��¾[� v�`�A�_]Zia;�]�fb>`�K�G\egD]W]^(X�AFe&=2I�?>7U7U7$uN¤(K�I�DFX�W¸�A*l�A�X�W��X[Z�G\DF_(^

A[<�Z\=Ye&K�SYKi?�?�oHS2=�P8K�SYKi?�?�Z\`HK�G\e&D(WH^[XVA�e&=2I�Kih/E�=YS2=YL�G�=2EHema �LN<CZ\`HK�G\e&D]W]^(X�A�e&=@I�WH=2?�K�h[EH=2SY=2LHG\=YE�ea �Ii<nd"AFG�^(=2XHq�o]S2=�P8K�Tk?�E�?UZ\AF=YXH=2XHqgZ�`�K�G\egD]W]^(X�AFe&=2I�K�h[EH=2S2=YLHG\=2EHema �WV<nK�SYd/K�?>=2X�IJ`�A�G\qFK/a �K*<n_NK�A/I�KMDFX���A�G�Z�`QAFX�WqFD(D]W]l~=2SYS�Z\Dg`(EHe�AFXHO(=YX�W�a �

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/�H��h/P8EHS2S�¾/¾H��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\K�d/K�GJ?U=2LHS2KRK�XHqF=2XHK*y*P8G�=2q&7�Fa~�R?U=2XHq±l�D/G\WH?�oBW]=@A�q/G\AFe�?�o~D/GQKih/EVA"Z�=2DFXV?QI�SYKiA�G\SY^{?�`HD"l�Z�`�A�Z�A�G\K�P8G\=Yq/K�GJA"Z�D/GCe&DFG\K�K���I�=YK�X[ZQZ\`�A�X�AG\K�d/K�GJ?U=2LHS2K6K�XHq/=YX�KsS2K�AFW�?cZ\DQAnI�DFX[Z�GJAFWH=2I�Z�=2DFX�D�PjZ\`HK&I�S@AF?\?U=@I�AFS�?UZ\A"Z\K�e&K�X[ZJ?BDFP�Z�`HK&?�K�I�D/X�WmS@A*l A�X�W�AFSYSD/L�?UK�G�d"A�Z�=2DFX�?�Z�D(DVa

¾/�H��h/P8EHS2S�¾/¾/��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujG\K�d/K�GJ?U=2LHS2KRK�XHqF=2XHK*y*P8G�=2q&7U7�]a~¸�K�Z�· ?jI�D/X�?�=2W]K�GjA�XgK�XHq/=YXHK~AFX�W6P8G\=2qRD/_VK�G\A�Z�=2XHqRLNK�Z:l�K�K�XgA�`HDFZ�A�X�WgARI�DFS@WsLVA"Z�`�a�b>`HK>K�XHqF=2XHK>=2?�EV?UKiW6Z\DW]G\=2dFKcZ\`HKRP8G�=2q�a�b>`HKRZ:l�D6LVA"Z�`V?�AFG�KB=YX?UK�S�P T�Z�`HK�G�e&D]W]^(X�AFeg=@IcKih[EH=YS2=2LHG�=2EHemaj�B?�KR_�G�=2e&K�?;Z�D4WH=2?UZ�=2XHqFE�=2?�`P8G\=YqgP8G\DFe K�XHqF=2XHK-d"A�G\=@A�LHS2K�?�u�=�a KFa2o]P8DFG>Z\`HKMP8G�=2q

� �� 58`HKiA"ZBAFL�?UD/G�LNK�WCP8G�D/e Z\`HK6I�D/S2WQL�A"Z\`V<$o� �� 5,`HK�A�ZcG�K9A:K�I$Z\K�WQZ�DgZ\`HK-`HD�ZcLVA"Z�`N<$oAFX�W � � 58l�DFG\OC=2XH_HE]Z$< )

AFX�WCP8D/G~Z�`�K-K�XHq/=YXHK� � 58`HKiA"ZcG\K"A:KiI$Z�KiWCZ\D&Z�`HK6I�DFS@WnLVA"Z�`N<$o� � 5,`HK�A�ZBA�L�?�DFG\LVKiWCP8G\DFe Z�`HK-`HDFZ~L�A"Z\`V<$oAFX�W � 5,l�D/G�OCD/E]Z�_�E]ZJ<�a

������ � b>`�=2?ch[EHKi?:Z\=YD/X A:EV?:Zc`�A/?�Z�D�LNK6?:Z\K�_H_NK�WQZ\`HG�D/EHqF`dFK�G�^CI�A�G\K�P8EHS2S2^FaA[<Q��=2dFK�X�Z\`�A"Z-Z\`HK�K�X�qF=2XHKCA�X�W�P8G\=Yqml�DFG\O�=YX�I�^]I�SYKi?�o�l~`VA"Z6=@?�Z�`HKCIJ`�AFXHqFK&=2X�Z\`HK�=2X/Z\K�G\X�A�SjK�XHK�G\qF^

� �P8DFGMZ\`HK&l�D/G�O(=2XHqn�VEH=2W±58D/G6?UE�L�?:ZJA�X�I�Ki<RD�P�K�=YZ�`HK�G-D"dFK�G�AmI�^]I�SYK ����=2dFK�X�Z\`HK�A�X�?�l�K�G�Z�DZ�`�K�VG\?UZBh[EHK�?UZ�=2DFXmA�X�WQZ\`HK���?UZcS2A*lzD�P�Z�`HK�G�e&D]W]^(X�AFeg=@I�? � $ ����, � � o�l~`�A"ZBAFG�K � A�X�W � �p=2XZ\K�G\e�?>D�P � �� A�XVW � �� A�XVWQDFP � �RA�X�W � � oHG\K�?�_NK�I$Z\=Yd/K�S2^Fa

LN<n»{`VA"Z6A�G\K6Z\`HK4K��]_HG�Ki?�?�=2DFX�?BP8DFGRZ�`HK&K���I�=YK�X�I�=2K�?�DFP�Z�`HKgK�X�qF=2XHK5 �F<RAFX�W�P8G\=2qx5 � � <��� cDFZ�Kgl�K&A�G\KX�D�ZsAF?�O(=YX�qQP8D/G-=2WHK�A�S>v�A�G\XHD�Z-K��]_HG\K�?\?�=YD/X�?�o�A:EV?:Z6Z\`HK�qFK�XHK�GJA�S�K��(_�G�Ki?�?�=YD/X�?�a ������ � ¤(=2X�I�K�=YZ6=2?_NK�G\`�AF_�?&=2WH=YD[?U^(X�I�G\A�Z�=@InZ\DrZ�`HK�AFE]Z�`�DFG�D�P�Z�`�=2?Qh/E�K�?UZ�=2DFX�o�l�K�l~=2S2S A:E�?UZ�Z�K�S2SB^/DFEtZ�`�A�Z�Z�`HK�P8G�=2qK��CI�=2K�X�I�^�=2?MXHDFZRZ\`HK�?:ZJA�X�W�A�GJW�I�D(K��CI�=YK�X/ZMD�P�_VK�GUP8D/G�e�AFX�I�K58=�a K/aYo � �� � � �,u�KFa q�a2op»�9jTkµ ½ µ[<$oNLHE]Z� � $ � �� � � �� a

Ii<Q|�DFG�Z�`�KRK�XHqF=2XHKM?UD/SYd/KcP8DFG � �cAFX�W�� A/?�P8E�X�I$Z\=YD/X�?>D�P � � A�X�W��ia�b>`�K�XQP8DFG�Z�`HK�P8G\=Yqg?UD/SYd/KcP8DFG � ��AFX�W � �pAF?�P8EHXVI$Z�=2DFXV?~D�P � �� A�X�W � ��a

WV<n»�G\=�Z\KQW]D"l~XrZ\`HKQK��]_HG�Ki?�?�=2DFX�?6AFX�A�S2DFq/DFE�?�Z\D � � � ��� $ � � , � �� P8D/G � � ����� AFX�W � � ��� a�b>`�K�?�KAFG�K<A:EV?:ZRZ�`HK4_�A�GJA�e&K�Z\K�GJ?>D�P�Z�`�KsXHK�ZRK�X�qF=2XHK�T�P8G�=2qC?�^(?UZ�K�e A/?�?�EHe&=2XHq�=�ZMAFI�Z\?~S2=YO/KsA�X�K�XHqF=2XHK/u�=�a K/aYoA/?�?�EHe&=2XHqgZ�`�A�Z~Z�`HK-XHK�Zc_�A�GJA�e&K�Z�K�GJ?�A�G\KMAFSYSp_ND/?�=YZ�=2dFKFa

K*<n7kP�l�KsA/?�?�EHe&KMZ�`HK4K�XHq/=YX�KsA�X�WP8G\=2qnA�G\K-=2WHK�X[Z�=@I�AFS�A�XVWmG�K�dFK�GJ?�=YLHS2KFo�l~`�A"ZMA�G\K � � � ��� o � � ����� oNAFX�W� � ��� ��»{`�A"Zc=@?�Z�`HK-G\K�S@A"Z\=YD/XQLNK�Z:l�K�K�X �&A�X�W � � =2XQZ\`H=@?c?U_NK�I�=2AFS�I�A/?UK �

P\<m BD"l�G�K�_HS2A/I�K�Z\`HKCG\K�d/K�GJ?U=2LHS2K�K�XHq/=YXHKnD�P~Z�`�KnG\K�dFK�G�=2LHS2K�K�XHq/=YX�K�T�P8G�=2q�_�A�=2GsDFPc_�A�G�ZQ5,Ki<-L(^rA�e&DFG\KK��CI�=2K�X[ZBK�X�qF=2XHK-l~=�Z\` ��� � �]a>�B?\?UEHe&K-Z\`HK6e&DFG\K-K��CI�=YK�X/ZRK�XHq/=YXHK-=@?B?\I�AFSYKiWQZ�DCG\K"A:KiI$ZcZ\`HKs?\A�e&K� � Z�DQZ�`HK�I�D/S2W�L�A"Z\`xA/?BZ\`HK&G�K�dFK�G\?�=YL�SYK6K�XHqF=2XHK/as9�G\D"dFK-Z\`�A"ZMZ\`HK4X�K�Z6?U^]?UZ�K�e�d[=2DFS@A"Z\K�?RZ�`�K&��X�WS@A*l�DFP�Z\`HK�G\e&D]W]^(X�A�e&=@I�?~A�XVWn`HK�X�I�K-=@?>=2eg_ND/?\?�=YLHS2KFa

q(<n BD"l�G\K�_HS@AFI�K;Z\`HK>G�K�dFK�GJ?�=YLHS2K�P8G\=2qRDFP�Z�`�K�G\K�d/K�G\=YL�SYK�K�XHq/=YXHK�T�P8G\=2qR_�AF=YG�D�PN_�A�G�Z~58Ki<�L(^sARe&DFG\K�K���I�=YK�X[ZP8G\=2q�l~=YZ�` � � � � ��ax�R?�?�EHe&KCZ\`HKne&DFG\KnK��CI�=2K�X[ZsP8G\=Yq�=2?g?�I�A�S2K�WrZ\D�A�LV?UD/G�LrZ\`HK?\A�e&K � �� P8D/G�e

Page 107: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;�H� b>`HK�G�e&D]W]^(X�AFeg=@I�?�7�7U7$uN¤]K�I�D/X�W¸�A*lzAFX�W��X[Z�G\DF_(^ ��¾ ³

Z\`HK�I�D/S2W�L�A"Z\`±A/?6Z\`HKmG�K�dFK�GJ?�=YLHS2KCP8G\=2q�a�9;G�D"d/K�Z�`�A�Z&Z�`HKmXHK�Z�?�^]?:Z\K�e d(=2DFS@A"Z�Ki?6Z\`HK��"X�W�S2A*l�D�PZ\`HK�G\e&D]W]^(X�A�e&=@I�?~A�XVWn`HK�X�I�K-=@?~=2e&_VD[?�?�=YL�SYK/a

¾/�H��h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK��CI�=YK�X�I�^A�X�WQl�A/?:Z\KM`HK�A�Z³ a~�t_VD"l�K�G�_HS@A�X[Z�K��[Z\G\A/I$ZJ?�K�XHK�G\qF^RP8G�D/e�?:Z\K�A�e�A�Z�� ¶ ¾ �iv�A�X�W6WHK�S2=Yd/K�GJ? ¼ ¾F¾�¯�» 5,egK�q/A*l>A"Z�Z\?J<�D�PHK�SYKiI$Z�G\=@I_ND"l�K�G�a�7kZcG\K"A:KiI$Z\?>l>AF?UZ�KM`HKiA"Z>Z�DCAgG\=Yd/K�G~A"Z ³ ¾ � vRaHb>`HK-D"dFK�G\AFSYSNK��CI�=2K�XVI�^n=@?~¾ � � ¼ aA[<C»{`VA"Z;=@?�Z�`�K~=2W]KiA�SNv�AFG�X�D�ZjK��CI�=2K�XVI�^6P8D/G;AM`HKiA"Z�K�X�qF=2XHK~DF_NK�GJA"Z\=YXHqMLNK�Z:l�K�K�X4Z\`HK~Z:l�DM`HK�A�Z�L�A"Z\`�?�o?UZ�KiA�e�AFX�WG�=2dFK�G� ������ � ¿~K�e&K�e4LVK�G>Z�D�E�?�K-²MK�S2d(=YXQZ�K�eg_NK�GJA"Z\EHG\K�?�a

LN<Q�R?U=2XHqQZ�`HK �C¦ � � ��K���I�=YK�X�I�^xA�X�W�Z�`HK&qFK�XHK�GJA�S�K��]_HG\K�?\?�=YD/X � $ � � � � � � � � ���Ho�l~`�A�Z�=@?�Z�`�KZ\D�ZJA�Sp_ND"l�K�G~K��(Z�GJAFI�Z�K�WnP8G\DFe Z\`HK6?:Z\K�AFeuj=�a KFa2oHW]K�S2=Yd/K�G\K�WQ_VD"l�K�G~_�SYE�?>l>AF?UZ�K�T�`�K�A"Z>_ND"l�K�G�

Ii<n»{`VA"Zc=@?�Z�`HK6A/I$Z�EVA�S�l>AF?UZ�K�T�`HKiA"Z>_VD"l�K�G~W]=@?\IJ`�A�G\qFKiW�Z�D&Z\`HK-G\=Yd/K�G �WV<Q£BD"l�e&AFX(^x`HD/E�?�K�?6G\K�h[EH=2G\=YXHq��i¾ � » KiAFIJ`rZ�D�`HK�A�ZgI�D/EHS@WrLVKQ`HK�A�Z�K�WrL(^�Z�`�KCl�A/?:Z\KC`HKiA"Z4=YPc=YZ

l�K�G\K-?UD/e&K�`HD"l�A/I�I�K�?\?U=2LHS2KFa

¾/�H��h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujK�X/Z\G�D/_(^nA�S2l�A*^]?�=YXVI�G\K�AF?�K�?� ª�¬"¨ �V«������V¬ ��­�� 7�`HD/_VK�Z\`H=2?Bh/E�K�?UZ�=2DFXm=2?B°�²fXHD"l-a

µ�a ��D/E�`�A*d/KCZ:l�Dx?�^(?UZ�K�e�?s=2X�Z\`HK�G\e�A�S~I�D/X/ZJAFI�Z�ojLHE]Z&=@?UD/S2A�Z�K�W�P8G�D/e Z�`HKG�Ki?:ZgD�PcZ\`HKl�D/G�S@Wpar7!XH=YZ�=@A�S2SY^?�^]?:Z\K�e��~`VAF?�Z\K�e&_VK�G\A�Z�EHG\K �

� A�XVWg?�^]?:Z\K�e��]o�Z\K�e&_NK�GJA"Z�E�G�K �

� a�»{=YZ�`HD/E]Z�S2D/?\?�D�PpqFK�XHK�GJA�S2=YZ:^s?�A*^6Z�`�A�Z�

� � �

� aA[<Q¤]=YX�I�K Z�`HK Z:l�D ?U^]?UZ�K�e&?�A�G\Kz=2X Z�`HK�G�e�A�SxI�DFX[ZJAFI$Z{l~`�A�Z�I�AFX}^/DFE�?�A*^�AFLVD/E]ZwZ�`HK�=YG���X�A�SZ\K�e&_NK�GJA"Z�E�G�Ki? �

LN<Q�R?�?�EHe&K�Z�`�A�Z�Z\`HK~?U^]?UZ�K�e�?�`�A*dFK�`HK�A�Z�I�A�_�A/I�=YZ�=2K�? � � 5� <�AFX�W � � 5

� <�Z�`�A�Z�AFG�K�A�_H_HG\DF_�G�=@A"Z\KjP8DFG�Z�`�KI�DFX�WH=�Z\=YD/X�?�EHX�W]K�G~l~`H=2IJ`Q^FD/EnS2K�Z>Z�`HK�e K�h[EH=2S2=YLHGJA"Z\KFu�KFa q�a2o]I�D/X�?:ZJA�X[Z>dFDFS2EHe&KFoHI�DFX�?UZ\AFX[Z�_HG\K�?\?UE�G�K/oD/G~?UD/egK-?UZ�GJA�XHq/KRDFZ�`HK�GcI�D/X�W]=YZ�=2DFX�a���=2dFK�Z�`HK-=2X[Z�K�qFGJA�S�K��]_HG\K�?\?U=2DFXV?;P8D/G�Z�`HK6IJ`�AFXHqFK�=2X`�K�A"Z~KiAFIJ`?�^]?:Z\K�e�?6K��]_VK�G�=2K�X�I�KC=2XrZ�`HKQK�h[EH=2SY=2LHGJA"Z�=2DFX�_�G�D]I�Ki?�?�us=�a KFa2o�Z\`HKnK��]_HG�Ki?�?�=2DFX�?�P8D/G � � � AFX�W � � � a»{`VA"ZBI�AFXQD/XHK-?�A*^QA�LNDFE]Z � � � � � � � A�X�WQl~`(^nI�AFXmDFXHK-?\A*^�=�Z �

Ii<Q¿cK�I�AFSYS�Z\`HK6W]= �NK�G�K�X[Z�=@A�S�K��(_�G�Ki?�?�=YD/XCP8D/GcAgIJ`VA�XHq/KR=2XmK�X[Z�G\DF_(^C=@?

��� $ ���� �

|�=2X�W�Z\`HK�=2X/Z\K�q/G\AFSCK��]_HG\K�?\?U=2DFXV?rP8DFG�Z\`HKzIJ`VA�XHq/K�?r=2X K�X[Z�G\DF_(^ D�PmZ�`HK�Z:l�Df?�^]?:Z\K�e�?�=2X Z�`�KKih[EH=YS2=2LHG\A�Z�=2DFXw_HG\D]I�K�?\?&=2XtZ\K�G\e�?�D�P�Z�`HK�`HK�A�ZnI�A�_VAFI�=YZ�=2K�?�u�=�a K/aYo>Z\`HK�K��]_HG\K�?\?U=2DFXV?gP8DFG ��� � AFX�W��� � a

WV<Q|�=2X�W�=2XHK�h[E�AFSY=YZ�=2K�?;G�K�S2A�Z�=2XHq ��� � AFX�W ��� � Z\D � � � ��

�]ajb>`HK�X&�VX�W&Z�`�KB=2XHK�h[E�AFSY=YZ:^sG\K�S@A"Z\=YXHq ��� �AFX�W � ��� � � aK*<n»{`VA"ZB=@?~Z\`HK4?�=Yq/XmD�P�Z�`HKsZ�DFZ\A�S�IJ`�A�X�qFK-=2X�K�X[Z�G\DF_(^Fa�7:?~Z\`H=@?cG\K�?�EHS�Z�I�DFXV?U=@?:Z\K�X[Zcl~=YZ�`�Z\`HK6K�X[Z\G�D/_[^?UZ\A�Z�K�egK�X[ZcD�P�Z\`HKs�"XVWQS@A*l �

¾/�H��h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujK�X/Z\G�D/_(^CIJ`�A�XHq/KM=YXmA�Xm=@W]K�AFSpq/AF?¶ a~� I�DFX�?UZ\AFX[ZcdFDFS2EHe&K-^FD/Em`�A*dFKM=2X�I�G\K�A/?UKiWnZ\`HK-Z\K�e&_VK�G\A�Z�EHG\K-D�PjA�X�=@W]KiA�S�W]=@A"Z\DFe&=@IMq/AF?cL[^AgP,AFI�Z�DFGBD�P�i¾Ha���DFEm`�A*d/K ¹ e&DFS2K�?�aj»{`�A"Zc=@?�Z�`�K6IJ`�A�XHq/KR=2XmK�X[Z�G\DF_(^��

Page 108: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 nAn � N[1_H ;75\*IH ¥ Da&:5<cT1

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/�/�sh[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@I�IJ`VA�G\qFKMW]K���X�=�Z\=YD/X�oH=2X�I�D/eg_�SYK�Z�K�Fa~�;SYKiI$Z�G\=@I�IJ`VA�G\qFK�=2?�u

A[<nA4P8EHXVWHA�e&K�X[ZJA�S�_HG\DF_NK�G�Z:^�D�P�e�A"Z�Z�K�G~l~`�=2IJ`�I�D/e&K�?>=2XmA&W]K���XH=YZ�K6h[E�AFX/Z\=Y��K�WQEHXH=YZ ��a

LN<QA&W]K�G�=2dFKiWn_�G�D/_VK�GUZ:^CDFP�e�A"Z�Z�K�G~l~`H=2IJ`�I�DFe&K�?>=2X�A4=2X�W]K���XH=YZ�K6h[E�AFX/Z\=Y��K�WEHXH=YZ���e&DFG\KMDFG>S2K�?\?�a

Ii<QAnP8EHX�W�A�e&K�X[Z\AFSj_HG\DF_NK�G�Z:^DFP�e�A"Z�Z�K�G�l~`�=2IJ`rI�D/egKi?�=YXrAQI�DFX[Z�=2X(EHEHe�DFP�h[E�A�X[Z\=�Z\=YKi?�uBZ�`HK�G�K&=@?RX�D?�e�A�S2SYKi?:Z~LH=YZcD�PjIJ`�AFG�q/KFa

WV<QAMW]K�G�=2dFKiWs_�G�D/_VK�GUZ:^6DFPNe�A�ZUZ�K�Gjl~`H=@IJ`&I�DFe&K�?�=2X�AMI�DFX[Z\=YX(EHEHe D�Pph[E�A�X[Z�=YZ�=2K�?�u�Z\`HK�G\K>=2?�XHD-?Ue�A�S2S2K�?UZL�=�ZcDFP�IJ`�AFG�q/KFa

K*<QAFesLNK�Gia

¾/�/�sh[e4EHS�ZB¾/¾H�i¾H�s�&� ¶ K�A/?U^�e&K�egD/G�^�u>��K�Xm|HGJA�X�O[S2=2XQX�AFe&K�WmIJ`�A�G\qFKi?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ³ º

�]a>»{`HD�XVA�e&K�WQ_VD[?U=YZ�=2dFK-AFX�WXHK�q[A"Z�=2dFK�K�S2K�I�Z�G\=2IMIJ`�AFG�q/K��A[<M��K�DFG\qFK4»�A/?U`�=YXHqFZ�D/X�a LN<��FD/`HXx�RWHA�e�?�a Ii< ��K�XHK�W]=@I$Z-�cG\XHD/S2Wpa W�<��RA�G\DFX ��EHG\GiaK*<<��K�Xm|HGJA�XHO(S2=YX�a

¾/�/�sh[e4EHS�ZB¾/¾H�i¾/���&���MK�A/?U^�e&K�egD/G�^�u�?�e�A�S2SYKi?:Z~_H`(^]?U=@I�AFSpIJ`�A�G\qFK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¹/½ TJ�

³ a~b>`HK6AFL�?�DFS2E]Z�K-d"A�S2EHK-DFP�Z\`HK6?Ue�AFSYS2K�?UZcXHDFX���K�G\Dg_H`(^(?�=@I�A�S�A�e&DFEHX[Z~D�P�K�S2K�I�Z�G\=2I-IJ`VA�G\qFK&58XHDFZBI�DFXV?U=@W]K�G\=2XHqh[E�AFG�O]?J<;=@?�u

A[<�D/G;A�LNDFEHZc� � ¹ �C�i¾ � ��#pvRa LN<>��vRa Ii<�=2X�W]K��VXH=�Z\K�S2^�?Ue�A�S2S�a WV<�=YXVW]K���X�=�Z\K�S2^4S@A�G\qFK/a

K*<�=YXVW]K�Z\K�G\eg=2X�A�Z�KFa

¾/�/�sh[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�e&K�X[ZJA�G\^nIJ`�A�G\qFK� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¹/½ TJ�

µ�a~b>`HK-K�SYKiI$Z\G�=@IMIJ`�A�G\qFKMI�D/egKi?~h[E�A�X[Z�=2��KiWn=2XmEHXH=YZ\?~DFP:uA[<r��I�DFEHS2DFe4L�a LV<

�$ � � º(� ¼ � ¼ � � � Ii< � � $ ¼ � ¼[¶ � ��¾ � ���p| �"ea WV< � $

¼ � ½/½ �x�i¾"#p ~Tke � �/v �"a K*<�$ � � ¹ ¾/������¾ � ��#�vRa

¾/�/�sh[e4EHS�ZB¾/¾/�H��¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj_ND/?�=�Z\=Yd/K�S2^nIJ`�AFG�q/KBe�A"Z�Z�K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¹/½ T ½

¶ aB°RGJW]=2X�A�G\^�e�A"ZUZ\K�G~=@?~_ND/?�=�Z\=Yd/K�S2^nIJ`�A�G\qFK�l~`HK�XHK�d/K�G>_HG\D�Z�D/X�?�uA[<�DFE]Z\X(EHesLNK�GcX�K�E]Z\G�D/X�?�a LV<�D/E]Z�d/D�Z\K-K�S2K�I$Z\G�D/X�?�a I�<�D/E]Z�X(EHe4LVK�GcK�S2K�I�Z�G\DFX�?�a WV<~A�G\KP8K�l�K�G>Z�`�AFXmK�S2K�I$Z\G�D/X�?�a K*<>A�G\K�AFL�?UK�X[Z�a

¾/�/�sh[e4EHS�ZB¾/¾/�/��¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\DFXV?�X�D�Zc_NK�G\e&AFXHK�X[Z\SY^CLNDFE�X�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¹/½ TUº

¹ a~�;SYKiI$Z�G\DFXV?�=2X�A&A"Z�D/e�A�G\KFu

Page 109: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a;�F� ��S2K�I$Z\G�=@I6v�`�A�G\qFK ��¾ ¶

A[<&_NK�G\e&AFXHK�X[Z\SY^wLNDFEHX�W{Z�D�Z\`HKxA�Z�DFema LV<�X�D�ZQ_NK�G\e�A�XHK�X[Z�S2^tLNDFEHXVWwZ�D�Z\`HKxA�Z�D/ea Ii<I�DFX]�VXHK�WQZ�DgZ\`HK-X(E�I�S2K�E�?�a W�<�e&DFG\KMe&A/?�?�=2dFKRZ�`�AFXQZ\`HK-X(E�I�S2EHKi?�a Ki<�q/G�K�K�X�a

¾/�/�sh[e4EHS�ZB¾/¾/�/�F���&� ¶ K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\DFXQDFG~_HG\D�Z\DFXG�K�e&D"d*AFS� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º]��T ³

º(a>»{`H=@IJ`mD�P�K�S2K�I�Z�G\DFX�?�o(_HG�DFZ�D/X�?�o]X�K�E]Z\G�D/X�?~A�G\KRKiAF?�=YK�G>Z�D&G\K�e&D"dFKRP8G�D/e�A�X�A�Z�DFe �A[<M9�G\D�Z\DFX�?�a LV<Mb>`HK�^xA�G\K�A�S2Sj=YG\G\K�e&D"d"A�LHS2KFa Ii<Mb>`HK�^�A�G\KgKih[E�A�S2SY^�K�AF?�=2SY^�G\K�e&D"d"A�L�SYK/aWV<> cK�EHZ�G\DFX�?�a Ki<>��S2K�I�Z�G\DFX�?�a

¾/�/�sh[e4EHS�ZB¾/¾/� ³ ¾4� ³�³ e&D]W]K�GJA"Z\K�e�A�Z�`�u�IJ`�AFG�q/KRD/Xx�Mq&D�P�_HG\D�Z\DFX�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º ³ TJ�

¼ ac��=2dFK�X&Z�`HKce�A/?�?;D�PpA-_HG\D�Z�D/X&=2?B� � ¹ º �C��¾ � � �Nq6AFX�WgZ�`�KBK�S2K�e&K�X/ZJA�G\^4IJ`�AFG�q/K>=2?B� � ¹ ¾/� �C�i¾ � � #pvRoFl~`�A�ZAF_H_HG\D*�(=2e�A"Z\K�S2^�=2?�Z\`HKMZ�DFZ\A�S�IJ`�A�G\qFKRD�P>��q&D�P�_�G�DFZ�DFXV? �

A[<�� � ¹ º�����¾ � ����vRa LV<�� � ¹ ¾/���x�i¾ � ��#�vRa Ii<B�i¾ � vRa W�<~� � ¶ �x�i¾ � � � vRa Ki<���K�G\D�a

¾/�/�sh[e4EHS�ZB¾/¾/� ¶ ¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�DFX�W]EVI$Z�=2DFXmI�S@AF?\?�K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

½ a~b>`HK�G�K-AFG�K�P8DFE�G~e&AF=YXmIJ`�AFG�q/K�I�DFX�W]EVI$Z�=2DFX�I�A"Z�K�qFD/G�=2K�?;P8DFG~e�A"Z\K�G\=2AFS�uA[<C=2X�?�EHS@A"Z�D/G�oHI�DFX�WHE�I$Z\DFGio(WHK�e&=2I�DFX�WHE�I$Z\DFGioHA�X�WDFGJIJ`HKi?:Z\G\A4I�DFXVW]E�I$Z\DFGiaLN<n=2X�?�EHS@A"Z�D/G�oHI�DFX�WHE�I$Z\DFGio(?�K�e&=@I�D/X�W]E�I�Z�DFGioHA�XVWQ=2X]P8GJAFI�DFX�W]EVI$Z�D/G�aIi<n=2X�?�EHS@A"Z�D/G�oHI�DFX�WHE�I$Z\DFGio(?�K�e&=@I�D/X�W]E�I�Z�DFGioHA�XVWm¤]EH_VK�G�e�AFX]TkI�DFX�WHE�I$Z\DFGiaWV<n=2X�?�EHS@A"Z�D/G�oHI�DFX�WHE�I$Z\DFGio(?�K�e&=@I�D/X�W]E�I�Z�DFGioHA�XVW?�EH_NK�GJI�D/X�W]E�I�Z�DFGiaK*<n=2X�?�EHS@A"Z�D/G�oHI�DFX�WHE�I$Z\DFGio(?�K�e&=@I�D/X�W]E�I�Z�DFGioHA�XVWWHK�e&=2?�K�e&=@I�D/X�W]E�I�Z�DFGia

¾/�/�sh[e4EHS�ZB¾/¾/� ¹ ¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/X�W]E�I�Z�DFGJ?~W]K���XHK�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

��¾Ha �\¸�K�Zi· ?�_HS@A*^ �]1\��D3�����"# 1 |HDFG �]��¾F¾�o�Z\`HK-A�X�?�l�K�G�=@?�u�b>`�K�?�KRe�A"Z\K�G\=2AFS2?�A�S2S2D"l�A�XnK�SYKiI$Z\G�=@IRI�EHG\G�K�X/Z�Z�D4��D"lZ\`HG�D/EHqF`QZ�`�K�ema �»{`�A�ZBA�G\K oH�BSYK����

A[<�=YXV?UEHS@A"Z\DFGJ? LV<>I�D/X�W]E�I�Z�D/G\? Ii<�d*A/I�EHE�e}?UZ\A"Z\K�? WV<>?UD/SY=@WH? K*<>I�G\^(?UZ\AFS2?

¾/�/�sh[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/X/ZJAFI�Z�P8D/G\I�K�?�F�Fa>»{`�A�ZBA�G\K-I�DFX[ZJAFI$Z�P8DFGJI�Ki? �

A[<n|�DFGJI�Ki?C?UD�?�`HD/GUZnGJA�X�qFKZ�`�A�ZQe�AFI�G�D[?�I�DF_H=@I�AFSYS2^rZ�`�K�^wG�Kih[EH=YG\K�LND(WH=YKi?�Z�D�_H`(^(?�=@I�A�S2S2^ � � ¦ �=2X�DFGJW]K�GZ�DwAFI�Z�a��cS2S-K�d/K�G\^(W�A*^wI�DFX[Z\A/I$ZP8DFGJI�Ki?AFG�KxZ�`�K �� ¦ � � � � � � � ¦ P8D/G\I�Ke�AFXH=�P8Ki?:Z\K�WL(^Ce�AFI�G�D[?�I�DF_H=@IBe�A�ZUZ�K�G�a

LN<Q|�DFGJI�Ki?�?UDc?�`HD/GUZ�GJA�XHq/K�Z�`�A�Z�e�AFI�G�D[?�I�DF_H=@I�AFSYS2^>Z�`HK�^RG\K�h[EH=2G\K�LND]W]=2K�?pZ\Dc_H`(^]?U=@I�AFSYS2^ � �� � �=2X�DFGJW]K�GZ�DwAFI�Z�a��cS2S-K�d/K�G\^(W�A*^wI�DFX[Z\A/I$ZP8DFGJI�Ki?AFG�KxZ�`�K �� ¦ � � � � � � � ¦ P8D/G\I�Ke�AFXH=�P8Ki?:Z\K�WL(^Ce�AFI�G�D[?�I�DF_H=@IBe�A�ZUZ�K�G�a

Ii<Q|�DFGJI�Ki?B?�Dn?U`�DFG�ZRGJA�XHq/KMZ�`�A�Z�e�AFI�G�D[?�I�DF_H=@I�AFSYS2^�Z\`HK�^mG\K�h[EH=2G�K6LND]W]=2K�?RZ�DC_�`[^]?�=2I�A�S2SY^ � � ¦ � =2XD/G\WHK�GRZ�DmAFI$Zias�cS2SjK�d/K�G\^]WHA*^I�DFX[Z\A/I$Z�P8DFGJI�Ki?�AFG�KsZ�`HK �4� � � �� � � � � � ��P8DFGJI�Kge�A�XH=YP8K�?UZ�KiWL(^Ce�A/I�G\D/?\I�DF_�=2IRe�A"ZUZ\K�Gia

WV<Q|�DFGJI�Ki?�?UDc?�`HD/GUZ�GJA�XHq/K�Z�`�A�Z�e�AFI�G�D[?�I�DF_H=@I�AFSYS2^>Z�`HK�^RG\K�h[EH=2G\K�LND]W]=2K�?pZ\Dc_H`(^]?U=@I�AFSYS2^ � �� � �=2X�DFGJW]K�G�Z�D6AFI�Z�a��cS2S�K�dFK�G\^]WHA*^6I�D/X[Z\AFI�ZjP8DFGJI�Ki?�A�G\K�Z�`HK �4� � � �� � � � � � ��P8DFGJI�K~e�A�XH=YP8K�?UZ�KiWL(^Ce�A/I�G\D/?\I�DF_�=2IRe�A"ZUZ\K�Gia

K*<Qb>`�KMP8DFGJI�K�?�`HD/S2WH=YXHqCI�DFX[Z\A/I$Z>SYK�X�?�K�?~=2XQ_�S2A/I�KFa�b>`�K�^�· G\KMXHD�Z>P8D/G~Z�`HK-?\h[EHK�AFeg=@?�`�a

¾/�/�sh[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ ¶ K�A/?U^�e&K�egD/G�^�ujXHD&e&=@I�G\D/?\I�DF_�=2I�IJ`�A�G\qFK�XHK�E]Z�GJA�S2=Y�iA"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

Page 110: Introductory Physics Problems David J. Jeffery Department of

��¾ ¹ v�`�A�_]Zia;�F� �;SYKiI$Z\G�=@I6v�`�A�G\qFK

�i�]a>»{`(^�W]D/X�· Zg_VD[?U=YZ�=2dFKA�X�W�XHK�q[A"Z�=2dFKIJ`�A�G\qFK�X�K�I�Ki?�?\A�G\=2SY^�XHK�EHZ�GJA�S2=Y��KnK�A/IJ`�D�Z\`HK�GgA"ZgZ�`HKe&=2I�G�D[?�I�DF_H=@IS2K�d/K�S�A:E�?UZcSY=2OFKMZ\`HK�^negD[?:Z\SY^W]D�A"Z>Z�`�K-e&A/I�G\D/?\I�D/_H=2IRS2K�dFK�S �7kZc=@?>P8D/G�LH=@WHW]K�XQL(^ a

A[<�I�S@AF?\?�=2I�A�S-_H`(^]?U=@I�? LV</�[A�e&Ki?�v�SYK�G�O ¯�A"�]l�K�S2S Ii<�¯�=@IJ`�A�K�Ss|�AFG\A/WHA*^ W�</��K�X|�G\AFXHO(SY=2X Ki<>h[E�AFX/Z\EHe�e&KiIJ`�A�XH=@I�?

¾/�/�sh[e4EHS�ZB¾/¾�µV��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\DFe�AFqFXHK�Z�=@?Ue� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ³ a~b>`HKsK�S2K�I$Z\G�=@I�=YZ:^QAFX�We�A�qFX�K�Z�=@?�e AFG�KMXHD"l EHX�WHK�GJ?:Z\D[D]WQZ�D�LNK4A&E�XH=�Z\K�W�?�K�ZBDFPj_H`HK�X�DFe&K�X�A&l~`�=2IJ`ml�KI�A�S2S

A[< e�A�qFX�D[K�SYKiI$Z\G�=@?Uema LN< e&AFqFe�A�K�SYKiI$Z\G�=@?Uema Ii< K�S2K�I�Z�G\DFe�A�q/=�Tk=2?�emaWV<�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@?�ea K*<�K�S2K�I�Z�G\DFe�A�q/X�A�XH=2e&DFE�?�=@?Uema

¾/�/�sh[e4EHS�ZB¾/¾�µ(��¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\D�Tke�A�q/XHK�Z\=2IRI�DFX�XHK�I�Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=p=YP�e&AFqFXHK�Z�=@?Ue}=2?~I�D"dFK�G�KiW

��µ�aBv�`HG\=@?:Z\=2AFX�°RK�G\?UZ�KiWn=2Xr� ¼ �F¾-P8D/EHX�WQZ�`�A�ZBA&I�EHG\G�K�X[Z-5,D�P�K�S2K�I�Z�G\=2IMIJ`�AFG�q/Ki<;qFK�X�K�GJA"Z�KiWQA�uA[< ��K�?\?UK�S]P8EHX�I�Z�=2DFX�a LN<jA6£cK�G�e&=YZ�Kc_NDFS2^(XHDFe&=@A�S�a I�<j¯�=@IJ`�AFK�S�|VA�GJAFWHA*^/a W�<�£cD(DFO/KF· ?S@A*l�P8D/G\I�KFa Ki<>Age�A�q/XHK�Z\=2IRP8DFGJI�K/a

¾/�/�sh[e4EHS�ZB¾/¾�µ ³ ¾C�&���MK�A/?U^�e&K�egD/G�^�u�v�D/EHSYD/esL�· ?�S2A*l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ¶ a~b>`HKMP8D/G�e4EHS@A�� ��� $

��� � � � ����

� ���

l~`HK�G�K � $ ¼ � ½F½ �x�i¾"#p �e � �Fv ��o�=2? S@A*l-aA[<cv�DFEHS2DFe4L�· ? LV<>|�AFG\A/WHA*^�· ? Ii<>�ce&_ (K�G�K/· ? W�<<��=2D�Z�T!¤]A*d"AFGUZi· ? K*<~�MA�E�?\?�·]S@A*l-a

¾/�/�sh[e4EHS�ZB¾/¾�µ ³ ���&� ¶ K�A/?U^�e&K�egD/G�^�u�I�A"Z�K�qFD/G�^&D�P;v�DFE�SYD/esL�· ?�S2A*l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¹/½ T ¶

� ¹ aBv�D/EHSYD/esL�· ?>S@A*l�=@?~AHuA[<B?�D]I�=2K�ZJA�S�S2A*l-a LV<RS@A*l�D�P�Z\`HK�G\e&D]W]^(X�A�e&=@I�?�a Ii<cS@A*l D�P�e&DFZ�=2DFX�a W�<�I�D/X�?�K�G\d*A�Z�=2DFXS@A*l-a Ki<�P8DFGJI�KMS@A*l-a

¾/�/�sh[e4EHS�ZB¾/¾�µ/µ/¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@I�AFX�WQqFGJA*d[=YZ:^&P8DFGJI�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ��µ[¾4?�DFG�Z�DFP

�*º(a~b>`HK-K�SYKiI$Z\G�D[?:ZJA"Z�=@IBP8DFGJI�K-A�X�Wq/G\A*d(=YZ:^&AFG�KMLND�Z\` P8DFGJI�K�S2A*lc?�aA[<�=YX(d/K�GJ?UK LV<�=2X(dFK�GJ?�K�T!?�h[E�AFG�K I�<�=2X[d/K�GJ?UK�TkI�EHLNK WV<�SY=2XHK�AFG Ki<>h[E�A/W]GJA"Z�=@I

¾/�/�sh[e4EHS�ZB¾/¾�µ/µ[���&�s�4K�A/?U^�e&K�egD/G�^�ujXHK�ZBIJ`�A�G\qFK�A�X�WQP8D/G\I�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*ºF�*T ½ b>`H=@?>=2?BAg?�=2eg_�SY=Y��K�Wd/K�GJ?U=2DFX�a

� ¼ a~|�DFGRZ:l�DC_VA�G�Z�=@I�S2K�?s5,=�a KFa2o�LVD]W]=2K�?RZ\`�A"ZMI�A�X�LVK4G�K�q/A�GJW]KiWA/?R?UZ�G\E�I�Z�EHG\K�S2K�?\?\<>Z�DnK��]K�G�Z�AQv�D/EHSYD/esL�P8D/G\I�KD/XQKiAFIJ`D�Z�`�K�Giu

A[<jLND�Z\`CesE�?UZ�LNKBE�X�IJ`�A�G\qFKiWpa LV<jLND�Z\`CesE�?UZ�LNKRIJ`VA�G\qFK�W�a Ii<jDFX�KcesE�?UZ�IJ`VA�G\qFK�W&AFX�W&Z�`�KDFZ�`HK�GRE�X�IJ`�A�G\qFKiWpa W�<~Z\`HK�=2G-IJ`�A�G\qFKi?ce4E�?:ZMLND�Z�`xLVK&q/G�KiA"Z�K�GcZ\`�A�Xt��vRa K*<~Z\`HK�=2G-IJ`�A�G\qFKi?e4E�?UZcLVDFZ�`mLVK-S2K�?\?�Z�`VA�Xr��vRa

¾/�/�sh[e4EHS�ZB¾/¾�µ/µ ³s³�¶ µ&`�AFG\WnZ�`H=2XHO(=2XHq�u���X�=�Z\K-LVD]W]^A"ZUZ\G\A/I$Z\=YD/X]T�G\K�_�EHS2?�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=YTJ�*º��"T ½ b>`H=@?>=2?>Z\`HK-`�AFG\WQdFK�G\?�=YD/X

� ½ aBv�AFXnZ:l�Dg��XH=YZ�K-LND(WH=YKi?~K�A/IJ`QK�SYKiI$Z�G\=@I�A�S2S2^�XHK�E]Z\G\AFS�D"dFK�G\AFSYSNK�d/K�GcA�ZUZ�GJAFI�Z~DFG>G�K�_VK�S�K�A/IJ`QDFZ�`HK�G�

Page 111: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a;�F� ��S2K�I$Z\G�=@I6v�`�A�G\qFK ��¾(º

A[<n BD�aLN<Q�BSYl>A*^]?�aIi<Q BDCA�X�WA�S2l>A*^(?�aWV< � ��aF|�DFGjK��HAFeg_�SYK/o/I�D/X�?�=2W]K�G�Z:l�D-?�e�A�S2S�o�X�DFX]T!I�D/X�W]E�I�Z�=2XHqML�A�S2S2?;A"ZUZJAFIJ`HKiWsL(^sAMX�DFX]T!I�D/X�W]E�I�Z�=2XHq

LVA�Giu�q/=Yd/K�DFX�K�L�A�S2SMA�_VD[?U=YZ�=2dFK�IJ`�A�G\qFK�AFX�W±Z�`�KxDFZ�`HK�GnL�AFSYS�A�XHK�q/A"Z\=Yd/K�IJ`�AFG�q/K�D�PMZ�`HKr?\A�e&Ke�AFqFXH=YZ�E�WHKFanb>`HKQ?:Z\G�E�I�Z�EHG\K&=2?sA�XrK�S2K�I�Z�G\=2I�W]=2_NDFS2K&Z�`�A�Z6=2?-D"d/K�GJA�S2S�XHK�E]Z\G\AFS�aQb>l�D�?�E�IJ`�W]=Y_NDFS2K�?l~=2S2S�Z�K�X�WmZ\DCG�K�_VK�S�=YPjSY=2OFK6K�X�WH?RA�G\K6I�S2D/?�K�?UZRA�X�WQZ\DnA"Z�Z�GJAFI$ZR=�PjEHXHS2=2OFK6K�X�WH?BAFG�K6I�SYD[?UKi?:Zia>7!X[d/K�GJ?UK�T?\h[E�A�G\KsXVA"Z�E�G�K&D�P;Z�`HKnv�DFE�SYD/esL�P8D/G\I�K4q/E�A�GJA�X[Z\K�K�?cZ�`�A�ZMZ�`HK�I�S2D/?�KgK�X�WH?MDFP�Z:l�DQD/L,A:K�I�Z\?M?U`�DFEHS@WWHDFe&=YXVA"Z�K4LVK�`�A*d(=YD/GB=YPjZ�`HK�^�A�G\K6LHG\DFEHq/`/ZRd*AFXH=@?U`H=2XHq/SY^�I�S2D/?�K-Z\DFqFK�Z�`HK�GRAFX�WmZ�`�KsD�Z\`HK�G�K�XVWH?R?UZ\A*^A4��X�=�Z\K6W]=2?UZ\AFX�I�K6AF_�A�G�Z�aj��W]=@A�q/G\AFe e&=Yq/`/Z~`HK�SY_Z\D�EHX�W]K�G\?UZ\AFX�WCZ\`HK6?�=�Z\E�A"Z\=YD/X�a

K*<Qb>`�K�^�I�A�X � ����coCL�E]ZzXHK�dFK�G � � �C¦ �a�|HD/G�K��HA�e&_HS2KFo�I�D/X�?U=@W]K�G{Z:l�D ?�e�A�S2S�o�XHDFTXVI�DFXVW]E�I$Z\=YX�qLVA�S2S2?MA"Z�Z\A/IJ`HK�W�L[^xAnXHD/X]T!I�DFXVW]E�I$Z\=YX�qQL�AFG�u�qF=2dFK4DFXHK&L�AFSYSjA_ND/?�=�Z\=Yd/KgIJ`�AFG�q/K4AFX�WZ\`HK�D�Z�`�K�G�L�A�S2SNAsXHK�q[A"Z\=Yd/KRIJ`�AFG�q/K~D�P�Z\`HK�?\A�e&KRe&AFqFXH=YZ�EVW]KFajb>`HK�?:Z\G�E�I�Z�EHG\KB=@?>A�XCK�SYKiI$Z\G�=@IBW]=2_NDFS2KZ\`�A"Z�=2?�D"dFK�G\AFSYS�XHK�E]Z\G\AFS�ajb>l�Ds?�E�IJ`nW]=2_VD/SYKi?;l~=2S2S�Z\K�X�WCZ�DsG\K�_NK�SN=YP�SY=2OFKRK�X�WH?�A�G\KBI�SYD[?UKi?:Zio/LHEHZ�Z\`HK�^WHD � � Z�K�XVWnZ\DCA"Z�Z�GJAFI$Z>=YP�E�XHSY=2OFKMK�X�WH?cAFG�KMI�S2D/?�K�?UZ�a

¾/�/�sh[e4EHS�ZB¾/¾�µ/µFµg� ³ �Me&D]W]K�GJA"Z\K�e�A�Z�`�u�v�D/EHSYD/esL�· ?�S2A*lz=YX�A/I$Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º]��T:� ½

��¾Ha>7kP�Z\`HK-W]=@?:ZJA�X�I�KRLNK�Z:l�K�K�XQIJ`�AFG�q/K�?�=@?>W]K�I�G�KiAF?�K�W&L(^CA4esEHSYZ�=2_HS2=2I�A"Z�=2dFKRP,AFI�Z�D/G�DFP;� �"µ�o/Z�`HK�e�A�qFX�=�Z\E�W]K�D�PK�SYKiI$Z�G\=@IBP8D/G\I�KMLVK�Z:l�K�K�XZ�`HK6IJ`VA�G\qFK�?�L(^QAgesE�S�Z\=Y_HS2=@I�A"Z\=Yd/K�P,AFI$Z\DFG~DFP:u

A[<�� ¹ a LV<�µ�a Ii<��Fa W�<�� �*µVa Ki<�� �(� ¹ a

¾/�/�sh[e4EHS�ZB¾/¾�µ ¹ ¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj_NDFS@A�G\=Y�iA"Z\=YD/X�]�FaBv�`�AFG�q/K�?�K�_VA�GJA"Z�=2DFXQ=YX�AgXHK�E]Z�GJA�SpD/L,A:K�I�Zc=2?~I�A�S2SYKiWpu

A[<-GJAF?UZ�K�G�=2��A�Z�=2DFX�a LN<-_�A/?:Z\K�EHG\=Y�iA"Z\=YD/X�a I�<6_VD/S2AFG�=2��A�Z�=2DFX�a W�<-X�DFG�Z�`�_NDFS@A�G\=Y�iA"Z�=2DFX�aK*<�e&=YXH=@A"Z\EHG\=Y�iA"Z�=2DFX�a

¾/�/�sh[e4EHS�ZB¾/¾ ¶ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujXHK�ZBIJ`�A�G\qFKRDFX�I�D/X�W]E�I�Z�D/G�F�]a>»{`HK�G�KM=@?cA�S2S�Z�`�KC58XHK�ZJ<~IJ`�AFG�q/KRD/XA&I�DFX�W]EVI$Z�D/G~=YX�AFXQK�SYKiI$Z�G\D/?UZ\A�Z�=@IM?U=YZ�E�A�Z�=2DFX �

A[<v�S2EHe&_NK�Wm=2XnZ\`HK-e&=2WHWHSYK/aLN<¤]_HG�KiAFWQEHXH=YP8DFG\e&SY^nZ�`HG\DFEHq/`HDFEHZ�aIi<¤]_HG�KiAFW�58=2XmqFK�X�K�GJA�S�XHDFXHT�EHX�=�P8D/G�e&S2^]<�D"d/K�G�Z�`HK6?�EHG�P,AFI�KFaWV<mv�S2EHe&_NK�Wm=2X/Z\DgZ:l�D&DFG\LH=YZ�=2XHq&e�AF?\?�=2XZ�`HK-=2X�?�=2WHKFaK*<Q�BSYS�A"Z~Z�`�K-LVDFZUZ�D/e l~`HK�G�K-q/G\A*d(=YZ:^g_�EHSYS@?~=YZ�a

¾/�/�sh[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�I�DFX�W]EVI$Z�D/G~?U`�AFG�__NDF=2X/ZJ?� ³ a~��Z~Z\`HK6?U`VA�G\_QKiW]qFKi?�AFX�W_VD/=YX[ZJ?>D�PjAgIJ`VA�G\qFK�WQI�D/X�W]E�I�Z�DFGiu

A[<�Z\`HK6?�EHGUP,A/I�K-IJ`�AFG�q/K�W]K�X�?�=�Z:^nAFX�WQK�S2K�I$Z\G�=@I���K�S2WmA�G\K�G�K�S2A�Z�=2dFK�S2^�`H=2qF`�aLN<CZ\`HK6?�EHGUP,A/I�K-IJ`�AFG�q/K�W]K�X�?�=�Z:^nAFX�WQK�S2K�I$Z\G�=@I���K�S2WmA�G\K�G�K�S2A�Z�=2dFK�S2^�S2D"l-aIi<CZ\`HK6?�EHGUP,A/I�K-IJ`�AFG�q/K�W]K�X�?�=�Z:^nAFX�WQK�S2K�I$Z\G�=@I���K�S2WmA�G\K�egKiW]=2D(I�G�K/aWV<CZ\`HK6?�EHGUP,A/I�K-IJ`�AFG�q/K�W]K�X�?�=�Z:^nAFX�WQK�S2K�I$Z\G�=@I���K�S2WmA�G\K�SYKi?�?�Z\`�A�Xm^FD/EQe&=2qF`[Z>Z�`H=2XHO�aK*<CZ\`HK6?�EHGUP,A/I�K-IJ`�AFG�q/K�W]K�X�?�=�Z:^nAFX�WQK�S2K�I$Z\G�=@I���K�S2WmA�G\K�G�K�S2A�Z�=2dFK�S2^�G\K�S@A"Z�=2dFK/a

¾/�/�sh[e4EHS�ZB¾/¾ ¼ ¾F¾ ³&³�³ `�AFG\WQe�A"Z�`�u�v�DFEHS2DFe4LAFX�Wnq/G\A*d(=YZ\A�Z�=2DFX�AFS�P8D/G\I�K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º]��T ¶

�"µ�aBv�D/EHSYD/esL�· ?�S@A*l{A�X�WgZ\`HK�_VD/=YX[ZUTke�AF?\?jqFGJA*d(=�ZJA"Z\=YD/X�A�S]P8D/G�e4EHS@AM=YXCX�DFX]TkdFKiI$Z�D/GjP8DFG\e�A"Z>A�G\KFoFG\K�?�_NK�I$Z\=Yd/K�S2^�u

� � $ ��� � � � �

A�X�W ����$ � � � � � �

l~`HK�G�K�� $ ¼ � ½F½ ����¾"#p �e � �Fv ��o � $ ¹ � ¹ º*µ(� ����¾ � � �M=2Xx¯�²6¤mE�XH=�ZJ?�o �n?:ZJA�X�WH?BP8DFGMIJ`�AFG�q/KFo � P8D/Ge�AF?\?�o��&A�XVWx�CP8DFG�_�A�G�Z�=@I�S2K�?g�4AFX�Wx�Ho�A�X�W =@?BZ\`HK&W]=2?UZ\AFX�I�KgLNK�Z:l�K�K�X�Z�`HK&_�AFGUZ\=2I�SYKi?�a6b>`�K4e�AF?\?RD�P

Page 112: Introductory Physics Problems David J. Jeffery Department of

��¾ ¼ v�`�A�_]Zia;�F� �;SYKiI$Z\G�=@I6v�`�A�G\qFK

K�SYKiI$Z�G\DFXV?~=2? ½ � ��¾ ½ ���i¾ � � �MAFX�WZ�`�K�=2GBK�S2K�I�Z�G\=2IsIJ`�A�G\qFKM=@?6� � ¹ ¾[� �r��¾ � ��#�vRaN�c_H_�G�D*�]=2e&A�Z�K�SY^/o�l~`�A�ZB=2?Z\`HKsGJA"Z\=YD�q/G\A*d(=YZ\A"Z\=YD/X�A�SNP8D/G\I�K-Z�D�Z\`HK6K�SYKiI$Z�G\=@I�A�S�P8DFGJI�K6LNK�Z:l�K�K�XmZ:l�D�K�SYKiI$Z�G\DFXV?658=�a K/aYo � � � � ��<�P8D/GRAFX[^W]=@?UZ\A�XVI�K �

A[<��Fa LV<��i¾Ha Ii< ³ �x�i¾ � � � a WV< ³ �x�i¾�� � a K*<���¾ � ��#�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/�/�sh/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujK�SYK�egK�X[Z\A�G\^CIJ`�AFG�q/K�?�=YX�A&I�D/EHS2DFesL�Fa~�fZ:^(_H=2I�A�S�I�EHG\G\K�X[ZB=@?s��� 5,�fP8DFG�A�e&_NK�G\Ki<BDFGs��v�DFEHS2DFe4L�_NK�GM?UKiI�DFXVWpa���=2dFK�X�Z�`VA"ZBZ\`HKgK�S2K�e&K�X[Z\AFG�^IJ`�AFG�q/Ks=@?

�$}� � ¹ ¾/� ����¾ � � #�vRop`HD"lfe�A�X(^�K�SYK�egK�X[Z\A�G\^�IJ`�AFG�q/K�?B��D"l _�A/?:Z6AQ_VD/=YX[Z6=2Xt�&?UKiI�D/X�W�=YP

Z\`HK6I�EHG\G\K�X[Z~=2?M��� �

¾/�/�sh/P8EHS2S�¾/¾/��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�A&dFK�I�Z�D/G>I�A�S@I�EHS@A"Z\=YD/XQl~=YZ�`�IJ`�AFG�q/K�?�]a~|�DFEHGc_NDF=2X[ZBIJ`�A�G\qFKi?>A�G\KM?�K�ZcA�Z~Z�`HKsI�DFG\XHK�GJ?�D�PjA&?�h[E�AFG�K6�ge&K�Z\K�GJ?>DFX�A&?U=@W]KFa���DF=2XHqCI�S2D]IJO[l~=@?�KBP8G\DFeZ\`HK�EH_H_NK�G6S2K�P Z6`VA�X�WrI�D/G�X�K�GiopZ�`HKCIJ`VA�G\qFK�?MAFG�KgS2AFLVK�SYKiWr��5:��v><�o � 5���v><$o�v�5 , ³ v><�o�A�X�Wr¡ 5,µ�v><$a»{`�A�Zc=2?~Z�`HK6X�K�Z~P8DFGJI�K-K��]K�G�Z�K�WQDFX�IJ`�AFG�q/K � �4¿~K�e&K�esLNK�G~Z\DC?U_NK�I�=�P8^A�W]=YG\K�I�Z�=2DFX�a �������� � 9;=2IJOQAI�DFX(dFK�XH=YK�X[ZM?�K�Z-D�P�A"�]K�?MA�XVWxI�DFe&_HE]Z\K4Z\`HKgP8DFGJI�K&I�D/eg_NDFX�K�X[Z\?-AFSYD/XHqCZ\`HD/?�K�A"�]K�?�a4b>`HK�I�DFe&_VD/XHK�X[ZJ?AFG�K A:E�?UZB?�I�A�S@A�GJ?�a�¿~KiI�A�S2S�v�DFE�SYD/esL�· ?>S2A*l�P8DFG>Z\`HKMP8DFGJI�KMW]EHKMZ\D�_�A�G�Z�=@I�S2K&��D/XQ_VA�G�Z�=@I�S2K-�g=@?�u

�� ��� $ �� � � � ����

� ���

l~`HK�G�K � $ ¼ � ½F½ �x�i¾ #  �e � �Fv � A�XVW � ��� _NDF=2X[Z\?�P8G\DFe _VA�G�Z�=@I�S2Kg�MZ\D&_�A�G�Z�=@I�S2K6�]a�¡RG\A*l�A�WH=2AFqFGJA�ema

¾/�/�sh/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK�S2K�e&K�X/ZJA�G\^nIJ`�AFG�q/KRW]=@?U_VA�G\=�Z:^³ a~�}I�DF_�_VK�Gs_NK�XHX(^rl�K�=Yq/`�?sAFLVD/E]Zg� � ¶ q�5,L(^rA/I$Z\E�A�S�o�LHE]Z4X�D�ZsZ\K�G\G�=2LHS2^�A/I�I�EHG\A�Z�K/o�e&K�A/?UE�G�K�egK�X[Zsl~=�Z\`e�A�=2S�l�K�=2qF`H=2XHq&?�I�A�S2Ki<�aA[<Q��=2dFK�XwZ�`�A�ZI�DF_H_NK�Gi· ?nA"Z�D/e&=2I�e�A/?�?n=2? ¹F³ � ¶ =2X�A"Z\DFe&=2I�e&A/?�?CEHXH=YZ\?�58=�a K/aYoc=2X{EHXH=YZ\?QD�PC� � ¹/¹ �

�i¾ � � ��O(q[<�op`HD"l e�A�X(^�I�DF_H_NK�G-A"Z\DFe�?MA�G\K6Z\`HK�G\K4=2XxZ�`HK&_NK�XHX(^�� ������ � 7kP�^FD/E�`�A*dFKQ��¾jO(qQD�PK�qFq[?�AFX�WK�A/IJ`QK�qFqgl�K�=Yq/`�? ¶ ¾jqVo[Z�`HK�X^/DFE`HD"l�e�AFX[^nK�qFq[? �

LN<��=2dFK�X�Z\`�A"Z&AxI�DF_H_NK�G&A"Z\DFe `�AF?&� ½ _HG\D�Z�D/X�?n5,=�a KFa2o�A�Z�D/eg=@ICX(EHe4LVK�G)? $M� ½ <�oj`HD"l esEVIJ`�qFG\D/?\?_ND/?�=YZ�=2dFK-IJ`�A�G\qFK�=2X�v�D/EHS2DFesLV?~W]D(K�?�Z�`�K-_VK�XHX(^n`�A*d/K��

Ii<n7!e�AFqF=2XHK 5,I�DFX[Z�GJA"P,A/I$Z�EVA�S2SY^ AF?rZ\`HK�^�?�A*^ =YX »rAF?�`H=2XHq�Z\DFXV<rZ�`�A�Z�Z�`HK�A�L�?�DFS2E]Z\K{d*AFSYE�K�D�PmZ�`�KK�SYK�e&K�X[Z\AFG�^ _HG\D�Z�D/X IJ`�A�G\qFK{l>AF?�� � ¾F¾/¾F¾F¾��±Z�=2egKi?�S@A�G\qFK�G�Z�`VA�X Z\`HKzAFL�?UD/SYEHZ�K�d"A�S2EHKzD�P�Z�`�KK�SYK�e&K�X[Z\AFG�^&K�S2K�I�Z�G\DFXnIJ`VA�G\qFK658=�a KFa2o(Z�`HK�G�KRl�A/?�A6P8G\A/I$Z�=2DFXVA�SVIJ`VA�G\qFKBW]= ��K�G\K�X�I�KRDFP;5��

���< $ �i¾ � ! <$o

l~`VA"Zcl�DFEHS@WLVK-Z\`HK-P8D/G\I�K�LNK�Z:l�K�K�XmZ:l�D&_NK�XHX�=YKi?BA�W]=@?:ZJA�X�I�K��-e&K�Z�K�GBA�_VA�G�ZBAF?\?UEHe&=2XHqgZ�`�A�ZcZ�`�K_NK�X�XH=YKi?~l�DFEHS@WnLNK-XHK�E]Z�GJA�Sp=YP�Z\`HK�G\K-l�K�G\K�X�D4P8GJAFI�Z�=2DFX�AFSpIJ`�A�G\qFKMW]= �NK�G�K�X�I�K/a

WV<n7:?-AIJ`�AFG�q/K4W]= �NK�G�K�X�I�KgLNK�Z:l�K�K�X�_HG\D�Z\DFXxAFX�WxK�S2K�I$Z\G�D/X�DFP�Z�`HK&D/G\W]K�G-?UEHq/qFKi?:Z\K�W�=2X�Z\`HK&_�A�G�ZC5,Ii<h[EHKi?:Z\=YD/XQS2=2OFK�S2^����j�]_HS@A�=2X�a

� � � � �B_HG\DF_ND/?�D�P(XHDFZ�`H=2XHqc=2XM_�A�G�Z�=@I�EHS@A�Gio�Z\`HK�l�DFGJWB_NK�X�X[^�DFG\=2qF=2X�A�S2SY^BegKiA�X[Z�I�D/=YXMDFP(²M=2XHqc9�K�XVWHA�D�P¯�K�G\I�=2AQ58_HG\DFX�DFEHX�I�K�W�¯�E�G\?�`H=@A/<�A�Xn�BXHqFS2D�T:¤]A"�]D/X�O[=2XHq[W]DFe D�P�I�K�X[Z�GJA�S���X�qFS@A�X�W&=2XCZ\`HK�¡�A�G\O��cq/K�? �Z\`HKCZ\`H=YX�q/?676WHDFX�· ZsO(XHD"l-a�9�K�XVWHAmSY=2dFKiWr=YX�Z�`HK�ºiZ�`�I�K�X[Z�E�G�^ �{EHXHS2K�?\?-Z�`�K�G\KCl�A/?6A�X�D�Z�`�K�G4¯�K�GJI�=@A�XO(=2XHq&D�P�Z�`HK6?\A�e&KMX�A�e&K-A"ZB?�DFe&KMD�Z\`HK�G>Z\=Ye&K/a

Page 113: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � � Da1 � N[1_H ;75\*IH ��*[1_N-,

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/� ³ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\=2IR��K�S2WmW]K���XH=YZ�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�Fa~b>`HK-K�SYKiI$Z\G�=@IR��K�S@W=2?~A�uA[<Cd/K�I�Z�DFG���K�S2WK�e&AFX�A"Z\=YX�q4P8G\DFe}IJ`�A�G\qFKMA�X�WmI�A�E�?�=YX�qsZ\`HK-K�S2K�I�Z�G\=2IRP8DFGJI�K/aLN<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�IJ`�AFG�q/K�AFX�WQI�A�E�?�=2XHqgZ�`HK-K�SYKiI$Z�G\=@IBP8D/G\I�KFaIi<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�I�E�G�G\K�X[ZcA�X�WI�AFE�?�=YXHqgZ\`HK-K�S2K�I�Z�G\=2IRP8DFGJI�K/aWV<nd/K�I�Z�DFG���K�S2WK�e&AFX�A"Z\=YX�q4P8G\DFe}I�EHG\G�K�X[Z~AFX�WmI�AFE�?U=2XHq4Z�`HK-e�AFqFXHK�Z�=@IBP8D/G\I�KFaK*<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�I�E�G�G\K�X[ZcA�X�WI�AFE�?�=YXHqgZ\`HK-e�A�qFX�K�Z�=@IRP,A�GJI�K/a

¾/� ³ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj�jT�P8DFGJI�K�DFX�IJ`�AFG�q/K�]a~b>`HKMP8D/G\I�KMDFXmAgIJ`VA�G\qFK �4I�A�E�?�K�WQL(^nA�XK�S2K�I�Z�G\=2IR��K�S2W � =2?cqF=2dFK�XQL(^Nu

A[< �� $ � ��Na LN< �� $ � � �(a Ii< �� $ �� � ��a W�< �� $f5 �s<���� �(a Ki< �� $ � �Ca

¾/� ³ h[e4EHS�ZB¾/¾/�H��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\DFe�AFqFXHK�Z�=@Ic��K�S2W³ a~��?�K�SYP T�_�G�D/_�A�q[A"Z�=2XHq4K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IB��K�S@W=2?�u

A[<BA?UZ\A"Z\=2I4K�S2K�I�Z�G\=2I6��K�S@Wpa LV<BA?UZ\A"Z\=2I4e�A�q/XHK�Z\=2Is��K�S@Wpa I�<RAQqFGJAF?\?~��K�S2Wpa W�<BSY=2qF`[Z�aK*<>?UD/EHX�Wpa

¾/� ³ h[e4EHS�ZB¾/¾/�/��¾C�&���MK�A/?U^�e&K�egD/G�^�uj_NDF=2X[Z~IJ`VA�G\qFK�K�S2K�I$Z\G�=@IR��K�S@Wµ�a~b>`HKBK�S2K�I$Z\G�=@I>��K�S2W�AFLVD/E]Z�A-_NDF=2X[Z�IJ`�AFG�q/K�D/G�AFX[^g?U_�`HK�G\=2I�A�S2SY^g?U^(e&e&K�Z\G�=@I~IJ`�A�G\qFKcWH=2?UZ�G\=YL�E]Z�=2DFX�=@?�q/=Yd/K�XL(^

� $ ���

��

l~`HK�G�K � $ ¼ � ½/½ �x�i¾"#p �e ���/v ��o =2?�Z\`HK-GJAFW]=2E�?�P8G\DFe Z\`HK-I�K�X[Z\K�G~D�Pj?�^(?UZ�K�emo �6=@?>Z�`HK-IJ`�AFG�q/KR=2X�?�=2WHKDFP�A&?�`HK�S2SpD�Pj?U=2��K oVAFX�W � =@?�uA[<nAgGJAFW]=@A�S2S2^CDFE]Z:l>A�GJWC_NDF=2X[Z�=2XHq&EHXH=YZcdFKiI$Z�D/G�aLN<QAgGJAFW]=@A�S2S2^C=YX(l>A�GJWC_NDF=2X[Z�=2XHq&EHXH=YZBdFKiI$Z�D/G�aIi<QAFXAF��=2esE]Z\`�A�S�A�XHq/SYK�EHXH=YZBdFKiI$Z\DFGiaWV<QAg_NDFS@A�GcAFXHqFS2KMEHXH=YZcdFK�I�Z�D/G�aK*<QAFX l~=YZ�`Z�=2S2WHK-DFX=�Zia

¾/� ³ h[e4EHS�ZB¾/¾/� ³ ¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@IB�VK�S@WQS2=2XHK¶ a~��I�EHG�d/K�Z�`HG\DFEHq/`Q?�_�AFI�K�Z�`�A�Zc=2?>ZJA�XHq/K�X[Z>Z�DgZ�`�K-K�S2K�I$Z\G�=@IR��K�S@WdFKiI$Z�D/GcA"Z~K�A/IJ`Q_NDF=2X[Zc=2?~A(y"AFX�u

A[<~?UZ�G\K�A�e}SY=2XHK/a LV<c?UZ�G\K�AFe}I�EHG�d/KFa I�<cK�S2K�I�Z�G\=2I���K�S2W�SY=2XHKFa WV<~e�A�q/XHK�Z\=2I���K�S2W�SY=2XHKFaK*<>?:Z\G\AF=Yq/`[Z�S2=YX�K6A�S2l�A*^]?�a

¾/� ³ h[e4EHS�ZB¾/¾/��µ/¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�P,AFG>��K�S@WSY=2e&=�Z¹ a~b>`HKsK�S2K�I$Z\G�=@IM��K�S2W�AFG�D/EHX�W�A&S2D]I�A�S2=2��K�W�WH=2?UZ�G\=YL�E]Z�=2DFX�DFPjIJ`VA�G\qFKC58l~=YZ�`xA�XHDFXHT���K�G\DgX�K�Z�IJ`VA�G\qFKi<�=2X�Z�`�KP,AFGUT���K�S@WQSY=2e&=�ZcS2D(DFO]?>SY=2OFK�Z\`HK-K�S2K�I�Z�G\=2IR��K�S2WD�PjA[y�A�X�u

Page 114: Introductory Physics Problems David J. Jeffery Department of

�F�i¾ v�`�A�_]Zia;� ³ b>`�K6��S2K�I$Z\G�=@I�|�=2K�S@W

A[<>W]=2_VD/SYK/a LN<>_VD/=YX[ZBIJ`�AFG�q/KFa I�<>=2X]��XH=YZ�Ks_HS2AFXHK-D�PjIJ`�AFG�q/KFa WV<>=YXH��XH=YZ�KsI�^[S2=2X�W]K�GBD�PIJ`VA�G\qFKFa K*<�=YX]�VXH=�Z\K-SY=2XHK-DFP�IJ`�AFG�q/KFa

¾/� ³ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2KRP,AFG>��K�S@Wº(a~b>`HKMP,AFGUT���K�S2WQK�S2K�I�Z�G\=2IR��K�S2WD�P�A�XmK�S2K�I�Z�G\=2IMW]=2_NDFS2KMP,A�S2S2?>D �xAF?�u

A[<�� � a LN<�� � � a I�<�� � � a W�<M� � � a Ki<R� � � a

¾/� ³ h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2K�K�SYKiI$Z\G�=@I���K�S@W¼ a~b>`HK-_VA"ZUZ\K�G\XQDFP�Z\`HK-K�S2K�I�Z�G\=2IR��K�S2WS2=YX�K�?~A�LNDFEHZBAgWH=Y_NDFS2K-=2?~?�DFG�Z~D�P:u

A[< L�E]ZUZ\K�G���^[T�S2=YO/KFa LV< S@AFW]^(LHEHqFT�S2=2OFKFa I�< W]G\AFqFD/X]��^[T�S2=2OFKFa WV< AF_H`H=@W(TkSY=2OFK/aK*<�_HGJA*^[=2XHqFT�e�A�X[Z\=2?UT�S2=2OFKFa

¾/� ³ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2K�?>=2XXVA"Z�E�G�K½ a~b>`HK-_NK�G\e�A�XHK�X[Z>D/G~=YXVW]E�I�KiWmW]=Y_NDFS2K�?~A�Z~Z�`HK-e&=@I�G\D/?\I�D/_H=2IRS2K�dFK�S�A�G\KFu

A[<QEHX�I�D/e&egD/X�a LV<mI�DFe&e&DFX�a I�<X�K�dFK�GP8DFEHX�W�a W�<XHK�d/K�GP8DFE�X�W�DFX �;A�G�Z�`�aK*<�XHK�d/K�G>P8D/EHX�WQ=YX�?�_�AFI�KFa

¾/� ³ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2KRZ\DFGJh[EHK��¾Ha~b>`HKMZ\DFGJh[EHKMDFXmA�XK�S2K�I$Z\G�=@IMW]=2_VD/SYK-DFP�W]=2_NDFS2K�e&D/egK�X[Z ��=2X�A�XmK�S2K�I�Z�G\=2IR��K�S2W � =2?�u

A[< � $ �� � �Ca LV< � $ , �� � �Ca Ii< � $ �� � �&a W�< � $ , ���� �&a K*< � $ , �� � ��a

¾/� ³ h[e4EHS�ZB¾/¾[º�¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2K�_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^�F�Fa~�BXK�SYKiI$Z\G�=@IMW]=Y_NDFS2KC58l~=YZ�`me&DFe&K�X/Z ���<�=YX�AFXQK�SYKiI$Z�G\=@IB�VK�S@W � `�A/?~Ag_VDFZ�K�X[Z\=2AFS�K�XHK�G�q/^�D�PjA�S2=Yq/XHe&K�X[Z�u

A[< � $ �� � �Ca LV< � $�, �� � ��a Ii< � $ �� � ��a W�< � $ , �� � ��a Ki< � $�, �� � ��a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/� ³ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�AFGUZ\=��VI�=2AFSpK�S2K�I�Z�G\=2IR��K�S2WD�P��;AFGUZ\`�Fa>7kP~Z\`HK��A�G�Z�`�`�A/W�A�X�K��HI�K�?\?6DFPBIJ`�A�G\qFKnD�P-�Fa ¾�K�SYK�egK�X[Z\A�G\^rIJ`�A�G\qFK�EHX�=�Zg_VK�Gg?\h[E�A�G\KCe&K�Z\K�Gm58l~`H=@IJ`=@?6XHDFZ6Z�`�KnI�A/?UKCA/I$Z�EVA�S2SY^H<$o�l~`�A�Zsl�D/EHS@WxLNKn=YZ\?sK�S2K�I�Z�G\=2Ig��K�S2W!A:EV?:Z&A"Z6Z\`HKn?�EHGUP,A/I�K � £BD"l WHD[Ki?-Z\`H=2?I�DFe&_�A�G\KRZ�D&Z�`�K-LHG�KiA�O]W]D"l~XQK�S2K�I$Z\G�=@IR��K�S@WQP8DFGcAF=YG65 ³ �x�i¾"!p  �/vRu�£B¿�»wT ¶ �]�i< �� � � � �B?>D/XHKMI�A�XQ_HG\D"dFKBKiAF?�=YS2^�E�?�=YX�q��MAFE�?\?�·(S@A*l-o/Z\`HKMK�S2K�I�Z�G\=2IB��K�S@WQDFE]ZJ?U=@W]KMD�P�E�XH=�P8D/G�emo]=2X]��XH=YZ�K_HS@A�X�KMI�DFX�WHE�I$Z\DFG658l~`�=2IJ`m=@?~A�S@?UD&=2X]��XH=YZ�K�SY^W]K�K�_V<�=2?cqF=2dFK�XQL(^

� $ �

� ��� �

l~`HK�G�K �x=2?~Z�`HK6?�EHG�P,AFI�KMA�G\K�A&IJ`�AFG�q/KRW]K�X�?�=�Z:^/o

��$ ¼ � ¼[¶ ����¾ � ��� v � �H5, �e � <

=@?~Z\`HK6d"AFI�EHEHe _VK�G�e&=YZ�=2d[=YZ:^mA�X�W ��r=2?BA�EHXH=YZBdFKiI$Z\DFG~_NDF=2X/Z\=YX�qCDFE]ZBP8G�D/e Z�`�Ks?UE�GUP,A/I�KFa>¿~K�egK�esLNK�GBAFSYSZ\`HKCIJ`�A�G\qFK4DFXrAmI�DFXVW]E�I$Z\DFGM=2XrAFXx=@W]KiA�SjK�S2K�I�Z�G\D/?UZ\A�Z�=@I4I�AF?�Kg=@?MS2D(I�A"Z\K�W�A"ZMZ�`HKC?�EHG�P,AFI�KgAFX�W�Z\`HK�G\K&=2?XHDnK�S2K�I$Z\G�=@I���K�S2Wm=2X�?�=2W]K6Z�`HKgI�DFXVW]E�I$Z\DFGia�»�KsAFG�K6A/?�?�EHe&=YX�q�DFE]ZJ?U=@W]KMZ�`�K4I�D/X�W]E�I�Z�D/Gs58=�a K/aYo�Z�`HKg�;AFGUZ\`V<I�A�XmLVK4A�_H_HG\D*�]=Ye�A�Z�K�WAF?cd*A/I�EHE�e A/?>P,A�GBA/?~_NK�G\eg=YZ�=2d(=�Z:^=@?BI�D/X�I�K�G�X�K�WpujP8D/GcDFE�GBI�D/X�?U=@W]K�G\A�Z�=2DFX�?�Z\`H=2?A/?�?�EHe&_]Z�=2DFX=@?c?UEH��I�=YK�X[Z�S2^Cd"A�S2=2Wpa

¾/� ³ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK�S2K�I�Z�G\DFXmI�G\D/?\?U=2XHqgLVK�Z:l�K�K�X_HS@A"Z�Ki?

Page 115: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia;� ³ b>`HK-��S2K�I$Z\G�=@IM|�=YK�S2W �F�/�

�]a~b>`HK�G�K�A�G\K~Z:l�D6S2AFG�q/Kc_�AFG\AFSYS2K�SV_HS2A�Z�Ki?B58_�S2A�Z�Kg�RA�XVW&_HS2A�Z�K-�F<;¾ � ¾ ¶ e A�_�AFGUZ;l~=YZ�`A�G\K�A6IJ`VA�G\qFKcW]K�X�?U=YZ�=2K�?� � � ¾�A�X�W � � � ¾HugXHDFZ�K � � �$ , � � X�K�I�Ki?�?\A�G\=2SY^/amb>`�KC_HS@A"Z�Ki?sI�A�X�LNK�Z�G\K�A�Z�K�W�A/?6=2X]��XH=YZ�KAF?6AFXAF_H_HG\D*�(=2e�A"Z\=YD/X�a��/E�?UZB?UD&l�K-A�S2S�A�q/G�K�KRD/XnZ\`HK6I�D(DFGJW]=2X�A"Z\K-I�DFX(d/K�X[Z�=2DFX�?�u�_HS2A�Z�K��M=@?~A"Z�� $�¾HoH_HS@A"Z\K6�=@?cA"Z � $ � $�¾ � ¾ ¶ emo]A�X�WQZ\`HK-EHXH=YZcdFKiI$Z�D/G>=YXZ�`�K-_VD[?U=YZ�=2dFK ��W]=2G\K�I$Z\=YD/XQ=@? ���a� � � � b>`�K6IJ`�A�G\qFK-W]K�X�?U=YZ�=2K�?B`�A*dFKM_HS@A�XVA�Gc?�^[e&e&K�Z\G�^/o�LHEHZBl�K6WHDFX�· ZBO(XHD"l�D/GcXHK�K�WZ�D�O(XHD"l�`HD"lZ\`HK6IJ`�A�G\qFKR=2?~WH=2?UZ�G\=YL�E]Z�KiWQl~=YZ�`mW]K�_]Z�`Z�`�G�D/EHqF`QZ�`HKM_HS@A"Z\K�?�a>��E]Z~l�K-W]D&O(XHD"l{Z\`�A"ZcKiAFIJ`QWH=���K�G\K�X[Z�=@A�S_HS@A�XVA�Gc?�S2AFL�?�l~=�Z\`�IJ`�A�G\qFK�W]K�X�?�=YZ:^ � ��=2X�A4_�S2A�Z�K-qF=2dFKi?�G�=@?UK�Z\D&A�WH=���K�G\K�X[Z�=@A�SpK�SYKiI$Z\G�=@IR��K�S@W

� � $ � �� � �

��

l~`HK�G�K ���_VD/=YX[ZJ?cA*l�A*^gP8G\DFe�Z�`HK6?�S2AFLQD/XQK�=�Z\`HK�GR?U=@W]K-D�P�Z�`HK4?US@A�LmA�X�W � � =2?~Z�`HK-d"AFI�EHEHe}_VK�G�e&=YZ�=2d[=YZ:^Fab>`H=@?~G\K�?�EHSYZ�P8D/SYS2D"lc?�P8G\DFe}�MAFE�?�?�·]S@A*l-a�»�K6I�AFXQ=2X[Z�K�qFGJA"Z�KMEH_�AFSYS�Z\`HK�?�K-?US@A�L�?>=2e&e&K�W]=@A"Z\K�S2^CZ�D�q/K�Z

� $ �

� � ���

l~`HK�G�K ��=2?�Z�`HKRK�S2K�I�Z�G\=2Ic��K�S@W�DFEHZ\?�=2W]KBD�PpZ�`�KB_HS@A"Z\KBA�X�W ��_NDF=2X[Z\?�A*l�A*^6P8G�D/e Z\`HKB_�S2A�Z�KcD/XCK�=YZ�`HK�G�?�=2WHKDFP�Z\`HK-_HS@A"Z�K/aA[<n|VA�G�P8G�D/e Z�`HK�K�W]q/K�?�o/l~`VA"Z>=2?�A�_H_�G�D*�]=2e&A�Z�K�SY^4Z�`HK�K�S2K�I�Z�G\=2Ic��K�S@WCLNK�Z:l�K�K�X�Z�`�KR_HS@A"Z\K�?����=Yd/KRLND�Z\`e�AFqFXH=YZ�E�WHK6A�X�WW]=2G�KiI$Z�=2DFX�a�°RX�SY^Ag?�^(esLNDFS2=2IMAFX�?Ul�K�G>=@?~_ND/?\?U=2LHS2KFa

LN<Q��Z;Z�=2egKR��K�G�DVoFA-_HG\D�Z\DFX&=2?;G�K�SYKiAF?�K�WsP8G�D/efZ\`HKc_ND/?�=�Z\=Yd/Kc_HS@A"Z\KBA�X�W&AFX�K�S2K�I$Z\G�D/XgP8G�D/efZ\`HKcXHK�q/A"Z\=Yd/K_�S2A�Z�KFa ��D�Z\`�_�A�G�Z�=@I�S2K�?�A�G\KcA"Z�G�Ki?:Z�A�Z�Z�`�KcZ�=2e&KBDFP�G�K�SYKiAF?�KFa�b>`�K�^&W]DFX�· Z�=2X[Z�K�G\A/I$Z;l~=YZ�`CKiAFIJ`�DFZ�`HK�GA/?cZ\`HK�^�e&D"d/K6EHX�W]K�GBZ\`HKgK ��K�I$ZMD�P;Z�`HKgK�S2K�I�Z�G\=2I6��K�S@Wpa-��Z�l~`VA"ZBZ\=Ye&K&W]DCZ\`HK�^�_VAF?\?BKiAFIJ`�DFZ�`HK�G=2X�?U^(e4LVD/S2?�

Ii<n»{`VA"Z;=@?jZ\`HK�=2G;W]=@?:ZJA�X�I�K~P8G\DFef_�S2A�Z�K-�c=2XCAFI�Z�E�AFSHX(EHesLNK�GJ?�A"ZjZ\`H=@?jZ�=2e&KcD�Pp_�A/?�?�=2XHq � ������ � b>`�KGJA"Z\=YD&DFP�_HG\D�Z\DFXQZ�D&K�S2K�I�Z�G\DFXe&A/?�?>=@?-� ¼F³F¹ aY� ¶ a

¾/� ³ h/P8EHS2S�¾/¾ ³ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�IJ`�A�G\qFK�G�D]Wpo]=2X[Z�K�qFGJA"Z�=2DFX³ a~b>`HK�G�Ks=2?�A�Z\`H=YX�EHXH=YP8DFG\egS2^�IJ`�A�G\qFKiWG�D]WmD�P�S2K�X�q�Z�` �caBb>`HKsZ�DFZ\A�S�IJ`�AFG�q/K-=2? �(aBb>`HK4G�D]Wp· ?cZ\`H=@IJO[X�K�?\?=@?~XHK�qFS2=Yq/=YLHS2KFu�=YZBI�AFXQLNKMZ�G\K�A�Z�K�WAF?~AgS2=YX�K-D�PjIJ`�A�G\qFK/aA[<C»{`VA"Z~=2?�Z\`HKRK��]_HG�Ki?�?�=2DFX�P8D/G;Z\`HKMK�S2K�I$Z\G�=@IB��K�S@WnAgW]=@?:ZJA�X�I�K���A*l>A*^sP8G\DFe D/XHK�K�X�WnD�P�Z\`HKMG�D]WCAFX�WAFSYD/XHqmZ�`�KnA"�]=@?MD�P>Z�`HKnG�D]W � �������� � |�=YXVW�Z�`HKCK��]_HG�Ki?�?�=2DFX�P8DFGsIJ`VA�G\qFK&_VK�G6EHXH=YZ4S2K�X�q�Z�`�AFX�WZ\`HK�X�W]=2d(=2WHK6A�X�WI�D/X�h[EHK�G~L(^C=2X[Z�K�q/G\A�Z�=2DFX�aj¡RG\A*l�A&W]=2AFqFGJA�ema

LN< 7!X�Z\`HK-P,AFGUT���K�S@WmS2=Ye&=YZ�oNl~`�A"ZRWHD[Ki?~Z\`H=2?RK��]_HG\K�?\?�=YD/XLNK�I�DFe&K��r BD�Z\KFu���K�G\DC=@?cXHDFZRA�X�A/I�I�K�_]ZJA�LHS2KAFX�?�l�K�G>AFS�Z\`HDFE�qF`QZ�`�A�Zc=2?>Z\`HK-AF?�^(eg_HZ�D�Z\K-l~`H=@IJ`nZ\`HKMP8EHX�I�Z�=2DFX�A�_H_�G�D[AFIJ`HKi?�a

¾/� ³ h/P8EHS2S�¾/¾�µ/¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�uj=YX]�VXH=�Z\K6S2=YXHK6IJ`VA�G\qFKµ�a>»{`�A�Z;=@?�Z�`HKBK�S2K�I$Z\G�=@I>��K�S2Wm5�?U=2��KBAFX�W&W]=2G�KiI$Z�=2DFXN<jA�G\DFEHXVW4AFX�=YX]�VXH=�Z\KcS2=YXHKBD�PpIJ`�A�G\qFK>l~=YZ�`�S2=YXHKiA�G;IJ`VA�G\qFKW]K�X�?�=�Z:^ � a �������� � ¡R=Yd(=@W]KcA�X�W&I�DFX�h[EHK�G�u�l~`VA"Z�=@?�Z�`HKBK�S2K�I$Z\G�=@I���K�S@W�A"Z;AFXgAFG�L�=�Z\G\AFG�^-_NDF=2X[Z;=YX�?�_�AFI�KW]E�KMZ�DCA�X�AFG�LH=YZ�GJA�G\^CW]= �NK�G�K�X[Z�=@A�S�LH=YZcD�P�Z�`�K6SY=2XHK ���BS2?�D�ujL(^Q?�^(e&egK�Z�G\^Cl~`�A�ZcesE�?UZBLNKMZ�`HKsWH=YG\K�I�Z�=2DFXDFP�Z\`HK6K�SYKiI$Z�G\=@I���K�S@W �r�cXVWmS2A/?:Z\SY^/oVA�I�D/X(dFK�GJ?�=YD/XnZ\DCA�XHq/EHS2AFGc=2X/Z\K�q/G\A�Z�=2DFXm?�A*d/K�?>XH=2XHKn5,D�Pjl~`�A"Z ��I�A"ZJ?�·S2=Yd/K�?�*<$u � $ Z\AFX �6l~`HK�G�K��Q=2?�Z�`HK�I�D(DFGJW]=2X�A"Z\KBA�S2DFX�qMZ�`HKRSY=2XHKBDFP�IJ`�A�G\qFK>G\K�A/IJ`H=YX�qMP8G�D/e , Z�D � AFX�W =2?�Z\`HK-_VK�G�_NK�XVW]=2I�EHS@A�G~W]=@?:ZJA�X�I�KRP8G\DFe ^/DFEHG~AFG�LH=YZ�GJA�G\^&_VD/=YX[Z>Z�DgZ\`HKMSY=2XHK-A"Z>Z�`�K���${¾gSYD]I�A"Z�=2DFX�a

¾/� ³ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u;¤]£M°�K�SYKiI$Z\G�=@IMW]=Y_NDFS2K¶ a~b>`HKMZ\DFGJh[EHKMDFXmAgWH=Y_NDFS2K-e&DFe&K�X[Z ���=YX�AFXQK�SYKiI$Z�G\=@IB�VK�S@W � =@?

�� $ �� � � �

7kP>l�K&l~G\=�Z\KgZ�`H=@?MP8DFG\esE�S2AQ=YX�?\I�AFS2AFGRP8D/G�e egKiAF?�EHG\=YXHq �P8G�D/e�Z�`�K�K�S2K�I$Z\G�=@I4��K�S@WrW]=2G�KiI$Z�=2DFXw58l~`�=2IJ`�=2?I�DFX(dFK�X/Z\=YD/X�A�S <$o[Z\`HK�X

� $ , � r?�=YX �

Page 116: Introductory Physics Problems David J. Jeffery Department of

�F�*� v�`�A�_]Zia;� ³ b>`�K6��S2K�I$Z\G�=@I�|�=2K�S@W

l~`HK�G�K �xA�XVW A�G\KFoVG�Ki?U_NK�I�Z�=2dFK�SY^/o�Z\`HKse�A�q/XH=YZ�E�W]Ki?BDFP ���A�XVW � A�XVWmZ�`HK4XHK�q[A"Z\=Yd/Ks?U=2qFX�?�`HD"lc?cZ�`�A�ZZ\`HK-Z�D/G\h[EHK-AFSYl>A*^]?�Z�G\^(?~Z�DCA�S2=2qFXZ�`HK6WH=Y_NDFS2K6e&DFe&K�X[Zcl~=YZ�`mZ\`HK-��K�S2Wpu�=�P � �{¾gZ�`�K-Z�D/G\h[EHK-_NDF=2X[Z\?~=2XZ\`HK&XHK�q[A"Z�=2dFK �WH=YG\K�I�Z�=2DFX )�=YP �$��¾nZ�`HKgZ\DFGJh/E�Ks_NDF=2X/ZJ?�=YXxZ�`HK&_ND/?�=�Z\=Yd/K �W]=2G�KiI$Z�=2DFX�asb>`HKgZ�D/G\h[EHK4D�PZ\`HK-K�S2K�I�Z�G\=2IR��K�S2W=@?>Z�`HK-D/XHS2^�Z�D/G\h[EHK-AFI�Z�=2XHq&DFXQZ�`HK6WH=Y_NDFS2KFa

A[<n|�G�D/e  cK�l>Z�DFX�· ?-?�K�I�DFX�W�S2A*l =2Xx?\I�AFS2AFGRG\D�ZJA"Z\=YD/X�A�S�P8DFG\e���X�W�Z�`HK�W]= ��K�G\K�X[Z�=@A�SjKih/EVA"Z�=2DFX�P8DFG�Z�`�Ke&DFZ�=2DFXD�P�Z�`HK6W]=2_NDFS2K-=YXZ�`�K-K�S2K�I$Z\G�=@IR��K�S@Wpa�¿~KiI�AFSYS�Z\`H=2?~P8DFG\e D�P�Z�`HK6?�K�I�DFX�WQS@A*l�=@?

� $���

l~`�K�G\K �m=@? � Z\DFGJh/E�KFo ��=@?~G�DFZ\A�Z�=2DFX�AFSN=2XHK�GUZ\=2A�oHA�X�W � $ ���� � � � �M=@?~A�XHq/EHS2AFG~AFI�I�K�S2K�GJA"Z\=YD/X�aLN<n7kP�^FD/Ene�A�O/KBZ\`HK6?�e&AFSYSpAFXHqFS2K-A�_H_HG\D*�]=Ye�A�Z�=2DFX�o[l~`�A"ZcW]= ��K�G\K�X[Z�=@A�SpKih/EVA"Z�=2DFXnP8DFGcA&?UZ\A�XVWHA�GJWCO(=2X�W

DFP�e&DFZ�=2DFXmW]D&^FDFE`�A*d/K��Ii<Q|�DFGjZ\`HKc?�DFS2E]Z�=2DFXgZ�DMZ\`HKBAF_H_HG\D*�(=2e�A"Z\K�Kih/EVA"Z�=2DFX&=2X&Z�`HK~_VA�G�ZB58LV<jAFX�?�l�K�G�o�l~`VA"Z�=@?�Z�`HKBK��]_HG\K�?\?U=2DFXP8D/G>Z�`HK6AFXHqFE�S2AFG�P8G\K�h[EHK�X�I�^QA�X�W_NK�G\=YD]WQD�P�Z�`HK-e&D�Z\=YD/X �

WV<Q BD"lzS2K�Zi· ?cLVKsI�DFX�I�G�K�Z�K-A�XVWI�DFX�?�=@W]K�GBAgl>A"Z\K�Gce&DFS2K�I�EHS2KC5,£ � °M<>=2XmAFX�A�_H_HS2=2K�WEHXH=YP8DFG\e�K�SYKiI$Z�G\=@I�VK�S@WQDFP�?UZ�G\K�XHqFZ�`mD�P���¾ �   �Fvf58S2=2OFKMXHK�AFGcA&IJ`�A�G\qFKiWnI�D/esL�uj£R¿�»wT ¶ �]�*<$ajb>`HK6W]=2_NDFS2K-egD/e&K�X[Z~D�PAl>A"Z\K�G-e&DFS2K�I�EHSYK&=@?-A�LNDFE]Z ¹ � � ���i¾ ��� � v;T�e 5,£R¿�»wT ¶�³ ºF<$a��B?\?�EHe&K&Z�`HK&l>A"Z�K�G-e&DFS2K�I�E�SYK&=@?-AE�XH=�P8D/G�e ?UD/SY=@W&?U_�`HK�G\K~D�P�G\A/W]=2E�?~�����5,=�a KFa2oV�i¾ � � � eC<�Z\D6I�A�S@I�E�S2A�Z�K~=YZ\?jG\D�ZJA"Z�=2DFXVA�S]=2XHK�G�Z�=@AHu�AM_HG�K�ZUZ:^?�D�T!?�DgAF_H_HG\D*�(=2e�A"Z\=YD/X�a�»{`VA"Zc=@?�Z�`HKMP8G\K�h[EHK�X�I�^�#�D�P�Z�`HK-e&DFZ�=2DFX �

¾/� ³ h/P8EHS2S�¾/¾ ¹ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�I�S2A/?�?�=2I�A�S�`(^]W]G�D/qFK�XQA"Z\DFe¹ a~b>`HK`(^]W]G�D/qFK�X�A"Z�D/e I�AFXHXHD�ZgG�KiA�S2SY^rLNKQE�X�W]K�GJ?UZ�D(D]W�=YX±I�S@AF?\?U=@I�AFS�_�`[^]?�=2I�?�uCh[E�AFX[Z�EHe e&K�IJ`VA�XH=@I�?4=2?G\K�h[EH=2G�KiWpaj cK�dFK�G�Z�`�K�S2K�?\?�o]D/XHK-I�A�XqFK�Zc?UD/egKM=@W]K�A&DFP�Z\`HK6?U=2��KMDFP�K.�NKiI$Z\?~P8G�D/e�I�S@AF?\?U=@I�AFS�K�?UZ�=2e&A�Z�Ki?�aA[<Q��=2dFK�X±Z�`�A�Z�Z�`HK�?�K�_VA�GJA"Z�=2DFXtD�PMZ�`�K�K�S2K�I$Z\G�D/X±AFX�W±_HG\D�Z�D/Xw=YX±Z�`�K�`(^(WHG�D/qFK�X±A"Z\DFe =@?C¾ � ¶ � ½ �

�i¾ � � � emo�l~`�A�Z�=@?�A�L�?�DFS2E]Z\K;d"A�S2EHK�D�PHZ\`HK>K�S2K�I$Z\G�=@IjP8D/G\I�K�LNK�Z:l�K�K�X6Z\`HK�?�K�_VA�G�Z�=@I�S2K�?�up=�a KFa2o"Z�`�K�K�SYKiI$Z�G\=@IP8D/G\I�KBKiAFIJ`nK��]K�G�Z\?�DFXCZ\`HKMD�Z\`HK�Gia�5�b>`HK-¾ � ¶ � ½ ����¾ � � � e =2?�Z�`�KRe&K�AFXQ?�K�_�AFG\A�Z�=2DFXCDFP�_HG\D�Z\DFXnAFX�WK�SYKiI$Z\G�D/XA/?~W]K�Z\K�G\eg=2XHKiWQL(^nh[E�AFX[Z�EHe}egKiIJ`�A�X�=2I�?�a <67:?�Z\`HKMP8DFGJI�K-A�ZUZ�GJAFI�Z�=2dFKMDFG>G\K�_HE�S2?�=Yd/K��

LN<��=2dFK�X�Z�`VA"Z�Z�`HKgK�S2K�I�Z�G\D/?UZ\A"Z\=2I-P8DFGJI�Ks=@?BZ�`HK4DFXHS2^P8DFGJI�KsLNK�Z:l�K�K�X�K�S2K�I�Z�G\DFX�AFX�W�_HG\D�Z\DFX�5,l~`H=@IJ`�=2?X�D�Z�h[EH=�Z\K�Z�G\EHKi<�A�XVW6Z\`�A"Z�Z�`�K�_�G�DFZ�DFXgI�AFXsLNK~G�K�q/A�GJW]KiW6AF?�A"Z�G\K�?UZ~5,l~`H=@IJ`4=@?jA�S2e&D/?UZ�Z\G�EHK�LNK�I�AFE�?�KDFP~=�ZJ?6esEVIJ`�qFG\K�A"Z\K�G-e�AF?\?J<$o�l~`�A"Zs=@?-Z\`HKCK�SYKiI$Z�G\DFX�· ?4AFI�I�K�S2K�GJA"Z\=YD/Xxe�A�q/XH=YZ�E�W]KQA�X�W�l~`H=@IJ`�l�A*^WHD[Ki?�Z�`HK6A/I�I�K�S2K�GJA"Z�=2DFXQ_VD/=YX[Z �

Ii<��=2dFK�X�Z\`�A"ZMZ�`�K&AFX�?�l�K�GBZ\D_VA�G�Z&5,LV<$o�l~`VA"Z6I�AFX�^FD/Ex?�EHqFq/K�?UZ�A/?BZ\`HK�I�S@AF?\?U=@I�AFS�G\K�A/?UD/X�l~`(^�Z�`�KK�SYKiI$Z\G�D/X±W]D(Ki?UX�· ZCI�GJAF?�`�=2X[Z�D�Z�`HK�_�G�DFZ�DFX � ������ � »{`[^tW]D(K�?�X�· Z�Z\`HK�¯�D(DFX±I�GJAF?�`t=2X[Z�D�Z�`�K��A�G�Z�` �

WV<Q�R?�?�EHe&=2XHq6Z\`HKBe&D�Z\=YD/XCD�P�Z\`HKRK�SYKiI$Z\G�D/X�=2?;EHXH=YP8DFG\e�I�=YGJI�E�S2AFG;e&D�Z\=YD/X�o/l~`VA"Z�=@?;Z�`HKRK�S2K�I$Z\G�D/XC?U_NK�KiW� �m»{`�A�Zc=2?~Z�`HK-GJA"Z\=YD � ��*���¿~KiI�AFSYS � �3*�=@?~I�DFX(d/K�X[Z�=2DFX�AFSYS2^CW]Ki?U=2qFX�A�Z�KiW��r=2XG\K�S@A"Z\=Yd(=YZ:^Fa

Page 117: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � �'&Ad�EGE � ��& �

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/��µgh[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u;�MAFE�?�?>S@A*l-o(`H=2qF`�?U^(e&e&K�Z\G�^�Fac�MAFE�?�?�·iS2A*l�q/=Yd/K�?�Acl>A*^RZ\DRKiAF?�=YS2^MDFL]ZJA�=2XsA�X4K��]_HG\K�?\?U=2DFXMP8D/G�Z\`HK�K�S2K�I$Z\G�=@I;��K�S@W6DFPVABIJ`�AFG�q/K;W]=@?:Z\G�=2LHE]Z\=YD/X=2X�I�AF?�K�?�DFP:uA[<C`�=Yq/`m?�^(e&egK�Z�G\^�u�_�G�=2X�I�=2_�AFSYS2^Fo]_HS@A�XVA�GioHI�^(SY=2X�W]G\=@I�A�S�AFX�W?U_H`�K�G\=2I�A�S�?�^[e&e&K�Z\G�^/aLN<nS2D"lz?�^(e&egK�Z�G\^�u�K/a qVaYo�=YG\G�K�qFEHS@A�G�DFL3A:K�I$ZJ?�oHIJ`VA�G\qFK�WQA"Z\egD[?U_�`HK�G\=2IMI�SYD/E�WH?�aIi<n=2X�W]= ��K�G\K�X[ZB?U^(e&e&K�Z\G�^/aWV<Q?UZ�GJA�X�qFKM?U^(e&e&K�Z�G\^FaK*<QIJ`VA�G\e�?U^(e&e&K�Z\G�^/a

¾/��µgh[e4EHS�ZB¾/¾/�F¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�h[EH=2d"A�S2K�X[Zc_H`(^]?U=@I�AFSNS@A*lc?�]a~b�D�?�A*^�Z\`�A"Z~Z:l�Dg_H`(^(?�=@I�A�SpS@A*lc?>DFG>_ND/?UZ�EHS@A"Z\K�?cAFG�K�K�h[EH=2d"A�S2K�X[Zce&K�AFX�?�u

A[<�Z\`�A"Z ��¦ ��=2e&_HSY=2K�?;Z�`�KRDFZ�`HK�G�a�b>`(E�? � �� � ��������Z�`�A�Z>I�A�XCLNKRW]KiW]E�I�K�W�P8G\DFe�D/XHKBI�AFXAFS2?�D�LNKsW]K�WHE�I�KiWP8G�D/e�Z\`HK6D�Z\`HK�Giacv�DFEHS2DFe4L�· ?cS2A*l A�X�W��MAFE�?\?�·HS@A*l�=YX�K�SYKiI$Z�G\D/?UZ\A�Z�=@I�? � � AFXK��HA�e&_HS2K�DFP�Kih[EH=Yd"AFSYK�X/Z~S@A*lc?�a

LN<CZ\`�A"Z � � �=Ye&_HS2=2K�?�Z\`HK�D�Z\`HK�Gio�LHE]ZCXHDFZCd[=@I�K�d/K�GJ?�A�a{b>`[EV? �� � � ������� Z\`�A"ZnI�A�XwLNKWHK�W]E�I�K�W�P8G�D/e D/XHKsI�A�X�AFS2?�DCLNKgW]KiW]E�I�K�W�P8G\DFe Z\`HKsDFZ�`HK�G�a6v�DFEHS2DFe4L�· ?cS@A*l AFX�Wx�MAFE�?\?�·VS2A*l�=2XK�SYKiI$Z\G�D[?:ZJA"Z�=@I�? � � � � A�XmK��]AFe&_HSYKMDFP�K�h[EH=2d"A�S2K�X[ZcS@A*lc?�a

Ii<CZ\`�A"Z � �� � �� =2e&_HSY=2K�?�Z\`HKMD�Z\`HK�Gia�b>`(E�? � � �������}Z\`�A"Z~I�AFXnLNK-W]K�W]EVI�K�WCP8G�D/e DFX�KRI�AFXAFS2?�D�LNKsW]K�WHE�I�KiWP8G�D/e�Z\`HK6D�Z\`HK�Giacv�DFEHS2DFe4L�· ?cS2A*l A�X�W��MAFE�?\?�·HS@A*l�=YX�K�SYKiI$Z�G\D/?UZ\A�Z�=@I�? � � AFXK��HA�e&_HS2K�DFP�Kih[EH=Yd"AFSYK�X/Z~S@A*lc?�a

WV<CZ\`�A"Z �C¦ � =Ye&_HS2=2K�?�Z�`�K-D�Z�`�K�Gia�b>`(E�? � � �������}Z\`�A"ZcI�A�XLVK-W]KiW]E�I�KiWCP8G\DFe�DFXHK-I�AFXQAFS2?�DLNK�W]K�WHE�I�KiW�P8G\DFe�Z\`HK4DFZ�`HK�G�a&v�DFEHS2DFe4L�· ?RS@A*lfA�X�W��MA�E�?\?�·NS@A*l =2X�K�SYKiI$Z�G\D/?UZ\A�Z�=@I�? � � � � AFXQK��HA�e&_HS2K-D�P�Kih[EH=Yd"AFSYK�X/Z~S@A*lc?�a

K*<CZ\`�A"Z~Z\`HK�^4� � � � K�AFIJ`D�Z\`HK�Gia

¾/��µgh[e4EHS�ZB¾/¾ ³ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@IB�VE]�³ a~b>`HK6h[E�AFX[Z�=YZ:^ �

��� � � � � �� � � ��

=@?>Z�`�KFuA[<�K�SYKiI$Z\G�=@I�_ND�Z\K�X[Z�=@A�S�a LN<�K�SYKiI$Z\G�=@I��VK�S@Wpa Ii<�K�SYKiI$Z\G�=@I��VE]� Z�`HG\DFE�qF`}A ?�EHGUP,A/I�K/aWV<�e&AFqFXHK�Z�=@IR��E]�nZ\`HG\DFEHq/`A&?�EHGUP,A/I�K/a Ki<�e�A�q/XHK�Z\=2I�_ND�Z�K�X[Z�=@A�S�a

¾/��µgh[e4EHS�ZB¾/¾�µ[¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u;�MAFE�?�?�·]S@A*lµ�a~b>`HK-K��]_HG�Ki?�?�=2DFX �

��� � � � � �� � � �� $ � � � � � � � � �

� �=@?�uA[<�Z\`HK6W]= �NK�G�K�X[Z�=@A�SpK�h[E�A�Z�=2DFXQP8DFG\e�DFP��MA�EV?�?�·]S2A*l-a

Page 118: Introductory Physics Problems David J. Jeffery Department of

�F��µ v�`�A�_]Zia;�"µ}�MAFE�?\?�·H¸�A*l

LN<CZ\`HK-=2X/Z\K�q/G\AFSNKih[E�A"Z\=YD/XnP8D/G�e}D�P��MAFE�?\?�·]S@A*l-aIi<mv�D/EHS2DFesL�· ?>S@A*l-aWV<Q|VA�GJAFWHA*^�· ?�S2A*l�DFP�=2X�W]EVI$Z�=2DFX�aK*<CZ\`HK6��=2X�?UZ�K�=YXmK�h[E�A�Z�=2DFX�a

¾/��µgh[e4EHS�ZB¾/¾ ¶ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u;�MAFE�?�?�·]S@A*l�?U_�`HK�G\=2I�A�S¶ a~|�DFG~A&?U_H`�K�G\=2I�A�S2SY^�?�^[e&e&K�Z\G�=@IMIJ`�A�G\qFK�W]=@?:Z\G�=2LHE]Z\=YD/X�o��MA�E�?\?�·[S@A*l�q/=Yd/K�?�Z�`HKMe�A�q/XH=YZ�E�W]KMDFP�Z�`HKMK�SYKiI$Z�G\=@I��K�S2WQZ\DgLNKA[< $ � � � � � �]5,µ�� � � �*<$aLN< $ � � � � � �H5�� � � � <�oHl~`HK�G�K � � � � � =@?~SY=2XHKiA�G~IJ`�A�G\qFKMW]K�X�?U=YZ:^FaIi< $ � � � � � �]5�� � � <�oHl~`HK�G\K � � � � �p=2?cAFG�KiA4IJ`VA�G\qFKRWHK�X�?�=�Z:^/aWV< $ � � � � � �]5,µ�� � � <$aK*< � $ � � � � � �]5,µ�� � � <�a

¾/��µgh[e4EHS�ZB¾/¾ ¹ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u;�MAFE�?�?�·]S@A*l�I�^(S2=YX�WHG�=@I�AFS¹ a~|�DFG�AMI�^(S2=YX�WHG�=@I�AFSYS2^6?U^(e&e&K�Z\G�=@I>IJ`�A�G\qFK>W]=@?:Z\G�=2LHE]Z\=YD/X�o/�MA�EV?�?�·"S2A*l�qF=2dFK�?�Z\`HK>e�A�qFX�=�Z\E�W]K~D�PVZ�`HK>K�SYKiI$Z�G\=@I��K�S2WQZ\DgLNKA[< $ � � � � � �]5,µ�� � � �*<$aLN< $ � � � � � �H5�� � � � <�oHl~`HK�G�K � � � � � =@?~SY=2XHKiA�G~IJ`�A�G\qFKMW]K�X�?U=YZ:^FaIi< $ � � � � � �]5�� � � <�oHl~`HK�G\K � � � � �p=2?cAFG�KiA4IJ`VA�G\qFKRWHK�X�?�=�Z:^/aWV< $ ��� � � � �]5,µ�� � � <$aK*< � $ � � � � � �]5,µ�� � � <�a

¾/��µgh[e4EHS�ZB¾/¾[º�¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u;�MAFE�?�?�·]S@A*l�_HS@A�X�AFGº(a~|�DFG�As_HS@A�X�AFG�?�^[e&e&K�Z\G�=@IBIJ`VA�G\qFKcW]=@?:Z\G�=2LHE]Z\=YD/X�oH�MA�E�?\?�·FS@A*l{qF=2dFK�?jZ�`HK�e�A�qFX�=�Z\E�W]KBDFPpZ�`HKRK�S2K�I�Z�G\=2Ic��K�S@WZ\D�LVKA[< $ ��� � � � �]5,µ�� � � �*<$aLN< $ �2� � � � �H5�� � � � <�oHl~`HK�G�K �)� � � �p=@?~SY=2XHKiA�G~IJ`�A�G\qFKMW]K�X�?U=YZ:^FaIi< $ � � � � � �]5�� � � <�oHl~`HK�G\K � � � � �p=2?cAFG�KiA4IJ`VA�G\qFKRWHK�X�?�=�Z:^/aWV< $ ��� � � � �]5,µ�� � � <$aK*< � $ � � � � � �]5,µ�� � � <�a

¾/��µgh[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u;�MAFE�?�?�·]S@A*l�?UE�GUP,A/I�KMD�PjI�D/X�W]E�I�Z�DFG¼ ac�MAFE�?�?�·]S@A*lzA�_�_HSY=2K�WnZ�D�A:EV?:ZcD/E]Z\?�=2WHK�DFP�AFXK�SYKiI$Z\G�D[?:ZJA"Z�=@I�I�DFXVW]E�I$Z\DFG~q/=Yd/K�?�Z�`HK-e�AFqFXH=YZ�E�WHK�DFP�K�SYKiI$Z�G\=@I��K�S2WQZ\DgLNKFuA[< $ ��� � � � �]5,µ�� � � �*<$aLN< $ �2� � � � �H5�� � � � <�oHl~`HK�G�K �)� � � �p=@?~SY=2XHKiA�G~IJ`�A�G\qFKMW]K�X�?U=YZ:^FaIi< $ � �]5 � � <$oHl~`�K�G\K �x=@?c?UE�GUP,A/I�KMA�G\K�A&IJ`�A�G\qFK�W]K�XV?U=YZ:^FaWV< $ ���]5,µ�� � � <$aK*< � $ ���]5,µ�� � � <$a

¾/��µgh[e4EHS�ZB¾/¾ ½ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u>��K�Xm|HGJA�X�O[S2=2XQ=2X(dFK�GJ?�K�T!?�h[E�AFG�K½ a ��K�X|HGJA�XHO(S2=YXr5:�"º"¾ ¹ �N�"º ½ ¾Hu�Z�`�K�=@W]KiA�S6��K�XmA�X(^(l�A*^/oFXHDFZ>X�K�I�Ki?�?\A�G\=2SY^gZ�`�KMI�G\A�P Z:^&DF_NK�GJA"Z�D/G�DFP�`H=@?UZ�DFG\^H<D/X�XHD�Z\=2I�=YXHq�Z�`�A�ZsLH=YZ\?4D�P~_�A�_NK�G6��D/A�Z�=2XHq�=2X�A�IJ`�A�G\qFKiW�e&K�Z\A�S;Z\AFXHO"A�GJWrl�K�G�K�XHDFZ4A"Z�Z�GJAFI�Z�K�W�Z\D�Z�`�KZJA�XHO"A�GJW�5�AF?;Z�`HK�^�LVK�=�P�Z�`HK�^�l�K�G�KcD/E]Z\?�=@W]KBZ\`HKRZ\A�X�O*AFG\WnW]EHKcZ\D4_NDFS@A�G\=2��A"Z\=YD/X�D�P�Z\`HKB_VA�_NK�G>e&DFS2K�I�E�SYKi?� ?U`HT\�"ºFº !�Z\`HDFEHq/`!��K�Xl�DFE�S2WQXHD�Zc`VA*dFK�O[X�D"l~XAFLVD/E]Z~_VD/S2AFG�=2��KiWne&DFS2K�I�EHS2K�?J<�WHK�W]E�I�K�WQZ�`VA"ZA[<�Z\`HKMZ\AFXHO"A�GJWnl>AF?>`VA�SYP�K�e&_]Z:^/aLN<CZ\`HKMZ\AFXHO"A�GJWnl>AF?>`VA�SYP�P8EHS2S�aIi<¤HA�e}�RWHA�e�?�·�5:�"º��F�"T\� ¼ ¾ ³ <jAFSYKMS@AFIJOFKiWnLND]W]^Fa

Page 119: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia;�"µ}�MAFE�?\?�·H¸�A*l �F� ¶

WV<CZ\`HKfK�SYKiI$Z\G�=@I � � � �� � � � =2X�Z�`�K Z\AFXHO"A�GJW l�A/?�A�_H_VA�G\K�X[Z�S2^}I�DFX�?UZ\AFX/Zio�AFX�W Z�`(E�?�Z�`�KK�SYKiI$Z\G�D[?:ZJA"Z�=@IRP8DFGJI�K�DFLNK�^/K�WmA�X=YX(d/K�GJ?UK�Tk?\h[E�A�G\KcS@A*l-a

K*<CZ\`HKgK�S2K�I$Z\G�=@I �� � ¦ f=2X�Z\`HK6ZJA�XHO"A�GJW�l>AF?RA�_H_�AFG�K�X[Z�S2^Q��K�G\D�o�A�X�WmZ\`(E�?cZ\`HKgK�S2K�I$Z\G�D[?:ZJA"Z\=2IMP8D/G\I�KD/LVK�^FKiWQAFXQ=2X(dFK�GJ?�K�T!?�h[E�AFG�KRS2A*l-a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/��µgh/P8EHS2S�¾/¾H��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu;�MA�E�?\?�·]S@A*lzAFX�WA�I�EHLNK�FaBv�D/X�?U=@W]K�G�AsIJ`VA�G\qFK�W&I�DFX�W]EVI$Z�=2XHqgI�EHLNKFajb>`HK�I�EHLNKR`VAF?�X�K�Z�IJ`VA�G\qFK � �${¾�a�b>`�KRI�E�LVKR=2?�=2?�DFS@A"Z\K�WgP8G\DFeAFX[^nK�S2K�I$Z\G�=@IR��K�S@WH?~X�D�ZcA�G\=2?�=2XHqsP8G\DFe}=�ZJ?UK�S�P:a�b>`�K6?U^]?UZ�K�e�=2?~K�SYKiI$Z\G�D[?:ZJA"Z�=@I�aA[<v�AFX±�MAFE�?�?�· ?4S@A*l LNKEV?UKiW�Z�D�W]K�G�=2dFKAx?�=2eg_�SYKK��]_HG\K�?\?U=2DFX�P8DFGgZ�`HKmK�SYKiI$Z�G\=@IC��K�S2WtA�G\DFEHXVW�Z�`�KI�EHLNK���»{`(^CX�D�Z�

LN<n»{`VA"ZBA�LNDFEHZc=YXQZ�`HKMP,AFGUT���K�S2WQSY=2e&=�Z ��7kPj?UDVo]l~`(^nA�X�Wl~`�A�Z~=2?>Z\`HK-K��]_HG\K�?\?�=YD/X �Ii<Q¡RK�G\=2dFK>Z�`�K~K��]_HG\K�?\?U=2DFX4P8DFG�Z\`HKcK�S2K�I�Z�G\=2I���K�S2W�A�ZjZ�`HKc?�EHG�P,AFI�K�=2X&Z�K�G�e�?�Z\`HKB?�EHGUP,A/I�K~IJ`�AFG�q/K�W]K�X�?�=�Z:^� ��� � � �� � 58l~`H=@IJ`m=2?>XHDFZBI�D/X�?:ZJA�X[ZJ<�a

¾/��µgh/P8EHS2S�¾/¾/��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�IJ`�AFG�q/K�WQ?U_�A/I�KiI�GJA"P Z� ª�¬"¨ �V«������V¬ ��­�� LHE]Z~Z�`�K�G\K-=2?~A4Z�D/EHqF`Z\`H=YX�O[=2XHq�W]=@?�I�E�?\?U=2DFXLH=YZ

�]ac¤(_VAFI�KiI�GJA"P Z�Z�GJA*dFK�S2=2XHqc=2X6Z�`�K�GJAFWH=2A�Z�=2DFX-LNK�SYZ\?jI�AFXsAFI�I�EHe4EHS@A"Z�K�ABX�K�ZjIJ`�A�G\qFK�L(^-=2X[Z�K�GJI�K�_]Z�=2XHqRK�S2K�I$Z\G�D/X�?�a¤]A*^m^/DFE�`�A*d/KsAn?�_H`HK�G�=@I�AFSYS2^?�^(e&egK�Z�G\=2IFopI�DFXVW]E�I$Z\=YX�qQ?\A"Z�K�SYS2=YZ�KsDFP�G\A/W]=2E�?s� � ¶ e�Z\`�A"Z-AFI�h/E�=YG\K�?RACXHK�ZIJ`�AFG�q/KRDFP�� � ³ � v{=YXmD/XHKMDFG\LH=�ZiaA[<C»{`VA"Zc=@?�Z�`HK6?�EHG�P,AFI�K-IJ`�AFG�q/K�WHK�X�?�=�Z:^��LN<mv�AFS2I�EHS@A"Z�K�Z\`HKMe&AFqFXH=YZ�EVW]KMD�P�?�EHG�P,AFI�K�K�SYKiI$Z\G�=@Ic�VK�S@WQ=2XQZ:l�Dgl�A*^]?�m£cD"l�WHD[Ki?>=�ZBI�DFe&_�AFG�KRZ�DgZ�`�K

L�G�KiA�O]W]D"l~XC�VK�S@WQDFP�AF=YG ��°BP�I�DFEHGJ?�KFo(Z�`�K�G\K�=@?�X�· Zce4E�IJ`mA�=2G~=YXmDFG\LH=YZ�aIi<Q�;SYKiI$Z\G�D/XH=2I4I�D/eg_NDFX�K�X[Z\?RDFX�Z\`HK&?U_�A/I�KiI�GJA"P Z�I�A�X�LNK&WHA�e�A�q/K�W�L(^Z�`�K4K�SYKiI$Z�G\=@I6��K�S2W�?RI�A�E�?�K�W�L(^Z\`H=@?cIJ`�A�G\qFKMLHE�=YS@W(TkEH_�a;£BD"lzI�AFXZ�`HK�^nLNK6_HG\D�Z�KiI$Z\K�W ���������� � b>`�=2?~=@?cA&W]=@?�I�E�?\?U=2DFXmh[EHK�?UZ�=2DFX�ab>`�K-=YX�?UZ�G\E�I�Z�DFG>=@?cA�S2e&D/?UZcI�DFe&_HS2K�Z\K�S2^C=2qFXHD/G\AFX/Z>D�P�G\K�A�SpK�SYKiI$Z\G�=@I�AFS�AFX�WK�S2K�I�Z�G\DFXH=@IMW]K�d(=@I�K�?�a

¾/��µgh/P8EHS2S�¾/¾ ³ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj_�A�GJA�S2SYK�S�_HS2A�Z�Ki?³ a ��D/E�`�A*dFK>Z:l�D-=YXH��XH=YZ�KRI�DFX�WHE�I$Z\=YXHq-_�S2A�Z�K�?;=YX�_VA�GJA�S2SYK�S�a�b>`HKc?�^(?UZ�K�e `VAF?�K��HAFI$Z�_�S2AFX�A�G;?�^(e&egK�Z�G\^4AFX�W=@?>K�S2K�I�Z�G\D/?UZ\A"Z\=2IFa;°RXnZ\`HK-SYK�P Zc_HS@A"Z�KM^/DFE`�A*dFKMA�XmA�G\K�AgIJ`�A�G\qFK�W]K�XV?U=YZ:^ � �±¾&AFX�WnD/XnZ\`HK-G\=Yq/`/Z>_HS@A"Z\K^/DFE�`�A*d/K4AFG�KiAnIJ`�AFG�q/K4W]K�X�?U=YZ:^ , � ��¾�a6b>`HK�?U^]?UZ�K�e =@?M=2X�P,AFI�ZMAFX�=@W]K�AFS�_�A�GJA�S2SYK�S�Tk_HS@A"Z\K4I�AF_�AFI�=�Z\DFGia¤(D/e&K�DFP�=2X[Z�K�G�Ki?:Z\=YXHq&_HG\DF_NK�G�Z�=2K�?>DFP�Z\`H=2?BI�A�_VAFI�=YZ�D/G~A�G\K�G\K�d/K�AFSYKiWC=2XQZ\`HK6A�XV?Ul�K�GJ?�Z\D&Z�`HK6h[EHKi?:Z\=YD/X�?�aA[<C»{`�K�G\K-DFXQZ�`HKMZ:l�D&_HS2A�Z�Ki?>esE�?UZBA�S2S�Z�`HK6IJ`VA�G\qFK�LVK �LN<n»{`VA"Zs=@?MZ�`�KCK�S2K�I�Z�G\=2Ig��K�S2Wr=2XrZ�`�K&��dFK�G\K�q/=YD/X�?�usSYK�P ZsD�P�Z�`HKn_HS2A�Z�Ki?�o�=YXV?U=@W]K&Z�`�KC_VD[?U=YZ�=2dFK�_�S2A�Z�KFo

LNK�Z:l�K�K�X�Z�`�Kn_HS@A"Z\K�?�o�=2X�?�=2WHK�Z�`HKQXHK�q[A"Z\=Yd/KC_HS@A"Z�K/o�G�=2qF`[ZsDFP~Z�`HKQ_HS2A�Z�Ki?�a ������ � ¿~K�I�A�S2S;Z\`�A"ZgA?�=2XHqFS2KM=YX]�VXH=�Z\K6_HS@A�X�AFG~?US@A�LD�PjIJ`�A�G\qFK�l~=YZ�`�A�G\K�AgIJ`�A�G\qFKMW]K�X�?U=YZ:^ �xqF=2dFKi?~As�VK�S@W

� $ �

� � ��� �

l~`�K�G\K ���_NDF=2X/ZJ?>DFE]Z:l>A�GJW�P8G\DFe}K�=YZ�`HK�Gc?U=@W]K-DFP�Z�`�K6?US@A�L�aIi<n»{`VA"Zc=@?�Z�`HK6IJ`�AFG�q/K�WHK�X�?�=�Z:^QDFXK�A/IJ`QDFP�Z�`�KMP8DFEHGBI�DFX�WHE�I$Z\DFG~?UE�GUP,A/I�K�?�WV<Q¡RD(K�?>Z\`HK6A�XV?Ul�K�G�Z�D&_�AFGUZ65�I�<�e�A�O/KM?�K�XV?UK �

Page 120: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � � N[1_H ;75\*IH8BC?A;71)>W;<*[&AN

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/� ¶ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\=2I�_ND�Z�K�X[Z�=@A�S� ª�¬"¨ �V«������V¬ ��­�� K�S2K�I$Z\G�=@I�_VDFZ�K�X/Z\=2AFS�oVW]K���X�=�Z\=YD/X

�Fa>»{`�A�Zc=2?>K�SYKiI$Z\G�=@IM_VDFZ�K�X/Z\=2AFS �A[<C7kZ�=2?�Z\`HKcK�SYKiI$Z�G\=@I>_VDFZ�K�X[Z\=2AFSHK�XHK�G�q/^ �����EHXH=YZ�IJ`�AFG�q/KFa�7kZ�=@?;A&� ¦ �1� ��K�S@W&S2=YO/K>Z�`HK~K�SYKiI$Z�G\=@I�VK�S@Wpa

LN<n7kZ4=2?6Z�`HKCK�SYKiI$Z\G�=@I&_VDFZ�K�X/Z\=2AFS;K�XHK�G\qF^ �1 �A�IJ`�A�G\qFK/an7kZs=@?6A � ¦ �1� ��K�S@WrSY=2OFK&Z\`HKCK�SYKiI$Z�G\=@I�VK�S@Wpa

Ii<n7kZc=@?>Z\`HK-K�S2K�I�Z�G\=2I�_ND�Z�K�X[Z�=@A�SpK�X�K�G\qF^ ���� EHXH=YZBIJ`�A�G\qFK/a�7kZ~=@?cA � � ���1���VK�S@WQE�XHSY=2OFKMK�SYKiI$Z�G\=@IIJ`VA�G\qFKFa

WV<n7kZ-=@?�Z�`HK�K�SYKiI$Z\G�=@Is_ND�Z\K�X[Z�=@A�SjK�XHK�G\qF^ �1 DFP�AmIJ`�A�G\qFK/a67kZ-=2?-A � � � � � ��K�S@W�EHXHS2=YO/K4K�SYKiI$Z�G\=@IIJ`VA�G\qFKFa

K*<n7kZc=@?>Z\`HK-K�S2K�I�Z�G\=2I�_ND�Z�K�X[Z�=@A�S�K�XHK�G\qF^ ���� _VK�GcEHXH=YZBIJ`�AFG�q/KFa�7kZc=2?~A � ¦&� � � � ��K�S2WEHXHS2=2OFKMZ�`�KK�SYKiI$Z\G�=@IR��K�S@Wpa

¾/� ¶ h[e4EHS�ZB¾/¾H�/��¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@IR_ND�Z\K�X[Z�=@A�S�?\I�AFS2AFG�]ac¤(=2X�I�K-K�S2K�I$Z\G�=@I�_VDFZ�K�X/Z\=2AFS�=@?~Ag?\I�AFS2AFG>=�ZBA/WHWH?�u

A[<RSY=2OFK&AdFK�I�Z�D/G�a LV<RSY=2OFK&Am?�I�A�S@A�Gia Ii<BS2=2OFK�ACZ\K�X�?�DFGia W�<BZ�Dm��K�G�DmA�S2l�A*^]?�a K*<X�D�ZBA"ZcAFSYS�a

¾/� ¶ h[e4EHS�ZB¾/¾H�*��¾C�&���MK�A/?U^�e&K�egD/G�^�uj_ND�Z\K�X[Z�=@A�SpEHX�=�Zcd/DFSYZ� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

³ a~b>`HK-E�XH=�ZJ?~D�P�K�S2K�I�Z�G\=2I�_ND�Z�K�X[Z�=@A�S�AFG�K/uA[<�dFD/S�ZJ?�5,´ $ �]yFv><�a LV<�A:D/EHSYKi?�a Ii<> �y/vRa W�<�l�K�LNK�GJ?�a Ki<�D(K�G\?UZ�KiWH?�a

¾/� ¶ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\DFX]TkdFD/S�Zµ�a>7kP�AFXnK�SYKiI$Z�G\DFXn=2?�AFI�I�K�S2K�GJA"Z\K�W&Z\`HG\DFEHq/`nA6_ND�Z\K�X[Z�=@A�SpW]= �NK�G�K�X�I�K�D�P��i¾F¾j´4o/l~`VA"Z>O[=2XHK�Z�=@IBK�XHK�G\qF^&W]D(K�?�=YZA/I�h[EH=2G�KM=2XQK�´R?65,K�S2K�I$Z\G�D/X]TkdFDFSYZ\?J<��

A[<���¾/¾jK�´4a[LN<>¾ � ¾H��K�´sa I�<�� � ¹ ����¾ � ����K�´4a W�<�� � ¹ ����¾ � ���6�Va K*<�� � ¹ �x�i¾ ���pK�´4a

¾/� ¶ h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�S2D/?�K�WQ_�A"Z\`�?cAFX�Wn_ND�Z\K�X[Z�=@A�S¶ a>7kPp^FD/E&qFD6A�G\DFE�X�W&A�X(^4I�SYD[?UKiW4_VA"Z�`�=2XCA�X&K�SYKiI$Z�G\=@I>��K�S@W�5,I�A�E�?�K�WgL(^&A�X�?:ZJA"Z\=2IcWH=2?UZ�G\=YL�E]Z�=2DFX�DFP�IJ`�AFG�q/Ki<�o^/DFEHG~IJ`�AFXHqFKM=2XK�SYKiI$Z\G�=@I�_VDFZ�K�X[Z\=2AFSp=2?�u

A[<g¾j´sa LN< �4��¾F¾�´sa I�<gA�S2l>A*^(?gq/G�KiA"Z�K�GsZ\`�A�X±��K�G�DVa WV<&A�S2l�A*^]?4SYKi?�?gZ\`�A�X±��K�G�DVaK*<>?U`�D(IJO(=2XHq�a

¾/� ¶ h[e4EHS�ZB¾/¾�µ[¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj_NDF=2X[Z~IJ`VA�G\qFK�_VDFZ�K�X[Z\=2AFS¹ a~b>`HK-_ND�Z\K�X[Z�=@A�SpDFP�Ag_NDF=2X[ZBIJ`�A�G\qFK&58G\K�S@A"Z\=Yd/KBZ\D�=YX]�VXH=�Z:^H<�=@?�u

A[< � $ ����� � a�LV< � $ ����� �/a I�< � $ ����� a WV< � $ ��� a K*< � $ � � �/a

Page 121: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a;� ¶ ��S2K�I$Z\G�=@IM9�D�Z\K�X[Z�=@A�S �F�"º

¾/� ¶ h[e4EHS�ZB¾/¾ ¶ ��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�W]=2_NDFS2K�_ND�Z\K�X[Z�=@A�Sº(a~b>`HKMP,AFGUT���K�S2WQK�S2K�I�Z�G\=2I�_ND�Z�K�X[Z�=@A�SpD�PjA�XK�S2K�I�Z�G\=2IMW]=2_NDFS2K-=2?

� $ � �BI�D[?�� �

l~`HK�G�K �g=2?�Z�`�KMAFXHqFS2KRP8G�D/e _VD[?U=YZ�=2dFKMW]=2_VD/SYK-A"�]=@?�o =@?�Z�`HK-W]=@?UZ\A�XVI�K�P8G�D/e�Z�`HK-W]=2_NDFS2K�I�K�X[Z�K�G�oHAFX�W��=2?Z\`HKFu

A[<~W]=2_VD/SYK4e&DFe&K�X[Z � � �(a LV<BW]=2_VD/SYKs?�K�I�DFX�W � � �(a I�<~W]=2_NDFS2K4?�K�I�D/X�W � �(a W�<cW]=2_NDFS2Ke&D/egK�X[Z � �(a K*<�e&DFe&K�X[Z�E�ea

¾/� ¶ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�I�DFX�W]EVI$Z�D/G>K�h[EH=2_VDFZ�K�X[Z\=2AFS¼ a~� I�DFX�WHE�I$Z\DFG�=2X�A�XwK�S2K�I�Z�G\D/?UZ\A"Z\=2ImI�AF?�Kr5�A�X�Ww=2X{?UD/e&K�_HG\A/I$Z\=2I�A�S~XHD/X]T�K�SYKiI$Z\G�D[?:ZJA"Z�=@ImI�A/?UKi?\<4=@?CA[y�A�X

D/L,A:K�I�Z�aA[< XHDFXHTKih[EH=Y_ND�Z\K�X[Z�=@A�S LV<6_�?�K�E�W]DFT�Kih[EH=Y_ND�Z\K�X[Z�=@A�S I�<-P,A�E]�(TkK�h[EH=2_VDFZ�K�X/Z\=2AFS WV<-K�h[EH=2_NDFG\_VD/=2?�KK*<�K�h[EH=2_VDFZ�K�X/Z\=2AFS

¾/� ¶ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�W]= ��K�G\K�X[Z�=@A�S�IJ`�AFXHqFK½ a~b>`HKMW]= �NK�G�K�X[Z�=@A�S�IJ`�A�XHq/K � � =2XnK�SYKiI$Z\G�=@Ic_ND�Z\K�X[Z�=@A�SpA�S2DFX�q4AsWH=���K�G\K�X[Z�=@A�SNLH=YZ~D�P�_�A�Z�` � ���=2XCZ�`�KRK�SYKiI$Z�G\=@I��K�S2W � D�P�_VD/=YX[ZBIJ`�AFG�q/Kg5,SYD]I�A"Z�KiWQA�Z~Z�`HK-D/G�=2qF=2XV<�=@?>qF=2dFK�XL(^�uA[< � � $�, � � � �� $ , � �HaLN< � � $ � � � �� $ � �HaIi< � � $ � � � �� $ � aWV< � � $�, � � � �� $ , � aK*< � � $ � ��a

¾/� ¶ h[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujq/G\A/W]=YK�X[Z�DFP�_ND�Z\K�X[Z�=@A�S��¾Ha~b>`HK-K�SYKiI$Z\G�=@IR��K�S@W=2?>q/=Yd/K�XL[^

� $ ,�� �

l~`HK�G�KM=2X�v�A�G�Z�K�?�=@A�XQI�D(DFGJW]=YXVA"Z�Ki?� � $

� � �� �

� �� �

� �� � �

=@?>Z�`�K D�P�Z�`HK-_ND�Z\K�X[Z�=@A�S�aA[<�q/G\A/W]=2K�X[Z LN<;¸�A�_HS@AFI�=2AFX I�<�W]=2dFK�G�q/K�X�I�K W�<�¡4· �BSYK�esLNK�G�Z�=@A�X Ki<���=2X�?UZ�K�=YXH=2EHe

¾/� ¶ h[e4EHS�ZB¾���¾/¾F¾C�6� ³ e&D]W]K�GJA"Z\K�e&K�egD/G�^�ujI�D/X[Z�=2X[E�DFE�?>IJ`�AFG�q/K�F�Fa~b>`HK4A�_H_HG\DF_�G�=@A"Z\K-qFK�X�K�GJA�S�=2X[Z�K�q/G\AFSpZ�DI�AFS2I�EHS2A�Z�KMZ\`HKs_ND�Z\K�X[Z�=@A�S�W]EHK6Z\DnACI�DFX[Z�=2X(EHDFE�?RW]=@?:Z\G�=2LHE]Z\=YD/X�D�P

IJ`�AFG�q/KR=@?�u

A[< � $ ��� � ��� � aLN< � $ � � � ��� �/aIi< � $ ��� � ��� aWV< � $ ��� � �(aK*< � $ � � � � �(a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

Page 122: Introductory Physics Problems David J. Jeffery Department of

�F� ¼ v�`�A�_]Zia;� ¶ �;SYKiI$Z\G�=@IM9�D�Z�K�X[Z�=@A�S

¾/� ¶ h/P8EHS2S�¾/¾H��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujl�D/G�O[TkK�XHK�G�q/^4Z\`HK�D/G�K�emo]K�S�aj_VDFZ�K�X[Z\=2AFS�Fa~� _�A�G�Z�=@I�S2KsDFP�IJ`�AFG�q/K � � =2?�`HK�S2WxA"Z�Z�`HKgDFG\=2qF=2X�a-� ?�K�I�DFX�W�_VA�G�Z�=@I�S2KsD�P�IJ`�A�G\qFK � � =@?�`HK�S@W�AQW]=@?:ZJA�X�I�K � � � � � � ��A*l�A*^mA�XVW�Z�`�K�X�G\K�S2K�A/?UKiWmP8G\DFe�G�Ki?:Zia ��DFZ�`�IJ`�A�G\qFKi?BA�G\Ks_ND/?�=YZ�=2dFKFa-b>`HKgDFX�SY^P8DFGJI�KgA�G\DFEHXVW�=2?Z\`HK4v�DFEHS2DFe4LnP8D/G\I�KMLVK�Z:l�K�K�XQZ�`HK-_�AFGUZ\=2I�SYKi?�aA[<C»{`VA"Z>=2?;Z�`HK�qFK�XHK�GJA�SVK��]_HG\K�?\?U=2DFX&P8D/G;Z\`HKM?U_NK�KiW�D�P�_�AFGUZ\=2I�SYKM��� ������ � ¿~KiI�A�S2SVZ�`HK�l�D/G�O[TkK�XHK�G�q/^Z\`HK�D/G�K�ema

LN<n»{`VA"Zc=@?�Z�`HK-K��(_�G�Ki?�?�=YD/XnP8D/G~_�A�G�Z�=@I�S2K6�]· ?~?U_NK�KiWnl~`�K�Xm=�ZcG\K�A/IJ`HK�?�=2X]��XH=YZ:^��Ii<Q�R?�?�EHe&K�Z\`HKxIJ`�AFG�q/K�?gZ\`HK�LND�Z�`�`�A*dFK�� � v D�P6IJ`�AFG�q/KFo � � � � � ����$ ³ emocAFX�W±Z�`HK�e&A/?�?nD�PMZ�`�K_VA�G�Z�=@I�S2K-�4=@?c¾ � ¾/�jq�a�»{`�A"Zc=@?>_�A�G�Z�=@I�S2K6�]· ?~?U_NK�KiWmA"Z~=YXH��XH=YZ:^ �

¾/� ¶ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_ND�Z�K�X[Z�=@A�S@?�P8DFG~`H=2qF`�?�^[e&e&K�Z\G�^�]a~¡RK�Z\K�G\eg=2XHKMZ\`HKMP8DFS2SYD"l~=2XHq&_ND�Z�K�X[Z�=@A�S�P8DFG\esE�S2AFKFu

A[<nb>`�Kn_ND�Z�K�X[Z�=@A�S�P8D/GgA�_VD/=YX[ZgIJ`VA�G\qFK&G�K�S2A�Z�=2dFK�Z\D�=2X]��XH=YZ:^Fax¿~K�I�A�S2S�Z�`�KnK�S2K�I�Z�G\=2IC��K�S@WrP8D/G4A�_NDF=2X[ZIJ`VA�G\qFK�=2?

� $ ���

�� �

LN<Qb>`�K�_ND�Z�K�X[Z�=@A�SMW]=���K�G\K�XVI�K�P8D/GQAFX�=YXH��XH=YZ�K�S2=2XHK�DFPsIJ`�A�G\qFK�LNK�Z:l�K�K�X�G\A/W]=@A�SB_NDF=2X[Z\? � A�X�W � a»{`VA"Z6`�AF_H_VK�X�?M=YP�K�=�Z\`HK�G6DFP � DFG � q/D(K�?�Z�Dm=2X]��XH=YZ:^�D/GM��K�G\D � 9;G\A/I$Z\=2I�A�S2SY^�?�_VKiA�O(=YX�q�o�`HD"l =2?Z\`HK-G\K�?�EHS�Z\=YX�qg_�G�D/LHSYK�e�A*dFD/=2WHK�W �m¿~KiI�AFSYS�Z\`HK-K�S2K�I�Z�G\=2IR��K�S2WQP8DFGcAFXQ=2X]��X�=�Z\K6SY=2XHK-DFP�IJ`�AFG�q/KR=@?

� $ �

� � � � �

l~`�K�G\K � =2?>Z\`HK-S2=YXHKiA�GcIJ`�AFG�q/KRW]K�X�?�=�Z:^A�X�W =@?>e&K�A/?UEHG\K�WQ_NK�G\_VK�X�W]=@I�EHS@A�G>Z\D&Z�`HK-S2=YX�KFaIi<Qb>`�K�_ND�Z\K�X[Z�=@A�S�W]=���K�G\K�XVI�K�P8DFGcAFXQ=2X]��XH=YZ�K-_�S2AFXHKMD�P�IJ`VA�G\qFK�LVK�Z:l�K�K�X_VD/=YX[Z\? � A�XVW � egKiAF?�EHG\K�W_NK�G\_NK�X�W]=@I�E�S2AFG�S2^�DFE]Z:l>A�GJW�P8G\DFe�Z\`HKM_HS@A�XHKMDFX�K�?�=2WHKFaj»{`�A�Z>`VA�_H_NK�X�?>K�=�Z\`HK�G~DFP � D/G � qFD(K�?�Z\D=2X]��X�=�Z:^�� 9�GJAFI$Z\=2I�A�S2SY^�?�_NK�A�O(=2XHq�o�`HD"lf=@?MZ\`HK�G�Ki?UE�S�Z\=YXHq�_�G�D/LHSYK�e A*dFD/=2WHK�W ��¿cK�I�AFSYS�Z�`HK�K�SYKiI$Z�G\=@I�VK�S@WnP8D/GcA�X=YXH��XH=YZ�K6_HS@A�X�K�DFP�IJ`VA�G\qFKB=@?

� $ �

� � ��

l~`�K�G\K �x=@?>Z�`HK6AFG�KiA4IJ`VA�G\qFKMW]K�X�?�=YZ:^nA�X�W =2?>e&K�A/?UE�G�KiWn_NK�G\_VK�X�W]=@I�EHS@A�G>Z\D&Z�`HK-_�S2AFXHKFa

¾/� ¶ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�� D�P�EHXH=YP8DFG\e�IJ`�AFG�q/KRLVA�S2S³ a ��D/EC`�A*dFK~E�XH=�P8D/G�e&S2^�IJ`�A�G\qFKiW4?�_H`HK�G�KcDFP�IJ`�A�G\qFK � AFX�W&GJAFW]=2E�? �ga�»�KF· G�Kcq/DF=2XHq-Z\D-��X�W&Z\`HKB_ND�Z\K�X[Z�=@A�S

� � � ��D�PcZ\`H=2?&IJ`�AFG�q/KCAF?\?UK�esLHS2^{58G\K�S@A"Z\=Yd/KCZ�Dx��K�G�Dxl~`HK�X�AFSYS�Z\`HKIJ`VA�G\qFKCLH=YZ\?&AFG�KnA�Zg=2X]��X�=�Z:^G\K�S@A"Z\=Yd/KBZ\D�K�AFIJ`D�Z\`HK�G$<$aA[<n|�=2G\?UZ�o�l~`�A"Z~=@?�Z�`HK6W]= ��K�G\K�X[Z�=@A�S�L�=�Zc_ND�Z\K�X[Z�=@A�SpK�XHK�G\qF^ � �fD�P�A&W]= ��K�G\K�X[Z�=@A�S�L�=�ZcDFP�IJ`�AFG�q/K � �s=2XmA_ND�Z\K�X[Z�=@A�S � �

LN<Q BD"l{l~`�A"Z�=2?;Z�`�KRW]= �NK�G�K�X[Z�=@A�SNLH=�Z�_VDFZ�K�X/Z\=2AFSVK�XHK�G\qF^ � ��D�P�A4W]=���K�G\K�X[Z\=2AFSVLH=YZ�DFP�IJ`�A�G\qFK � �6A�Z;Z�`�K?�EHG�P,AFI�K�DFP�EHX�=�P8D/G�e&S2^QIJ`�AFG�q/K�Wn?�_H`HK�G�KMDFP�IJ`�AFG�q/K �gA�X�WQGJAFW]=2E�? �

Ii< ��D/EnI�AFX&Z�`H=2XHO�DFP�L�G�=2XHqF=2XHq6E�_CLH=YZ\?�D�P�IJ`�AFG�q/K � ��P8G\DFe�=2X]��XH=YZ:^�A�X�W�A/WHW]=2XHq6Z\`HK�e Z�DsZ�`HK�?U_�`HK�G\KDFP>IJ`VA�G\qFK � Z�`VA"Z6^FD/E�AFG�K&AF?\?�K�esL�SY=2XHq�a�b>`(E�?M^/DFErI�A�X�=2X/Z\K�q/G\A�Z�K4Z�`HK�K��(_�G�Ki?�?�=YD/X�^/DFE�qFD�ZMP8D/GZ\`HKsAFX�?Ul�K�G�Z\D�_�A�G�Zs58LV<>P8G�D/e ��$z¾gZ�D ��$ � =YPj^FDFEmI�AFXmK��]_HG\K�?\?�Z�`HK6=2X[Z�K�qFGJA�X�WQ=YXZ\K�G\e&?cD�PjA?�=2XHqFS2K-d"A�G\=2AFLHSYK/u�=�a K/aYo �4D/G ac¤(D�K��]_HG\K�?\? =YXmZ\K�G\e&?BD�P �gDFG �g=2XmZ�K�G\e�?~D�P a>b>`HK-P8DFG\e&K�GBI�AF?�K=@?~KiAF?�=YK�G�a�7!XZ�`HK-S@A"Z\K�GcI�A/?UKM^/DFEnl~=2S2S�A�S@?UD&XHK�K�WnZ�`HK-K��]_HG�Ki?�?�=2DFXQP8DFG � �s=2XnZ\K�G\e�?~D�P � a

Page 123: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a;� ¶ ��S2K�I$Z\G�=@IM9�D�Z\K�X[Z�=@A�S �F� ½

WV<¤]EHL�?UZ�=YZ�E]Z\KRZ\`HKMK��]_HG\K�?\?U=2DFXV?jP8G\DFe�Z�`�K�_VA�G�Z�5,Ii<�A�X�?�l�K�G�=2X[Z�DsZ�`HKM_�AFGUZ-58LV<�AFX�?Ul�K�G�A�X�Wn=YX[Z\K�qFGJA"Z\KP8G\DFe ¾nZ\D � 5,DFG-¾QZ�D � =YP>^FDFErA�G\KgE�?U=2XHq A/?�Z�`HK�=2X[Z�K�qFGJA"Z�=2DFXxd"A�G\=2AFLHSYK*<$a�|HD/GMXHK�D/_H`(^/Z\K�?�Z\D=2X[Z�K�qFGJA"Z�=2DFX�o ���

#�5 �N<�� ��$ ��5 � < , ��5 �(< �l~`�K�G\K � =@?�Z�`HK6AFX/Z\=2WHK�G\=Yd"A"Z\=Yd/KMD�P5#�uj=�a KFa2o � � ��� � $ #�a

K*</���]� �"��+@)R3g�]�8���N��+@)�l~`�A"Z>=2?;Z�`�K�q/G\A*d(=YZ\A�Z�=2DFX�AFSH_VDFZ�K�X/Z\=2AFS�K�XHK�G�q/^4DFP�AsE�XH=�P8D/G�e W]K�X�?�=�Z:^C?�_H`HK�G�KRD�Pe�A/?�? � A�X�WGJAFW]=2E�? ���

¾/� ¶ h/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_ND�Z�K�X[Z�=@A�S�DFP�W]=@?UOQD�P�IJ`�A�G\qFKµ�a ��D/E`VA*dFKMAsZ\`H=2X�W]=2?�OCDFP�IJ`�AFG�q/K �4l~=�Z\`Z�`HK6IJ`�AFG�q/K�?�_HG\K�A/WnEHX�=�P8D/G�e&S2^CD"dFK�G�Z\`HK6W]=@?UO�a

A[<C»{`VA"Zc=@?�Z�`HK6AFG�KiAgIJ`VA�G\qFKRWHK�X�?�=�Z:^ ��DFP�Z\`HK6W]=@?UOQqF=2dFK�XQZ�`VA"Zc=YZc`�AF?>GJAFW]=2E�? ���LN<n»{`VA"ZM=2?BZ�`HKgW]= �NK�G�K�X/Z\=2AFS�IJ`VA�G\qFK-DFXxACG\=YXHqn=YX�Z�`HKgW]=2?�OmD�P�GJAFW]=2E�? �AFX�W�l~=@W(Z�` � �No�l~`HK�G\K �=2?

Z\`HK-GJAFW]=2E�?~I�D(D/G\W]=2X�A�Z�K�D�P�Z�`HK6W]=@?�ONaIi<n»{`VA"Z�Z�`HK�_VDFZ�K�X/Z\=2AFS � �zA"Z�AB`HK�=2qF`[Z �BAFLVD"d/K�Z�`�K�W]=@?UO6AFSYD/XHq~Z\`HK�A��]=2?�D�P]Z\`HK�WH=2?�O-W]EHK�Z�DRABG�=2XHqRD�PIJ`VA�G\qFK�DFPHl~=2W(Z\` ��Va�¿~K�egK�esLNK�G�_VDFZ�K�X/Z\=2AFS/=@?�AB?\I�AFS2AFG�A�X�W4AFWHW�?�S2=YO/K�AR?�I�A�S@A�GpZ\`HK�G\K�P8D/G�K/a��B?\?�EHe&KZ\`HK-_ND�Z�K�X[Z�=@A�S�=@?>��K�G�D�A"Z~=2X]��XH=YZ:^QA/?>=2?~I�DFX(dFK�X[Z�=2DFX�AFSVP8D/GcAgSYD]I�AFSY=2��AFLHS2KMIJ`VA�G\qFKMW]=2?UZ�G\=2LHE]Z�=2DFX�a

WV<Q|�=2X�WZ�`�K6Z�DFZ\AFS�_VDFZ�K�X/Z\=2AFS�A�Zc`HK�=2qF`[Z �CWHEHK-Z�DCZ�`HK6l~`�DFS2K-G�=2XHq�a>��S2=2eg=2X�A�Z�K ��=2XmP,A*dFDFG~DFP �6P8G\DFeZ\`HK-K��]_HG\K�?\?�=YD/X�a

K*<Q�R?U=2XHq�b�A*^[S2DFGi· ?�?�K�G\=2K�?�Z�Dm�i?:Z~DFGJW]K�G�o[��X�WQZ\`HKMP,A�G�T��VK�S@WnK��(_�G�Ki?�?�=YD/XCP8D/G>Z�`HK-_ND�Z\K�X[Z�=@A�S�DFP�Z\`HK6W]=@?UOD/XnZ\`HK6A"�]=@?�a

P\<m�R?U=2XHq6b�A*^(SYD/G�· ?�?�K�G\=2K�?�o"��X�W4Z�`�K>��G\?UZjDFGJW]K�Gj=2X&?Ue�A�S2S)� ���±P8D/G�e DFPVZ\`HKc?�DFS2E]Z�=2DFX4P8DFG�Z\`HK~_VDFZ�K�X/Z\=2AFS�u=�a KFa2o�Z�`�KcA�_H_HG\D*�]=Ye�A�Z�K�P8DFG\e�Z�`�Kc?UD/SYE]Z\=YD/XgP8DFGjLNK�=2XHq-dFK�G�^sI�SYD[?UK�Z\DMZ�`HKcW]=@?�ONa���S2=2eg=2X�A�Z�K �R=YXgP,A*dFD/GDFP ��A�XVW �Q=2XQP,A*d/DFG�D�P � � a�¿~KiI�A�S2S

� $ �µ�� � �

q(<C»{`VA"Zc=@?�Z�`HK �FTkI�DFe&_NDFXHK�X/Z~DFP�Z�`�K-K�S2K�I$Z\G�=@IR��K�S@W ��-P8D/G>Z�`HK6?�e�A�S2S.������I�A/?UK �

¾/� ¶ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj=2X[Z�K�q/G\A�Z�=2DFXQP8DFG~_ND�Z\K�X[Z�=@A�S¶ a ��D/EQ`�A*d/KRAgW]=@?UOCDFP�GJAFW]=2E�? �ga�b>`�KM?�EHG�P,AFI�K�IJ`�AFG�q/KRW]K�X�?�=�Z:^�=@?>qF=2dFK�XCL(^ �j5 < $ � � � l~`�K�G\K =@?�Z�`�KGJAFW]=@A�S�I�D(DFGJW]=YXVA"Z�K�D�P�Z�`HK6WH=2?�O�a

A[<C»{`VA"Zc=@?�Z�`HKMZ\D�Z\AFS�IJ`�AFG�q/K �sDFXZ�`HK6WH=2?�O��LN<n»{`VA"Z6=@?�Z�`HK�K�SYKiI$Z�G\=@I4_ND�Z\K�X[Z�=@A�S�A�ZsW]=@?:ZJA�X�I�K���AFLVD"d/KsZ\`HKCW]=@?UO�DFX�=�ZJ?6A"�]=@?�a ������ � ��DFErl~=2SYS

_�G�D/L�A�LHS2^CXHK�K�WA4Z\A�L�SYK-DFP�=2X[Z�K�q/G\AFS2?�aIi<n»{`VA"Zc=@?�Z�`HK-_ND�Z\K�X[Z�=@A�S�A�Z�&=�P � � �

WV<�»{`�A�Zc=2?�P,AFGUT���K�S@WQSY=2e&=�Z\=YXHq&P8D/G�e P8DFG>Z�`�K-_VDFZ�K�X[Z\=2AFS�A"Z��58=�a KFa2o�l~`HK�X4� � � �-<��

Page 124: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � ¥ &A9a&THJ*O;7?T5\E &T>a, ¥ &:9�&AH *O;7&A>�H^1

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/� ¹ h[e4EHS�ZB¾/¾H�i¾F¾C�&� ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�AF_�AFI�=�Z\DFG~W]K��VXHK�W�Fa �\¸�K�Zi· ?;_HS@A*^ �]1J� D+�"����# 1 |HD/G��]��¾F¾�o"Z�`�KRA�XV?Ul�K�G�=2?�u��BXCK�S2K�I�Z�G\=2I�A�SNW]K�d(=@I�KRI�DFX�?�=@?:Z\=YXHqsD�P�Z:l�D4I�DFXVW]E�I$Z\=YX�q?�EHG�P,AFI�Ki?;?�K�_�AFG\A�Z�KiW&L[^&d"AFI�EHEHe�DFG�AsW]=2K�S2K�I�Z�G\=2IcZ�`�A�Z�I�A�G\G�=2K�?;K�h[E�A�S�A�XVW�DF_H_ND/?�=YZ�KBIJ`�AFG�q/K�?jD/X�Z�`�KBZ:l�D?�EHG�P,AFI�Ki?~A�X�WQ=@?>E�?UKiWQZ�D�?:Z\DFG\KMK�S2K�I$Z\G�=@I�AFSp_VDFZ�K�X/Z\=2AFSpK�XHK�G�q/^nA�XVWQIJ`�AFG�q/K�� �A[<C»{`VA"Zc=@?~A&G�Ki?U=@?:Z\DFGio]�cS2K�� �LN<n»{`VA"Zc=@?~A�Xm=YXVW]E�I$Z\DFGioH�cS2K�� �Ii<n»{`VA"Zc=@?~AgZ�GJA�X�?�=2?UZ�D/G�o]�BSYK����WV<n»{`VA"Zc=@?~A�X�W(Tkq/A�Z�K/oH�cS2K�� �K*<n»{`VA"Zc=@?~A�I�DFXVW]K�X�?�K�G��{XHD�o(XHD�A&I�AF_�AFI�=�Z\DFGio(�BSYK�� �

¾/� ¹ h[e4EHS�ZB¾/¾/�F¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�I�A�_�A/I�=YZ\A�XVI�K�qFK�D/e&K�Z�G\^�]a~b>`HK6I�A�_�A/I�=YZ\AFX�I�K�D�PjA&I�A�_VAFI�=YZ�D/G>=2W]KiA�S2SY^QW]K�_NK�X�W�?~DFXHS2^CD/X�u

A[<C=YZ\?BW]=YK�SYKiI$Z\G�=@I�=YX�?�EHS@A"Z\=YD/X�aLN<n=YZ\?cqFK�D/e&K�Z�G\^FaIi<n=YZ\?cqFK�D/e&K�Z�G\^CA�XVWQ=YZ\?~WH=YK�SYKiI$Z�G\=@IM=YX�?�EHS@A"Z\=YD/X�aWV<CZ\`HK-_ND�Z�K�X[Z�=@A�S�_HEHZcDFXQZ�`HK6I�A�_�A/I�=YZ�DFGiaK*<CZ\`HK6IJ`�AFG�q/KR_HEHZcDFXQZ�`HK6I�A�_�A/I�=YZ�DFGia

¾/� ¹ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�v $�hHy*´³ aBv�AF_�AFI�=�ZJA�X�I�K�=@?>qF=2dFK�XQL(^�u

A[< � $ � � �(aLN< � $ � ��� �(aIi< � $ � ��� �CaWV< � $ ��� �&aK*< � $ � , �&a

¾/� ¹ h[e4EHS�ZB¾/¾�µ[¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�P,AFG\A/Wµ�a~b>`HK4¯�²6¤EHXH=YZRDFPjI�A�_�A/I�=YZ\AFX�I�K-=@?cZ\`HK-P,AFG\A/W�5�| $-v~y*´�<�aV7!XmP,A/I$Zio���|t=@?B?�E�IJ`�A�`(EHqFK6I�A�_�A/I�=YZ\AFX�I�K��^/DFEmesE�?UZB`HD/S2W�Av�DFEHS2DFe4LDFP�IJ`�A�G\qFKMl~=YZ�`�AC?�=YX�qFS2K-dFDFSYZcP8D/GBA���|tI�A�_VAFI�=YZ�D/G �wZ�`VA"ZBI�AF_�AFI�=�Z\DFGJ?~A�G\Kq/K�XHK�G\AFSYS2^�G\A�Z�KiWn=2X�uA[<CO]|�o�¯�|�o�AFX�Wm�M|�aLN<n_V|�o�X�|�o�A�X�W � |�aIi<Qb~|�o�9�|�oHA�X�Wm�;|�aWV<QA/|�A�XVWnP,|�aK*<CP8K�G�G\K�ZJ?�oH?UZ�D[A"ZJ?�oHAFX�Wnl�K�A/?UK�S2?�a

¾/� ¹ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�A�_�A/I�=YZ�DFG~?�^(esLNDFS¶ a~b>`HK6?UZ\AFX�WHAFG\WQI�=2G\I�EH=�ZBWH=2AFqFGJA�e ?�^[e4LVD/S�P8DFGcA&I�AF_�AFI�=�Z\DFG>=@?�u

Page 125: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia;� ¹ v�AF_�AFI�=�Z\DFGJ?>A�X�W�v�A�_VAFI�=YZ\AFX�I�K �i�H�

A[< � � aLN<��� aIi< � aWV<CT��8T�aK*<��4a

¾/� ¹ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj_HS@A�XVA�G~I�AF_�AFI�=�Z\DFG¹ a~b>`HK&?�=Ye&_HS2K�?UZRDFP�A�S2S�I�A�_�A/I�=YZ�D/GRI�AF_�AFI�=�ZJA�X�I�K6P8D/G�e4EHS2AFK-Z�DG\K�e&K�e4LVK�GR=@?cZ\`�A"Z�P8DFGRZ�`�KgAF_H_HG\D*�(=2e�A"Z\K�S2^=2X]��XH=YZ�KQ_HS@A�X�AFGsI�AF_�AFI�=�Z\DFG-l~=YZ�`�d"AFI�EHEHe LVK�Z:l�K�K�X�Z�`�Kn_HS@A"Z\K�?�ab>`HKCP8DFG\esEHS@Am=YX(d/DFS2dFK�?6DFXHS2^ � 58Z�`HKAFG�KiACD�P�Z�`HK&_HS@A"Z\K�?J<$o �Z\`HK�?UK�_�A�GJA"Z\=YD/X�D�P�Z\`HK&_HS@A"Z�Ki?�o�A�X�W�Z�`HK&d"AFI�EHEHe _NK�G\e&=�Z\=Yd(=YZ:^ � � 5,l~`H=2IJ`�`�A/?EHX�=�ZJ?~D�P � � ��<$a>��^nW]=2e&K�X�?�=2DFX�AFS�A�X�AFSY^]?�=2?M58=�a KFa2o�A�X�AFSY^]?�=2?>DFP�Z\`HK-EHXH=YZ\?J<$o]Z\`HKMP8DFG\esE�S2AgesEV?:ZcLNKFuA[< � $ � � � � � � aLN< � $ � � �����6aIi< � $ � � � ����aWV< � $ � �]5 � � � <$aK*< � $f5��0, �[< � � � a

¾/� ¹ h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�AF_�AFI�=�Z\DFG�P8DFG\esEHS@A�Kº(a~b>`HKwI�AF_�AFI�=�Z:^�P8D/G�e4EHS2AFK�P8DFGxZ�`�KtZ\`HG\K�K�=@W]KiA�S�o4`H=2qF`HTk?�^(ege&K�Z�G\^Fogd*A/I�EHE�e4T!?�K�_�AFG\A�Z�K�W�I�A�_�A/I�=YZ�D/G\? �_HS@A�XVA�GioHI�^(SY=2X�W]G\=@I�A�S�o]A�X�Wm?�_H`HK�G�=@I�AFS �{=YXDFGJW]K�G>AFG�K/uA[<

� $ �

�� ��� $ -

� ��� ��� $ -

�� �

LN<� $ �

� � � � ��$ � � � $ �

µ��� � � ��

Ii<� $ ���

�� $ � � � �

S2X�5 � � � � � � � � ��� �k< � ${µ�� � � ��� � �� , � ��� � ��� � � � � �

WV<� $ � � � �

SYX�5 � � � � � � � ��� � �!< � $ ����

� ${µ�� � � ��� � �� , � ��� � ��� � � � � �

K*<� $�µ�� � � ��� � �

� , � � ��� ��� � � � � � � $ ����

� $ ��� � �S2X�5 � � � � � � � � ��� �k<

¾/� ¹ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�I�A�_�A/I�=YZ�DFGJ?�=YXm_�AFG\AFSYS2K�S¼ a>7kP�^FDFEn`�A*dFK�A4?�K�Z>D�P � � ��� I�A�_VAFI�=YZ\AFX�I�Ki?;=2X_�A�GJA�S2SYK�S�o/Z�`�K�XQZ�`HK�K�h[EH=2d"A�S2K�X[Z>I�A�_�A/I�=YZ\AFX�I�K � ��� �4=2?�q/=Yd/K�XL(^�uA[<�� � � ��� ��$��

�� � � � aLN<�� � � ��� � $ ��� � a

Ii< � ��� � $ ��� � � � aWV<�� � � ��� � $ ��� � � �

�a

K*< � ��� � $ ��� � a

¾/� ¹ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�I�A�_�A/I�=YZ�DFGJ?�=YXm_�AFG\AFSYS2K�S½ a>7kP�^FDFEn`�A*dFK�A4?�K�Z>D�P � � ��� I�A�_VAFI�=YZ\AFX�I�Ki?;=2X_�A�GJA�S2SYK�S�o/Z�`�K�XQZ�`HK�K�h[EH=2d"A�S2K�X[Z>I�A�_�A/I�=YZ\AFX�I�K � ��� �4=2?�q/=Yd/K�XL(^�u

Page 126: Introductory Physics Problems David J. Jeffery Department of

�i�/� v�`�A�_]Zia;� ¹ v�AF_�AFI�=�Z\DFGJ?>A�X�W�v�A�_�A/I�=YZ\AFX�I�K

A[<�� � � ��� ��$ ��� � � � a

LN<�� � � ��� ��$ ��� � a

Ii< � ��� ��$ ��� � � � a

WV<�� � � ��� ��$ ��� � � �� aK*< � ��� ��$��

�� � a

¾/� ¹ h[e4EHS�ZB¾/¾ ½ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�I�A�_�A/I�=YZ�DFGJ?�=YX�?�K�G\=YKi?��¾Ha>7kP;^/DFE�`VA*dFK4AQ?UK�Z�DFP � � � � I�AF_�AFI�=�ZJA�X�I�K�?B=YX�?UK�G�=2K�?�oNZ�`HK�X�Z�`�K4Kih/E�=Yd"A�S2K�X[ZMI�A�_VAFI�=YZ\AFX�I�K � ��� � =2?�q/=Yd/K�X

L(^�uA[<�� � � ��� � $ �

�� � � � a

LN<�� � � ��� � $ ��� � a

Ii< � ��� ��$ ��� � � � a

WV<�� � � ��� ��$ ��� � � �� aK*< � ��� ��$��

�� � a

¾/� ¹ h[e4EHS�ZB¾���¾/¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj�jT���K�S@WQK�XHK�G�q/^nW]K�XV?U=YZ:^�F�Fa �\¸�K�Zi· ?Q_HS@A*^ �(1J��D3�����"# 1 |�DFG��(�i¾F¾Ho>Z\`HKrA�X�?�l�K�Gn=@?�utb>`HKxK�XHK�G\qF^wW]K�X�?U=YZ:^{D�P-Z\`HKrK�S2K�I�Z�G\=2I���K�S@W�=2X

d"AFI�EHEHema �A[<C»{`VA"Zc=@? � $ 5U� �F�F< � � ��o��BSYK����LN<n»{`VA"Zc=@? � $ � ���H5�� � � <$o��BSYK�� �Ii<n»{`VA"Zc=@? � $�, � � ��o��BSYK����WV<n»{`VA"Zc=@? � $ 5U� �F�F< � � Co��cS2K�� �K*<n»{`VA"Zc=@? � $ 5U� �F�F< � � � o��BSYK����

¾/� ¹ h[e4EHS�ZB¾��F�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]=2K�S2K�I�Z�G\=2I�i�]a~��W]=2K�S2K�I�Z�G\=2I�=@?cAHu

A[<C_NDFS@A�G\=2��A�L�SYK�=YXV?UEHS@A"Z\DFGiaLN<QI�DFX�WHE�I$Z\DFGiaIi<Q?�K�e&=YTkI�DFX�WHE�I$Z\DFGiaWV<Q?�EH_NK�GJI�D/X�W]E�I�Z�DFGiaK*<n=2X�?�EHS@A"Z�D/G>Z�`�A�ZBI�AFX�· Z~LNK-_VD/S2AFG�=2��KiWpa

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/� ¹ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�I�AF_�AFI�=�ZJA�X�I�KBP8D/G�e4EHS@A�K�Fa~b>`HK�I�A�_VAFI�=YZ\AFX�I�K�P8D/G�e4EHS@A�KjD�P]`H=2qF`HTk?�^(ege&K�Z�G\^�I�A�_�A/I�=YZ�DFGJ?pA�G\KjK�A/?U^BZ�DBI�A�S@I�EHS@A"Z\K;?UZ\A�G�Z�=2XHq>P8G\DFe��MA�E�?\?�·S@A*l-u �

��� � � �� �� � � �� $ � � � � � � � � �

� ��

°RXHK-EV?UKi?c�MA�E�?\?�·�S2A*l�Z�DCI�AFS2I�EHS@A"Z�K�Z\`HK-K�S2K�I�Z�G\=2I���K�S2WLNK�Z:l�K�K�XQZ\`HK-_HS@A"Z\K�?~DFP�Z\`HK6I�AF_�AFI�=�Z\DFG>=YXZ\K�G\e&?DFP>q/K�D/egK�Z�G\^xAFX�W�IJ`�A�G\qFK �D/XrZ�`HKQ_VD[?U=YZ�=2dFKC_�S2A�Z�K�58Z�`HKQXHK�q[A"Z�=2dFKn_HS2A�Z�KC`VAF?sIJ`VA�G\qFK�, ��<-A�XVWrZ�`HK�XW]K�Z�K�G�e&=2XHK�?�Z\`HK-_VDFZ�K�X/Z\=2AFS�W]= �NK�G�K�X�I�K-q/DF=2XHq4P8G�D/e Z�`HK-X�K�q/A�Z�=2dFKM_HS@A"Z\KRZ\D&Z�`HK-_ND/?�=YZ�=2dFKM_HS@A"Z�KME�?�=2XHq

� $ , � �� �

� � �� � � �� �

b>`HK6I�A�_�A/I�=YZ\AFX�I�K�=2?cqF=2dFK�XQL(^� $ �

Page 127: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia;� ¹ v�AF_�AFI�=�Z\DFGJ?>A�X�W�v�A�_VAFI�=YZ\AFX�I�K �i� ³

l~`H=@IJ`�?U`�DFEHS@WCZ\EHG\XD/E]Z>Z�D�LNK-=YXVW]K�_NK�X�WHK�X[ZcD�P �sAFX�W ��aA[<C»{`VA"ZR=@?BZ�`HK&I�AF_�AFI�=�ZJA�X�I�K-P8DFG\esEHS@A&P8D/GRA�X�=2W]KiA�S�_�A�GJA�S2S2K�S�_�S2A�Z�K4I�A�_�A/I�=YZ�D/G���R?�?�EHe&Kg_HS2A�Z�KgA�G\K�A� A�XVW�_HS@A"Z�Kg?UK�_�A�GJA"Z\=YD/X ��a�»�Ks`�A*d/K6Z�DAF?\?UE�egK6Z�`HK&IJ`�A�GJAFI�Z�K�G�=@?:Z\=2IMS2K�X�q�Z�`�D�P��f=2?RdFK�G�^mS@A�G\qFKI�DFe&_�AFG�KiW �gP8D/G>Z�`HK-=2X]��XH=YZ�Ks_HS2A�Z�K-A�_�_HG�D*�]=2e�A"Z�=2DFXnZ�D�LNK-d"A�S2=2Wpa

LN<n»{`VA"Zc=@?�Z�`HK6I�A�_�A/I�=YZ\A�XVI�K�P8DFG\esEHS@AsP8DFGBAFXQ=@W]K�AFS�I�^(S2=YX�WHG�=@I�AFSp_HS2A�Z�K-I�AF_�AFI�=�Z\DFG �m�B?\?UE�egK-I�^[S2=2X�W]K�GS2K�X�q�Z�` �Bo�=YX�XHK�G�AFX�WsD/E]Z�K�GjG\A/W]=2=2�6A�X�W � o/A�X�WsZ�`HK~_ND/?�=YZ�=2dFK~IJ`�A�G\qFK�DFX4Z�`�K~=YXHX�K�Gj_HS@A"Z\KFa�»xK~`�A*d/KZ\DCAF?\?UE�egK � � ���QA�X�W � � � � P8DFG>Z\`HK-`H=2qF`�?�^[e&e&K�Z\G�^QA�G\qFEHe&K�X[ZJ?;Z\DCA�_H_�SY^nAF_H_HG\D*�]=Ye�A"Z\K�S2^Fa

Ii<n»{`VA"Zc=@?�Z�`HK6I�A�_�A/I�=YZ\A�XVI�K�P8DFG\esEHS@AsP8DFGcA�Xm=@W]K�AFS�?U_�`HK�G\=2I�A�S�_HS@A"Z\K6I�A�_VAFI�=YZ�D/G��R?�?�EHe&K-=YX�XHK�GcAFX�WD/E]Z�K�G�G\A/W]=2=-�tA�X�W � o�A�X�W�Z�`HK�_ND/?�=YZ�=2dFK�IJ`�A�G\qFKQDFXtZ�`HK�=2XHXHK�G�_HS@A"Z�K/aw7!X�Z\`H=2?�I�AF?�KZ�`HK�`H=2qF`HT?�^(e&egK�Z�G\^nI�D/X�W]=YZ�=2DFX�A�_�_HSY=2K�?>K��HAFI$Z\SY^/a

WV<n»{`VA"Z6S2=Ye&=YZ�=2XHq�I�AF?�KgP8DFG\esEHS@AW]Dm^FDFExqFK�Z�P8G\DFe Z�`HK&_�AFGUZC5,Ii<MA�X�?�l�K�GM=�P � � ��7!XxZ�`�=2?6I�AF?�K^/DFEx_HE]ZMZ�`HK&D/E]Z�K�G�_�S2A�Z�K�A"ZM=YXH��XH=YZ:^Fas7kZi· ?-?�`�AF_VK&?UDQP,A�G-A*l>A*^m`�AF?�XHDK ��K�I�Z-?�=2X�I�KgZ�`�K4K�SYKiI$Z�G\=@I�VK�S@W�l~`HK�G\K�=YZ4=@?6=2eg_NDFG�Z\AFX[ZsDFLNK�^]?s?�_H`HK�G�=@I�AFS;?�^[e&e&K�Z\G�^/a�¿~K�e&K�esLNK�G6Z\`HKnE�XH=Yd/K�GJ?UK�=@?6D"d/K�GJA�S2SX�K�E]Z\G\AFS�5,=�Z-?UK�K�e�?J<$a�¤]DC=�P�^FDFE�=@?�DFS@A"Z�K4An?�_H`HK�G\=@I�A�S�_HS@A"Z�K4D�P�_ND/?�=�Z\=Yd/K4IJ`�AFG�q/KFoN?UD/egK�l~`HK�G\K6D ��=2XZ\`HK-EHXH=2dFK�G\?�KM=2?>X�K�q/A�Z�=2dFK-IJ`�AFG�q/KcZ�D�LVA�S@A�X�I�K�=YZ�a

¾/� ¹ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�I�AF_�AFI�=�Z\DFG~A�XVW?�l~=YZ\IJ`�]a~¸�K�Z�· ?�AFX�A�S2^(��K�Z\`HK�?UZ\A�Z�=@I�?:ZJA"Z\K�?�DFPHA~dFK�G�^�?U=2e&_HSYK�I�=2G\I�EH=�Z�I�DFXV?U=@?:Z\=YX�qcD�PHA�X-=@W]KiA�SFLVA"ZUZ\K�G\^Bl~=YZ�`6_ND�Z\K�X[Z�=@A�S� � opAnI�A�_�A/I�=YZ�DFGRD�P;I�A�_�A/I�=YZ\A�XVI�K � � op?Ul~=YZ\IJ`�DFP;I�AF_�AFI�=�ZJA�X�I�K � � l~`HK�X�DF_NK�X�opA�XVW�I�D/XHXHK�I�Z�=2XHqnl~=2G\K�?�a�BX{=2W]KiA�SB?�l~=YZ\IJ`{l�DFEHS@W±`�A*dFKm��K�G�D�I�A�_�A/I�=YZ\AFX�I�K/o�LHEHZnDFEHGQ?Ul~=YZ\IJ`w=@?�XHD�ZQ=2W]KiA�SBAFX�Ww`�A/? � � � ¾Ha£BD"l�K�dFK�Gio � � ��� � � a�b>`HK4A/?�?�K�e4LHS2K�W�I�=2GJI�EH=YZR=@?RAQ?U=2XHq/SYK6S2D(DF_�G\EHXHX�=YXHqnL�A"Z�Z�K�G\^Fo�I�AF_�AFI�=�Z\DFGioV?�l~=�ZJIJ`=2XtA�I�S2D]IJO[l~=@?�KQW]=2G�KiI$Z\=YD/X�unl~=2G�Ki?4I�DFXHX�K�I$ZgZ�`�KmI�DFe&_NDFXHK�X/ZJ?�a�b>`�KQl~=2G�Ki?g`�A*dFKQXHDx_ND�Z\K�X[Z�=@A�S~W]G\DF_V?A/I�G\D/?\?sZ\`HK�e�l~`HK�XwXHD�I�EHG\G�K�X/Z�=@?&��D"l~=2XHq�a�b>`�K�_VDFZ�K�X[Z\=2AFScIJ`�A�XHq/K�A�G\DFEHX�W�Z�`�K�I�DFe&_HS2K�Z\K�I�=2G\I�EH=YZ?�`HDFE�S2W�LVK���K�G\DQA"Z6AFSYS�Z�=2e&K�?�uBZ\`H=@? A:E�?:ZMP8D/SYS2D"lc?RP8G�D/e�Z�`HK�I�D/X�?�K�G\d*A�Z�=2dFK4X�A"Z\EHG�KgD�P�Z�`HK&K�SYKiI$Z�G\D/?UZ\A�Z�=@IP8D/G\I�KFa���DFE�?�`HDFEHS@WW]G\A*l�A&I�=2G\I�EH=�ZcW]=@A�q/G\AFemaA[<C7!X�=�Z\=2AFSYS2^Fo[Z�`�KRI�AF_�AFI�=�Z\DFG�A�X�W�?�l~=�ZJIJ`nA�G\KcEHXVIJ`�A�G\qFKiW�A�X�WCI�DFXHX�K�I$Z\K�WgZ\D6Z�`�KRL�A�ZUZ\K�G\^Fa�b>`HKR?�l~=�ZJIJ`=@?MDF_NK�X�a47:W]KiA�S2SY^/opXHD�I�EHG\G\K�X[ZM?�`HD/EHS2W���D"lfA�Z6A�S2S�l~`�K�XxZ�`HK�I�=2GJI�EH=YZ-=2?-I�DFXHXHKiI$Z\K�Wpa���E]Z-=YXxP,AFI�ZZ\`HK�G\Ksl~=2S2S�LNK4ACZ�=2X[^Z\G\AFX�?U=2K�X[ZRI�EHG\G�K�X/ZBZ�`�A�ZRl~=2SYS�_HE]Z-ACIJ`�AFG�q/K � � DFX�LND�Z�`�Z�`HKgI�AF_�AFI�=�Z\DFGBAFX�W?�l~=YZ\IJ`�a�b>`HKsI�E�G�G\K�X[Zc?:Z\DF_�?cl~`HK�X�_ND�Z\K�X[Z�=@A�S�WHG�D/_mA/I�G\D/?\?�Z�`HKsI�A�_�A/I�=YZ�D/GcA�X�Wm?�l~=�ZJIJ`Kih[E�A�S@?>Z�`�K_ND�Z\K�X[Z�=@A�S�G\=2?�K4A/I�G\D/?\?~Z\`HK&L�A"Z�Z�K�G\^�u � � $�� � � � � a6¡BK�Z�K�G\e&=YX�K � � A�XVW � � =YXxZ�K�G�e�?RD�P �

�o � � o

AFX�W � � a&£cD"l W]DnZ\`HK�?U=2��Ki?�D�P � � AFX�W � � I�DFe&_�AFG�KsZ�D ����»{`�A"Z-l�DFEHS@W � � AFX�W � � LNK�=YP;Z�`�K

?�l~=YZ\IJ`�l�K�G\KC=@W]K�AFSR58=�a KFa2o�`�AFW � � $ ¾[<$a �������� � ¿~K�e&K�esLNK�G � $ � ��axb>`�=2?4=2?4A�X�AFSYq/K�LHGJA_�G�D/LHSYK�emu�Z:l�D&EHXHO(XHD"l~X�?�P8D/G~l~`H=@IJ`QZ:l�D&K�h[E�A�Z�=2DFX�?>A�G\KMXHK�KiW]K�WQP8D/Gc?UD/SYE]Z\=YD/X�a

LN<Q BD"lt^/DFE�I�S2D/?�K�Z�`HKR?Ul~=YZ\IJ`&l~`H=@IJ`�K�?\?UK�X[Z�=@A�S2SY^sI�DFX(dFK�GUZJ?�=�Z�=2X[Z�DsAM_�=YKiI�K~D�P�l~=2G�K~l~=YZ�`�XHD-_ND�Z\K�X[Z�=@A�SWHG�D/_mA/I�G\D/?\?>=�Zia~b>`HK�G\K-=2?B?UD/egK6Z�GJA�X�?�=YK�X[ZBI�EHG\G�K�X[Z~P8DFGBA*l~`H=2S2KFoHLHEHZBZ�`�Ks?U^]?UZ�K�e}?�K�ZUZ\SYKi?BW]D"l~XZ\DA&?UZ\A�Z�K-l~=YZ�`�IJ`�A�G\qFK � � D/XnZ\`HK6I�AF_�AFI�=�Z\DFGia�»{`VA"ZBA�G\K�� �RA�X�W � � �

Ii<Q BD"lz^/DFE�D/_VK�XQZ\`HK4?�l~=YZ\IJ`�A�q[A�=2X�a�»{`VA"ZB`�AF_H_NK�X�?� ������ � b>`�K�G\K-=2?BXHD�_VDFZ�K�X/Z\=2AFS�W]= ��K�G\K�X�I�KA/I�G\D/?\?�Z�`HK6?�l~=�ZJIJ`�a

WV<Q BD"lw^FDFE&ZJA�O/K>Z�`HKRL�A"Z�Z�K�G\^gDFE]Z;DFP�Z�`HK�I�=2G\I�EH=�Z�SYKiA*d[=2XHqMZ\`HKBl~=2G�Ki?jZ\`�A"Z�I�DFXHX�K�I$Z\K�W&Z\D-Z�`�KBL�A�ZUZ�K�G�^Z\K�G\e&=YX�AFS2?�P8G\K�K/aj»{`�A"Zc`VA�_H_NK�X�?�

K*<Q BD"l ^FD/Et?�=Ye&_HS2^�I�D/XHXHKiI$Z&Z�`HKZ\K�G\eg=2X�AFS�l~=2G\K�?�a�b>`HK�G\Kl~=YS2S~LVKZ\G\AFX�?U=2K�X[Z&I�EHG\G�K�X[Z�a�b>`HKmK�X�WG\K�?�EHSYZ�l~=YS2SHLNKBAF?�=YP�Z�`HKRI�A�_VAFI�=YZ�D/GjA�X�WgDF_NK�XCI�=YGJI�E�=�Z�l�K�G\K~I�A�_VAFI�=YZ�D/G\?�=2X�_�A�GJA�S2S2K�S]=2X&A-?UZ\A�Z�=@I~I�A/?UK/a»{`VA"Z&=2?sZ�`HKmIJ`�AFG�q/KCDFXtK�AFIJ`�=2X�Z\K�G\e�?4DFP � � A�X�W�Z�`HKmI�AF_�AFI�=�ZJA�X�I�K�?� �������� � �B?�KIJ`VA�G\qFKI�DFX�?�K�G\d"A"Z\=YD/X�A�X�W�Z�`HKP,A/I$ZgZ�`�A�ZgZ\`HKm_VDFZ�K�X/Z\=2AFS~W]=���K�G\K�XVI�K�?&A/I�G\D/?\?6Z\`HKI�A�_�A/I�=YZ�D/GgAFX�W�?�l~=�ZJIJ`e4E�?UZcLVK-Kih/EVA�S�a���D/E�A�G\K�?�DFS2d(=YXHqgP8D/G>Z:l�D&EHXHO(XHD"l~XV?~A�q/AF=YX�a

¾/� ¹ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujK�X�K�G\qF^n?UZ�D/G�KiWC=2XmA&I�A�_�A/I�=YZ�DFG³ a~b>`HKM_ND�Z\K�X[Z�=@A�S�K�XHK�G\qF^C?UZ�D/G�KiWC=2X�AgI�A�_�A/I�=YZ�D/G�=@?~A4P8EHX�I$Z\=YD/XmD�P�Z\`HK6IJ`�AFG�q/KRA�XVWQ=YZ\?~WH=2?UZ�G\=YL�E]Z�=2DFXDFXHS2^Fa

Page 128: Introductory Physics Problems David J. Jeffery Department of

�i��µ v�`�A�_]Zia;� ¹ v�AF_�AFI�=�Z\DFGJ?>A�X�W�v�A�_�A/I�=YZ\AFX�I�K

7kZ&W]D(K�?6X�D�ZgWHK�_NK�X�W�DFX�`HD"l Z�`�KQW]=@?:Z\G�=2LHE]Z\=YD/X�l>AF?sA/?�?�K�e4LHS2K�Wpa�b>`HKQl�D/G�O�W]DFX�K�Z�D�AF?\?UK�esLHS2K�Z�`�KW]=@?UZ�G\=YLHEHZ�=2DFX�o~`HD"l�K�d/K�Gio�Kih[E�A�S@?&Z�`�=2?Q_VDFZ�K�X/Z\=2AFSBK�XHK�G\qF^/a ¤(D�^/DFE�I�A�Xw=Ye�AFqF=2XHK�A�X(^±?U=2e&_HSYK�l�A*^tD�PA/?�?�K�e4LHSY^�^/DFEQSY=2OFK-AF?�e&K�AFX�?>D�P�I�AFS2I�EHS2A�Z�=2XHq4Z�`HK-_ND�Z\K�X[Z�=@A�SpK�XHK�G\qF^/a�¤]A*^CZ�`�A�Z>^/DFE A:E�?:Z~Z\D(DFO�_ND/?�=�Z\=Yd/KIJ`�AFG�q/KsP8G\DFe DFXHK�_HS@A"Z\K&SY=YZUZ\SYKCL�=�ZsA�ZsAnZ\=Ye&KCAFX�W�egD"d/K�W�=�Z6Z\DZ�`HK�DFZ�`HK�G-_HS2A�Z�K/a���DFE�?:ZJA�G�Z�KiW�P8G\DFeEHXVIJ`�A�G\qFKiW�?:ZJA"Z�KgA�X�W�LHEH=2S�ZMEH_�Z\DQIJ`�AFG�q/K �&DFX�Z\`HK4I�A�_�A/I�=YZ�D/G�aBb>`�KgIJ`�AFXHqFKs=YX�_ND�Z\K�X[Z�=@A�S�K�X�K�G\qF^D�PZ\`HK6?U^]?UZ�K�e�W]EHKMZ\`HKMZ�GJA�X�?UP8K�G~DFP � � ��=@?

� � $ � � � � � l~`HK�G�K � � =2?�Z�`�K-_VDFZ�K�X[Z\=2AFS�W]=���K�G\K�XVI�K�LVK�Z:l�K�K�XQZ�`HK-_HS@A"Z\K�?>A"Z>Z\`HK�Z�=2egK-DFP�Z\G\AFX�?:P8K�G�G\=2XHq � � � aj»{`VA"Z~=2?Z\`HK�Z�D�ZJA�S(_ND�Z�K�X[Z�=@A�S]K�X�K�G\qF^MD�PVIJ`VA�G\qF=2XHqcZ\`HK~I�A�_VAFI�=YZ�D/G�Z\D ��� ������ � ��D/E4XHK�K�WsZ�DMW]DMA�Xs=2X[Z�K�qFGJA"Z�=2DFX�a

¾/� ¹ h/P8EHS2S�¾���¾F¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�I�S2A/?�?�=2I�A�S�K�S2K�I�Z�G\DFXG\A/W]=2E�?µ�a~9�K�DF_HS2KMDFX�I�KRZ\G�=2K�WnZ�DCWHK�d(=2?�K-A�?UK�e&=�T!I�S@AF?\?U=@I�AFSVe&D]W]K�S�D�PjA�XK�S2K�I�Z�G\DFX=YXml~`H=@IJ`Z�`HK-G\K�?UZ~e&A/?�?>K�XHK�G\qF^q/=Yd/K�X�L[^x��=2X�?:Z\K�=2X�· ?�P8DFG\esEHS@A $ ��*���5 }P8D/G-K�XHK�G�q/^�`HK�G\Ki<�l>AF?�K�X[Z\=YG\K�S2^�?UZ�DFG\K�W�AF?MK�SYKiI$Z\G�=@I4��K�S@W_ND�Z\K�X[Z�=@A�S>K�X�K�G\qF^Fa�b>`HKQP8DFG\esEHS@A�P8D/G4_ND�Z\K�X[Z�=@A�S�K�XHK�G�q/^�W]K�X�?�=YZ:^�=@? � $ 5:� �F�F< � � �x5 �P8D/G4K�SYKiI$Z�G\=@I��K�S2WC`HK�G\Ki<�a�»{`VA"Z;Z\`HK�^�W]=@W�l>AF?�A/?�?�EHe&K~Z\`�A"Z>A�S2S�Z\`HKBK�SYKiI$Z�G\DFXCIJ`VA�G\qFK>l�A/?�EHX�=�P8D/G�e&S2^&?�_HG\K�A/W4D/X�Z�`�K?�EHG�P,AFI�K-DFP�A�?U_H`�K�G\K-D�PjG\A/W]=2E�?��ga�b>`HK�^I�A�S@I�EHS@A"Z\K�WQZ�`�K-Z�DFZ\A�S�K�XHK�G�q/^CD�P�Z\`HK6K�S2K�I�Z�G\=2I��VK�S@W�58l~`H=@IJ`�=2?��K�G\D-=YX�?�=@W]KcZ\`HKB?�_H`HK�G\KFo[D�P�I�DFEHGJ?UK/oFL(^��MA�E�?\?�·/S2A*lB<�A�X�W&Kih/EVA"Z�KiWgZ�`�A�Z�Z�D �4*��65 � LVK�=YX�q-Z�`HKRK�S2K�I�Z�G\DFXe�AF?\?J<$asb>`HK�X�Z\`HK�^x?UD/SYd/K�WmP8D/G �4o�Z\`HK �UK�SYKiI$Z�G\DFX�G\A/W]=YEV?�a � »{`�A"Z-=@? � � 5, BD�Z\KFuRZ�`H=@?-?UK�e&=�T!I�S@AF?\?U=@I�AFSe&D]W]K�S�=2?�XHDFZ�o/D�PNI�DFEHGJ?�KFo�I�D/G�G\K�I�Z�AFS�Z\`HDFE�qF`4Z:l~=2I�K�Z\`HK~d"A�S2EHK~I�AFS2I�EHS2A�Z�KiW �{I�A�S2SYKiW6Z\`HKcI�S@AF?\?�=2I�A�S(K�S2K�I�Z�G\DFXGJAFW]=2E�? �w=@?~Ag_�A�GJA�e&K�Z�K�G�Z\`�A"Z~Z\EHG�XV?>EH_m=YX�?�DFe&K-I�A�S@I�E�S2A�Z�=2DFX�?�a <

¾/� ¹ h/P8EHS2S�¾��i��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�I�A�_VAFI�=YZ\AFX�I�KMl~=YZ�`m_(^(G�K��nW]=YK�SYKiI$Z\G�=@I¶ a ��D"^rDFGgqF=2G�S�l~=2��A�GJW�?\I�=2K�X[Z�=@?UZsZ�`VA"Z&^FDFEtA�G\KFoj^FD/E�W]KiI�=@W]KnZ\D�I�DFX�?UZ�G\E�I�Z4^FD/EHGgD"l~X�I�AF_�AFI�=�Z\DFGQ5,SY=YZUZ\SYKG\K�IJO(=2XHq�`HD"l WHA�XHq/K�G\DFE�?~Z�`HK�^I�A�X�LNKFa < ��D/E�E�?�KsAgZ\AFSYS�_(^(G�K��W]G\=YX�O[=2XHq�q/S2A/?�?cA/?BW]=2K�S2K�I�Z�G\=2IsA�X�WmS2=YX�KZ\`HKc=2X�?U=@W]KBAFX�W&DFEHZ\?�=2W]KBD�P�Z�`HKRI�EHG\dFKiWg?�EHG�P,AFI�K�?jl~=YZ�`&Z\=YX�P8D/=YS�a�b>`HKcqFS@AF?\?j=@?c� ¶ I�e `�=Yq/`CA�X�W&`�A/?j=2XHXHK�GAFX�W�D/E]Z�K�GgGJAFWH=Y=>D�P ³ � ¹ I�e AFX�W ³ � ¼ I�emo�G\K�?�_VKiI$Z�=2dFK�SY^/a�»{`�A�Z&=@?4Z�`HK�I�A�_�A/I�=YZ\A�XVI�KQAFX�WtLHG�KiA�O]W]D"l~X_ND�Z\K�X[Z�=@A�SND�P�^/DFEHG�I�A�_VAFI�=YZ�D/G�Qb�D6��X�W�Z�`HK�LHG\K�A�O]W]D"l~X&_ND�Z\K�X[Z�=@A�SNK��HAFI�Z�S2^&G�Kih/E�=YG\K�?��VX�W]=2XHq6Z\`HKRS2=2XHK�AFGIJ`�AFG�q/K�WHK�X�?�=�Z:^nD�P�Z�`HK-=2XHXHK�G>P8DF=2S�l~`HK�XZ\`HK6W]=2K�S2K�I$Z\G�=@I�LHG\K�A�O]?>W]D"l~X�a� � � � ��^ Z�`HK±L(^FogZ�`H=@?rW]K�d(=@I�K±=2?rI�A�S2SYKiW Az¸�K�^]W]K�X �[A�GxAFX�W l>AF?xDFX�KtDFP:o4=YPQXHDFZxZ\`HKt��G\?UZ�oI�DFX�?\I�=2DFE�?�S2^gI�DFX�?UZ�G\E�I$Z\K�W�I�A�_�A/I�=YZ�DFGJ?�a���=2qF`[Z\K�K�X[Z\`CI�K�X[Z\EHG�^&=2X(dFK�?UZ�=2q/A�Z�D/G\?���GJ?UZ�S2K�A�G\X[Z;`HD"l{WHAFXHqFK�G�D/E�?XHD/X]TkSY=2qF`[Z�X�=YXHq&K�SYKiI$Z�G\=@I�=YZ:^nI�D/EHS2WQLNKMP8D[D/SY=2XHq�A�G\DFE�X�Wnl~=YZ�`Z\`HK�?�KMZ�`H=2XHq[? �{DFG~?�Dg7>?�K�K�e Z�D�G\K�I�AFSYS�a

Page 129: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � ¥ da5\5<1_>2;<E &A>�, � 1)EG*IE�;7&A>�H^1

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/�[º6h[e4EHS�ZB¾/¾F¾���¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\=2I�A�SpEHXH=YZ\?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º�¾"TJ�F�

�Fa �\¸�K�Zi· ?n_HS@A*^ �]1J� D+�"����# 1 |HD/G �(�i¾F¾�o;Z\`HKxAFX�?Ul�K�G�=@?�u�b>`HK�^±AFG�K/o~G�Ki?U_NK�I�Z�=2dFK�SY^/o�Z\`HK�EHX�=�ZJ?nDFPM_ND"l�K�GioI�EHG�G\K�X[Zio]_VDFZ�K�X[Z\=2AFS�oHAFX�WG�Ki?U=@?:ZJA�X�I�KFa �»{`�A�ZBA�G\KFo]G\K�?�_VKiI$Z\=Yd/K�S2^Fo oH�cS2K�� �

A[<+A:DFEHS2KFo�l>A"Z�Z�o�X�K�l>Z�D/X�o/AFX�W6_VAF?\I�A�S LN<�DF`Hemo�l>A"Z�Z�o�d/DFSYZ�oFAFX�W4AFe&_VK�G�K I�<�AFesLH=2q�o"d/DFSYZ�K�TP,A/I�K/o/D/egK�X�o]A�X�WCl�A�Z�O(=YX W�<;AFe&_VK�G�K/o/d/DFSYZ�o[DF`He A�XVW�l�A�ZUZ Ki<;l�A�ZUZ�o(A�e&_NK�G\KFo[dFD/S�Zio[AFX�WD/`He

¾/�[º6h[e4EHS�ZB¾/¾H�i¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�²M=2G\IJ`�`HDB�~· ?�I�EHG\G�K�X/Z~S@A*l�]aBv�`�AFG�q/K�I�DFX�?�K�G\d"A"Z\=YD/XQA�_�_HSY=2K�WQZ\D&?UZ�KiAFW]^Q?:ZJA"Z�K6I�EHG\G�K�X/ZJ?�=YX�I�=2GJI�EH=YZ\?>S2K�A/WH?�Z�DVu

A[< ²M=2G\IJ`�`HDB�~· ? dFD/S�ZJA�q/K S2A*l-a LV< °R`Hem· ? S2A*l-a I�< ²M=YGJIJ`H`HD �~· ? I�EHG\G\K�X[Z S@A*l-aWV<> cK�l>Z\DFX�· ?B��X�WnS@A*l-a Ki<�K�XHK�G\qF^QI�DFXV?UK�G�d"A"Z\=YD/X�a

¾/�[º6h[e4EHS�ZB¾/¾/�F¾F¾C�6���4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�K ��K�I�Z�=2dFK-?�_VK�K�W³ a~b>`HKMK.�NKiI$Z�=2dFKM?�_VK�K�WQD�P�GJA�X�WHDFe�Z�`�K�G\e&AFS�egDFZ�=2DFXQD�P�K�SYKiI$Z�G\DFXV?�=2XegK�Z\AFS2?>A"Z>G\D[D/e�Z�K�eg_NK�GJA"Z\EHG\KR=@?�D�PD/G\W]K�G�u

A[< ³ �x�i¾�e��"?�a LV<��i¾"!�e��"?�a I�<��i¾ � !�e ��?�a WV< ³ �x�i¾ � � e ��?�a Ki<���e��"?�a

¾/�[º6h[e4EHS�ZB¾/¾ ³ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�I�DFX(dFK�X/Z\=YD/X�A�S�I�E�G�G\K�X[Zµ�aBv�D/X[d/K�X[Z�=2DFXVA�SpI�EHG\G\K�X[Z>P8DFG~K�=YZ�`�K�G~_ND/?�=�Z\=Yd/K�D/G~XHK�q[A"Z\=Yd/K�IJ`�AFG�q/K�I�A�G\G�=2K�GJ?�=2?~WHK���XHKiWmAF?>qFD/=YX�q

A[<C=2XZ�`HK6WH=YG\K�I�Z�=2DFXD�P�Z�`HK-K�SYKiI$Z�G\=@IB�VK�S@WQD/G~W]D"l~XnZ\`HK-_ND�Z�K�X[Z�=@A�S�q/G\A/W]=YK�X[Z�aLN<nD/_H_ND/?�=�Z\KRZ\`HK6W]=2G�KiI$Z\=YD/XQDFP�Z\`HK-K�S2K�I�Z�G\=2IR��K�S2WDFG~E�_QZ\`HK-_ND�Z�K�X[Z�=@A�SpqFGJAFWH=YK�X/ZiaIi<n_NK�G\_NK�X�W]=@I�E�S2AFG>Z�D&Z�`�K6W]=YG\K�I�Z�=2DFXD�P�Z�`HK-K�SYKiI$Z\G�=@IR��K�S@WDFG~W]D"l~XQZ�`HK-_ND�Z\K�X[Z�=@A�S�q/G\A/W]=2K�X[Z�aWV<CZ\D&Z�`HK-S2K�P ZiaK*<CZ\D&Z�`HK-G\=2qF`[Z�a

¾/�[º6h[e4EHS�ZB¾/¾�µ[¾F¾4�4µ�µ&e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�°R`Hem· ?~S@A*l� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ��µ ½

¶ aB°R`Hem· ?>S2A*lz=2?�uA[< � $ � �Va LV< � $ ��� �Ca I�< � $ � ���ga W�< � $ � �ga Ki< � � � � �� $ � � � � � � � a

¾/�[º6h[e4EHS�ZB¾/¾�µ(��¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujK�XHK�G\qF^�S2D/?UZ~=YXmG\K�?�=2?UZ�D/G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º�¾"TJ� ³

¹ a~b>`HK-K�SYKiI$Z\G�=@I�AFSNK�XHK�G\qF^nSYD[?:Z~=2XmAgG\K�?�=2?UZ�D/G>=2?cI�DFX(dFK�GUZ\K�Wn=YX[Z�DVuA[<jK�SYKiI$Z�G\=@I>��K�S@W�K�XHK�G\qF^/a LV<�`HK�A�Z;K�X�K�G\qF^Fa I�<�e�A�qFX�K�Z�=@I>��K�S2WCK�XHK�G�q/^Fa W�<je�AFI�G�D[?�I�DF_H=@Ie&KiIJ`�A�XH=@I�AFSpK�XHK�G�q/^Fa Ki<�q/G\A*d(=YZ\A"Z\=YD/X�A�SN_ND�Z�K�X[Z�=@A�SpK�X�K�G\qF^Fa

Page 130: Introductory Physics Problems David J. Jeffery Department of

�i� ¹ v�`�A�_]Zia;�/º v�E�G�G\K�X[Z\?>AFX�Wm¿~K�?�=2?UZ\AFX�I�K

¾/�[º6h[e4EHS�ZB¾/¾�µ ³ ¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�EHG�G\K�X[Z>=YXZ\D/AF?UZ�K�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º]��T ³ �

º(a>»{`�A�Zc=2?�Z\`HK6I�E�G�G\K�X[Z~=YX�A4Z�D[AF?UZ�K�G~D�P��*� �{l~=YZ�`�A&¡-v{_ND�Z\K�X[Z�=@A�S;5,DFG~d/DFSYZ\A�q/Ki<�AFI�G�D[?�?�=�ZcDFP��*��¾j´ �A[<>¾��6a LV<���µ/µ/¾��sa I�<��*��¾��sa WV<���¾��sa Ki<��*�j�6a

¾/�[º6h[e4EHS�ZB¾/¾ ¶ ¾F¾4�4µ�µ&e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�°R`Hem· ?~S@A*lzAFX�WQeg=@I�G\DgP8DFG\e¼ aB°R`Hem· ?>S2A*l I�AFXQLNK6W]K�G\=2dFK�WnP8G\DFe Z\`HK-e&=2I�G�D[?�I�DF_H=@IBS@A*l A/?�?�EHe&=2XHq a

A[< � $ � �4u �� $ 5U� ���/< �� � u�I�DFX�?UZ\AFX[Z~WHK�X�?�=�Z:^/aLN< � $ � �4u �� $ 5U� ���/< �� �"u�I�DFX�?UZ\AFX[Z~I�A�_�A/I�=YZ\AFX�I�K/aIi< � $ � �4u �� $ � �nu�I�DFX�?UZ\AFX[Z>K�SYKiI$Z\G�=@I���K�S@WpaWV< � $ � �4u �� $ � �nu�I�DFX�WHE�I$Z\=Yd(=YZ:^n=2X�W]K�_NK�XVW]K�X[ZcD�P �aK*< � $ � �4u �� $ � �nu�I�DFX�WHE�I$Z\=Yd(=YZ:^Q?UZ�G\DFXHq/SY^CW]K�_VK�X�W]K�X/ZcD/X �a

¾/�[º6h[e4EHS�ZB¾/¾ ¹ ¾F¾C� ¶ �MK�A/?U^&Z\`H=2XHO(=YXHqVu�EHXH=YZcD�P�I�D/X�W]E�I�Z�=2d[=YZ:^½ a~b>`HK6¯�²6¤CEHX�=�ZcDFP�I�DFX�W]EVI$Z�=2d(=�Z:^x5 P8DFG\esE�S2A � $ � � � � � ��<�esE�?UZ~LVK/u

A[<v ��?He ��� O(q � �iaLN<mv � ?He ��� O(q � �iaIi<mv � ?He � � O(q � � aWV<mv ��?He ��� O(q � ��aK*<mv ��?He � ��O(q � ��a

¾/�[º6h[e4EHS�ZB¾/¾[º�¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�?�K�e&=YTkI�DFX�W]EVI$Z�D/G\?��¾Hac¤(K�e&=�T!I�D/X�W]E�I�Z�DFGJ?

A[<CD/LVK�^°R`Hem· ?~S2A*lzl~`H=@IJ`Qe�A�O/K�?�Z\`HK�e ?UD&E�?�K�S2K�?\?�aLN<nD/LVK�^°R`Hem· ?~S2A*lzl~`H=@IJ`Qe�A�O/K�?�Z\`HK�e ?UD&E�?�K�P8EHS�aIi<QWHDFX�· ZcDFLNK�^°R`�e· ?~S@A*l�l~`H=@IJ`me&AFOFKi?�Z�`HK�e}?�DgEV?UK�P8EHS�aWV<QWHDFX�· ZcDFLNK�^°R`�e· ?~S@A*l�l~`H=@IJ`me&AFOFKi?�Z�`HK�e}?�DgEV?UK�SYKi?�?�aK*<Q?�K�e&=YT�D/LVK�^°R`Hem· ?>S2A*lzl~`H=2IJ`me�A�O/K�?�Z�`�K�e}?�D&e&K�W]=2D]I�G\KFa

¾/�[º6h[e4EHS�ZB¾/¾ ¼ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj²M=YGJIJ`H`HD �~· ?>d/DFSYZ\A�q/KRS@A*l�F�Fa~b>`HK~_ND�Z\K�X[Z�=@A�SHIJ`VA�XHq/K>AFG�D/EHX�W4A�X(^sI�S2D/?�K�W4_�A�Z�`&=2?���K�G\D�oFAFX�WsZ�`(E�?j=2XgZ�`HKc?�_VKiI�=@A�SHI�AF?�K�DFP�AFX4K�SYKiI$Z\G�=@I�AFS

I�=YGJI�EH=YZ~Z�`�K-_VDFZ�K�X[Z\=2AFS�IJ`�A�XHq/K�?>?�EHe&egKiWD"dFK�G~AFSYSpK�SYK�egK�X[Z\?~=2XZ�`HK6I�=YGJI�EH=YZ~esE�?UZcLNKFuA[<C=2X]��X�=�Z\KFujZ\`H=2?c=2?~¯�D/��AFGUZi· ? ³ GJWQS2A*l-aLN<n_ND/?�=YZ�=2dFKFu�Z\`H=@?>=2?c²MGJA�X�O[`�K�=YZ�· ?R�i?:ZcS@A*l-aIi<nX�K�q/A�Z�=2dFK/u�Z\`H=@?~=2?>»{=2S@?UD/X�· ?6��µ�Z\`Q_NDF=2X[Z�aWV<n=2X�W]K���XH=YZ�K/ujZ�`H=@?~=@?~£cK�eg=2XHq/l�A*^�· ?�I�DFX A:KiI$Z\EHG�K/aK*<n��K�G\D�u�Z�`�=2?~=@?~²M=2G\IJ`H`�DB�~· ?>d/DFSYZ\AFqFK�S2A*l-a

¾/�[º6h[e4EHS�ZB¾/¾ ½ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj_ND"l�K�G>D�P�_ND�Z\K�X[Z�=@A�S�W]G�D/_� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ� ¶ �

�i�]a~b>`HK-K��]_HG�Ki?�?�=2DFXCP8D/G~_VD"l�K�G>q/K�XHK�G\A�Z�K�WQL(^nA&I�EHG\G\K�X[Z �&Z�`HG\DFE�qF`QA&_ND�Z\K�X[Z�=@A�S�WHG�D/_ � =@?�uA[< � $ ��� �&a LV< � $ � � �Va Ii< � $ ��, �Va W�< � $ � �Ca Ki< � $� � �Ca

¾/�[º6h[e4EHS�ZB¾���¾/¾F¾C� ³ �MK�A/?U^�e�A�Z�`�u�_ND"l�K�G~I�AFS2I�EHS2A�Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ³ a~�}I�EHG\G�K�X[ZsD�P6�i¾�� 5,AFX�A�e&_NK�G\KC=@?4A�I�DFEHS2DFe4L�_VK�Gg?�K�I�DFX�WV<MqFD(K�?6Z�`HG\DFE�qF`�A�d/DFSYZ\A�q/KCW]= �NK�G�K�X�I�KQD�P�i¾j´�5�A�d/DFSYZB=@? A:DFE�SYK4_VK�GRI�D/EHS2DFesLN<$a>»{`�A"Z�=2?cZ�`HK4_VD"l�K�G458K�X�K�G\qF^_VK�GBEHXH=YZBZ\=Ye&K4l~=�Z\`�¯�²6¤mEHXH=YZ\?DFP�l�A�ZUZ\? � ?U^(esLNDFS�» !kuN=�a KFa2o7A:D/EHS2K�?R_VK�G�?�K�I�DFX�W�<BW]K�S2=2dFK�G\K�W�L[^Z\`HKsd/DFSYZ\A�q/KsW]= �NK�G�K�X�I�KsZ�DnZ�`HK&I�EHG\G\K�X[ZO(=2XHK�Z\=2IMK�XHK�G\qF^CAFX�WQP8G�D/e Z�`HK6I�EHG\G�K�X/Z~O(=2XHK�Z\=2IMK�XHK�G\qF^�_HG\DFLVA�LHS2^�=Ye&e&K�WH=2A�Z�K�S2^CZ\DC?UD/e&K�DFZ�`HK�G>P8DFG\ema

Page 131: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia;�/º v�EHG\G\K�X[Z\?~AFX�WQ¿cK�?�=2?UZ\AFX�I�K �i�[º

������ � ¡BD&Z\`HK-e�A"Z�`Z\Dge�AFOFK�Z�`HK-E�XH=�ZJ?cI�D/e&K�D/E]ZcG\=Yq/`/ZiaA[<���¾/¾j»�a LV<���¾/¾>�Va I�<��i¾j»�a W�<���¾>�Va Ki<���»�a

¾/�[º6h[e4EHS�ZB¾��F�i¾F¾4� ³�³ e&D]W]K�GJA"Z\K�e�A�Z�`�ujK�SYKiI$Z�G\DFXV?�=2X�A&I�EHG\G�K�X[Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��TJ�*º ³ T ½

��µ�a~��I�EHG\G\K�X[Z�DFP��j�{�VD"lc?;_�A/?:Z>As_NDF=2X[Z�=2XQAsl~=YG\KFaj£BD"l{e&AFX(^gK�SYKiI$Z\G�D/X�?��VD"l{_�AF?UZ�_NK�G~?�K�I�D/X�W �r5�¯�DFG\KK��]A/I$Z\SY^Cl~`VA"Zc=@?�Z�`HK-XHK�Z~��D"l�DFP�K�SYKiI$Z\G�D/X�?�_VK�GB?UKiI�D/X�W �*<

A[< ³ � � � ��¾ � � #�K�S2K�I$Z\G�D/X�?$y"?�a LV<{� K�S2K�I$Z\G�D/X�?$y"?�a I�<�� � � ¶ � ��¾ � #�K�S2K�I�Z�G\DFX�?$y"?�aWV<~� �x�i¾ � #RK�SYKiI$Z\G�D/X�?Jy�?�a K*<�XHDFXHK/a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/�[º6h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�P8E�?�K-e&K�SYZ�=2XHq�Fa~��P8E�?�KQ=@?4A�l~=YG\K=YX�A�I�=2GJI�EH=YZgW]Ki?U=2qFX�K�WrZ\Dxe&K�SYZ�A"ZgA�_HG\K�?\I�G\=YLNK�W�I�EHG\G�K�X/Ziax7kZgZ�`�K�G\K�L(^rDF_NK�X�?4Z�`�KI�=YGJI�EH=YZ6A�X�W�?UZ�DF_V?BZ\`HKg��D"l-a&b>`HK&_VD/=YX[Z-=2?RZ\DD/_VK�X�Z\`HK�I�=2G\I�EH=YZMLNK�P8D/G�K�AFX[^[Z\`H=YX�qQ=2e&_VD/GUZJA�X[Z-egK�S�ZJ?�a¤]A*^�Asl~=YG\KRe�A�Z�K�G\=@A�SNegK�S�ZJ?>A"Z�AgI�E�G�G\K�X[Z�W]K�X�?�=�Z:^�µ/µ/¾�� �"I�e �*aj»{`�A�Z>WH=2AFegK�Z�K�G�DFP�I�^(S2=YX�WHG�=@I�AFSVl~=2G�KR=2?XHK�K�W]KiWmZ�Dne&AFOFK-Z\`HKse&K�S�Z\=YXHqQI�EHG\G�K�X[ZR¾ � ¶ � �4�B?\?�EHe&K6Z�`�K4I�E�G�G\K�X[Zcl~=2SYS�?U_�G�KiAFWmEHXH=YP8DFG\e&SY^D"dFK�G~Z�`�Kl~=2G�K-I�G�D[?�?>?�K�I$Z\=YD/X�a�£cD"lz=2?�Z\`HK6A�G\K�A4D�PjAgl~=YG\KMG�K�S2A�Z�KiWCZ\D&Z�`HK-e&K�SYZ�=2XHqCI�EHG�G\K�X[Z �

¾/�[º6h/P8EHS2S�¾/¾/��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�I�EHG�G\K�X[Z>P8G\DFe�I�EHG�G\K�X[ZcW]K�X�?U=YZ:^�]a~b>`HK6I�EHG\G�K�X/Z~W]K�X�?U=YZ:^n=2X�AgdFK�G\^�S@A�G\qFKMI�^(SY=2X�W]G\=@I�A�Spl~=2G\KFo(P8DFGBl~`�A"Z\K�dFK�G>G�KiAF?�DFX�o(DFLNK�^]?�Z\`HK-K��]_HG\K�?\?U=2DFX

� $�� � � ��� � ��� l~`HK�G�K � � =@?�Z�`�K&I�K�X[Z�GJA�S�I�EHG\G�K�X/Zio =@?�Z�`�K�G\A/W]=2AFSjI�D(DFGJW]=2X�A"Z\K4=2X�Z�`HK&l~=2G�K/o�A�X�W �� =@?�Z�`HK � T�P8DFS@W]=2XHqGJAFW]=2E�?�D�P;Z�`HK�I�E�G�G\K�X[Z-W]K�X�?�=YZ:^�W]=2?UZ�G\=2LHE]Z�=2DFX�a4�B?\?�EHe&=YXHqQZ�`VA"ZMZ�`HK&GJAFW]=2E�?�D�P;Z�`HK&l~=2G�Kg=2?-?�DS2AFG�q/Ks=YZI�A�X�LNKQ?�K�Z4Z�D�=2X]��X�=�Z:^/ojl~`�A"Zg=2?sZ�`HKK��]_HG\K�?\?�=YD/XxP8D/GsZ\`HKCZ\D�ZJA�S>I�EHG\G�K�X[Zs=YX�Z�`HKl~=YG\KFa ������ � ��D/Ee&=2qF`[Z~��X�WQZ�`�KMP,AFI$Z\DFG\=2AFS�=YX[Z�K�qFGJA�S�E�?�K�P8EHS�u

� 1 $�� +�

�� � � � � � �

¾/�[º6h/P8EHS2S�¾/¾ ³ ¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�ujegKiA�X�?�_VK�K�WLVK�Z:l�K�K�XmI�D/SYS2=2?�=2DFX�?� ª�¬"¨ �V«������V¬ ��­�� 7;Z\`H=YX�OCZ�`�K6h/E�K�?UZ�=2DFX=2?cAFSYSpG\=2qF`[Z�o]LHEHZc7$· e ?:Z\=YS2SpZ�`�DFEHq/`/Z�P8EHS�a

³ a~b>`HK�_HG\DFL�AFLH=2SY=YZ:^-D�P�K�SYKiI$Z\G�D/X]T�=2DFX4I�DFS2S2=2?�=YD/X6=2XgARe&K�Z\AFS(`�A�_H_NK�X�=YXHq�=2XsZ\`HK;Z\=Ye&K~?�_�A�XsP8G�D/e�S2A/?:ZjI�D/SYS2=2?�=2DFXZ\D&Z�=2egK � =2?

��5 � < $ � ,�� � ���

l~`HK�G�K �g=@?jZ\`HK�T�P8DFS@W]=2XHqMZ�=2e&K~P8DFG�I�DFS2S2=2?�=YD/X�?�a � � � �  BD�Z�Z\`�A"Z�=�Z>?U`HD/EHS@W4l�DFG\G\^s^FD/E�oFL�E]Z�Z�`�=2?;Z�=2e&K

W]=@?UZ�G\=YLHEHZ�=2DFX�AF_H_HS2=YKi?4?�=YXVI�KCZ\`HKdFK�S2D]I�=YZ:^xDFPcZ�`�Kn=2X�W]=2d[=@W]E�AFS>K�S2K�I$Z\G�D/X�?sI�A�X�LNKQZ\A�O/K�X�A/?4AxI�DFXV?:ZJA�X[ZAFSYe&D/?UZRE�X�A ��K�I�Z�K�W�L(^mAF_H_HS2=YKiW�K�S2K�I�Z�G\=2I6��K�S@WH?�a-�cS@?UDA"ZRS2K�A/?:ZMAFI�I�DFGJW]=2XHq�Z\DQ»�9�T ¹ µ ¹ oV=�ZM=@?BK�SYKiI$Z�G\DFXHT=2DFXmI�D/SYS2=2?�=2DFX�?�Z\`�A"ZBAFG�K�=Ye&_NDFG�Z\AFX/ZioHXHDFZ>K�SYKiI$Z\G�D/X]T�K�SYKiI$Z\G�D/XQI�D/SYS2=@?U=2DFX�?�u�7;l�DFX�WHK�G~l~`(^��A[<nb�A�O/K�Z�`HK6W]K�G�=2d"A"Z\=Yd/KRDFP ��5 � <�l~=�Z\`G\K�?�_NK�I$Z~Z\DgZ�=2egK/aLN<Qb>`�KgW]K�G�=2d"A"Z\=Yd/KsP8G\DFe�_�AFGUZ&5,A[<B=@?MAn_�G�D/L�A�LH=2S2=�Z:^�W]K�X�?U=YZ:^ ��5 � <BP8DFGMI�D/SYS2=2?�=2DFX�?�uc=�a K/aYo ��5 � < � � =2?RZ�`�K

_�G�D/L�A�LH=2S2=�Z:^nP8DFGBA�I�DFS2SY=@?U=2DFXm`�AF_H_NK�XH=2XHq�=2XmZ�`HKsWH=���K�G\K�X[Z�=@A�S�Z�=2egK4=YX[Z\K�G\d*AFS � � a�b>`HK6Z�=2egKs=YX[Z�K�G�d"AFSD"d/K�G�l~`H=@IJ`nZ\`HK6W]K�XV?U=YZ:^nA�_�_HSY=2K�?>=@?�P8G\DFe�Z�=2e&K6¾m58=2ege&KiW]=2A�Z�K�SY^nA�P Z�K�G>Z�`HKMS@AF?UZ~I�DFS2SY=@?�=YD/XV<;Z�DgZ�=2e&K=2X]��X�=�Z:^/at��=Yd/K�X�Z�`HKm_HG\DFL�AFLH=2SY=YZ:^�W]K�X�?�=YZ:^Fo�l~`�A�Zg=@?4Z�`HKme&K�AFX�d"A�S2EHKD�P � � 58=�a K/o;l~`�A�Zg=@?� � �� <LNK�Z:l�K�K�X�I�DFS2SY=@?�=YD/X�?�o�l~`HK�G\K ��=@?-A�X�=YX[Z�K�qFK�G6A�X�W � � ¾Ha�b>`HKCh[E�AFX[Z�=YZ:^�� � �� =@?-I�AFSYS2K�W�Z�`HK���Z\`

Page 132: Introductory Physics Problems David J. Jeffery Department of

�i� ¼ v�`�A�_]Zia;�/º v�E�G�G\K�X[Z\?>AFX�Wm¿~K�?�=2?UZ\AFX�I�K

e&D/egK�X[ZcD�P�Z�`HK6_�G�D/L�A�LH=2S2=�Z:^nWH=2?UZ�G\=YL�E]Z�=2DFX�a�»{`�A"ZBAFG�K�Z\`HKs¾"Z\`�A�X�W���?UZce&DFe&K�X[ZJ?cA�X�Wl~`�A�ZBA�G\KZ\`HK�^I�AFSYS2K�W � ������ � ��DFEe&=Yq/`/Z~�VX�WQZ�`HKMP,A/I$Z�D/G�=@A�S�=2X[Z�K�q/G\AFSpE�?�K�P8EHS�u

� 1 $ � +�

�� � � � � � �

Ii<n7!X�e&K�Z\A�S�I�D/X�W]E�I�Z�D/G\?jl~=YZ�`CAF_H_HS2=YKiW&K�S2K�I�Z�G\=2I>�VK�S@W�D�P�Z:^(_H=@I�A�SVK�S2K�I�Z�G\=2I�A�SHKih/E�=Y_NK�e&K�X[Z>?U=2��K/o�Z�`�K�G\Kc=2?AFX4K�SYKiI$Z\G�=@I�AFSFP8D/G\I�K�D/X6Z\`HK>K�S2K�I$Z\G�D/X�?�Z�`�A�Z�I�A�EV?UKi?�A�I�E�G�G\K�X[Z�a�b>`HK�P8DFGJI�K>AFI�I�K�S2K�GJA"Z\K�?�Z�`HK>K�SYKiI$Z�G\DFXV?=2X�A_�A�G�Z�=@I�E�S2AFG6W]=YG\K�I�Z�=2DFX�P8DFG6Z�`HK&Z\=Ye&KCLNK�Z:l�K�K�XrI�DFS2SY=@?�=YD/X�?�aQb>`H=2?sAFI�I�K�S2K�GJA"Z\=YD/X�DFX�SY^�I�A�EV?UKi?-Ae&=2X(E]Z�K�K��[Z\G\Ad/K�S2D(I�=�Z:^�Z�D�LNKCAFWHW]KiWxZ�DmZ�`�K�G\AFX�W]DFe Z�`HK�G�e�A�Sjd/K�S2D]I�=YZ:^�D�P�Z�`HK�K�SYKiI$Z\G�D/X�?�aCb>`�KGJA�XVW]DFe dFK�SYD]I�=�Z:^M=@?�ZJA�O(=YX�qcZ�`�K�A*d/K�GJA�qFKjK�SYKiI$Z\G�D/X6XHD"l~`HK�G�K/a�b>`HK�eg=2X(E]Z�K>K��[Z\G\AcdFK�S2D]I�=YZ:^MqF=2dFK�?�Z�`�KK�SYKiI$Z\G�D/X�?;A-X�K�Z;�VD"lwWH=YG\K�I�Z�=2DFX�a�»{`HK�XnA6I�D/SYS2=@?U=2DFX�D]I�I�EHGJ?jZ�`�KBK�S2K�I�Z�G\DFXCW]=2G\K�I$Z\=YD/X�=2?�GJA�X�W]D/e&=Y��K�WAFX�WgZ�`�KcK��(Z�GJAMdFK�SYD]I�=�Z:^4=2?jS2D/?UZ�u�Z�`�KcK�XHK�G�q/^sq[A�=2XHK�W4P8G\DFe Z�`HKcK�SYKiI$Z\G�=@I�P8DFGJI�K~=@?;W]=@?\?U=2_�A"Z\K�W4Z�Ds`HK�A�Z=2X�Z�`HKQI�DFXVW]E�I$Z\DFGia�b>`HK�K��(Z�GJAdFK�SYD]I�=YZ:^�=@?6?�De&=2X(E]Z�K�Z\`�A"Z6=YZsW]D(K�?6XHD�ZsAB�NKiI$Z-Z�`�K�_HG�D/L�A�L�=YS2=�Z:^WH=2?UZ�G\=YL�E]Z�=2DFXCDFP�Z�`HKBZ�=2egKRLVK�Z:l�K�K�XnI�DFS2SY=@?�=YD/X�?�a�¡RK�Z�K�G�e&=2XHKcZ\`HKcK��(_�G�Ki?�?�=YD/X&P8DFG;Z�`HKRegKiA�X�d/K�S2D(I�=�Z:^DFPjZ�`HKgK�S2K�I�Z�G\DFX�?�W]EHKsZ�DQZ�`HKgK�S2K�I�Z�G\=2I6��K�S@W�q/=Yd/K�X�Z\`�A"Z�Z�`HKge�A�q/XH=�Z\E�W]K4D�PjZ�`�KgA/I�I�K�SYK�G\A�Z�=2DFX�W]E�KZ\DZ�`HK&��K�S2Wx=@?-AI�DFX�?UZ\AFX[Z � $

� � � � � b>`H=@?MdFK�SYD]I�=YZ:^�=@?-I�A�S2S2K�W�Z�`HK�W]G\=�P Z6d/K�S2D]I�=YZ:^Fas7kZ6=@?�Z�`�K

A*d/K�GJA�q/K-dFK�S2D]I�=YZ:^mD�PjZ�`�K4K�SYKiI$Z�G\DFXV?�u>Z\`HK4GJA�XVW]DFe�dFK�SYD]I�=�Z\=YKi?BDFP�=YX�WH=Yd(=@W]E�A�S�K�SYKiI$Z�G\DFXV?BA*dFK�G\AFqFKMZ\D��K�G\D�a

¾/�[º6h/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�A"Z\e&D/?�_H`HK�G\=@I�I�EHG\G�K�X/Zµ�a~b>`HKx�;A�G�Z�`�· ?�S2D"l�K�GnA�Z�e&D/?�_H`HK�G�K�I�DFX[Z\AF=YX�?C_VD[?U=YZ�=2dFK�SY^wA�X�W±XHK�q/A�Z�=2dFK�S2^tIJ`VA�G\qFK�W±=2DFX�?n_HG\D(WHE�I�KiWtL(^GJAFW]=2D/A/I$Z\=Yd/KK�SYK�e&K�X[Z\?�=2XwZ�`�K�?UD/=YS�A�X�WwI�D/?�eg=@ImGJA*^(?�az�R?�?�EHe&K�Z\`HK�=2GnW]K�X�?U=YZ�=2K�?QA�G\K ¹ �F¾�I�e ��� AFX�W¶/¶ ¾�I�e � � o�G�Ki?U_NK�I�Z�=2dFK�S2^Fo>A�XVW�Z\`�A"Z�Z\`HK�^±A�G\K � ������� � IJ`�AFG�q/K�Wpa�5�¸�D"l�K�GCA"Z\e&D/?�_H`HK�G\=@Ine&DFS2K�I�EHS2KW]K�X�?�=�Z:^�=@?6AFLVD/E]Zs� � ¶ ���i¾ � #pI�e ��� P8D/G6I�D/eg_VA�G\=2?�DFX�uRZ�`�Kge&D/SYKiI�EHS2K�?-AFG�K&e&D/?UZ�S2^�XHK�E]Z�GJA�S�a <t�B?\?�EHe&KAFS2?�D�A�XmA"Z�e&D[?U_H`�K�G\=2IRK�S2K�I�Z�G\=2I���K�S2WQD�P>�i�F¾j´ �*e _NDF=2X/Z\K�WmW]D"l~X(l>A�GJWpaA[<C7!Xml~`H=@IJ`mW]=YG\K�I�Z�=2DFX�W]D(K�?>KiAFIJ`O(=YX�WQD�P�=2DFXegD"d/K��LN<��=2dFK�X�Z�`VA"ZBZ\`HK4I�DFX�WHE�I$Z\=Yd(=YZ:^DFPjZ�`HKgA�=2GB=@?Bq/=Yd/K�X�L(^�� $f� � º"¾ ����¾ � ��� � � �Ne � �*o�l~`�A"Z�=2?BZ�`�K

I�EHG\G�K�X/ZcW]K�X�?�=�Z:^��Ii<Q�R?�?�EHe&K�Z\`�A"Z6Z\`HKC=2DFX�?s`�A*dFKgZ\`HKn?\A�e&KnW]G\=�P Zg?U_NK�KiWrl~`H=2IJ`�=@?-_HS@A�EV?U=2LHS2Kn?U=2X�I�K�Z�`HK�^�AFG�K�=2XrZ�`�K?\A�e&K�K�S2K�I�Z�G\=2IB��K�S@Wpo]`�A*d/KcZ\`HK-?�AFegK�e�AF?\?;D/XQA*d/K�GJA�qFK/o�Z\`HK-?�AFegKMA�LV?UD/SYE]Z\KRd"AFSYEHK�D�P�IJ`�A�G\qFK/o[AFX�WZ\`HKR?\A�e&KBI�DFS2SY=@?�=YD/X&Z�=2egKRDFXnA*d/K�GJA�q/KFa�»{`�A�Z�=@?jZ\`H=2?�W]G\=�P Z>?U_NK�KiW ��5� cD�Z\KcZ\`�A"Z�I�EHG\G�K�X/Z�=2?�XHK�Z���E]�DFP�IJ`VA�G\qFKFo(XHDFZ>��E]�QDFP�D/XHK-O(=YX�WQDFGcAFXHD�Z\`HK�G~DFP�IJ`�AFG�q/KFa ��K6I�A�G\K�P8E�S�A�LNDFE]Zc?�=Yq/X�?�a <

¾/�[º6h/P8EHS2S�¾/¾ ¶ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj_ND"l�K�G>=YX � TkGJA*^&Z�EHLNK¶ a~�BX � T�GJA*^�Z\EHLVK-D/_VK�G\A�Z�Ki?~A"ZBA&I�EHG\G\K�X[Z~D�P;º � ¾je���AFX�WmA&_VDFZ�K�X/Z\=2AFS�W]= �NK�G�K�X�I�K-DFP ¼ ¾jO(´sa]»{`�A�Zc=2?~=YZ\?_ND"l�K�G>=YXml>A"ZUZJ? �

¾/�[º6h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj_ND"l�K�G�=2X[Z�K�qFGJA"Z�KiWCP8D/G~`HK�A�Z�K�G¹ a~���*� ¶ ¾�» G\A/W]=@A�X[Z�`�K�A"Z\K�G~D/_VK�G\A�Z�K�?>l~=YZ�`�Ag_ND�Z�K�X[Z�=@A�S�W]= ��K�G\K�X�I�KMA/I�G\D/?\?�=�ZcDFP��F� ¶ ´sa

A[<C»{`VA"Zc=@?�Z�`HK6I�EHG�G\K�X[Z~=2XQZ\`HK-`HKiA"Z�K�G�LN<n»{`VA"Zc=@?�Z�`HK-G\K�?�=2?UZ\AFX�I�K � � D�P�Z�`HK-`HKiA"Z\K�GcI�D/=YS �Ii<Q£BD"l�esEVIJ`CK�XHK�G�q/^�58=2X¯�²6¤CEHXH=YZ\?J<;WHD[Ki?�Z�`HKM`HKiA"Z�K�G�AFL�?�DFG\LnA�X�WCK�e&=�Z65,=�Zi· ?�Z�`�KM?\A�e&K�A�e&DFEHX[Z$<=2X�A4Z�=2egK � � $ ��`HD/EHGia

WV<Q BD"l ?\A*^mZ�`�A�ZsW]EHK&Z\DmAmW]K�P8K�I�Z-Z�`HK�G\K�?�=2?UZ�D/G�?UZ\AFGUZJ?�Z�Dm=2X�I�G\K�A/?UKg=YXrG\K�?�=2?UZ\AFX�I�K4P8G\DFe =YZ\?-_�G�D/_VK�Gd"AFSYEHK � � I�AFS2I�EHS@A"Z�KiWn=2X_�A�G�Zs58LV<�a�b>`HK-G\K�?�=2?UZ\AFX�I�K�=YXVI�G\K�AF?�K�?>A/I�I�D/G\WH=YXHq4Z�D&Z\`HK-K��]_HG\K�?\?�=YD/X

�&5 � < $�� � 5 � � � � < � l~`�K�G\K � � $ ��`HD/EHG�AFq/AF=YXnAFX�W�Z\=Ye&K � ?UZ\AFGUZJ?�A�Z�Z\`HKMDFXHK�`HD/EHG>e&AFG�O�u�=�a KFa2oHA"Z � � a;��=2dFK�XCZ\`�A"Z>Z�`�K� � � �� � � ��=2?B`HK�S@WmI�DFXV?:ZJA�X[Z�oH`�D"l�esEVIJ`mZ�`HK�G�e�A�SpK�XHK�G\qF^Q=YXm_HG\=2X�I�=2_HS2K-=2?~q/K�XHK�G\A�Z�KiWCP8G\DFe

Page 133: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia;�/º v�EHG\G\K�X[Z\?~AFX�WQ¿cK�?�=2?UZ\AFX�I�K �i� ½

Z\`HK�DFX�Kg`�DFEHG-e�A�G\OmZ�DmZ\=Ye&K�Kih/EVA�S@?R=2X]��X�=�Z:^/a �������� � ��D/E�· SYS�`VA*dFK4Z�Dm=YX[Z\K�qFGJA"Z\K&_VD"l�K�GMD"dFK�GZ\=Ye&K/aj7:W]K�X[Z�=YP8^l~`�A"Zi· ?~I�DFX�?UZ\AFX/ZcAFX�Wnl~`VA"Z�· ?~XHDFZ�a

Page 134: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � ¥ *-5\HJd�*[;<E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/� ¼ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�egPjW]K�d(=@I�K�Fa �\¸�K�Zi· ?R_HS@A*^��]1J� D+�"�\�"# 1 |HD/G��]��¾F¾�oHZ\`HKgAFX�?�l�K�GB=@?�uc� W]K�d(=@I�K4Z�`�A�Z�I�D/X(dFK�G�Z\?BK�XHK�G�q/^nP8G\DFe�?�DFe&K-P8D/G�eZ\DsK�S2K�I�Z�G\=2I�A�SN_VDFZ�K�X/Z\=2AFSVK�XHK�G\qF^gL(^&egD"d(=2XHqs_ND/?�=YZ�=2dFKRIJ`VA�G\qFK>P8G\DFe A6S2D"l{_VDFZ�K�X/Z\=2AFS�Z\K�G\e&=YX�AFS�Z\D4As`H=Yq/`_ND�Z\K�X[Z�=@A�S�Z�K�G\e&=YXVA�SHZ\D6e�A�=2X[Z\A�=2X�A-G\K�S@A"Z�=2dFK�SY^gI�D/X�?:ZJA�X[Z�DFG;_VK�G�=2D]W]=2Ic_VDFZ�K�X[Z\=2AFSVW]= �NK�G�K�X�I�KBLVK�Z:l�K�K�X&Z�`�KZ:l�DmZ�K�G�e&=2X�A�S@?6K�dFK�X�l~`�=YS2K�Z�`�KQI�E�G�G\K�X[Z-��D"lc?-K��(Z�K�G\X�AFSYS2^�Z\`HG\DFEHq/`rA�I�=2G\I�EH=�ZsP8G�D/e Z\`HKn`H=2qF`rZ\D�Z�`�KS2D"l{Z�K�G�e&=2X�A�S�AFX�WQl�D/G�O�=@?~W]DFX�K�L(^�Z\`HK�Z�K�G�e&=2X�A�Sp=2XH=YZ�=@A"Z�KiWK�S2K�I$Z\G�=@IR��K�S@WH?�Z\Dge�AF=YX[Z\AF=YXQZ�`VA"ZcI�EHG\G\K�X[ZW]Ki?U_�=�Z\K-K��(Z�K�G�X�AFSpSYD[?�?�K�?�a»{`�A�Zc=2?~A(y"AFX W]K�d(=@I�K/o��cS2K�� �

A[<�P8e&K LV<�egP8K I�<�e&K�P WV<�K�P8e Ki<�K�egP

¾/� ¼ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj=2X[Z�K�G\X�AFSpG�Ki?U=@?:ZJA�X�I�K�]a~¿~KiA�SpK�e4PjW]K�d[=@I�Ki?cA�G\K�XHD�Zc_NK�G�P8K�I�ZcLVKiI�A�EV?UKMD�P:u

A[<Ce�AFqFXHK�Z�=@I���K�S2W�?�a LN<nK�SYKiI$Z\G�=@I��VK�S@WH?�a I�<Q=YX[Z\K�G\X�A�S�G�Ki?U=@?UZ\A�XVI�KFa WV<nK��(Z�K�G\X�AFSG\K�?�=@?:ZJA�X�I�KFa Ki<�S@Ag¿ �K�?�=2?UZ\AFX�I�K/a

¾/� ¼ h[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�=2G\I�EH=YZBW]K���X�=�Z\=YD/X³ a �\¸�K�Zi· ?�_HS@A*^ �]1J� D+�"����# 1 |�DFG �(�i¾F¾�oVZ\`HK�A�X�?�l�K�G�=2?�u���I�SYD[?UKiW�S2D[D/_�D/G�S2D(DF_�?�DFP�I�D/X�W]E�I�Z�D/G\?R=YX�l~`H=@IJ`I�EHG�G\K�X[ZJ?~I�A�XQ��D"l-a �»{`�A�ZBA�G\K oH�BSYK����

A[<pe�A�q/XHK�ZJ? LN<�|�AFG\A/WHA*^�· ?�A�X�W6¸�K�XH�/· ?�S2A*lc? I�<�I�AF_�AFI�=�Z\DFGJ? W�<�I�=2G\I�EH=�ZJ? Ki<pL�G�KiAFWAFX�WmI�=2G\I�EH=YZ\?

¾/� ¼ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�?�DFS2d(=YXHq&I�=2GJI�EH=YZ\?µ�a~�R?U=2XHq�²M=YGJIJ`H`HD �~· ?>d/DFSYZ\A�q/K�AFX�WmI�EHG\G\K�X[Z�S@A*lc?�oH?U=2e&_HSYK6I�=YGJI�E�=�ZJ?~I�A�XLNK6?UD/SYd/K�WQL[^�u

A[<-W]= �NK�G�K�X[Z�=@A�S�I�A�S@I�EHS2E�?�a LV<-AFSYq/K�LHGJAHa I�<-d*AFG�=@A"Z\=YD/X�A�S�I�A�S@I�E�SYE�?�a W�<M=2X[Z�K�qFGJA"Z�=2DFX�aK*<�qFEHKi?�?�l�DFG\ONa

¾/� ¼ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujG\K�?�=2?UZ�D/G\?�?�K�G\=YKi?Jy"_�A�GJA�S2SYK�S¶ a~b>`HK-Kih[EH=Yd"AFSYK�X/Z~G\K�?�=2?UZ�D/G�P8DFG\esEHS@A�K�P8DFG~G\K�?�=@?:Z\DFGJ?;=2X�?UK�G�=2K�?~AFX�Wn_VA�GJA�S2SYK�S�A�G\KFo(G�Ki?U_NK�I�Z�=2dFK�SY^�u

A[< � ��� $ ��� � AFX�Wx� ��� ��� $ �

�� ��� � a

LN<�� ��� ��� $ ��� ��� � A�X�W � ����$ �

�� � a

Ii< � ��� $���� � A�X�Wx� ��� ��� $��

�� ��� � a

WV< � ��� $ # ��� �� A�XVW � ��� $ �

�� � a

K*< � ��� $�# ��� �� A�XVW � ��� $ �

�� ��� � a

¾/� ¼ h[e4EHS�ZB¾/¾[º�¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj_�AFG\AFSYS2K�S�G\K�?�=2?UZ�D/G~I�A�S@I�E�S2A�Z�=2DFX¹ a>»{`�A�Zc=2?�Z\`HK-K�h[EH=2d"A�S2K�X[ZcG\K�?�=2?UZ\AFX�I�K�D�P>��¾ ��A�X�W�� ��G�Ki?U=@?:Z\DFGJ?;=2Xm_�A�GJA�S2S2K�S �

Page 135: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� ¼ v�=2G\I�EH=YZ\? � ³ �

A[<��F� ��a LV<�� � � ��a I�<>¾ � ½ � ��a W�<�� � ¾ ��a Ki<R�i¾ ��a

¾/� ¼ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\=@IRK�K�Sº(a ��D/EAFG�K�?Ul~=2e&eg=2XHq&l~=YZ�`^FDFE�G�_NK�Z~K�SYKiI$Z�G\=@IBK�K�S�|HG\K�WQA�X�WQ_HS@A*^[P8EHSYS2^�qFGJA�LQ`H=@?>`HK�A/WnA�XVW�Z\AF=YSpLNK�Z:l�K�K�Xl~`H=@IJ`gZ�`HK~_ND�Z\K�X[Z�=@A�S]=@? �zº ¶ ¾�´sa"»�K�ZjZ�`�K>Z:^[_�=2I�A�S]G\K�?�=2?UZ\AFX�I�K>LNK�Z:l�K�K�Xg`(EHe�A�X&LND(WH^6_�A�G�Z\?�=@?jDFPVDFGJW]K�G�i¾F¾F¾ ��587RZ�`H=2XHOH<$u6=YZ�· ?MesEVIJ`�`�=Yq/`HK�G-=YP�^/DFE�A�G\K&WHG�^�uMD�P>DFGJW]K�G&�i¾ � ��aC��=Yd/K�X�Z�`VA"Z6W]K�A�Z�`r=@?M_HG�K�ZUZ:^I�K�G�Z\A�=2X=�P�^FD/EI�A�G\G�^CA&I�E�G�G\K�X[Z~D�P�¾ � �j�6o]l~`�A�ZBA�G\KR^/DFEHGcIJ`VA�X�I�K�?�A[<v�S2D/?�K�Z�D&XH=2S�aLN<¤]D�T!?UDVaIi<��G\K�A�Z�aWV< ��D/Em`�A*dFK�XHK�d/K�G~LNK�K�Xm?\A"P8K�G�aK*< ��D/E�A�G\KREHXVW]K�GR� ¶ o]^/DFEQAFG�KM=2e&egD/GUZJA�S�a

¾/� ¼ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�e&e&K�Z\K�G~dFD/S�Z\e&K�Z�K�G¼ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �]��¾F¾�o[Z�`HKsAFX�?�l�K�G�=@?�u�°RXHK-e&K�AF?�EHG\=YX�qgW]K�d(=2I�K-=2?>_HEHZB=YX�?�K�G\=YKi?~A�X�WQ`�A/?~Ad/K�G\^�SYD"lzG�Ki?U=@?:ZJA�X�I�K )(Z\`HK-D�Z\`HK�G~=@?>_HE]Zc=2Xm_�A�GJA�S2SYK�S�A�X�WQ`�A/?~A4d/K�G\^C`H=2qF`G�Ki?U=@?UZ\A�XVI�KFa �A[<C»{`VA"ZBA�G\KMD]W]DFe&K�Z\K�GcAFX�WQ?�_NK�K�WHDFe&K�Z\K�GioH�cS2K�� �LN<n»{`VA"ZBA�G\K�Z\A��(=2e&K�Z\K�GcA�XVWQAFS�Z\=Ye&K�Z\K�Gio��cS2K�� �Ii<n»{`VA"ZBA�G\KMesEHSYZ�=2e&K�Z\K�GcA�XVWQD/`He&e&K�Z�K�G�oH�BSYK�� �WV<n»{`VA"ZBA�G\KMO(=YS2DFe&K�Z\K�GcAFX�WQ¡RK�e&K�Z�K�Gio��BSYK����K*<n»{`VA"ZBA�e&e&K�Z\K�GcAFX�WdFDFSYZ�e&K�Z�K�Gio]�cS2K�� �

¾/� ¼ h[e4EHS�ZB¾���¾/¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¿cv�I�=YGJI�EH=YZ>Z�=2e&K6I�DFXV?:ZJA�X[Z½ a~b>`HK

�T�P8DFS@W]=2XHqsZ\=Ye&K6D/G�Z�=2egK6I�DFX�?UZ\AFX[Z>DFP�A&?�=Ye&_HS2K6¿cv�5,G�Ki?U=@?:Z\DFG�TkI�A�_�A/I�=YZ�D/GJ<;I�=2G\I�EH=�Z~=@?~qF=2dFK�XnL(^�uA[< � $ � ���ga LV< � $�� �]5 � � <�a I�< � $ � � � a W�< � $ � � a Ki< � $�� � � � a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/� ¼ h/P8EHS2S�¾/¾H��¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVujG�Ki?U=@?UZ�DFG>e�A���K� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¹[¶�³ u ¹ <

�Fa~£R¿�»�o�_�a ¹/¶F³ o�®REHKi?:Z\=YD/X ¹ aCb>`HK�G\K�=@?6Ae&AF��K�DFP�G\K�?�=2?UZ�D/G\?MA�XVWx=@W]KiA�S�L�A�ZUZ\K�G\=YKi?�aC�BSYSjZ\`HKCL�A�ZUZ\K�G\=YKi?`�A*d/K � � � � $ µ�´4a�b>`�K�G\K4=@?MAQ?�_VKiI�=Y��K�W�G�Ki?U=@?UZ�DFG�l~=YZ�`�G\K�?�=@?:ZJA�X�I�K������ $fµ ��a-»{`�A"ZM=@?BZ\`HK�I�EHG\G\K�X[ZZ\`HG�D/EHqF`=YZ�������� � °BP�I�D/EHGJ?UK/o(Z�`HK�G�K/· ?~A4Z�G\=@IJONa

¾/� ¼ h/P8EHS2S�¾/¾/��¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVu�I�AF_�AFI�=�Z\DFG>e�A���K� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¹[¶�³ u ¼ <

�]a~£R¿�»�o�_�a ¹[¶�³ oj®REHK�?UZ�=2DFX ¼ a�b>`HK�G\K�=2?4A�e�A���KCD�PcI�AF_�AFI�=�Z\DFGJ?-A�X�Wr=@W]KiA�S;LVA"ZUZ\K�G\=YKi?�amb>`HKn?�^]?:Z\K�e =2??UZ\A�Z�=@I�u~=�a K/aYopA�S2S�Z�`HK&I�AF_�AFI�=�Z\DFGJ?BA�G\KsIJ`�AFG�q/K�WmEH_xA�X�W�X�DQI�E�G�G\K�X[ZR=@?B��D"l~=YX�q�aR�BSYS�Z\`HK4LVA"ZUZ\K�G\=YKi?c`�A*d/K� $���¾j´4a�b>`HK�=@?sA�?�_VKiI�=Y��K�W�I�A�_�A/I�=YZ�DFGMl~=YZ�`�I�A�_�A/I�=YZ\A�XVI�K � ��� $ ¹ � |�a»{`�A"Z6=@?-Z\`HKnIJ`�AFG�q/K4D/X� ��� �������� � b>`H=2XHOnS2=2OFK-AgegD/E�?�KFa

¾/� ¼ h/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u~�MS2D[D/_I�=YGJI�E�=�Z� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿~T ¹[¶ µ�u ¶ ��<

³ a~b>`HK�G�Kg=@?-AQ?�=YX�qFS2K4S2D(DF_rI�=2G\I�EH=�ZMl~=YZ�`�Z:l�DG\K�dFK�G\?�=2LHSYK4K�egP,?�5 �)� � ���� $}�i�j´ AFX�W �)� � �

� � $ ¹ ´M<BAFX�WZ:l�DmG�Ki?U=@?:Z\DFGJ?&5 � � $�µ � AFX�W � � $ ¼ � ¾ �~<�a�5,¿~K�dFK�GJ?�=YLHS2K&=YX�Z\`H=2?sI�DFX[Z\K��(Z6e&K�A�XV?�Z�`HK�^xI�AFX�?�EH_H_�SY^D/GcA�L�?�DFG\LnK�XHK�G\qF^/a <�v�DFXV?U=@W]K�G>Z\`HK-S2D[D/_nZ\D�LVK-G\K�I�Z\AFXHqFEHS@A�G~A/?>E�?UEVA�S�u � � =@?~DFXZ�`�KMZ�DF_m?�K�qFe&K�X/Z ) � �=@?�DFXxZ�`HK&G\=Yq/`/ZM?UK�qFe&K�X[Z ) � � � �

��� =@?RD/X�Z\`HK&LVDFZUZ�D/e ?�K�qFe&K�X/ZMl~=YZ�`�_VD[?U=YZ�=2dFK4Z�K�G�e&=2X�A�SjA�=2e&K�WxG�=2qF`[Z )� � � �

� � =@?~D/XnZ\`HK-SYK�P ZB?UK�qFe&K�X[Z~l~=YZ�`m_VD[?U=YZ�=2dFKMZ\K�G\e&=YX�AFS�A�=2e&K�WQEH_�a

Page 136: Introductory Physics Problems David J. Jeffery Department of

� ³ � v�`�A�_]Zia;� ¼ v�=2GJI�EH=YZ\?

A[<n¡RGJA*lzA&I�=2G\I�EH=YZBW]=2AFqFGJA�e l~=YZ�`�I�D/G�G\K�I�Z>?�^(esLNDFS@?�P8DFG>Z\`HK6I�D/eg_NDFX�K�X[Z\?�aLN<n»{`VA"Zc=@?�Z�`HK6I�EHG�G\K�X[Z~=2XQZ\`HK6I�=2GJI�EH=YZ�Ii<n»{`VA"Zc=@?�Z�`HK-_ND"l�K�GcW]=@?�?�=Y_VA"Z�KiWn=2XmK�A/IJ`QG\K�?�=2?UZ�D/G�WV<n»{`VA"Zc=@?�Z�`HK-_ND"l�K�G~D�P�K�AFIJ`L�A�ZUZ�K�G�^QA�X�W=@?>=�ZcK�eg=YZUZ\K�WmD/G>AFL�?�DFG\LVKiW �

¾/� ¼ h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj_ND"l�K�G~A�L�?�DFG\LVKiWn=2X�?UK�qFe&K�X[Z� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿~T ¹[¶ µ�u ½ ��<

µ�a~b>`HK�G�K~=@?;AsI�=2G\I�EH=�Z�?UK�qFe&K�X[Z;I�D/X[Z\A�=2XH=2XHq6AMG\K�?�=2?UZ�D/G � $�� � ¾ ��AFX�W�A�X�K�egP�DFPpEHXHO(XHD"l~X&_VDFZ�K�X/Z\=2AFSVAFX�WEHX�O[X�D"l~XD/G�=2K�X[ZJA"Z�=2DFXml~=YZ�`�G\K�?�_VKiI$Z~Z\D�Z�`HK4I�EHG\G�K�X[Z�a�b>`�KsI�EHG\G\K�X[Z~��D"l�=2?BSYK�P ZcZ�DCG\=2qF`[ZBA�X�W=@?cq/=Yd/K�XL(^ � $ � � ¾��saHb>`HK6?UK�qFe&K�X[ZcA�LV?UD/G�L�? � $ ¶ ¾j»�aA[<n¡RGJA*lwAsW]=2AFqFGJA�e D�PpZ�`�KRI�=2GJI�EH=YZ�?�K�q/egK�X[Z�aj¤(=YXVI�KcZ\`HKBD/G�=2K�X[Z\=2A�Z�=2DFX&D�PpZ\`HKBK�e4P�=@?�XHD�Z;O(XHD"l~X�o/^/DFEl~=2S2S�`�A*dFKRZ�D&�VXH=2?�`Z�`HK-_�G�D/LHSYK�e Z�D&_HEHZ~Z�`�A�ZBI�DFe&_NDFXHK�X[Zc=YX�a

LN<n»{`VA"Zc=@?�Z�`HK-_ND�Z\K�X[Z�=@A�S�WH=���K�G\K�X�I�K6AFI�G�D[?�?;Z�`HK6?�K�q/e&K�X[Z�Ii<Q�R?�?�EHe&=2XHq&Z�`HK-K�egP�`�A/?>XHD&=YX[Z\K�G\X�A�SpG\K�?�=2?UZ\AFX�I�K�l~`�A�Zc=2?>=YZ�· ? � � � � �WV<n»{`VA"Z>=2?�Z�`�K�_NDFS@A�G\=YZ:^gDFP�Z�`�KRK�e4P:uj=�a KFa2o[l~`VA"Z>=2?�Z�`�KRD/G�=2K�X[Z\A�Z�=2DFXCDFP�=YZ\?�Z�K�G�e&=2X�A�S@?�Z�D4Z�`HKMI�EHG\G\K�X[Z

WH=YG\K�I�Z�=2DFX �

¾/� ¼ h/P8EHS2S�¾/¾�µ��i¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj_VD"l�K�G>=2Xm?�=2eg_�SYK-S2D(DF_� ª�¬"¨ �V«������V¬ ��­�� l~=�Z\`mAgd"A�G\=@A�LHS2KMG�Ki?U=@?:Z\DFG

¶ a ��D/E�`�A*d/KsAn?�=YX�qFS2KsS2D[D/_�I�=2GJI�EH=YZ�l~=YZ�`�ACL�A�ZUZ\K�G\^DFPj�H�]K�W�_VDFZ�K�X[Z\=2AFS � �QAFX�W�Z:l�DCG\K�?�=2?UZ�D/G\?458=2Xx?�K�G\=YKi?DFP�I�DFEHGJ?UK*<�l~=YZ�`mG\K�?�=2?UZ\AFX�I�Ki? � � AFX�W �4a�b>`�K�G\K�?�=@?:Z\DFG���=@?~d"A�G\=2AFLHSYK/aA[<n¡RGJA*lzA&I�=2G\I�EH=YZBW]=2AFqFGJA�emaLN<��=2dFK�Z\`HK6A�X�AFSY^[Z\=2I�K��]_HG\K�?\?�=YD/XCP8DFGcZ�`HK-I�E�G�G\K�X[Z~=YXZ\`HK6I�=2G\I�EH=YZ�aIi<��=2dFK4Z�`�K&AFX�A�S2^[Z�=@IsK��]_HG�Ki?�?�=2DFX�P8D/GRZ\`HK&_VD"l�K�G � q/K�XHK�G\A�Z�KiW�=2XxG\K�?�=2?UZ�D/G ��=2XxZ�K�G\e�?�D�P � �Ho � � oAFX�W �4aj»{`VA"Z~=2?�Z\`HKM_VD"l�K�G>=2XZ�`HKMS2=Ye&=YZ\?>Z\`�A"Z � $�¾gA�X�W � $ ��¤(OFK�Z\IJ`QAgq/G\AF_H`nDFP �fA/?>AP8E�X�I$Z\=YD/XDFP ���

WV<Q¡RK�G\=2dFK6Z\`HK4AFX�A�S2^[Z�=@I6K��(_�G�Ki?�?�=YD/XmP8DFG � Z�`�A�ZRe�A"�]=2eg=2e&=Y��K�?BZ�`HKg_ND"l�K�G ��qFK�XHK�GJA"Z\K�Wm=2X�G\K�?�=2?UZ�D/G� =YXZ�K�G�e�?~DFP � �Ho � � o�AFX�W �ga�»{`VA"Zc=@?>Z�`HK-K��]_HG�Ki?�?�=2DFXCP8D/G � ������

¾/� ¼ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�uj_ND"l�K�G~=YXmd"A�G\=@A�LHS2KRG\K�?�=@?:Z\DFG� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¹[¶F¶ u ³ µ[<

¹ a~£R¿�»�o�_�a ¹[¶F¶ o;|�=YqVa;� ¼ T ³F¹ a�b>`HKm��q/EHG\K?�`HD"lc?&AxZ:l�DFT�S2D(DF_�I�=YGJI�EH=YZ�l~=�Z\`{A�X±K�egP �)� � �$o;Z:l�D����(KiWG\K�?�=2?UZ�D/G\?�l~`H=@IJ`l�KMZJA�OFKRZ�D�`VA*dFK�G�Ki?U=@?:ZJA�X�I�K � � AFX�W � � oVA�X�WA&d"A�G\=2AFLHSYK�G\K�?�=2?UZ�D/G �gaA[<C»{`VA"Zc=@?�Z�`HK-_ND"l�K�G~qFK�XHK�GJA"Z\K�WC=2XmG�Ki?U=@?UZ�DFG���=YP � $�¾4D/G � $ �

LN<n»{`VA"Z�AFG�K~S2D"l�K�G;A�XVW4E�_H_VK�G;LNDFEHXVWH?�D/X&Z�`HKc_ND"l�K�G�q/K�XHK�G\A�Z�K�Wg=2X�G�Ki?U=@?UZ�DFG ���mb>`HKBEH_H_NK�G;LNDFE�X�W=@?~Z\G�=@IJO(^Q?�=YXVI�KMZ�`�K�G\KsA�G\K6?UK�dFK�G\AFSpl�A*^]?>D�P�Z\`H=YX�O[=2XHqnAFLVD/E]Z~Z�`�KsEH_H_NK�GBLVD/EHX�Wpa ��E]ZB^/DFEml�AFX[ZBAG\K�AFS�A�L�?�DFS2E]Z\KgE�_H_VK�G6LNDFEHX�WxZ\`�A"ZsW]D(Ki?UX�· ZsW]K�_VK�X�WrDFXxZ�`HKnd*AFSYE�KgDFP �}A"Z6A�S2S�an¿~K�I�A�S2S � � o�� � oAFX�W � � � � A�G\KR���(KiWQAFX�WQ��XH=YZ�K/a�b>`HK-EH_H_NK�GcLNDFE�X�WmW]D(K�?�X�· Z~`�A*d/K�Z�D&LVK6AgS2K�A/?:ZcEH_�_VK�G~LVD/EHX�Wpa

Ii<¤]`HDFEHS@WQZ�`HK�G�KMLNK6Age&A��]=Ye4EHe�_ND"l�K�G>qFK�X�K�GJA"Z�KiWn=2X ������=Yd/K6A�XmA�G\qFEHe&K�X[ZiaWV<Q|�=2X�WQZ�`HK6AFX�A�S2^[Z�=@I�K��]_HG\K�?\?U=2DFXnP8DFG �&Z\`HG�D/EHqF`G\K�?�=2?UZ�D/G � =YXZ�K�G�e�?>DFP �go � � o � � A�X�W �)� � �$aK*<Q|�=2X�WQZ�`HK6AFX�A�S2^[Z�=@I�K��]_HG\K�?\?U=2DFXnP8DFG �fP8DFG~G\K�?�=2?UZ�D/G � =YXZ�K�G�e�?>DFP �go � � o � � A�X�W � � � � aP\<m|�=2X�WQZ�`HK6AFX�A�S2^[Z�=@I�K��]_HG\K�?\?U=2DFXnP8DFG ��Z\`�A"Zce�A��(=2e&=Y��K�? �&a�»{`�A�Zc=2?>Z\`HK � ����sK��]_HG�Ki?�?�=2DFX �

¾/� ¼ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�W]=@?Uq/EH=@?UKiWn_�AFG\AFSYS2K�SpG\K�?�=@?:Z\DFGJ?

Page 137: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� ¼ v�=2G\I�EH=YZ\? � ³/³

� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¹[¶�¹ u µ[¾/<º(a~£R¿�»�oH_�a ¹/¶�¹ o]9�Gia]µ/¾Ha

¾/� ¼ h/P8EHS2S�¾/¾[º"¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�W]=2?�qFE�=2?�K�W?UK�G�=2K�?>G\K�?�=@?:Z\DFGJ?¼ a~£R¿�»�oH_�a ¹/¶�¹ o]9�Gia]µ��Fa

¾/� ¼ h/P8EHS2S�¾/¾ ¼ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�Z�KiW]=2DFE�?cI�=YGJI�E�=�Z~_HG\DFLHS2K�e½ a~£R¿�»�oH_�a ¹/¶�¹ o]9�Gia]µ[�]a ������ � ¡RD�_�AFGUZ658LN<���G\?UZ�a

¾/� ¼ h/P8EHS2S�¾/¾ ½ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�¿cv�I�=YGJI�E�=�ZcIJ`�AFG�q/=YXHq��¾Ha~b>`HK�G�K~=@?c� ¶�� ¾jO ��G\K�?�=2?UZ�D/G;A�XVWgAsI�A�_VAFI�=YZ�D/Gj=YXC?�K�G\=2K�?�a�b>`HKRI�A�_VAFI�=YZ�D/Gj=2?;=YX�=�Z\=2AFSYS2^4E�X�IJ`�A�G\qFKiWpa���Z�Z�=2e&K

��K�G\DsAFI�DFX�?UZ\AFX/Z�_VDFZ�K�X[Z\=2AFSNDFP � $��*��´�=@?>?UE�W�W]K�XHS2^�A�_H_�SY=2K�WCA/I�G\D/?\?jZ\`HKRG\K�?�=@?:Z\DFG;AFX�WCI�AF_�AFI�=�Z\DFGia�b>`�K_ND�Z\K�X[Z�=@A�S�WH=���K�G\K�X�I�K-AFI�G\D/?\?�Z�`HK6I�A�_�A/I�=YZ�D/G�G\=@?UKi?;Z\D ¶�� ¾j´ =YXr� � ³ ¾ � ?�aA[<C»{`VA"Zc=@?�Z�`HK

�T�P8DFS@W]=YX�q4Z\=Ye&K-D/G>Z�=2egK6I�DFX�?UZ\AFX[Z>DFP�Z\`HK6I�=2GJI�EH=YZ�

LN<n»{`VA"Zc=@?�Z�`HK6I�A�_�A/I�=YZ\A�XVI�KMD�P�Z�`HK6I�A�_�A/I�=YZ�DFG �

¾/� ¼ h/P8EHS2S�¾���¾F¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�¿cv�I�=YGJI�E�=�ZcIJ`�AFG�q/=YXHq&W]=@?Uq/EH=@?UKiW�F�Fa~£R¿�»�oH_�a ¹/¶ º]o]9�Gia ¶ �]a ������ � b>`�=2?~_�G�D/LHSYK�e =@?~K�A/?U^�D/X�I�KM^FD/E?�K�KM_�A/?:Z~Z\`HK6I�AFe&DFE]�VAFqFK/a

Page 138: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0 n � � &:cT>a14;<*-H ��*[1_N-,�E ¥ &Ad�EG*I>Sc �F?A5\HJ1)E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾/� ½ h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uje�A�q/XHK�Z\=2IR��K�S2WmW]K���XH=YZ�=2DFX� ª�¬"¨ �V«������V¬ ��­�� e&AFqFXHK�Z�=@IR��K�S@WmW]K���X�=�Z\=YD/X

�Fa~b>`HK-e�AFqFXHK�Z�=@IB�VK�S@WQ=@?~AHuA[<Cd/K�I�Z�DFG���K�S2WK�e&AFX�A"Z\=YX�q4P8G\DFe}IJ`�A�G\qFKMA�X�WmI�A�E�?�=YX�qsZ\`HK-K�S2K�I�Z�G\=2IRP8DFGJI�K/aLN<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�IJ`�AFG�q/K�AFX�WQI�A�E�?�=2XHqgZ�`HK-K�SYKiI$Z�G\=@IBP8D/G\I�KFaIi<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�I�E�G�G\K�X[ZcA�X�WI�AFE�?�=YXHqgZ\`HK-K�S2K�I�Z�G\=2IRP8DFGJI�K/aWV<nd/K�I�Z�DFG���K�S2WK�e&AFX�A"Z\=YX�q4P8G\DFe}I�EHG\G�K�X[Z~AFX�WmI�AFE�?U=2XHq4Z�`HK-e�AFqFXHK�Z�=@IBP8D/G\I�KFaK*<Q?\I�AFS2AFG���K�S@WK�e�A�X�A�Z�=2XHqgP8G�D/e�I�E�G�G\K�X[ZcA�X�WI�AFE�?�=YXHqgZ\`HK-e�A�qFX�K�Z�=@IRP,A�GJI�K/a

¾/� ½ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\DFe�A�q/XHK�Z\=2IB��K�S@WH?cAFG�KMG\K�AFS�]a~b>`HKte�A�=2X�G�KiAF?�DFX�P8DFG�G�K�q/AFG\W]=2XHqwK�S2K�I�Z�G\=2I�A�X�W�e�AFqFXHK�Z�=@Ir��K�S@WH?�AF?xAFI$Z\E�A�SsZ�`H=2XHq[?�A�XVW�XHD�Z A:E�?:ZW]Ki?�I�G�=2_]Z\=Yd/K�W]K�d(=@I�K�?�P8DFG�I�A�S@I�EHS@A"Z\=YXHq{K�SYKiI$Z\G�=@I�A�X�W�e�A�q/XHK�Z\=2I�P8DFGJI�K�?m=@?�5,=YX Z\`HK�=2X�?UZ�G\E�I$Z\DFGi· ?md(=2K�lAFX[^(l>A*^H<jZ\`�A"ZiuA[<�Z\`HK�^A�G\K�?�D&E�?�K�P8EHS�A/?~W]K�?\I�G\=2_]Z�=2dFK-W]K�d[=@I�Ki?�aLN<Q?�K�SYP Tk_HG�D/_�A�q[A"Z\=YXHqtK�S2K�I�Z�G\DFe�A�q/XHK�Z\=2I�GJAFW]=@A"Z\=YD/X 5,I�DFX�?�=@?:Z\=YXHqwDFPgI�D/EH_HS2K�W�K�S2K�I�Z�G\=2IrAFX�W�e&AFqFXHK�Z�=@I

�VK�S@WH?\<g`VAF?gXHD�I�D/XHXHK�I�Z�=2DFX±l~=�Z\`t=YZ\?n?UD/EHG\I�K�5�A"P Z\K�G�=YZ\?&K�e&=@?�?�=2DFXV<gA�XVW�XHD/XHKml~=�Z\`t=YZ\?CG�KiI�K�=2dFK�GE�X/Z\=YSN=YZ�=@?;G\K�I�K�=2dFK�W�a�¤(EVIJ`CG\A/W]=@A"Z�=2DFX�I�A�XC_HG\DF_VA�q/A�Z�K~AFI�G�D[?�?�LH=YS2S2=YD/X�?;DFPpSY=2qF`[Z�^/K�AFG\?jDFP�?U_VAFI�KBSYD/XHqA�P Z�K�G�=YZ\?M?�DFEHGJI�K4`�AF?�LNK�K�X�l~=2_VKiW�P8G\DFe�K��(=@?UZ�K�XVI�K&A�X�W�SYD/XHqnLNK�P8D/G�Kg=�ZJ?MG�KiI�K�=Yd/K�GB`VAF?MI�D/egK4=YX[Z\DK��]=2?UZ�K�X�I�K/a�b>`[EV?>K�S2K�I$Z\G�=@IMA�X�We�A�q/XHK�Z\=2IR��K�S2W�?~A�G\KMA/?>G�KiA�S�A/? �{l�K�SYS ��AF?�SYDFZ\?>DFP�D�Z\`HK�G>Z\`H=2XHq/?�a

Ii<CZ\`HK�^A�G\KRLND�Z\`�dFKiI$Z�D/G���K�S@WH?WV<CZ\`HK�^A�G\KRLND�Z\`�?�I�A�S@A�G���K�S@WH?�aK*<CZ\`HK�^A�G\K�?�D&E�?�K�S2K�?\?~AF?~W]Ki?�I�G�=2_]Z�=2dFK-W]K�d(=2I�K�?�a

¾/� ½ h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�e�A�qFX�K�Z�=@IRP8DFGJI�KMS@A*l� ª�¬"¨ �V«������V¬ ��­�� e&AFqFXHK�Z�=@IRP8DFGJI�KMS2A*l-a

³ a~b>`HK-e�AFqFXHK�Z�=@IBP8D/G\I�KMS2A*l�P8DFG~_NDF=2X/ZcIJ`�AFG�q/KR=@?�uA[< �� $ � ��aLN< �� $ � �� � �naIi< �� $ � �� � ��QaWV< �� $ �� � ��QaK*< �� $ �� � �Ca

¾/� ½ h[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�P,A�=2G�S2^n?UZ�G\DFXHq&e�A�q/XHK�Z\=2IR��K�S2Wµ�aB°RXQZ�`HK6��A�G�Z�`�· ?~?�EHGUP,A/I�K-A4P,A�=2G�S2^CS@A�G\qFK�e�A�qFX�K�Z�=@IR��K�S@Wr58=2X�I�S2E�W]=2XHq�S@A�LNDFGJA"Z\DFG\^&?�^]?:Z\K�e�?J<�l�D/EHS2WQLNKFu

A[<��i¾pbMaLN<��i¾ � ��bMaIi<��i¾ � ���MA�E�?\?�aWV<����MA�E�?\?�aK*<���bMa

Page 139: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� ½ ¯�AFqFXHK�Z�=@I�|�=2K�S@WH?Rv�AFE�?U=2XHq�|HD/G\I�K�? � ³[¶

¾/� ½ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�G\D/?\?UKiW���K�S2W�?� ª�¬"¨ �V«������V¬ ��­�� I�G\D/?\?UKiW���K�S2WH?�o�I�G�D[?�?�K�WnK�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IB��K�S@WH?

¶ aBv�G\D/?\?UKiW���K�S2W�?~=2?~AFXmK��]_HG\K�?\?U=2DFXnZ�`�A�ZBI�E�?UZ�D/e&AFG�=2S2^�egKiA�X�?�uA[<�Z:l�D&K�S2K�I�Z�G\=2IR��K�S2WH?~Z�`�A�ZBA�G\KR_NK�G\_VK�X�W]=@I�EHS@A�G>Z\D�K�A/IJ`QDFZ�`HK�G�aLN<n_NK�G\_NK�X�W]=@I�E�S2AFG~K�S2K�I$Z\G�=@I-A�XVWne�A�q/XHK�Z\=2IR��K�S2W�?�aIi<CZ:l�D&e�A�qFX�K�Z�=@IR��K�S@WH?>Z\`�A"ZBAFG�K�_NK�G\_VK�X�W]=@I�EHS@A�G>Z\D�K�AFIJ`D�Z\`HK�GiaWV<n_VA�GJA�S2SYK�SpK�S2K�I$Z\G�=@IMA�X�WQe�A�q/XHK�Z\=2IR��K�S2WH?�aK*<nD/LHS2=2h[EHKMK�S2K�I�Z�G\=2I-AFX�WQe&AFqFXHK�Z�=@IR��K�S@WH?�a

¾/� ½ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\DFXmW]=2?\I�D"d/K�G\^� ª�¬"¨ �V«������V¬ ��­�� K�S2K�I$Z\G�D/XWH=2?\I�D"d/K�G\^Fo,��a3�VaHb>`HD/e&?�DFX

¹ a~b>`HK6WH=2?\I�D"d/K�G\^gDFP�Z\`HK-K�S2K�I�Z�G\DFX=2?>EV?UE�AFSYS2^nI�G�KiW]=�Z\K�WQZ�DVuA[<Q��K�DFG\qFK��FD/`HX�?UZ�D/XHK6¤[Z�D/XHK�^C=2XZ�`HK�� ¼ º"µ�aLN<#��K�Xm|�G\AFXHO(SY=2X=YXZ�`�K��*º ¹ ¾H· ?�aIi<#�Va ��aHb>`HD/e�?UD/XQ=2Xr� ½F½ º(aWV<#�Va ��aHb>`HD/e�?UD/XQ=2Xr� ¼F½ º(aK*<Q�;G�X�K�?UZ~¿cE]Z�`HK�GUP8D/G\WQ=2Xe&D/G�KMDFG>S2K�?\?-� ½ �F�/a

¾/� ½ h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj£BAFSYS�K.�NKiI$Z� ª�¬"¨ �V«������V¬ ��­�� £BA�S2S�K.�NKiI$Z

º(a~b>`HK6£RA�S2SpK ��K�I�ZB?U`HD"l�K�WnZ�`VA"Z*)A[<�Z\`HK6IJ`�AFG�q/K�I�A�G\G�=2K�GJ?;=2Xme&K�Z\AFS2?>`VAFWXHK�q[A"Z\=Yd/K�IJ`�AFG�q/KFaLN<CZ\`HK6IJ`�AFG�q/K�I�A�G\G�=2K�GJ?;=2Xme&K�Z\AFS2?>`VAFW_VD[?U=YZ�=2dFK-IJ`�AFG�q/KFaIi<CZ\`HK6IJ`�AFG�q/K�I�A�G\G�=2K�GJ?;=2Xme&K�Z\AFS2?>`VAFWXHK�EHZ�GJA�S�IJ`�AFG�q/KFaWV<CZ\`HK6IJ`�AFG�q/K�I�A�G\G�=2K�GJ?;=2Xme&K�Z\AFS2?>`VAFWLVDFZ�`mXHK�q/A"Z\=Yd/K�AFX�W_VD[?U=YZ�=2dFK-IJ`�AFG�q/KFaK*<ne&K�Z\A�S@?>`�A/WQX�D&IJ`VA�G\qFKMI�A�G\G\=YK�G\?�a

¾/� ½ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�=2G\I�SY=2XHq�IJ`�AFG�q/K�?� ª�¬"¨ �V«������V¬ ��­�� I�=2G\I�SY=2XHq�IJ`�A�G\qFKi?�a

¼ a~|�G�K�KMIJ`VA�G\qFK�Wn_�A�G�Z�=@I�S2K�?>e&D"d(=2XHq&=YXe�A�qFX�K�Z�=@I���K�S2WH?�Z\K�X�WQZ\D�uA[<�Z\G\A*d/K�S�=2Xm?UZ�GJA�=2qF`[Z~S2=YXHKi?�aLN<CZ\G\A*d/K�S�=2Xm?�=2X[EV?UD/=2WHAFS�I�EHG\dFKi?�aIi<ne&D"d/K�=2X��=2qF��AFq/?�aWV<Q?UZ�D/_AFX�Wm?:ZJA�G�ZcI�DFXV?:ZJA�X[Z�S2^FaK*<ne&D"d/K�=2XmI�=2G\I�SYKi?>DFG~`HK�SY=Y�]K�?�a

¾/� ½ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�EHG\DFGJA� ª�¬"¨ �V«������V¬ ��­�� A�EHG\DFGJA

½ a~b>`HK6AFEHG\DFGJAHuA[<C=@?±K�?\?UK�X[Z�=@A�S2SY^�I�AFE�?UKiW L(^ ¦ � � � � � _�AFGUZ\=2I�SYKi?�?�_H=YGJA�S2S2=YXHq EHX�W]K�G�Z\`HK�=YX]�VEHK�X�I�KzDFP�Z�`�K��A�G�Z�`�· ?�e�A�qFX�K�Z�=@Is��K�S@W�=2X[Z�DQZ�`HK�A�Z�e&D/?�_H`HK�G�Kge�A�=2XHSY^�A�Z-`H=Yq/`�S@A"Z\=�Z\E�W]K�?-AFX�W�I�A�EV?U=2XHqne�A/?�?�=Yd/KA�Z�e&D/?�_H`HK�G�=@IR��EHD/G�Ki?�I�K�X�I�KFa

LN<n=@?wK�?\?�K�X[Z�=@A�S2SY^ I�A�E�?�K�W}L(^ � � � � � _�AFGUZ\=2I�SYKi?{?U_H=2GJA�S2SY=2XHq EHX�W]K�GwZ�`HK =2X]��EHK�X�I�K�DFP�Z�`�K��A�G�Z�`�· ?�e�A�qFX�K�Z�=@Is��K�S@W�=2X[Z�DQZ�`HK�A�Z�e&D/?�_H`HK�G�Kge�A�=2XHSY^�A�Z-`H=Yq/`�S@A"Z\=�Z\E�W]K�?-AFX�W�I�A�EV?U=2XHqne�A/?�?�=Yd/KA�Z�e&D/?�_H`HK�G�=@IR��EHD/G�Ki?�I�K�X�I�KFa

Ii<n=@?cI�A�E�?�K�WQL(^Ce�A�qFX�K�Z�=@IR��K�S@WH?c?�l~=@?U`H=2XHqgZ�`�KMZ�G\K�K�?>=2XZ�`HK-b>=@A�q[AHaWV<n=@?cI�A�E�?�K�WQL(^Ce�A�qFX�K�Z�=@IR��K�S@WH?c?�l~=@?U`H=2XHqgZ�`�K6I�A�G\=2LVD/E�aK*<n=@?cI�A�E�?�K�WQL(^CK�S2K�I�Z�G\=2IR��K�S2WH?B?Ul~=@?U`�=YXHqgZ\`HK6I�AFG�=2LVD/E�a

Page 140: Introductory Physics Problems David J. Jeffery Department of

� ³/¹ v�`�A�_]Zia;� ½ ¯�A�qFX�K�Z�=@IM|�=YK�S2WH?�v�A�E�?�=YX�qg|�DFGJI�K�?

¾/� ½ h[e4EHS�ZB¾���¾/¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�e�A�qFX�K�Z�=@IRP8DFGJI�KMDFX�Agl~=2G�K��¾Ha~b>`HK-e�AFqFXHK�Z�=@IBP8D/G\I�KMS2A*l�P8DFGcAgl~=YG\KM=2?�u

A[< �� $ � ��aLN< �� $ � �� � �naIi< �� $ � �� � ��QaWV< �� � $� � �0 � ��naWV< �� � $� � �0 � �Ca

¾/� ½ h[e4EHS�ZB¾��F�i¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�e�A�qFX�K�Z�=@I�e&DFe&K�X[Z� ª�¬"¨ �V«������V¬ ��­�� e&AFqFXHK�Z�=@I�egD/e&K�X[Z

�F�Fa~|�DFGcAge�A�qFX�K�Z�=@I�e&DFe&K�X[Z�uA[< �� $ �� � ��A�X�W � $ , �� � ��aLN< �� $ �� � �� A�XVW � $�, �� � ��naIi< �� $ , �� � �� A�X�W � $ �� � ��naWV< �� $ , �� � � AFX�W � $ �� � ��aK*< �� $ �fAFX�W � $ �� � ��a

¾/� ½ h[e4EHS�ZB¾��i�F¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�K�S2K�I�Z�G\=2I�e&D�Z\DFG� ª�¬"¨ �V«������V¬ ��­�� K�S2K�I$Z\G�=@I�e&D�Z�D/G�o]=2X�W]EVI�K�WK�e4P:oVI�DFXV?UK�G�d"A"Z\=YD/XnDFP�K�XHK�G\qF^

�i�]a~b>`HK-_�`[^]?�=2I�A�S�G\K�AF?�DFXQl~`(^QA�XK�S2K�I�Z�G\=2I�e&D�Z\DFGcW]D(Ki?>XHD�Zcq/=Yd/KRK�XHK�G\qF^�P8D/G>P8G�K�KM=2?�uWV<CZ\`HK�e&AFqFXHK�Z�=@I���K�S2W�=YXVW]E�I�Ki?mA�I�D/EHX[Z�K�GQK�e4P4=YX�Z�`HK�G�DFZ\A�Z�=2XHq�I�D/=YSMl~`H=@IJ`{P8D/G\I�K�?nZ�`HKrI�EHG\G\K�X[Z

?�DFE�G\I�K~Z�D4K��]_VK�X�W�K�XHK�G\qF^ � � � �� � ¦ zl~`�A"Z�Z�`HKRegDFZ�D/G;_HE]ZJ?;D/E]Z�aj RA"Z�E�G�KRK�X�WH?�EH_�� � ¦ � � � �� � ������K�X�K�G\qF^nA�P Z�K�GcAFSYS�o]LHE]Zc=YZBW]D(K�? � � � � ��� � =YZ~Z�D&LVKMZ\G\AFX�?UP8DFG\egKiWpa

LN<CZ\`HK�e&AFqFXHK�Z�=@I���K�S2W�=YXVW]E�I�Ki?mA�I�D/EHX[Z�K�GQK�e4P4=YX�Z�`HK�G�DFZ\A�Z�=2XHq�I�D/=YSMl~`H=@IJ`{P8D/G\I�K�?nZ�`HKrI�EHG\G\K�X[Z?�DFE�G\I�K&Z�D�K��]_NK�X�WrK�XHK�G\qF^ � � � �� � � � Z\D�l~`�A"Z-Z\`HKne&DFZ�DFG-_�E]Z\?sDFE]Ziam RA"Z\EHG�K�K�X�WH?sEH_¦ � � � �� � ������K�X�K�G\qF^nA�P Z�K�GcAFSYS�o]LHE]Zc=YZBW]D(K�? � � � � ��� � =YZ~Z�D&LVKMZ\G\AFX�?UP8DFG\egKiWpa

Ii<CZ\`HK�e&AFqFXHK�Z�=@I���K�S2W�=YXVW]E�I�Ki?mA�I�D/EHX[Z�K�GQK�e4P4=YX�Z�`HK�G�DFZ\A�Z�=2XHq�I�D/=YSMl~`H=@IJ`{P8D/G\I�K�?nZ�`HKrI�EHG\G\K�X[Z?�DFE�G\I�K&Z�D�K��]_NK�X�WrK�XHK�G\qF^ � � � �� � � � Z\D�l~`�A"Z-Z\`HKne&DFZ�DFG-_�E]Z\?sDFE]Ziam RA"Z\EHG�K�K�X�WH?sEH_� � ¦ � � � �� � ������K�X�K�G\qF^CA"P Z\K�GcAFSYS�oHLHE]Zc=YZBW]D(K�? � � ��� � =YZ~Z�D&LVKMZ\G\AFX�?UP8DFG\egKiWpa

WV<CZ\`HK�e&AFqFXHK�Z�=@I���K�S2W�=YXVW]E�I�Ki?mA�I�D/EHX[Z�K�GQK�e4P4=YX�Z�`HK�G�DFZ\A�Z�=2XHq�I�D/=YSMl~`H=@IJ`{P8D/G\I�K�?nZ�`HKrI�EHG\G\K�X[Z?�DFE�G\I�K&Z�D�K��]_NK�X�WrK�XHK�G\qF^ � � � �� � � � Z\D�l~`�A"Z-Z\`HKne&DFZ�DFG-_�E]Z\?sDFE]Ziam RA"Z\EHG�K�K�X�WH?sEH_¦ � � � �� � ������K�X�K�G\qF^nA�P Z�K�GcAFSYS�o]LHE]Zc=YZBW]D(K�? � � ��� � =YZ~Z�D�LNKMZ�GJA�X�?UP8DFG\e&K�Wpa

K*<CZ\`HK�e&AFqFXHK�Z�=@I���K�S2W�=YXVW]E�I�Ki?mA�I�D/EHX[Z�K�GQK�e4P4=YX�Z�`HK�G�DFZ\A�Z�=2XHq�I�D/=YSMl~`H=@IJ`{P8D/G\I�K�?nZ�`HKrI�EHG\G\K�X[Z?�DFE�G\I�K�Z�D±K��]_NK�X�W�K�XHK�G�q/^ � ��� �� � ¦ l~`VA"ZZ�`HKre&D�Z\DFG_HE]Z\?D/E]Z�a� RA"Z\EHG�K�K�XVWH?EH_¦ � � � �� � ������K�X�K�G\qF^nA�P Z�K�GcAFSYS�o]LHE]Zc=YZBW]D(K�? � � ��� � =YZ~Z�D�LNKMZ�GJA�X�?UP8DFG\e&K�Wpa

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾/� ½ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(We�A"Z\`�ujK�S2K�I�Z�G\DFX=YX��wA�XVW#�zI�G\D/?\?UKiW���K�S2WH?�Fa~�±P8G\K�K~K�SYKiI$Z�G\DFXg=@?�=YXCA�G\K�qF=2DFX4D�P�EHXH=YP8DFG\efK�SYKiI$Z�G\=@I�AFX�Wge�A�qFX�K�Z�=@I���K�S@WH?�a~5,¿~KiI�A�S2S

�$ � � ¹ ¾[� �&��¾ � � #Nv

AFX�W � � $ ½ � �i¾ ½ �x��¾ ��� �VO[qNa <4b>`�KM?�^]?:Z\K�e =@?~W]Ki?�I�G�=2LVKiWCL(^v�AFGUZ\K�?�=2AFXQI�D(D/G\W]=2X�A�Z�K�?�a�b>`HKMK�S2K�I$Z\G�D/X�· ?=2XH=YZ�=@A�S�dFK�S2D]I�=YZ:^n=@?s5�¾� ¶ � ¾ ¶ � ¾[< ���i¾ � e��"?RA�X�Wm=YZB`�A/?BACI�DFX�?UZ\AFX[ZRAFI�I�K�S2K�GJA"Z\=YD/XQ=2X�Z\`HK �HT!W]=2G�KiI$Z\=YD/X�D�P� � ¾����i¾ ����e��"? ��a�7!XnZ\`HK��/T �4_HS2AFXHKB=YZ~=2?�e&K�G\K�S2^�I�=2G\I�SY=2XHqVa�b>`�KRe�A�q/XHK�Z\=2Ic��K�S@WC=@?M58µ[¾F¾�\¾�\¾/< � bMu�XHD�Z\KZ\`HK-EHXH=YZ\?cAFG�KMe&=@I�G\D�Z�Ki?US@AF?�aA[<n¡RGJA*lzA&W]=@A�qFGJA�e DFP�Z\`HK6?�^(?UZ�K�emaLN<n»{`VA"Zn=@?�Z\`HK�K�S2K�I�Z�G\=2I���K�S@Wpo~e�A�q/XH=�Z\E�W]K�AFX�W{W]=2G�KiI$Z\=YD/X � ������ � 7kP6A�X(^±I�DFe&_NDFXHK�X[ZnD�PMZ�`�K

K�SYKiI$Z\G�=@IR��K�S@Wl�K�G�KM=2XQZ\`HK��[T��g_HS@A�X�KFoHI�D/EHS@WnZ\`HK-K�S2K�I�Z�G\DFX&A:E�?UZcLVK6I�=YGJI�S2=YX�q4Z\`HK�G\K��

Page 141: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a;� ½ ¯�AFqFXHK�Z�=@I�|�=2K�S@WH?Rv�AFE�?U=2XHq�|HD/G\I�K�? � ³ º

Ii<n»{`VA"Zc=@?�Z�`HK6?�_VK�K�W=2XQZ\`HK��[T��g_HS@A�X�K6A"ZcA�X(^�Z\=Ye&KFaWV<n»{`VA"Zc=@?�Z�`HK-GJAFW]=2E�?>DFP�Z\`HK6I�=2G\I�EHS@A�G>e&D�Z�=2DFXmA�XVWQl~`VA"Z~=2?~Z�`HK6W]=2G\K�I$Z\=YD/XQDFP�I�=YGJI�S2=2XHq �

¾/� ½ h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(We�A"Z\`�uje�AF?\?~?U_NK�I�Z�G\DFe&K�Z\K�GioHA�X�AFSY^[Z\=2IMA�XVWnX(EHe&K�G\=@I�A�S� ª�¬"¨ �V«������V¬ ��­�� e&A/?�?~?�_NK�I$Z\G�D/e&K�Z�K�G�oHAFX�A�S2^[Z�=@IMA�X�WQX(EHe&K�G\=2I�A�S

�]a~� _�AFGUZ\=2I�SYKMDFP�IJ`�AFG�q/K �4=2?BAFI�I�K�S2K�GJA"Z\K�W�Z\`HG\DFEHq/`Ag_ND�Z�K�X[Z�=@A�Sp´saA[<C»{`�A�Zc=2?�Z\`HK-K��]_HG\K�?\?�=YD/XnP8D/G~=�ZJ?���X�A�S�?U_NK�KiWA/?�?�EHe&=2XHq4=YZB?UZ\A�G�Z�KiWCP8G\DFe}G�Ki?:Z �LV<b>`HK�_�A�G�Z�=@I�S2K�=@?�Z�`�K�X�=2X A:K�I�Z�KiW{=YX[Z\D�Are�AF?\?n?�_VKiI$Z�G\DFe&K�Z�K�Gnl~`H=2IJ`{=@?A�IJ`�A�e4LVK�Gnl~=YZ�`�A�EHX�=�P8D/G�e

e�A�q/XHK�Z\=2IB��K�S2Wpajb>`HKR��K�S2WQ=2?�_NK�G\_VK�X�W]=@I�EHS@A�G�Z\DsZ\`HKR_VA�G�Z�=@I�S2KRe&D�Z\=YD/X�ajb>`HK�_�A�G�Z�=@I�S2KcZ\G\A*d/K�S@?�P8D/G�`�AFS�P�AI�=YGJI�S2KsA�XVW�?:Z\G�=2OFKi?BA�l>A�S2S�aBb>`HKsGJAFWH=YE�?BD�PjZ\`HK4I�=YGJI�S2K6=@?Be&K�A/?UE�G�KiWpac»{`�A�ZR=@?cZ\`HKsK��(_�G�Ki?�?�=YD/X�5,?\A�X�?RAd/K�S2D(I�=�Z:^CP,AFI$Z\DFG$<;P8DFG>Z�`�K-e&A/?�?>DFP�Z\`HK-_�A�G�Z�=@I�S2K��

I�<�R?�?�EHe&KcZ\`HKB_�AFGUZ\=2I�SYKB=2?�A6W]D/EHLHS2^&IJ`VA�G\qFK�Wg_ND/?�=�Z\=Yd/Kc=2DFX�58=�a KFa2o[_ND/?�=YZ�=2dFKBIJ`�AFG�q/KB��<$o/Z�`�KB_ND�Z�K�X[Z�=@A�SNl�A/?

�i¾���´so�Z�`�Kne�A�q/XHK�Z\=2I&�VK�S@W�?:Z\G�K�XHq�Z\`�l�A/?6¾ � ��bMo�A�X�W�Z\`HK'� � � � ��� DFP~Z�`HKnI�=YGJI�S2KCl>AF?n� � ¶ ema»{`�A�Zc=2?�Z\`HK-e�AF?\?>D�P�Z�`HK-_VA�G�Z�=@I�S2K��

¾/� ½ h/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uje�A�q/XHK�Z\=2IRP8D/G\I�K�D/XAgl~=2G�K³ a~� � � ¾je}l~=YG\K-I�AFG�G\=YKi?~A&I�EHG\G�K�X[ZcD�P ¶�� ¾��6aHb>`HK�G�K-=@?cAgEHXH=YP8DFG\e�e�AFqFXHK�Z�=@I���K�S@WD�P�¾ � ��¾�b�A"ZBA�X�AFXHqFS2KDFP ³ ¾ �BZ�D&Z\`HK-l~=YG\KFa�»{`�A�Zc=2?~Z�`HK-e�A�q/XHK�Z\=2IRP8D/G\I�K�D/XnZ\`HK-l~=2G�K/a

¾/� ½ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾&?UE�_VK�G>Z�DFE�qF`Z�`H=2XHO�u�A�G\LH=YZ�GJA�G\^�SYD(D/_Qe�A�q/XHK�Z\=2IRZ\DFGJh/E�Kµ�a~9;G�D"d/K58Z�D�q/K�XHK�G\AFS�?�A�Z�=@?:P,A/I$Z�=2DFXr=YP~XHD�Zsl~=YZ�`�I�DFe&_HS2K�Z\KCG�=2qFD/GJ<BZ\`�A"Z6Z\`HKCe�A�q/XHK�Z\=2IgZ\DFGJh[EHKCA�LNDFE]ZsAFXA��(=@?BZ�`HG\DFEHq/`�Z�`�KgI�K�X[Z�K�GRDFP;e�AF?\?BD/X�A�X�A�G\LH=�Z\G\AFG�^Q_HS@A�X�AFGRS2D(DF_�DFP�I�EHG\G\K�X[ZR=2XxAnEHXH=YP8DFG\e�e&AFqFXHK�Z�=@I��K�S2W=@?

�� $ � � �� � ��

l~`HK�G�K �g=2?;Z�`HKMI�E�G�G\K�X[Z�=2XCZ\`HK�SYD(DF_�o ��=2?�Z\`HK�AFG�KiA-D�P�Z�`HK�SYD(D/_�o[AFX�W ��mZ\`HK�XHDFG\e�A�SVZ�D6Z\`HK�SYD(DF_�a�b>`�K?�K�X�?�KMD�P�Z�`HKsXHDFG\e�A�Sp=@?��H�]K�WL(^QAgG�=2qF`[Z�T�`�AFX�WQG�EHS2KFu�I�EHG\S�^FD/EHG~G�=2qF`[Z�T�`�AFX�W��VXHqFK�G\?>l~=YZ�`mZ\`HK6I�EHG\G\K�X[ZW]=2G\K�I$Z\=YD/X�A�X�Wg^FD/EHG�Z�`(EHe4L&_VD/=YX[Z\?�=YX&Z\`HKcW]=2G�KiI$Z�=2DFX&DFPVZ\`HKcXHD/G�e�A�S�a �������� � 7!e�AFqF=2XHK~G�K�_HS@AFI�=2XHq�Z�`�KS2D(DF_nL(^�S2DFXHqVo[Z�`H=2XQG\K�I�Z\AFXHqFEHS@A�G�S2D[D/_�?�D�P�I�EHG\G�K�X/Z �Vo]l~`HK�G\KcZ\`HKMSYD/XHqg?�=@W]KR=@?>=2XCZ�`�K�_�S2AFXHK-W]K���X�K�WCL(^Z\`HK ��T���K�S2W&AFX�W4Z�`HKcX�DFG\e&AFSHA�X�W4Z\`HKc?U`�DFG�Zj?�=@W]K~=2?�_VK�G�_NK�X�WH=2I�EHS2AFGjZ�DMZ\`H=@?j_HS@A�XHK/a�b>`�KcI�EHG\G�K�X[Z\?�D�PNZ�`�KG\K�I�Z\A�X�qFS2K�?�AFSYSN`�A*dFK>Z\`HKR?\A�e&KB?�K�XV?UKBA/?jZ\`HKRI�EHG�G\K�X[Z;DFP�Z�`HKRDFG\=Yq/=YX�AFSHS2D[D/_�a~5%�J¤(K�X�?�K��6=YX�e�A"Z\`HK�e�A�Z�=@I�A�SAUAFG�q/DFXm=2?�W]=2G�KiI$Z\=YD/X�l~`HK�XmZ\`HK�G\K4AFG�K-D/XHSY^QZ:l�DC_VD[?�?�=2LH=YS2=YZ�=2K�?�a <mb>`HK4G�KiI$ZJA�XHq/SYKi?>Z�=2SYKsZ�`HK4DFG\=Yq/=YXVA�SpS2D[D/_l~=YZ�`Z�`�K�=2Gc?U`HD/GUZc?�=2WHK�?~A�XVWnK�X�WLH=�ZJ?>D�P�SYD/XHq&?U=@W]K�?~Z�GJAFI�=2XHq4Z�`HK-D/G�=2qF=2X�AFSVS2D(DF_mAF?~I�S2D/?�K�S2^nA/?�_ND/?\?�=YLHS2KFab>`HKi?UKG\K�I$ZJA�XHq/SYKi?sAFG�KQLVD/EHX�WtG�=2qF=@W]S2^xZ\DFq/K�Z�`�K�GgL[^�?�DFe&KEHX�?�_VKiI�=Y��K�W�P8DFGJI�K/a�»xKDFXHS2^�`�A*d/KCZ�D�LNKI�DFX�I�K�G\XHK�W�l~=�Z\`�Z\DFGJh/E�K&I�DFe&_NDFXHK�X/Z-A�S2DFX�qnZ\`HK�A"�]=2?M_NK�G\_NK�X�W]=@I�E�S2AFGRZ\DZ�`HK&e�A�q/XHK�Z\=2I4��K�S2W�A�X�W�Z�`�KXHD/G�e�AFS�Z�D&Z�`�K-SYD(DF_�ujSYK�ZcE�?cI�AFSYS�Z�`H=@?>Z�`�K-_H=Yd/D�ZBA��(=@?�P8DFG~L�G�K�d[=YZ:^Fa��BSYS�Z�`HK-DFZ�`HK�G>Z�D/G\h[EHK6I�DFe&_VD/XHK�X[ZJ?I�A�X�I�K�S]Z\D6��K�G�DMZ\`HDFEHq/`&Z�`H=@?�=@?�X�· Z�?UD-KiAF?�^6Z�D4?UK�K~l~=�Z\`HDFE]Z>A-W]=@A�qFGJA�ema���W]=@A�qFGJA�e D�P�Z�`�KcG�K�_HS@AFI�K�e&K�X[ZS2D(DF_l�D/EHS2WQ`HK�SY_�a

¾/� ½ h/P8EHS2S�¾/¾ ¶ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u���A�G�Z�`QI�EHG\G�K�X/ZioH�;AFGUZ\`Qe�A�q/XHK�Z\=2I�e&DFe&K�X/Z¶ a~b>`HK�e�A�q/XHK�Z\=2IBegD/e&K�X[Z�DFP�Z�`HKM�;AFGUZ\`�=2? ¼ � ¾ �m��¾�� �6� �"bMaj�R?�Ag?U=2e&_HS2KBe&D]W]K�S�D�P�Z�`HKM�;AFGUZ\`�· ?�I�EHG\G\K�X[ZA/?�?�EHe&K&Z�`�A�Zs=YZ6��D"lc?-=2X�A�I�=2G\I�EHS@A�G6_�A�Z�`�DFP�GJAFW]=2E�? ³[¶ ¾/¾jO(e =YXrZ\`HKn��A�G�Z�`�· ?-I�D/G�K/a�v�AFS2I�EHS2A�Z�K&Z\`H=2?I�EHG�G\K�X[Zia

¾/� ½ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVujLVKiA�e�DFP�K�SYKiI$Z�G\DFXV?¹ a~��LVKiA�e D�P~K�S2K�I�Z�G\DFX�?s=2?4A�S2=Yq/XHK�W�=2X�A�_HS@A�XHKn_VK�G�_NK�X�WH=2I�EHS2AFG6Z\D�Z�`HKQSYD]I�A�S;W]=2G\K�I$Z\=YD/X�D�P~Z\`HKn�;AFGUZ\`�· ?e�A�q/XHK�Z\=2I���K�S2W�a�b>`H=@?je�A�q/XHK�Z\=2I���K�S2WgI�AFX4LNKcI�D/X�?�=2W]K�G�KiW4I�DFX�?UZ\AFX[Z�D"d/K�G�Z�`HKc?�=2��K>D�PVZ�`HK~LNK�AFef?U^]?UZ�K�eab>`HK�LNK�AFe l>AF?MD/G�=2qF=2X�A�S2S2^�I�G\K�A"Z\K�W�Z�Dm��^x=YX�A�?UZ�GJA�=2qF`[ZMSY=2XHKFa ��DFEr_HS@AFI�K�^/DFEHGJ?�K�SYP�?�DQZ\`�A"Z6^/DFErA�G\KS2D(DFO(=YX�q&WHD"l~XQD/XnZ\`HK-LVKiA�e A�X�WQ=YXZ\`HK6W]=2G�KiI$Z�=2DFXD�P�Z�`�K-e&AFqFXHK�Z�=@IR��K�S@WpaA[<nb>`�K-K�XHK�G�q/^�D�P�K�AFIJ`K�S2K�I�Z�G\DFXQ=2?-�*� � ¾jOFK�´6aj»{`�A�Zc=2?>Z\`HK�=2Gc?�_VK�K�W �

Page 142: Introductory Physics Problems David J. Jeffery Department of

� ³/¼ v�`�A�_]Zia;� ½ ¯�A�qFX�K�Z�=@IM|�=YK�S2WH?�v�A�E�?�=YX�qg|�DFGJI�K�?

LN<m®REVA�S2=�ZJA"Z�=2dFK�SY^�l~`VA"Z6l~=2SYS�`VA�_H_NK�X�Z�DZ\`HK�LVKiA�e AF?M=YZ�Z\G\A*d/K�S@?�=YX�Z�`�K�e&AFqFXHK�Z�=@I4��K�S@W � 7!Xrl~`�A�ZWH=YG\K�I�Z�=2DFXmW]=YG\K�I�Z�=2DFXmW]D(K�?>Z\`H=@?~`�A�_�_VK�XH=YX�qg`VA�_H_NK�X �

Ii<��=2dFK�X6Z\`�A"Z�Z�`�K�e�A�q/XHK�Z\=2I;��K�S2Wse&AFqFXH=YZ�EVW]K�=@? ¶F¶ � ¾ � bMoil~`VA"Z�=2?�Z�`�K�e�A�q/XH=YZ�E�W]K>DFPHZ�`HK�e�A"�]=2esEHeWH=2?�_HS@AFI�K�e&K�X[Z�DFP�Z�`HK�K�S2K�I�Z�G\DFX�P8G\DFe�=YZ\?>?UZ\A�G�Z�=2XHq6_NDF=2X[Z>AFX�WC`�D"l±S2DFX�q4W]D(K�?�Z\`HKRK�SYKiI$Z\G�D/X&Z\A�O/KcZ\DG\K�Z\EHG\XnZ\D�=�ZJ?~?:ZJA�G�Z�=2XHq&_VD/=YX[Z�a

Page 143: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� o ¥ da5\5<1_>2;<E ¥ &Ad�EG*->ac � &:cT>a14;<*-H ��*[1_N-,�E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³ ¾4h[e4EHS�ZB¾/¾F¾ ½ ¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�I�A�E�?�KRDFP�e�AFqFXHK�Z�=@IB�VK�S@WH?�Fa>7!XZ�`�K6A�L�?�K�X�I�KMD�P�Z\=Ye&K�T�d"A�G\^(=YX�qgK�SYKiI$Z\G�=@IR��K�S@WH?�oHe�A�qFX�K�Z�=@IR��K�S@WH?~AFG�K-I�AFE�?�K�WQL[^�u

A[<Ce�AFqFXHK�Z�=@IRe&D/XHDF_NDFS2K�?�aLN<ne�AFqFXHK�Z�=@IBZ\DFGJh[EHK�?�aIi<Q?UZ\A�Z�=@I-IJ`�A�G\qFK�W]=@?:Z\G�=2LHE]Z\=YD/X�?�aWV<QI�EHG\G�K�X/ZJ?~A�X�WQK�S2K�e&K�X/ZJA�G\^C_�AFGUZ\=2I�SYKMe�A�q/XHK�Z\=2IMW]=2_VD/SYKi?�aK*<Q?UZ�G\K�AFe�?�a

¾ ³ ¾4h[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u>��=2D�ZUT:¤]A*d"A�G�Z�S@A*l�]a~b>`HK ��=2D�Z�T!¤]A*d"AFGUZ>S2A*l�=2?�u

A[<� �� $ � �

µ��� � ������ �

LN<�C5 � < $

���

�� �

Ii< ��� � � �� $ � � � � � � �

WV< �� � � �� $ � � � �

� ��

K*< $ �4*���a

¾ ³ ¾4h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj�ce&_NK�G\KF· ?~S2A*l� ª�¬"¨ �V«������V¬ ��­�� �ce&_ �K�G�K/· ?>S@A*l

³ a~�Beg_ �K�G\KF· ?�S2A*lz=2?�uA[<

� �� $ � �µ��� � ������ �

LN<�C5 � < $

���

�� �

Ii< ��� � � �� $ � � � � � � �

Page 144: Introductory Physics Problems David J. Jeffery Department of

��µ[¾ v�`�A�_]Zia ³ ¾}v�E�G�G\K�X[Z\?cv�AFE�?U=2XHq�¯�AFqFXHK�Z�=@I�|�=2K�S@WH?

WV< �� � � �� $ � � � �

� ��

K*< $ �4*���a

¾ ³ ¾4h[e4EHS�ZB¾/¾ ³ ¾F¾4�Q���Me&D]W]K�GJA"Z\K�e&K�egD/G�^�u�e�A�q/XHK�Z\=2IR��K�S2WD�P�A�Xm=2X]��XH=YZ�K-l~=2G�Kµ�a~b>`HK-e�AFqFXH=YZ�E�WHK�DFP�Z\`HK-e�A�q/XHK�Z\=2IR��K�S2WD�P�A�Xm=2X]��XH=YZ�K-l~=2G�KM=@?~qF=2dFK�XnL(^�u

A[<'� $ � � � �]5�� � <$aLN<�� $ � � � � �H58µ�� <�aIi<�� $ � � � �VaWV<�� $ � � � ���H5�� � <�aK*< �� $ � � �� �H5����.� � <�a

¾ ³ ¾4h[e4EHS�ZB¾/¾ ³ ��¾C�&�s�4K�A/?U^�e&K�egD/G�^�uje�A�q/XHK�Z\=2IR��K�S2WS2=YX�K�?~A�LNDFEHZcl~=YG\K¶ a~b>`HKe�A�q/XHK�Z\=2In��K�S@WtSY=2XHK�?&AFLVD/E]Z&AFX�=2X]��XH=YZ�Kml~=2G�KmA�G\KQI�=YGJI�S2K�?gl~`HD[?UK?UK�X�?�KQ=@?&W]K�Z\K�G\eg=2XHKiW�L(^rZ�`�KW]=2G\K�I$Z\=YD/X�?>D�P�Z�`�KR�VXHqFK�G\?>E�?�K�Wl~=YZ�`�uA[<nAgS2K�P Z�T�`�AFX�WG�E�SYKMl~`HK�G�K�Z�`�KMZ�`(EHesL�AFSY=2qFX�?>l~=YZ�`Z\`HK6I�EHG\G\K�X[Z�aLN<QAgG\=Yq/`[ZUTk`�A�X�WQG\EHSYKMl~`HK�G�K�Z\`HKMZ�`(EHe4LmAFSY=2qFXV?>l~=�Z\`QZ\`HK6I�E�G�G\K�X[Z�aIi<QAgG\=Yq/`[ZUTk`�A�X�WQG\EHSYKMl~`HK�G�K�Z\`HKMZ�`(EHe4LmAFSY=2qFXV?>DF_H_ND/?�=�Z\K�Z�DgZ�`HK6I�EHG\G�K�X/ZcW]=2G\K�I$Z\=YD/X�aWV<nl~=2X�WmW]=2G�KiI$Z\=YD/X�aK*<nq/EHK�?\?�l�D/G�O�a

¾ ³ ¾4h[e4EHS�ZB¾/¾�µ[¾F¾4�Q� ³ e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�e�A�q/XHK�Z\=2IR��K�S2W=2X=@W]KiA�S�?�DFS2K�XHD/=2W¹ a~b>`HK-e�AFqFXH=YZ�E�WHK�DFP�Z\`HK-e�A�q/XHK�Z\=2IR��K�S2W=2X�?U=@W]K-A�Xm=@W]K�AFS�?UD/SYK�XHDF=@WQ=2?>q/=Yd/K�XL[^�u

A[<'� $ � � � �]5�� � <$aLN<�� $ � � � � �H58µ�� <�aIi<�� $ � � � �VoHl~`HK�G�K �x=2?>Z\`HK-X(EHesLNK�G~DFP�Z\EHG\X�?>_VK�GcEHXH=YZcS2K�XHqFZ�`�aWV<�� $ � � � ���H5�� � <�aK*< �� $ � � �� �H5����.� � <

¾ ³ ¾4h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujG\=Yq/`[ZUTkG�EHS2KRP8DFGcI�D/=YS@?º(a~b>`HK~e�AFqFXHK�Z�=@I;�VK�S@W4S2=2XHK�?jG\EHXHX�=YXHq�Z\`HG�D/EHqF`4Z�`�K~eg=@WHW]S2K~G\K�qF=2DFX4D�PpAMI�DF=2SH`�A*d/K;Z\`HK�=2G;?�K�X�?�K~W]K�Z\K�G\e&=YXHKiWZ\`HK6W]=2G�KiI$Z�=2DFXD�P�Z�`�KMZ�`(EHesLmE�?�K�WQl~=YZ�`�uA[<nAgG\=Yq/`[ZUTk`�A�X�WQG\EHSYKM=2Xml~`H=2IJ`QZ�`�KM��XHqFK�G\?~I�EHG\Sp=YXZ�`�K6W]=YG\K�I�Z�=2DFXD�PjI�EHG\G\K�X[Z>��D"l-aLN<QAgS2K�P Z�T�`�AFX�WG�E�SYKM=2Xl~`�=2IJ`Z�`�KM��XHqFK�G\?>I�EHG�S�=YXQZ�`HK6WH=YG\K�I�Z�=2DFXmD�P�I�EHG\G�K�X[Z��VD"l-aIi<QAgG\=Yq/`[ZUTk`�A�X�WQG\EHSYKM=2Xml~`H=2IJ`QZ�`�KM��XHqFK�G\?~I�EHG\Sp=YXZ�`�K-DF_H_ND/?�=�Z\K�Z�D&Z�`�K6W]=YG\K�I�Z�=2DFXD�P�I�EHG\G�K�X[Z��VD"l-aWV<nl~=2X�Wm?�_VK�K�WpaK*<nq/EHK�?\?�l�D/G�O�a

¾ ³ ¾4h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA�e&_NK�G\KMWHK���XH=2XHq&P8D/G\I�K� ª�¬"¨ �V«������V¬ ��­�� A�e&_VK�G�K-W]K���XH=2XHq&P8DFGJI�K

¼ a>»{`�A�Z�=@?�Z\`HKRP8DFGJI�Kc_NK�G�EHXH=YZ�S2K�X�q�Z�`nLVK�Z:l�K�K�X�Z:l�D6l~=2G�Ki?�DFX�KBe&K�Z\K�G>A�_�AFGUZ;KiAFIJ`�l~=YZ�`A6I�EHG\G\K�X[Z;D�P����=2XZ�`HK6?\A�e&K-W]=2G�KiI$Z�=2DFX �A[<��� 6aLN<���SYL�aIi<���O[qVaWV<� ����¾��p �y"eaK*<� ����¾ � �p My*ema

Page 145: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia ³ ¾}v�EHG\G\K�X[Z\?Bv�AFE�?U=2XHq&¯�A�q/XHK�Z\=2IM|�=2K�S@WH? ��µV�

¾ ³ ¾4h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujGJA�=2S�qFEHX½ a~� GJA�=2SpqFEHX=@?cAge&AFqFXHK�Z�=@I�u

A[<C_�=2?UZ�D/S�aLN<nl>A"Z\K�G~_H=@?UZ�DFS�aIi<nS@A�E�X�IJ`H=2XHq�W]K�d(=@I�KFaWV<nS2EHX�IJ`�=YXHq�W]K�d(=2I�KFaK*<CZ\G\AF=YXG\DFLHLNK�G~=2XZ�`HK-D/S2WQ»xKi?:Ziuj=�a KFa2o]Z\`�A"ZcD/S2WmIJ`�AFG�e&K�G ��E]ZJIJ`�v�A/?�?�=2WH^Fa

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³ ¾4h/P8EHS2S�¾/¾H��¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u���XH=YZ�Ks?UZ�GJA�=2qF`[Z>l~=YG\KMe&AFqFXHK�Z�=@IR��K�S@W�Fa~��Z\`H=YX�o�?:Z\G\AF=Yq/`[Z>l~=2G\K�DFP�S2K�XHqFZ�` �wI�AFG�G\=YKi?>I�EHG\G�K�X[Z �Va

A[<n¡RGJA*lzA&W]=@A�qFGJA�e DFP�Z\`HK6?�^(?UZ�K�emaLN<n»{`VA"Z�=@?jK��]_HG\K�?\?U=2DFXsP8DFG�Z\`HK~e�A�qFX�K�Z�=@I���K�S@W&A"Z;A�_NDF=2X/Z;AMW]=@?UZ\A�XVI�K���A*l>A*^�P8G�D/e Z�`�K ¦ �����

DFPHZ�`�K�l~=2G\K�A�S2DFX�qRARSY=2XHK�_VK�G�_NK�X�WH=2I�EHS2AFG�Z�DRZ�`HK�l~=YG\KFa �������� � ¡R=2d[=@W]K>A�X�W4I�D/X�h[EHK�Gia���D/Ese&=Yq/`[ZX�K�K�WQZ\`HKMZ\AFLHSYKM=2X[Z�K�q/G\AFS � � �

5 � � � ��� < � � � $ �� + � � � �� �

Ii<n7kP � � �oHl~`�A�Z~WHD[Ki?�Z�`HK-e�AFqFXHK�Z�=@IB�VK�S@WQLNK�I�DFe&K6A�XVWnl~`HK�G�K-AFSYD/XHqgZ�`HK-l~=2G�K-W]D(Ki?>=�ZBAF_H_HS2^Fa

¾ ³ ¾4h/P8EHS2S�¾/¾/��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uje�A�q/XHK�Z\=2IRP8DFGJI�KM_NK�GcE�XH=�ZcS2K�X�q�Z�`�]a~b>`HK�G�KgA�G\K6P8D/EHGMSYD/XHqQ?UZ�GJA�=2qF`[ZRl~=2G\K�?RK�AFIJ`xI�A�G\G\^[=2XHqnI�EHG\G�K�X/Z �G�EHX�XH=YX�qn_�AFG\AFSYS2K�S�Z�DK�A/IJ`�D�Z\`HK�Giu~Z�`�KI�EHG�G\K�X[ZJ?-A�S2Sj��D"lf=2X�Z�`HKQ?�AFegK�W]=2G\K�I$Z\=YD/X�anb>`HKCI�G�D[?�?M?�K�I�Z�=2DFXrD�P�Z�`HK�l~=2G\K�?MP8D/G�e�?-A�?\h/EVA�G\K4DFP>?�=2WHK�Na~»{`�A�ZB=2?cZ�`HK4e�A�qFX�=�Z\E�W]K6DFP�Z\`HK6P8D/G\I�K-_VK�GRE�XH=�ZRSYK�XHq�Z\`�A�X�W�WH=YG\K�I�Z�=2DFX�D�P�Z\`HK6XHK�ZRe�A�q/XHK�Z\=2IMP8D/G\I�KA/I$Z�=2XHq&DFXmA�X(^/DFXHK�D�P�Z�`HK�ema ������ � ¡RG\A*l�AgWH=2AFqFGJA�e A�XVWnK��(_�SYD/=�ZB?�^(ege&K�Z�G\^Fa

¾ ³ ¾4h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�Z:l�D�I�^(S2=YXVW]G�=@I�AFS�I�EHG\G\K�X[Z\?� ª�¬"¨ �V«������V¬ ��­�� Z:l�D�I�^(S2=YXVW]G�=@I�AFS�I�EHG\G\K�X[Z\?�o]?UEH_NK�G\_ND/?�=�Z\=YD/X�oH�ce&_ (K�G�K/· ?>S@A*l

³ ac¤]A*^nZ�`�A�ZR^/DFEm`�A*dFK4A�Xm=YXH��XH=YZ�K�S2^mSYD/XHqnI�^[S2=2X�W]G\=2I�A�S�I�DFX�W]EVI$Z�D/GBl~=YZ�`�EHX�=�P8D/G�e�I�EHG\G\K�X[ZRW]K�X�?U=YZ:^ �rAFX�WGJAFW]=2E�? �NaA[<C»{`VA"Z6=@?MZ�`HKne&AFqFXHK�Z�=@Ig��K�S@WrA"ZsA�W]=@?UZ\A�XVI�K P8G\DFe I�K�X/Z\K�G6=2X�?�=2WHKCA�X�W�DFEHZ\?�=2W]K&Z\`HKCI�D/X�W]E�I�Z�D/GK��]_HG�Ki?�?�K�WnE�?�=YXHq � � �/E�?UZ�=YP8^�Z�`�K-E�?UK-DFP��Beg_ (K�G\KF· ?�S2A*l�A�X�WQG�K�e&K�esLNK�G>Z\D�qF=2dFKRZ�`HK6WH=YG\K�I�Z�=2DFXD�PZ\`HKM��K�S2Wpa

LN<n7!e�AFqF=2XHK~Z�`VA"Z�^/DFEC?�EH_NK�G\=Ye&_ND/?�KRA�X�D�Z�`�K�G�I�^(SY=2X�W]G\=2I�A�SNI�DFXVW]E�I$Z\DFG�D�PpG\A/W]=2E�? � D/X�Z�`�Kc��GJ?:Zia�7kZ>`�A/?I�EHG\G�K�X/Z , �jaj7kZ~=2?~?�e�A�S2SYK�G>Z�`�AFXnZ\`HK���G\?UZcI�^(S2=YX�WHK�GcA�XVWnK�X/Z\=YG\K�S2^C=2X�?�=2W]KM=YZ�oHL�E]Z~DB�NTkI�K�X[Z�K�G�L(^nAFXAFe&DFEHX[Z *"uM=�a KFa2o *4=2?�Z\`HKCW]=@?:ZJA�X�I�KgP8G�D/e�Z�`HKCI�K�X[Z�K�G�DFP�Z\`HKg��GJ?:Z6I�^(S2=YXVW]K�GMZ\DQZ\`HK�I�K�X/Z\K�G-DFP;Z�`�K?�EH_NK�G\=Ye&_ND/?�K�W�D/XHKFaM»{`�A�Z�=@?BZ�`HKge�A�qFX�K�Z�=@I-�VK�S@W�A"ZRZ�`HK&I�K�X[Z�K�G�D�P�?UKiI�DFXVW�I�^(S2=YX�WHK�GMW]EHK6Z\DQ=YZ\?D"l~X�I�EHG�G\K�X[Z~DFX�SY^���»{`�A"ZB=@?>Z\`HK6XHK�ZBe�A�qFX�K�Z�=@IR��K�S@W�A"Z~Z\`HKsI�K�X[Z�K�GcD�Pj?UKiI�D/X�WmI�^(SY=2X�W]K�G��»{`�A�Z=@?~XHK�ZBI�EHG\G\K�X[Z>WHK�X�?�=�Z:^Q=YXV?U=@W]K�Z�`HK6?�K�I�DFX�WI�^(S2=YXVW]K�G �������� � ¡RG\A*l�A&W]=2AFqFGJA�ema

Ii<n»{`VA"Zc=@?>Z�`HK-X�K�Zce�A�q/XHK�Z\=2IR��K�S2Wm=2X�?�=2W]K�Z\`HKs?�K�I�D/X�WI�^(SY=2X�W]K�GcA"ZBAFX[^n_VD/=YX[ZBA�S2DFX�qsZ\`HK-SY=2XHKMP8G\DFeZ\`HK4I�K�X[Z�K�GBDFP�Z\`HK6�VG\?UZRI�^(S2=YXVW]K�G�A�X�Wm_�A/?�?�=2XHq�Z�`�G�D/EHqF`mZ\`HKs?�K�I�D/X�W�I�^(S2=YXVW]K�Gi· ?RI�K�X/Z\K�G � ��K6dFK�G�^I�A�G\K�P8EHS�AFLVD/E]ZcqFK�ZUZ\=YXHqgZ\`HK6?U=2qFXV?>D�P�Z\`HK6I�D/e&_VD/XHK�X[Z\?~I�DFG\G�KiI$Zia

WV<n»{`VA"Zc=@?�Z�`HK-XHK�ZBI�EHG\G\K�X[Z~D�P�Z�`HKMZ:l�D�I�^(SY=2X�W]K�G\?�

¾ ³ ¾4h/P8EHS2S�¾/¾�µ/¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�uje&AFqFXHK�Z�=@I���K�S@WA�S2DFXHq�?�DFS2K�XHD/=2WA"�]=@?µ�a ��D/E`VA*dFKMAg?�DFS2K�X�DF=@WnDFP�S2K�XHqFZ�` �co � Z�E�G�X�?�oHI�E�G�G\K�X[Z ��=2XKiAFIJ`QZ�EHG\X�oHAFX�WG\A/W]=YEV? �ga

Page 146: Introductory Physics Problems David J. Jeffery Department of

��µ(� v�`�A�_]Zia ³ ¾}v�E�G�G\K�X[Z\?cv�AFE�?U=2XHq�¯�AFqFXHK�Z�=@I�|�=2K�S@WH?

A[<C»{`VA"ZB=@?~Z\`HKsI�E�G�G\K�X[Zc_NK�GBE�XH=�ZRSYK�XHq�Z\` � �w5,7>egKiA�XmZ\`HKsI�E�G�G\K�X[Z~��D"l~=2XHqCA�G\DFE�X�WCZ\`HK4?�DFS2K�X�DF=@WQ=YPZ\`�A"Zc`�K�S2_�?�a <

LN<n7!Xml~`�A�ZcW]=YG\K�I�Z�=2DFX�W]D(K�?�Z\`HK-e�A�q/XHK�Z\=2IR��K�S2W_NDF=2X/ZBAFSYD/XHq4Z�`HK6A��(=@?>D�P�Z�`HK6?�DFS2K�X�DF=@W �Ii<Q¸�K�Z�4LVK�Z�`�KMI�D(DFGJW]=YXVA"Z�K�A�S2DFXHqsZ�`HK-A��(=@?�a�7kZ~=@?�_VD[?U=YZ�=2dFK�=YXQZ�`�K�W]=2G\K�I$Z\=YD/XnDFP�Z�`�KR�VK�S@WnA�XVW'��$�¾=@?-A"ZMZ\`HKCI�K�X/Z\K�G-DFP;Z�`�KC?UD/SYK�XHDF=@Wpag»{`�A"Z-=@?MZ�`HK&e�A�q/XHK�Z\=2I4��K�S2Wr?UZ�G\K�XHqFZ�`rA"Z6A_VD/=YX[Z ��W]EHKgZ\DAmW]= ��K�G\K�X[Z�=@A�SjLH=YZ6D�P>?UD/SYK�XHDF=@W�A�Z � � � ¿~K�I�A�S2S�Z�`�A�ZMP8DFG6?�=YXHq/SYK�I�DF=2S�Z�`HK&e�A�q/XHK�Z\=2I4��K�S2Wr?UZ�G\K�XHqFZ�`D/X]T!A"�]=2?>A�ZBAgWH=2?UZ\AFX�I�K ��P8G\DFe Z\`HK6I�K�X[Z�K�G~=@?

�n5 �(< $ � � � � ��~5 � � � � � < � � � �

b>`�K6W]=YG\K�I�Z�=2DFXD�P�Z�`HKM��K�S2W=@?cA�S2DFX�qsZ\`HK ��T!A"�]=@?�aWV<#��^=YX[Z\K�qFGJA"Z\=YD/Xn�VX�WZ�`HK6Z�D�ZJA�S���K�S@W�?:Z\G�K�XHq�Z\`�A"Z �CWHEHK-Z�D&Z\`HKs?�DFS2K�XHD/=2W�a ������ � � ¡R=Yd(=@W]KsAFX�W

I�DFX�h[EHK�G�a���D/Ee&=2qF`[Z~XHK�KiWQZ�`HKMZJA�LHS2KM=YX[Z�K�qFGJA�S

� � �5 � � � ��� < � � � $ �

� + � � � �� �

K*<n»{`VA"Zc=@?�Z�`HK-S2=Ye&=YZ�=2XHq�P8D/G�e =YP � � P8DFG>�H�]KiW4�VaP\<m|�DFGK��(Z�GJA�I�G�KiW]=�Zr58=2X�=2X�?�=Yq/`/ZiocXHDFZQe�A�G\O]?\< A:EV?:ZmqFEHKi?�?nl~`�A"ZQZ�`HKxP,A�G�T���K�S@WwSY=2e&=�ZmD�P-Z\`HKx��K�S@W?UZ�G\K�X�q�Z�`Q=2?�aj�BI�Z�E�AFSYS2^&Z�`HKMA�XV?Ul�K�G>W]K�_NK�XVWH?�DFXnl~`�K�Z�`�K�G����� ��D/G����� �caj¡BD/X�· Z>LND�Z\`HK�G�Z\G�^(=2XHqZ\D�l�D/G�O�D/E]Z>Z�`HK-S2=2eg=YZ�=2XHq�K��(_�G�Ki?�?�=YD/X�?�u�=YZ�· ?>Z�D(D&Z\K�W]=2DFE�?�Z\DCW]D&=�ZcG\=2qF`[Z�a

Page 147: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� p �+&:5\&A,a& 6 � E ��& � ?A@CQR>a,�d�H ;<*-?T>/&A>�,/QR>�,�daH^;7?A5\E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³ ��h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�|VA�GJAFWHA*^�· ?;S@A*l�DFP�=2X�W]E�I�Z�=2DFX�Fa~|VA�GJAFWHA*^�· ?;S@A*l�DFP�=2X�W]E�I�Z�=2DFXm=2eg_�SY=2K�?>Z\`�A"Ziu

A[<�Z\=Ye&K�T�d"A�G\^(=YX�qgK�SYKiI$Z\G�=@IR��K�S@WH?>=2X�W]E�I�K-e&AFqFXHK�Z�=@IR��K�S@WH?�aLN<CZ\=Ye&K�T�d"A�G\^(=YX�qge�AFqFXHK�Z�=@IB�VK�S@WH?>=YXVW]E�I�K-K�SYKiI$Z\G�=@IR��K�S@WH?�aIi<CZ\=Ye&K�T�d"A�G\^(=YX�qge�AFqFXHK�Z�=@IB�VK�S@WH?>=YXVW]E�I�K6I�A�_�A/I�=YZ�D/G��VK�S@WH?�aWV<CZ\=Ye&K�T�d"A�G\^(=YX�qge�AFqFXHK�Z�=@IB�VK�S@WH?>=YXVW]E�I�K-=2X�W]EVI$Z�D/G~��K�S2WH?�aK*<CZ\=Ye&K�T�d"A�G\^(=YX�qgK�SYKiI$Z\G�=@IR��K�S@WH?>=2X�W]E�I�K6I�A�_VAFI�=YZ�D/G���K�S@WH?�a

¾ ³ ��h[e4EHS�ZB¾/¾/�F¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�|VA�GJAFWHA*^�· ?;S@A*l�DFP�=2X�W]E�I�Z�=2DFXP8DFG\esEHS@A� ª�¬"¨ �V«������V¬ ��­�� |�A�GJAFW�A*^N· ?�S2A*l�D�P�=YX�WHE�I$Z\=YD/XQP8D/G�e4EHS@A

�]a~|VA�GJAFWHA*^�· ?;S@A*l�DFP�=2X�W]E�I�Z�=2DFXm=@?�uA[<

� �� $ � �µ��� � ������ �

LN< �� � � ���$�, �

� � � � � � �� �

Ii< ��� � � �� $ � � � � � � �

WV< �� � � �� $ � � � �

� ��

K*< $ �4*���a

¾ ³ ��h[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¸�K�XH�F· ?>S2A*l� ª�¬"¨ �V«������V¬ ��­�� ¸�K�X��F· ?>S2A*l

³ a �\¸�K�Zi· ?M_�S2A*^ �(1J��D3�����"# 1 |�DFG �]��¾/¾Ho�Z�`�KCA�X�?�l�K�G-=2?�u6b>`HKC?�K�X�?�K&D�P~A�Xr=2X�W]E�I�K�W�K�egP>=2?6?�E�IJ`�Z�`VA"Z-Z�`�K=2X�W]E�I�K�WQI�EHG\G�K�X[Z�=YZ�l�DFEHS@WCI�A�E�?�K45,=�P�Z\`HK�G\KBl�K�G\KRI�DFX�WHE�I$Z\DFGJ?�_HG\K�?�K�X[ZJ<;l�DFEHS@WCI�G\K�A�Z�KBA4e�A�q/XHK�Z\=2Ic��K�S@WZ\D�DF_H_ND/?�KBZ\`HK6IJ`�AFXHqFKMqF=2d(=YX�qgG\=@?UKRZ�D&Z\`HK-=YXVW]E�I�KiWK�egP:a �A[<C»{`VA"Zc=@? ��K�G�X�DFEHS2SY=p_�G�=2X�I�=2_HS2KFo��BSYK�� �LN<n»{`VA"Zc=@?~|HK�G\e�A"Zi· ?~S@AF?UZ>Z�`HK�DFG\K�emoH�cS2K�� �Ii<n»{`VA"Zc=@?c¤]IJ`(EHLVK�GUZi· ?cEHX]��XH=@?�`HK�WS@AF?UZ~?�^(e&_H`HDFX(^/oH�cS2K�� �WV<Q¸�K�XH�/· ? �{K��HI�E�?�KMe&KFoHl~`�A�Z~=2?c¸�K�XH�/· ?>S@A*l-oH�cS2K�� �K*<n»{`VA"Zc=@?~|�A�GJAFW�A*^N· ?~�"X�WQS@A*l�D�P�=2X�W]E�I�Z�=2DFX�o��BSYK�� �

¾ ³ ��h[e4EHS�ZB¾/¾�µ[¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujKiWHW]^nI�EHG�G\K�X[ZJ?µ�a~9;EHSYS�A&S@A�G\qF=@?�`QI�D/X�W]E�I�Z�D/G>Z�`HG\DFEHq/`QA&G\K�q/=YD/XnD�P�XHDFXHT�EHX�=�P8D/G�e e�AFqFXHK�Z�=@I���K�S@WQAFX�W^FD/EQl~=2SYS�=YX�WHE�I�K/u

Page 148: Introductory Physics Problems David J. Jeffery Department of

��µ/µ v�`�A�_]Zia ³ �f|VA�GJAFWHA*^�· ?�¸�A*l�DFP�7!X�WHE�I$Z\=YD/XmAFX�WQ7!X�W]E�I�Z�DFGJ?

A[<CL�=YS2SY^I�EHG\G\K�X[Z\?�aLN<ne&=2OFK�^nI�EHG\G\K�X[Z\?�aIi<nKiWHW]^I�EHG\G�K�X[Z\?�aWV<CP8G\=YZ���=�I�EHG\G�K�X[Z\?�aK*<nG\E�W]=�I�EHG\G�K�X[Z\?�a

¾ ³ ��h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=YXVW]E�I$Z\DFG¶ a~�BX=2X�W]EVI$Z�D/G~=2?BAgWHK�d(=2I�K-W]K�?�=Yq/XHK�W�u

A[<�Z\Dm`�A*dFK�AS2AFG�q/K � ��� � ����� � ¦ � � ¦ l~`HK�XrAQZ�=2egK�T�d"AFG�^(=2XHq�I�EHG\G�K�X[Z&5,=Ye&_HS2^(=YXHq�AQZ\=Ye&K�Td"AFG�^(=2XHq&e&AFqFXHK�Z�=@IR��K�S@W�< � � � � �xZ�`HG\DFE�qF`=�Zia

LN<CZ\Dm`�A*dFK�AS2AFG�q/K � ��� � ����� � ¦ � � ¦ l~`HK�XrAQZ�=2egK�T�d"AFG�^(=2XHq�I�EHG\G�K�X[Z&5,=Ye&_HS2^(=YXHq�AQZ\=Ye&K�Td"AFG�^(=2XHq&e&AFqFXHK�Z�=@IR��K�S@W�<-� � � � � � � � �xZ�`�G�D/EHqF`=�Zia

Ii<CZ\D�`�A*dFK-AgS@A�G\qFK ¦&� � �C¦ �� � � ¦ l~`�K�X�A4Z�=2egK�T�d"AFG�^(=2XHq�I�EHG\G�K�X[Z-5,=Ye&_HS2^(=YX�qnA4Z�=2egK�T�d"AFG�^(=2XHqe�AFqFXHK�Z�=@IB�VK�S@W�< � � � � ��Z�`HG\DFEHq/`Q=YZ�a

WV<CZ\D�`�A*dFK-AgS@A�G\qFK ¦&� � �C¦ �� � � ¦ l~`�K�X�A4Z�=2egK�T�d"AFG�^(=2XHq�I�EHG\G�K�X[Z-5,=Ye&_HS2^(=YX�qnA4Z�=2egK�T�d"AFG�^(=2XHqe�AFqFXHK�Z�=@IB�VK�S@W�<-� � � � � � � � �xZ�`�G�D/EHqF`=�Zia

K*<CP8D/G~E�?�K-L[^CZ�`HK6W]GJA"P Z~LND/AFG\Wpa

¾ ³ ��h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�¿c¸rI�=YGJI�EH=YZcLNK�`�A*d(=2DFG¹ a>7!X�A�X�¿cv�I�=2GJI�EH=YZRZ\`HKg_VDFZ�K�X[Z\=2AFS�D/X�AQI�A�_�A/I�=YZ�D/GB=@?B_HG\DF_NDFG�Z�=2DFXVA�S�Z\DCZ\`HK4=2X[Z�K�qFGJA�S�DFP�I�E�G�G\K�X[ZRAFX�W�=2XAFX¿c¸�I�=YGJI�E�=�Z~Z\`HK-_VDFZ�K�X/Z\=2AFSpDFXmA�Xm=2X�W]E�I�Z�DFG~=@?>_HG\DF_NDFG�Z�=2DFX�AFSNZ�D�uA[<�Z\`HK6W]K�G�=2d"A"Z�=2dFKMDFP�I�E�G�G\K�X[Z�aLN<CZ\`HKs�"XVWWHK�G\=Yd"A"Z\=Yd/KRDFP�I�EHG\G�K�X/ZiaIi<CZ\`HK6I�E�G�G\K�X[Z�aWV<CZ\`HK6I�E�G�G\K�X[Zc?�h[E�AFG�KiWpaK*<CZ\`HK6?\h/EVA�G\K�I�EHG�G\K�X[Zia

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³ ��h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(We�A"Z\`�ujK�S2K�I�Z�G\=2I�q/K�XHK�G\A�Z�DFGio(K�egP:oH_ND"l�K�G�Fa~�BX�K�S2K�I�Z�G\=2I-q/K�XHK�G\A�Z�D/G~`�AF?���¾F¾gZ\EHG\X�?BD/X�ACI�=2GJI�EHS@A�GBI�DF=2S�DFP�G\A/W]=YEV?c¾ � ¶ emacb>`HK4I�DF=2S�=@?c=2X�A�EHX�=�P8D/G�ee�A�q/XHK�Z\=2IC��K�S@W�DFPcµ;bMa�b>`HKI�D/=YS�=2?4G\D�Z\A�Z�KiW�A"ZgA�I�DFXV?:ZJA�X[ZgAFXHqFEHS@A�G6P8G�Kih/E�K�X�I�^�� D/X�A�X�A��]=2?6Z�`�A�Z_�A/?�?�K�?�Z\`HG\DFEHq/`A�W]=@A�e&K�Z�K�G~DFP�Z\`HKsI�DF=2S�A�X�WnZ�`�=2?RA"�]=2?>=@?~_NK�G\_VK�X�W]=@I�EHS@A�GcZ�D&Z�`�K-e&AFqFXHK�Z�=@I���K�S@Wpa;b>`�KAFXHqFEHS@A�G�_VD[?U=YZ�=2DFXnD�PpZ�`�KRI�D/=YS �s=@?�egKiAF?�EHG\K�WgP8G\DFe Z�`HKB��K�S@WnWH=YG\K�I�Z�=2DFX&Z�DsZ�`HK�XHD/G�e�A�S�Z�DsZ�`HKMI�D/=YS�58=�a K/aYoZ\D4Z\`HK-?U^(e&e&K�Z\G�^CA��(=@?�D�P�Z\`HK-I�D/=YSpl~`H=@IJ`n=@?>_NK�G\_VK�X�W]=@I�EHS@A�G�Z�DgZ\`HK-A"�]=2?�D�P�G�DFZ\A�Z�=2DFXV<�a�b>`�KRP8G\K�h[EHK�X�I�^DFP�G\D�ZJA"Z�=2DFXQ=2?6��¾F¾/¾6G\_He 5,G�K�dFD/SYE]Z\=YD/X�?�_VK�G � ����� �M<$aA[<n¡RGJA*lzA&W]=@A�qFGJA�e DFP�Z\`HK6?�^(?UZ�K�emaLN<n»{`VA"Z�=@?;Z�`HKRK��]_HG\K�?\?U=2DFX&=2Xn?U^(e4LVD/S2?�P8DFG�Z\`HKBe�AFqFXHK�Z�=@I~��E]������S2=2XHOFKiW�L(^4Z\`HKRI�DF=2SHP8D/G�A-q/K�XHK�G\AFS

AFXHqFS2K ���Ii<n»{`VA"ZR=@?�A�e&_HS2=�Z\E�W]KgD�PjZ�`�KsqFK�XHK�GJA"Z\K�WmK�e4P� ������ � �R?UKg|�A�GJAFW�A*^N· ?~S@A*l A�X�WmG\K�e&K�esLNK�GRZ�`�A�ZZ\`HK-G\D�Z\A�Z�=2DFXG\A�Z�K�=2?BI�DFXV?:ZJA�X[Z�a

WV<¤HA*^6DFXHK~I�DFXHXHKiI$Z\K�W4Z�`HK~q/K�XHK�G\A�Z�D/G�Z\D6A�G�Ki?U=@?:Z\=Yd/K�S2D/A/WgD�P��i¾F¾jO ��a�»{`�A"Z�=@?�Z�`�K~e&A��]=Ye4EHe _ND"l�K�Gq/K�XHK�G\A�Z�KiWn=2XA�I�^]I�S2K��

K*<n»{`VA"Z-=2?RZ\`HK�A*dFK�GJA�q/K6_ND"l�K�GRq/K�XHK�G\A�Z�K�W�=YX�AQI�^]I�S2Kgq/=Yd/K�X�Z\`HKm��¾/¾jO ��G�Ki?U=@?:Z\=Yd/KsS2D/A/W � ������ ���D/Emeg=2qF`[Z>��X�WQZ\`HKMZ�G\=Yq/DFXHD/e&K�Z�G\=@IB=@W]K�X[Z\=�Z:^

?�=YX � 5��< $ �� ��� ,rI�D[?�5�� �N<4!

Page 149: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia ³ �f|VA�GJAFWHA*^�· ?>¸�A*l�DFP�7!X�WHE�I$Z\=YD/XmAFX�WQ7!X�W]E�I�Z�DFGJ? ��µ ¶

`�K�S2_]P8EHS�aP\<�¤HA*^sZ\`HKBe�A�q/XHK�Z\=2I~��K�S@W�l>AF?~�cq[A�E�?\?c5U��¾ � ��b±l~`H=@IJ`C=2?;D�P�D/G\W]K�G�D�P�Z\`HKR��A�G�Z�`�· ?je�A�q/XHK�Z\=2I>�VK�S@W�<$ol~`VA"Zcl�DFEHS@WnLNKMZ�`�K6A�e&_HS2=�Z\E�W]K-D�P�Z�`HK-q/K�XHK�G\A�Z�KiWnK�e4P�

¾ ³ ��h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj=YX�WHE�I$Z\DFGJ?>=YX�?�K�G\=YKi?�]ac¤]A*^M^/DFEs`VAFWsAR?UK�Z�DFP�=2X�W]E�I�Z�DFGJ?�=YXg?UK�G�=2K�?�l~=YZ�`g=YX�WHE�I$ZJA�X�I�K�? � � � � a�b>`HK�=YX�WHE�I$Z\DFGJ?�AFG�K�l�K�SYS]?�K�_�AFG\A�Z�K�W�a

A[<n|�=2X�WQZ�`HK-K��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK-X�K�ZcDFG~Kih[EH=Yd"AFSYK�X/Z~=2X�W]E�I�Z\AFX�I�K/aLN<n»{`(^Q=2?�Z\`HK-G�Ki?UE�S�Z~D�P�_�AFGUZ65,A[<�XHD�Zcd"AFSY=@Wn=YP�Z�`HK-=2X�W]E�I�Z�D/G\?>l�K�G\KMXHD�Zcl�K�S2S�?UK�_�A�GJA"Z\K�W �

¾ ³ ��h/P8EHS2S�¾/¾ ³ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj=YX�WHE�I$Z\DFGJ?>=YXm_�AFG\AFSYS2K�S³ ac¤]A*^w^/DFE�`�A/W�At?UK�ZDFPs=YXVW]E�I$Z\DFGJ?n=2X�_VA�GJA�S2SYK�SRl~=YZ�`z=YX�WHE�I$ZJA�X�I�K�? � � � � a b>`HK�=YXVW]E�I$Z\DFGJ?mA�G\K�l�K�SYS?�K�_�AFG\A�Z�KiWpaA[<n|�=2X�WQZ�`HK-K��]_HG�Ki?�?�=2DFXCP8D/G>Z�`HK-X�K�ZcDFG~Kih[EH=Yd"AFSYK�X/Z~=2X�W]E�I�Z\AFX�I�K/aLN<Q|�=2X�WmAgE�?UK�P8EHS�EH_�_VK�GcLVD/EHX�WDFXZ\`HKMK�h[EH=2d*AFSYK�X[Zc=YX�WHE�I$ZJA�X�I�KFaIi<n»{`(^Q=2?�Z\`HK-G�Ki?UE�S�Z~D�P�_�AFGUZ65,A[<�XHD�Zcd"AFSY=@Wn=YP�Z�`HK-=2X�W]E�I�Z�D/G\?>l�K�G\KMXHD�Zcl�K�S2S�?UK�_�A�GJA"Z\K�W �

¾ ³ ��h/P8EHS2S�¾/¾�µ/¾/¾ ³&³ ¾4Z�D/EHqF`e�A"Z�`�u�?UD/SYd(=2XHq�Ag¡��±P8DFGc¿B¸�I�=YGJI�E�=�Zµ�a>7kZi· ?4A�LNDFE]Z6Z\=Ye&KQ^FDFEHTkAFSYS;?�DFS2dFKiWrA�W]= �NK�G�K�X/Z\=2AFS;Kih/EVA"Z�=2DFX{5�¡R��<$a�v�DFX�?�=2WHK�G-Z\`HKQ?�=Ye&_HS2KCD/XHK�TkSYD(D/_r¿B¸I�=YGJI�EH=YZB¡��tl~=YZ�`�A4�H�]K�WmW]G\=2d[=2XHq&K�egP ��58=�a K/aYoVA�XK�egP:oHG\K�?�=2?UZ�D/G>AFX�W=YXVW]E�I$Z\DFG~=2X�?UK�G�=2K�?J<$u

� � � � � � $ � �

A[<n¡RGJA*lzA&W]=@A�qFGJA�e DFP�Z\`HK6I�=2GJI�EH=YZ�aLN<¤(Z�K�_gDFX�K�W]=2d(=2WHK;Z\`HK~¡R��Z�`HG\DFE�qF`sL(^ �Ba�¤[Z\K�_4Z:l�DR��X�W4A�Xs=2X[Z�K�qFGJA"Z�=2XHqBP,AFI$Z\DFG #�a�b>`�K #&P8EHX�I$Z\=YD/X

?\A"Z\=2?U��Ki?>K�h[E�A"Z\=YD/X# � � � �

�# � $f5%# �(< �

l~`�K�G\K � $ � ��� =@?~Z\`HK4¿B¸�I�=2G\I�EH=YZcZ�=2e&K4I�D/X�?UZ\A�X[ZBD/G�T�P8D/S2WH=YXHqCZ�=2egK/acb�DC��X�W #xK��]_�AFX�W�5%# �(< �

EV?U=2XHqgZ�`HK6IJ`VA�=2XQG\EHS2KFa ��DFEml~=2SYS�Z\`HK�X�q/K�ZcW]= �NK�G�K�X[Z�=@A�SpK�h[E�A�Z�=2DFXD�PjA4P,A�e&DFE�?�Z:^(_NK

� � $ � � �

b>`�=2?>P,AFe&DFE�?>Z:^(_NKsI�AFXmLVKs?�DFS2dFKiWnL(^W]=Yd(=@W]=2XHq�Z�`�G�D/EHqF`L(^ ��AFX�WZ�`HK�X�=YX[Z\K�qFGJA"Z\=YX�qgLND�Z\`�?U=@W]K�?l~=YZ�`xG�Ki?U_NK�I�ZBZ\DCZ�=2e&KFa-¤(DFS2dFKsP8DFG�#�aRb>`HKg?�I�A�S2KsDFP�#�=2?REHXH=2e&_VD/GUZJA�X[Z�opA�XVW�?UD #�5 � $�¾/<B?U`�DFEHS@WLNK6?�K�Z~Z�Dm�/a

Ii<Q BD"l esE�S�Z\=Y_HS2^rZ�`�K¡��}5�W]=2d[=@W]KiW�Z\`HG�D/EHqF`�L[^ ��<6L(^ #�a*��D�Z\`t?�=2W]Ki?sDFPcZ�`�Km¡�� I�A�X�XHD"l LNK=2X[Z�K�qFGJA"Z�KiWCP8G\DFe Z�=2egK-��K�G\DgZ�D�AgqFK�X�K�GJA�SNZ�=2e&KFa;¡RDgZ�`H=@?cA�XVWn�VX�WQZ�`HK6?�DFS2E]Z�=2DFX�a

� $ ��5U� ,

���� ��� < �

b>`�K-=YXH=YZ�=@A�S�I�DFXVW]=�Z\=YD/XQD/XnZ\`HK6¡��w=2?�Z\`�A"ZBI�EHG�G\K�X[Z~=@?>��K�G\D�A"Z>Z�=2e&K6��K�G�DVaWV<¤]OFK�ZJIJ` �nAF?~A4P8EHX�I�Z�=2DFXmD�P�Z�=2e&KFa

¾ ³ ��h/P8EHS2S�¾/¾�µ��i¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�¿c¸�I�=YGJI�E�=�ZBW]=@?\IJ`�A�G\qFK¶ a ��D/E�`�A*dFKCA�D/XHK�TkS2D[D/_�I�=2G\I�EH=�Z4l~=�Z\` � � � � A�G\K�?�=@?:Z\DFG � A�X�Wr=2X�W]EVI$Z�D/G �Bu6Z�`�K�G\KC=2?sXHD��H�]KiW�K�egP?�DFEHGJI�K/aj��Z~Z�=2egK-��K�G\D�o[Z�`�K6I�EHG\G�K�X[Z>=2XZ�`HK6I�=YGJI�E�=�Z~=@? � � aA[<n¡RGJA*l�Z�`�K6I�=2G\I�EH=�ZcW]=@A�q/G\AFema�7!XVW]=2I�A"Z\KMA4�VWHE�I�=@A�S;5,=�a KFa2oHG\K�P8K�G�K�X�I�K*<�I�EHG\G�K�X/ZcW]=2G\K�I$Z\=YD/X�a

Page 150: Introductory Physics Problems David J. Jeffery Department of

��µ ¹ v�`�A�_]Zia ³ �f|VA�GJAFWHA*^�· ?�¸�A*l�DFP�7!X�WHE�I$Z\=YD/XmAFX�WQ7!X�W]E�I�Z�DFGJ?

LN<n»�G\=�Z\KW]D"l~X�²M=2GJIJ`H`HDB�~· ?sd/DFSYZ\AFqFK�S@A*l�P8DFG&A�X(^�Z\=Ye&KQP8DFGsZ�`H=@?&I�=2G\I�EH=�Zia �������� � b>`HKQd/DFSYZ\AFqFKWHG�D/_�?MAFI�G\D/?\?BZ�`HK�G\K�?�=2?UZ�D/G�AFX�Wx=YX�WHE�I$Z\DFG6A�G\KgLVDFZ�`�Z\AFOFK�Xx=YX�Z\`HK�W]=YG\K�I�Z�=2DFX�D�P>I�EHG\G�K�X[ZR��D"l-ag7kPZ\`HK�G\KM=2?BAgA/I$Z\E�A�S2SY^QA4d/DFSYZ\AFqFK�G�=@?UK�Z\`HK�XZ�`�K6W]G�D/_nZ\EHG\X�?~DFEHZ�Z\D�LVK-=2e&_HS2=2I�=�Z\SY^QXHK�q[A"Z�=2dFK/a

Ii<Qb>`�KgKih[E�A"Z\=YD/X�=2X�Z\`HK&_�A�G�Z&5,LV<�A�X�?�l�K�G�=2?-A/I$Z�EVA�S2SY^�AW]= �NK�G�K�X/Z\=2AFSjK�h[E�A�Z�=2DFX�P8D/G-I�EHG\G�K�X[Z�a4¤(D/SYd/KZ\`H=@?BKih/EVA"Z�=2DFXmP8D/G �AF?~P8E�X�I$Z\=YD/X�D�P�Z�=2e&KFa �������� � ¿~K�e&K�e4LVK�GcZ\`HKs=2XH=YZ�=@A�S�I�EHG\G�K�X[Zc=2? � � u>=�a K/aYo7�58Z $�¾[< $�¾Ha�¿~K�T�D/G\WHK�G-Z\`HKCK�h[E�A�Z�=2DFX�?�D�Z�`VA"ZsLND�Z\`�?U=@W]Ki?6D�P>Z\`HKnKih/EVA�S�?�=2qFX�I�AFX�LVKQ=YX[Z�K�qFGJA"Z\K�WD"d/K�GBZ�=2egK/a-¸�K�Z � $ � ���ga ��D/ExW]D/X�· ZMXHK�K�W�AFX�=2X/Z\K�q/G\A�Z�=2XHq�P,AFI�Z�D/GBZ\`H=2?BZ�=2e&KFa-7kP;^/DFEHG�I�EHG\G\K�X[Zq/D(K�?�Z�D&=2X]��XH=YZ:^Fo�^FDFEe�A*^C`�A*d/KRe�AFWHK6Ag?�=2qFXK�G\G�D/G�a

WV<n»{`VA"Zc=@?�Z�`HK-K��(_�G�Ki?�?�=YD/XnP8D/G>Z�`HK-=2XH=YZ�=@A�SpK�XHK�G\qF^n?UZ�D/G�KiWn=2XZ�`HK-=2X�W]EVI$Z�D/G�K*<n»{`VA"Zc=@?�Z�`HK-K��(_�SY=@I�=YZcK��]_HG\K�?\?U=2DFXnP8DFG~Z\`HK-_ND"l�K�G>WH=2?\?U=2_�A�Z�K�WQ=2XQZ\`HK-G\K�?�=2?UZ�D/G>A�ZBA�X(^&Z�=2e&K��P\<7!X[Z\K�qFGJA"Z\K~Z�`�KRK��(_�G�Ki?�?�=YD/X&P8DFG�_VD"l�K�G�W]=@?�?�=Y_VA"Z�KiW�=2X�Z�`HK�G\K�?�=2?UZ�D/G�P8G\DFe Z�=2e&KB��K�G�DsZ�D4=YX]�VXH=�Z:^/aj£BAF?K�XHK�G\qF^nLVK�K�X�I�D/X�?UK�G�d/K�W �

¾ ³ ��h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(We�A"Z\`�ujK�X�K�G\qF^CW]K�X�?U=YZ:^n=2X�AgLH=Yq�?�DFS2K�XHD/=2W¹ ac¤]A*^^FD/Em`�AFW�A�L�=YqC=@W]KiA�S�?�DFS2K�X�DF=@Wml~=�Z\`�A�X�=2X�W]E�I�Z\A�XVI�KsDFP � $ �i¾"!p£fAFX�WmdFD/SYE�egKsD�P � $ �*� ¶ e � ab>`HK6I�EHG\G�K�X/Z>=2XQZ\`HK6?�DFS2K�XHD/=2WQ=2? � $ �i¾F¾��saA[<v�AFS2I�EHS@A"Z�KMZ\`HK6e�A�q/XHK�Z\=2I-��K�S@WmK�XHK�G�q/^nW]K�X�?U=YZ:^l~=�Z\`HDFE]Z�I�A�S@I�E�S2A�Z�=2XHq&Z�`HK&�;T���K�S2W � ������ � b>`H=2?=@?~KiAF?�=YK�G�Z\`�A�Xm7;Z�`HD/EHqF`[Z�a

LN<mv�AFS2I�EHS@A"Z�K�Z\`HK-X(EHesLNK�GcDFP�Z\EHG\X�?>_VK�GcEHXH=YZcS2K�XHqFZ�`m=YX�?�^(esLNDFS@?>G�K�_HG�Ki?UK�X[Z�=2XHq4O(XHD"l~XV?-58=�a K/aYo �co ��oAFX�W �[<�AFX�WX[E�egK�G�=@I�AFSYS2^Fa

Ii<mv�AFS2I�EHS@A"Z�K�Z\`HK-e�A�qFX�K�Z�=@IR��K�S@W=YXZ\K�G\e&?>DFP�?�^(esLNDFS@?>G�K�_HG\K�?�K�X[Z�=2XHqgO[X�D"l~X�?>A�X�WX(EHe&K�G\=2I�A�S2SY^/aWV<Q BD"l I�AFS2I�EHS2A�Z�KnZ�`HKK�XHK�G�q/^�WHK�X�?�=�Z:^�P8G\DFe Z\`HKne�A�q/XHK�Z\=2IC��K�S@W�=YZ\?�K�SYP:a�¡BD(Ki?sZ\`HKmA�X�?�l�K�G4AFqFG\K�K

l~=YZ�`Z\`HK-_�A�G�Z65,A[<>A�X�?�l�K�G�

¾ ³ ��h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(We�A"Z\`�uje�A�q/XHK�Z\=2IR��E]�poHq/G�D"l~=2XHq4SYD(DF_º(a~b>`HK�G�K>=@?jA�`HDFG\=Y��DFX[Z\AFS]I�=2G\I�EHS2AFGjI�DFXVW]E�I$Z\=YX�q�S2D(DF_g=YX&A�EHXH=YP8DFG\e e�A�q/XHK�Z\=2I���K�S2WgD�PNe�A�qFX�=�Z\E�W]K �Ca~5,b>`�K��K�S2WQ=@?�AF_H_HS2=YKiWpuj=YZ>=@?�XHD�ZcW]E�KRZ\DsZ\`HKMSYD(D/_�a <4b>`HKMe�A�q/XHK�Z\=2IB��K�S@WQ_VD/=YX[Z\?>?UZ�GJA�=2qF`[Z>EH_�a�b>`HK�G\A/W]=2E�?�D�PZ\`HK-SYD(D/_Q=2X�I�G\K�A/?UKi?�l~=�Z\`QZ\=Ye&KsA/I�I�DFGJW]=YX�q6Z�D 5 � < $ � � ac5,��Z � $�¾Ho(Z�`�K-SYD(DF_`�A/?>��K�G\D&G\A/W]=2E�?�a <A[<C»{`VA"Zc=@?�Z�`HK-e�A�q/XHK�Z\=2I��VE]�CZ�`�G�D/EHqF`QZ�`HK-S2D(DF_mAF?~AgP8EHXVI$Z�=2DFXmDFP�Z�=2e&K��LN<n»{`VA"Z;=@?je�A�q/XH=�Z\E�W]K~DFPVZ\`HKc=2X�W]E�I�K�W&K�egPp=2X4Z\`HKcS2D(DF_ �Q»{`�A�Z;=2?jZ�`HKB?�K�XV?UK~DFPVZ\`HKcK�egPj58=�a K/aYo[l~`�A�Z

=@?�Z�`HK-W]=2G\K�I$Z\=YD/XCD�P�I�EHG\G\K�X[Z;��D"l�Z�`�A�Z�=YZ~l�D/EHS2WnI�A�EV?UK*<�l~`HK�Xnd(=2K�l~=2XHqsZ\`HKMSYD(D/_C=YXQZ�`�KMWH=YG\K�I�Z�=2DFXDFP�Z\`HK6A�_�_HSY=2K�W!��T��VK�S@Wpaj»{`(^ � ������ � ¿~K�e&K�esLNK�GB¸�K�XH�/· ?>S@A*l-a

Ii<��=2dFK�XCZ\`�A"Z�Z�`HK�S2D[D/_C`�A/?�I�DFX�?UZ\AFX[Z�G\K�?�=2?UZ\AFX�I�K �go(l~`�A�Z�=@?�Z�`HK�_VD"l�K�G�W]=@?�?�=Y_VA"Z�KiWC=2XCZ\`HKRS2D(DF_CL(^Z\`HK-=2X�W]E�I�K�WmI�EHG\G\K�X[ZcAF?~A4P8EHX�I�Z�=2DFXmD�P�Z�=2e&K � �

WV<n»{`VA"Z~=2?�Z\`HKBZ\D�ZJA�S�K�XHK�G�q/^�W]=2?\?�=Y_�A�Z�KiWnL(^gZ�`HKMG\K�?�=2?UZ\AFX�I�KR=YXQZ�`�KRS2D(DF_n=2XQZ�`HK�=YX[Z\K�G\d*AFSNP8G�D/e � $�¾Z\D � �

Page 151: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� n � ¥ &A>�, ��� ¥ ¥ *-5\HJd�*O;<E ` �8NO;71)5\>a&X;<*->ac ¥ da5<5\1)>W;J`S&A>�, � 5<&A>�ER@ ?A5 =!145 E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³ �sh[e4EHS�ZB¾/¾H�i¾F¾C�&� ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=YXVW]E�I$Z\DFGBAFX�WI�EHG\G�K�X[Z� ª�¬"¨ �V«������V¬ ��­�� =YX�WHE�I$Z\DFGcA�XVWI�EHG\G�K�X/Z

�Fa~�BX=2X�W]EVI$Z�D/G~G�Ki?U=@?UZ\?>GJA�_H=@WQIJ`VA�XHq/K�?�=YX�uA[<Cd/DFSYZ\AFqFKFaLN<nG\K�?�=@?:ZJA�X�I�KFaIi<QI�A�_�A/I�=YZ\AFX�I�K/aWV<n=2X�W]EVI$Z\AFX�I�K/aK*<QI�EHG\G�K�X/Zia

¾ ³ �sh[e4EHS�ZB¾/¾/�F¾F¾C�&� ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¸�v�D/?\I�=2SYS@A"Z\DFGio(G\A/W]=YDgK�e&=@?�?�=2DFX� ª�¬"¨ �V«������V¬ ��­�� ¸�v�D/?\I�=2SYS@A"Z\DFGio[GJAFWH=YDgK�e&=@?�?�=YD/X

�]a~�BX=2e&_VD/GUZJA�X[Z~E�?�K-D�P�AFX�¸�vwD[?�I�=YS2S@A"Z�D/G>=2?~=2X�uA[<C`�DFG�Z�=@I�EHSYZ�EHG\KFaLN<nS2=YZ�K�GJA"Z\EHG\KFaIi<n_NDFS2=YZ�=@I�?�aWV<nX�K�EHGJAF?UZ�`HK�XH=@AHaK*<nGJAFWH=YDgK�e&=@?�?�=YD/X�a

¾ ³ �sh[e4EHS�ZB¾/¾ ³ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�¸�¿~v�WHA�e&_NK�WmI�=2GJI�EH=YZ\?� ª�¬"¨ �V«������V¬ ��­�� ¸�¿cv{WHAFe&_VKiWI�=YGJI�E�=�ZJ?

³ a~b>`HK6¸�¿cv{I�=2GJI�EH=YZc=2?~AFX�A�S2DFq/DFE�?;Z�D&Z\`HK-e&K�IJ`�AFXH=@I�A�SpWHAFe&_VKiWQ`VA�G\egD/XH=@IRD[?�I�=YS2S@A"Z�D/G�a�7kZcK��]`H=2`H=YZ\?�uA[<CD"d/K�GJWHA�e&_H=2XHqVo(I�G�=YZ�=@I�AFS�WHA�e&_H=2XHqVoHA�X�WQSY=2XHKiA�GcWHAFeg_�=YXHqVaLN<nD"d/K�GJWHA�e&_H=2XHqVo(I�G�=YZ�=@I�AFS�WHA�e&_H=2XHqVoHA�X�WQEHX�W]K�G\W�A�e&_H=2XHq�aIi<nD"d/K�GJWHA�e&_H=2XHqVo(I�G�=YZ�=@I�AFS�WHA�e&_H=2XHqVoHA�X�Wh[E�AFW]GJA"Z\=2IMWHAFe&_H=YX�q�aWV<Q?�EH_NK�GJWHA�e&_H=2XHqVoHI�G\E�I�=@A�S�WHAFe&_H=YX�q�oHA�XVWQE�X�W]K�GJWHAFeg_�=YXHqVaK*<Q?�EH_NK�GJWHA�e&_H=2XHqVoHI�G\E�I�=@A�S�WHAFe&_H=YX�q�oHA�XVW�BX�W]K�G\W]D/qgW�A�e&_H=2XHq�a

¾ ³ �sh[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujW]G\=Yd/K�Xm¸�¿cv{I�=YGJI�EH=YZ\?�oHG\K�?�DFX�AFX�I�Kµ�a~b>`HK6WHG�=2dFK�X¸�¿~v�I�=2G\I�EH=YZ>K��]`H=YL�=�ZJ?�u

A[<CG\K�?�DFXVA�X�I�K�A�Z>��K�G\D�A�XHq/EHS2AFG�P8G�Kih/E�K�X�I�^FaLN<QI�DFG\G�Ki?U_NDFXVW]K�X�I�K�A�Z~��K�G\D�A�XHq/EHS@A�G�P8G�Kih[EHK�X�I�^FaIi<nG\K�?�DFXVA�X�I�K�A�Z~AFXHqFE�S2AFG�P8G\K�h[EHK�X�I�^ � $ � � + � � aWV<QI�DFG\G�Ki?U_NDFXVW]K�X�I�K�A�ZcA�XHq/EHS2AFG�P8G�Kih/E�K�X�I�^ � $ � � + � � aK*<QWHK�?�_VD/X�W]K�XVI�K6A"ZcAFXHqFEHS@A�G�P8G\K�h[EHK�X�I�^ � $ � � + � � a

¾ ³ �sh[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¸�¿cv�I�=2G\I�EH=�Zio]G�Ki?UD/X�A�XVI�K� ª�¬"¨ �V«������V¬ ��­�� ¸�¿cv{I�=YGJI�EH=YZ�o�G�Ki?UD/X�A�X�I�K

¶ a~� e�A A:D/G>E�?UK-DFP�A�¸�¿~v�I�=2G\I�EH=YZ>=@?>Z\D�uA[<�Z\EHXHK-=2X�AgWHK�?�=YG\K�WnP8G�Kih[EHK�X�I�^�u�P8DFG~K��HAFeg_�SYK-Ag_�A�G�Z�=@I�E�S2AFG�GJAFWH=YD&DFG>Z\K�S2K�d(=@?U=2DFXQP8G�Kih[EHK�X�I�^Fa

Page 152: Introductory Physics Problems David J. Jeffery Department of

��µ ¼ v�`�A�_]Zia ³ � ¸�v{AFX�Wm¸�¿cv�v�=2G\I�EH=YZ\?�o��cSYZ�K�G�X�A�Z�=2XHqnv�EHG\G�K�X/ZioHA�X�Wb�G\AFX�?:P8D/G�e&K�G\?

LN<Q?�EH_H_�G�Ki?�?rA�_�A�G�Z�=@I�E�S2AFGrWHK�?�=YG\K�W P8G�Kih/E�K�X�I�^Nu P8DFG�K��HA�e&_HS2K±A�_�AFGUZ\=2I�EHS2AFGrG\A/W]=YDzDFGrZ\K�S2K�d(=2?�=2DFXP8G\K�h[EHK�X�I�^/a

Ii<Q?�EH_H_�G�Ki?�?QAr_�A�G�Z�=@I�EHS@A�GnEHX�W]Ki?U=2G�KiW±P8G�Kih[EHK�X�I�^�u�P8D/GnK��HAFeg_�SYK�A�_�A�G�Z�=@I�EHS@A�GnG\A/W]=YD�D/GCZ\K�S2K�d(=2?�=2DFXP8G\K�h[EHK�X�I�^/a

WV<ne4EHSYZ�=2_HSY^A�XEHX�W]Ki?U=2G\K�WQP8G�Kih[EHK�X�I�^FaK*<QWH=Yd(=@W]K6A&W]K�?�=YG\K�WnP8G\K�h[EHK�XVI�^Fa

¾ ³ �sh[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u��Bv{_VD"l�K�Gio]_H`�A/?UK-?�`H=�P Z� ª�¬"¨ �V«������V¬ ��­�� �Bv{_ND"l�K�G�o(_H`VAF?�KM?�`H=YP Z

¹ a~b>`HK-_ND"l�K�G~?UE�_H_HS2=YKiWQL(^nAFX�A�SYZ�K�G\X�A�Z�=2XHqgI�=YGJI�E�=�ZcK�e4P�=@?>qF=2dFK�XL(^�uA[< � $ �2� � �

�� � � � � � � a

LN< � $ �2� � ��� � � � � � � I�D/?�5 � <$o�l~`�K�G\K � =2?~Z�`HK-_H`VAF?�KMWH=���K�G\K�X�I�KMLVK�Z:l�K�K�Xm_VDFZ�K�X/Z\=2AFS�A�X�WmI�EHG�G\K�X[Zia

Ii< � $ � � � ��� � � � � � � �"µ�a

WV< � $ � � � ��� � � � � � �]I�D/?�5 � <�y*µVoHl~`HK�G�K � =@?>Z\`HK-_H`�A/?UK-W]= �NK�G�K�X�I�KMLNK�Z:l�K�K�X_ND�Z\K�X[Z�=@A�S�AFX�WmI�EHG\G\K�X[Z�a

K*< � $ � � � ��� � � � � � � � ¶ a

¾ ³ �sh[e4EHS�ZB¾/¾[º�¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�Z\G\AFX�?:P8D/G�e&K�G� ª�¬"¨ �V«������V¬ ��­�� Z�GJA�X�?UP8DFG\e&K�G

º(a~b�G\AFX�?UP8DFG\egK�G\?�A�S2S2D"l�DFX�KRZ\D�uA[<n?UZ�K�_mDFE]ZcA&_ND�Z�K�X[Z�=@A�S�aLN<Q?UZ�K�_Z�`HG\DFEHq/`Ag_ND�Z\K�X[Z�=@A�S�aIi<Q?UZ�K�_mEH_�A�X�WW]D"l~XmA4_ND�Z\K�X[Z�=@A�S�aWV<Q?UZ�K�_mDFXmA4_ND�Z\K�X[Z�=@A�S�aK*<nD"d/K�GJ?:Z\K�_A4_ND�Z\K�X[Z�=@A�S�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³ �sh/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(We�A"Z\`�u�¸�¿ I�=YGJI�EH=YZ�oH¸�¿zZ�=2egK6I�DFX�?UZ\AFX[Z�Fa~� ?�=2eg_�SYK ���I�=2GJI�EH=YZ6`�AF?6LVK�K�X�?�K�Z6EH_�l~=YZ�`�AFX�K�egP � � � � $���¾j´4o�G�Ki?U=@?UZ�DFG�� � ¾�O ��o�A�X�W�=2X�W]E�I�Z�DFG¶ e�£w=2XC?UK�G�=2K�?�a�7!X�=�Z\=2AFSYS2^sZ\`HK�G\K~=@?j��K�G�D-I�E�G�G\K�X[Zj��D"l~=2XHq�o�Z�`HK�XCA-?Ul~=YZ\IJ`&=@?�Z�`HG\D"l~X�I�S2D/?�=YX�qRZ\`HKBI�=YGJI�EH=YZ�a

A[<C»{`�A�Zc=2?�Z\`HK6I�E�G�G\K�X[Z~l~`HK�XZ\`HKMZ�=2e&K � $����aLV<��Zsl~`VA"Z6Z\=Ye&K�5,=YX�X(EHe&K�GJA�S@?J<MW]D(K�?MZ\`HKnI�E�G�G\K�X[Z6G\K�AFIJ`�`�AFS�P~=YZ\?M��XVA�S;d"AFSYEHK�5,=�a KFa2o�=�ZJ?6d"A�S2EHKCA�Z6Z�=2e&K

=2X]��XH=YZ:^H<��

¾ ³ �sh/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVuj=YX�WHE�I$Z\DFGJ?>=YX�?�K�G\=YKi?~A�X�WQ_�A�GJA�S2S2K�S� ª�¬"¨ �V«������V¬ ��­�� =YX�WHE�I$Z\DFGJ?>=YX�?�K�G\=YKi?~A�X�WQ_�A�GJA�S2S2K�S

�]a-5�A/<;7kP�^FD/EC`�A*dFKB=YX�WHE�I$Z\DFGJ?;=2XQ?�K�G\=YKi?;l~`VA"Z�=@?�Z�`HK�=2X�W]E�I�Z\A�XVI�KBDFP�Z�`�KRKih/E�=Yd"A�S2K�X[Z�=YX�WHE�I$Z\DFG �r58LV<�7kP�^/DFE`�A*d/KR=2X�W]EVI$Z�D/G\?c=YX_�A�GJA�S2S2K�Spl~`�A�Z>=@?>Z\`HK-=YXVW]E�I$ZJA�X�I�K-D�P�Z�`HK-Kih/E�=Yd"A�S2K�X[Z~=2X�W]E�I�Z�DFG �

¾ ³ �sh/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�¸�vwD/?\I�=2S2S2A�Z�DFGio(G\A/W]=2D4P8G\K�h[EHK�X�I�^� ª�¬"¨ �V«������V¬ ��­�� ¸�v�D/?\I�=2SYS@A"Z\DFGio[GJAFWH=YD4P8G�Kih[EHK�X�I�^

³ ac¤]A*^w^/DFE{l>A�X[Z�KiWwZ�DtLHEH=2S2WzA�X � � D/?\I�=2SYS@A"Z\DFGCZ\D�_HG\D]W]E�I�KxA�GJAFWH=YD�?�=2qFX�AFSRA"Z���¾ �£c�±5,A�`(EHXVW]G�KiWe&K�q[AFI�^(I�SYKi?�_VK�GB?UKiI�D/X�W�<$a���D/E`VAFWAQ� � |�I�A�_�A/I�=YZ�DFGia�»{`�A"ZB?�=Y��KM=YX�WHE�I$Z\DFGBW]D&^/DFEXHK�KiW �

¾ ³ �sh/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾gK�A/?U^Ce�A�Z�`�uj_H`VAF?�KMI�DFX�?UZ\AFX[Z>DFP��Bv�I�=2G\I�EH=YZ� ª�¬"¨ �V«������V¬ ��­�� _H`�AF?�K-I�D/X�?:ZJA�X[Z~D�Pj�Bv{I�=YGJI�EH=YZ

µ�a~b>`HKR_VD"l�K�G�?UE�_H_HS2=YKiWCL(^�As�BvtK�egP�=@?R��¾F¾�»�a/b>`HK�¿c¯�¤�_ND�Z\K�X[Z�=@A�S�A�XVWCI�EHG\G\K�X[Z\?�A�G\KR��¾j´�A�X�W���¾ �soG\K�?�_VKiI$Z\=Yd/K�S2^ �»{`VA"Zc=@?>Z�`HK-_�`�AF?�K-I�DFXV?:ZJA�X[Z�

Page 153: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_]Zia ³ � ¸�v�AFX�W¸�¿cvzv�=2GJI�EH=YZ\?�oH�cSYZ�K�G�X�A�Z�=2XHqnv�EHG\G�K�X/ZioHA�X�Wmb�G\AFX�?UP8DFG\egK�G\? ��µ ½

¾ ³ �sh/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(We�A"Z\`�u�Z�GJA�XV?:P8D/G�e&K�Gio]?:Z\K�_mEH_�oV?:Z\K�_mW]D"l~X� ª�¬"¨ �V«������V¬ ��­�� Z�GJA�X�?UP8DFG\e&K�Gio(?UZ�K�_mEH_�o�?UZ�K�_W]D"l~X

¶ a ��D/E�l>A�X[ZRZ\D�?:Z\K�_�E�_�AFXx�Bv�_ND�Z\K�X[Z�=@A�SjL(^�AnP,AFI$Z\DFG�D�P ³ aC5,A[<R»{`�A"ZMZ�E�G�XxG\A�Z�=2D � � � � ����� � � ��e4E�?UZ^/DFEE�?UK ��58LN<�»{`�A"Zcl�DFEHS@WQLVKMZ\`HK-G\A�Z�=2D&D�P�Z\`HK6?�K�I�D/X�WHAFG�^&Z\D&Z�`HK-_HG\=2e&AFG�^CI�EHG\G�K�X/Z �

Page 154: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � � &�� � 1)NIN � E ���Wda&X;<*[? >�E ` � N-1)H^;75<?T=!&AcT>a1 ;<*IH�� &)(A1_E `�&A>�, U+9�1_HJ*[&TN&�L1_N[&:;<*[(+*O; 6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³/³ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¯�A"�]l�K�S2S�· ?>K�h[E�A�Z�=2DFX�?�Fa �\¸�K�Zi· ?z_HS@A*^ �]1J� D+�"�\�"# 1 |HDFG �(�i¾F¾�o�Z\`HK AFX�?Ul�K�Gz=2?�u b>`HK µ P8EHX�WHAFe&K�X[Z\AFSxS@A*lc?�DFPtI�S@AF?\?U=@I�AFSK�SYKiI$Z�G\D]W]^(X�A�e&=@I�?�a �A[<C»{`VA"ZBA�G\KMe�A�qFX�K�Z\?�oH�cS2K�� �LN<n»{`VA"ZBA�G\K-|�AFG\A/WHA*^�· ?�A�X�W¸�K�XH�F· ?~S@A*lc?�o]�BSYK����Ii<n»{`VA"ZBA�G\K-¯�A"�]l�K�S2S�· ?>W]K�e&D/X�?�oV�cS2K�� �WV<n»{`VA"ZBA�G\K�Z�`HK6I�DFXHKi?�D�Pj?U=2SYK�X�I�K/oH�cS2K�� �K*<n»{`VA"ZBA�G\K-¯�A"�]l�K�S2S�· ?�K�h[E�A�Z�=2DFX�?�oH�cS2K�� �

¾ ³/³ h[e4EHS�ZB¾/¾/�F¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�W]=@?�_HS2A/I�K�egK�X[Z~I�EHG\G�K�X/Zio]K�S2K�I�Z�G\=2IR��E]��]a~b>`HK6WH=2?�_HS@AFI�K�e&K�X[ZcI�EHG\G�K�X[Z>=@?�u

A[<nA&W]=@?�_HS2A/I�KiWQI�EHG�G\K�X[Z~D�P�K�S2K�I�Z�G\=2IMIJ`�AFG�q/KFaLN<CZ\`HK-e�A�q/XHK�Z\=2IR��E]�paIi<CZ\`HK-K�S2K�I�Z�G\=2IR��EH��aWV< � � � � � ��� � � � u�A�Z�K�G\e�AFWHW]KiWZ�Dn�Be&_ (K�G\KF· ?~Kih/EVA"Z�=2DFXm=2X�DFGJW]K�G>Z�DnA/I�I�D/EHX[ZcP8DFGcZ�`HK4=YX�WHE�I$Z\=YD/X�D�P

�� ¦ ��� ¦ ��K�S2WH?>L(^nZ�=2egK�T�d"AFG�^(=2XHq4e�AFqFXHK�Z�=@IB�VE]�paK*< � � � � � � � � � � u�A�Z�K�G\e�AFWHW]KiWZ�Dn�Be&_ (K�G\KF· ?~Kih/EVA"Z�=2DFXm=2X�DFGJW]K�G>Z�DnA/I�I�D/EHX[ZcP8DFGcZ�`HK4=YX�WHE�I$Z\=YD/X�D�P

� � � � � ¦ ��K�S@WH?~L(^�Z\=Ye&K�T�d"A�G\^(=YX�q4K�SYKiI$Z�G\=@I���E]�pa

¾ ³/³ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�¯�A��]l�K�SYS�· ?�_HG\K�WH=2I�Z�=2DFXD�Pj�;¯ l�A*d/K�?� ª�¬"¨ �V«������V¬ ��­�� ?U_NK�KiWQDFP�S2=Yq/`[Z

³ a~|�G�D/e `H=@?~µ&K�h[E�A"Z\=YD/X�?�oH¯�A"�]l�K�S2Spl�A/?�AFLHS2KRZ\D�_HG\K�W]=@I$Z~Z\`�A"ZiuA[<CS2=2qF`[Zcl�A/?�e&A/W]KMD�P�_�A�G�Z�=@I�S2K�?�Z\`�A"ZBAFG�K�XHD"l�I�A�S2S2K�WQ_H`HD�Z\DFX�?�aLN<nS2=2qF`[Zcl�A/?�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IRl�A*d/K�?�l~=�Z\`m_H`�AF?�KMdFK�SYD]I�=YZ:^�* $ � � + � � aIi<nS2=2qF`[Zcl�A/?�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IRl�A*d/K�?�l~=�Z\`m_H`�AF?�KMdFK�SYD]I�=YZ:^�* $ � � + � � � � aWV<nS2=2qF`[Zcl�A/?�e&A/W]KMD�P�_�A�G�Z�=@I�S2K�?�Z\`�A"ZBAFG�K�XHD"l�I�A�S2S2K�Wn��E]�]DFX�?�aK*<nS2=2qF`[Zcl�A/?�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IRl�A*d/K�?�l~=�Z\`m_H`�AF?�KMdFK�SYD]I�=YZ:^�* $ # � � � a

¾ ³/³ h[e4EHS�ZB¾/¾�µ[¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_VD[?:Z\EHS@A"Z�Ki?>D�Pj?U_NK�I�=2AFSpG�K�S2A�Z�=2d(=�Z:^µ�a �\¸�K�Zi· ?�_HS@A*^ �]1J� D+�"����# 1 |HDFG �]��¾F¾�oiZ�`HKcAFX�?Ul�K�G�=@?�u�5:�i<�b>`HK>S@A*lc?�D�PV_�`[^]?�=2I�?�A�G\K;Z\`HK~?�AFegK>=2XgAFSYS(=2XHK�G�Z�=@A�SP8GJA�e&K�?>DFP�G\K�P8K�G�K�X�I�K/a>5��F<>b>`HK6?�_NK�K�WDFP�S2=Yq/`/Zc=2Xd*A/I�EHE�e�=@?>Z�`HK6?\A�e&K�P8DFGcAFSYSpD/L�?�K�G\dFK�GJ?�a �A[<C»{`VA"ZBA�G\K�Z�`HK-S@A*lc?�D�PjI�S@AF?\?U=@I�AFS�K�S2K�I$Z\G�D]W]^(X�AFe&=2I�?�oH�BSYK����LN<n»{`VA"ZBA�G\K�Z�`HK-_�G�=2X�I�=2_HS2K�?>DFP�h[E�A�X[Z\EHe�e&K�IJ`VA�XH=@I�?�oH�cS2K�� �Ii<n»{`VA"ZBA�G\K-��E�I�SY=@Wp· ?~A"�]=2DFe�?�D�P�qFK�D/e&K�Z�G\^Fo]�BSYK����WV<n»{`VA"ZBA�G\K-I�D/X/Z\G\A/W]=@I$Z�D/G�^&`(^(_VDFZ�`HKi?UKi?�oH�BSYK�� �K*<n»{`VA"ZBA�G\K�Z�`HKMZ:l�Dg_VD[?:Z\EHS2A�Z�Ki?~D�P���=2X�?:Z\K�=2X�· ?c?U_NK�I�=2AFSpG�K�S2A�Z�=2d(=�Z:^/oH�cS2K�� �

¾ ³/³ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�6�gµ&e&D]W]K�GJA"Z\K�e&K�egD/G�^�uj cK�l>Z�D/X�· ?>S@A*lc?�oH¯�A"�]l�K�S2S�· ?>K�h[E�A�Z�=2DFX�?� ª�¬"¨ �V«������V¬ ��­�� ¸�DFG\K�X[Z\��=2X(d"A�G\=2AFX�I�K

Page 155: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/³ ¯�A"�]l�K�S2S�· ?~�;h[E�A�Z�=2DFX�?�o]��S2K�I�Z�G\DFe�A�q/XHK�Z\=2IR»�A*d/K�?�oHA�X�Wm¤(_NK�I�=2AFS�¿~K�S@A"Z\=Yd(=YZ:^ � ¶ �

¶ a>»{`H=@IJ` Z�E�G�XHKiW DFE]Z�Z�D{LNK�e&DFG\K�I�D/G�G\K�I�Zm=2X�G\K�S@A"Z�=2d(=2?UZ�=@Ir_H`(^]?U=@I�?�uz BK�l>Z\DFX�· ?�S@A*lc?�DFG�¯�A"�]l�K�SYS�· ?Kih/EVA"Z�=2DFXV?~A�X�WQl~`(^ �A[<nb>`�K�^ l�K�G\K�LND�Z\` �� � � ����� ��� ¦ � �'� ¦ ?U=2X�I�KzZ\`HK�^ LND�Z\` IJ`VA�XHq/K�W P8D/G�e E�X�W]K�G��� � �� �±Z�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aLN<Qb>`�K�^ l�K�G�K�LVDFZ�` �� � � ��� � ¦ � �'� ¦ ?U=2X�I�K�Z�`HK�^ l�K�G�K LND�Z\` =2X(d*AFG�=@A�X[ZfE�X�W]K�G��� � �� �±Z�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aIi<Q BK�l>Z\DFX�· ? S@A*lc? l�K�G\K � � � ¦ � �'� ¦ ?�=YXVI�K�Z\`HK�^ DFX�SY^ l�K�G�K�=2X(d"A�G\=2AFX/Z E�X�W]K�G��� � �� �±Z�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aWV<Q¯�A"�]l�K�SYS�· ?mK�h[E�A"Z\=YD/X�?�l�K�G\K � � � ¦ � �'� ¦ ?�=YXVI�KrZ�`�K�^�D/XHS2^�l�K�G\K�=YX(d"A�G\=2AFX[ZmE�X�W]K�G��� � �� �±Z�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aK*<Q¯�A"�]l�K�SYS�· ?mK�h[E�A"Z\=YD/X�?�l�K�G\K � � � ¦ � �'� ¦ ?�=YXVI�KrZ�`�K�^�D/XHS2^�l�K�G\K�=YX(d"A�G\=2AFX[ZmE�X�W]K�G� � � ��� � � Z�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

Page 156: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � � N[1_H ;75<? =!&:cT>a14;<*-H��L&A,�*[&:;<*[?T>

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³ µgh[e4EHS�ZB¾/¾F¾���¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujK�SYKiI$Z�G\DFe�AFqFXHK�Z�=@IBl>A*dFKi?�o[Z�GJA�XV?Ud/K�GJ?UKRl�A*d/K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�Fa~�;SYKiI$Z�G\DFe�AFqFXHK�Z�=@IBl>A*dFKi?�AFG�K/uA[<'��� ��� �� �'� ��� � ��l>A*dFKi?cl~=YZ�`�Z\`HKgK�S2K�I$Z\G�=@IsAFX�W�e�A�q/XHK�Z\=2Is��K�S2W�d/K�I�Z�DFGJ? � � � � � � �zZ\DKiAFIJ`D�Z\`HK�Gia

LN< � � � � � �� � {l>A*dFKi?�l~=YZ�`gZ\`HKcK�S2K�I�Z�G\=2I~AFX�Wge�A�qFX�K�Z�=@I���K�S@W&dFKiI$Z\DFGJ? � � � � � � ��Z�D-KiAFIJ`DFZ�`HK�G�a

Ii< � � � � � �� � l>A*dFKi? l~=�Z\` Z�`�K K�S2K�I�Z�G\=2I A�X�W e�AFqFXHK�Z�=@I ��K�S@W d/K�I$Z\DFGJ?���� �� ��� � ¦ ��� � � Z�D�KiAFIJ`QD�Z�`�K�Gia

WV<���� ��� �� �'� ��� � � l>A*dFKi? l~=YZ�` Z�`HK K�S2K�I�Z�G\=2I A�X�W e�A�qFX�K�Z�=@I �VK�S@W d/K�I$Z\DFGJ?���� �� ��� � ¦ ��� � � Z�D�KiAFIJ`QD�Z�`�K�Gia

K*<nLND�Z\` � � � � � �� � A�X�W � � � � � �� � l>A*dFKi?�u Z\`HKfK�SYKiI$Z\G�=@I���K�S@W�d/K�I$Z\DFGJ?{A�G\KS2DFX�qF=YZ�E�W]=2X�AFS�A�X�WQZ�`�K-e&AFqFXHK�Z�=@IR��K�S@WdFK�I�Z�D/G\?>A�G\KRZ�GJA�X�?�dFK�G\?�KFa

¾ ³ µgh[e4EHS�ZB¾/¾F¾[��¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujS2=Yq/`[Z~?�_NK�K�W=2Xmd*A/I�EHE�e� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]� ³ TJ� ¶

�]a~b>`HK-d"A/I�EHEHe}?U_NK�KiWQDFP�S2=2qF`[ZcW]K�_NK�X�W�?~DFX�uA[<�P8G\K�h[EHK�X�I�^/a LN<jl>A*dFK�S2K�X�q�Z�`�a Ii<�W]=@?:ZJA�X�I�KcZ\G\A*d/K�S2K�Wpa W�<�AFe&_HSY=YZ�EVW]KFa K*<jXHDFZ�`H=2XHq�u=YZc=@?cAgEHXH=2dFK�GJ?\A�SpI�D/X�?:ZJA�X[Z�a

¾ ³ µgh[e4EHS�ZB¾/¾H�i¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj?U_NK�KiWD�P�SY=2qF`[Z�o]l>A*dFK�SYK�XHq�Z\`� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

³ a~b>`HK-G\K�S@A"Z\=YD/XnLNK�Z:l�K�K�X�*�o #�oHA�X�W � =@?�uA[<�* $ # � � aLN<'* $ # � aIi<'* $ � � + # � aWV<'* $ + # � aK*<'* $ # � � a

¾ ³ µgh[e4EHS�ZB¾/¾ ³ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/SYD/G\?�D�P�d(=2?�=2LHSYK-?�_VKiI$Z\G�EHe� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a~b>`HK6I�DFS2DFGJ?�D�P�Z\`HK-d(=2?�=2LHSYK6?�_NK�I$Z\G�E�e =YXmD/G\W]K�G>D�P ��� ¦ � � � ������l>A*dFK�SYK�XHq�Z\`QA�G\KFuA[<CG\K�W�o]DFGJA�XHq/KFo(^FK�SYS2D"l-o]qFG\K�K�X�o(LHSYE�KFoHd(=2DFS2K�Z�aLN<nd(=2DFS2K�Zio]LHSYE�KFoHq/G�K�K�X�o]^/K�S2SYD"l-o]D/G\AFXHqFK/o/G\K�WpaIi<nd(=2DFS2K�Zio]qFG\K�K�X�o]LHSYE�K-^FK�S2S2D"l-o[G\K�W�oHDFGJA�XHq/KFaWV<nd(=2DFS2K�Zio]LHSYE�KFo]P8D/G�Ki?:Z�T�S@A*l~X�o(^FK�SYS2D"l-o(Z\AFXHqFK�G�=2XHKFo]G\K�W�aK*<nd(=2DFS2K�X[Z�oH?UZ�G\=2_VK/o]P8DFG\K�?UZUTkS2A*l~X�o[e&D/E�?UK/o(Z\AFXHqFK�G�=2XHKFo]K��]`�A�E�?UZ�a

¾ ³ µgh[e4EHS�ZB¾/¾ ³ ¾/�s� ¶&³ e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�v�A�X�A/W]=@A�XC�NA�q&=YXmG\K�WQSY=2qF`[Z

Page 157: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia ³ µ��;SYKiI$Z�G\DFe�AFqFXHK�Z�=@IR¿cA/W]=@A"Z�=2DFX � ¶F³

� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]� ³ T:�/º¶ a~b>`HK4v�AFX�AFWH=2AFXC�VAFqg=2XmDFGJW]=2X�A�G\^�SY=2qF`[Z\=YXHq&=@?>G�KiWmA�X�WQl~`H=YZ�KFaj»{`�K�X�d(=YK�l�KiWn=2XG�KiWQS2=2qF`[Z~=�Zc=@?�u

A[<cAFSYS�l~`H=�Z\KFa LV<cG�KiW�A�X�W�L�S2A/IJONa I�<BA�S2S�G\K�W�a W�<RA�S2S�LHS@AFIJO�a Ki<~G\K�W�A�X�W�l~`�=�Z\K?UZ�=2S2S�a

¾ ³ µgh[e4EHS�ZB¾/¾ ³ ¾�µn� ³ �MK�A/?U^�e�A�Z�`�u;AgGJAFW]=2Dgl�A*d/K�S2K�XHqFZ�`QI�A�S@I�EHS@A"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]��µ�T ³ º

¹ a~�{GJAFWH=YD-?UZ\A"Z\=YD/X&LHG�D[AFWHI�AF?UZ\?jA�Z ¹ ¾F¾�O(£B�-58O(=YS2DF`�K�G�Z��i<�a���=2dFK�XgZ�`�A�Z�Z�`HKR?U_NK�KiW4DFPpSY=2qF`[Z�=2XCA�=2Gj=2?�Z\D6qFD(D]WAF_H_HG\D*�(=2e�A"Z\=YD/X ³ � ¾ �x�i¾�e��"?�o]Z\`HK-l�A*d/K�S2K�XHqFZ�`QD�P�GJAFWH=YDgl�A*d/K�?�=@?

A[< ¶ ¾/¾jema LN< ¹ ¾F¾�ea Ii<>¾ � ¾F¾[��ema WV< ³ � ¾ ����¾ �ema Ki<>¾�ea

¾ ³ µgh[e4EHS�ZB¾/¾ ³ ��¾C�&�s�4K�A/?U^�e&K�egD/G�^�uj=2X(dFK�GJ?�K�T!?�h[E�AFG�KcS@A*lº(a~b>`HK-=2X[Z�K�X�?U=YZ:^�P8G\DFe�A&_NDF=2X[Zc?UD/EHG\I�KMD�P�S2=2qF`[Z~P,A�S2S2?>D ��l~=YZ�`mG\A/W]=2E�? S2=YO/KFu

A[<�� � a LN<�� � �Fa I�<�� � � a WV<�� � �/a Ki<�� � � a

¾ ³ µgh[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D/X�?�oHWHA�XHq/K�G\DFE�?�o(DFG\q/AFXH=2IBe&DFS2K�I�E�SYKi?� ª�¬"¨ �V«������V¬ ��­��  cK�KiWH?>Z\DgLNK6I�D/G�G\K�I�Z�KiW�P8DFGcP,AF?UZ>K�SYKiI$Z\G�D/X�?�a

¼ a>»{`(^n=@?~�c´ AFX�W`H=2qF`HK�G>P8G�Kih/E�K�X�I�^CK�S2K�I�Z�G\DFe�A�q/XHK�Z\=2IRG\A/W]=@A"Z�=2DFXWHA�X�qFK�G\DFEV?;Z\D�SY=YP8K��A[<nb>`�Ks_H`HDFZ�D/X�?~D�P;?�E�IJ`�`H=2qF`mP8G\K�h[EHK�X�I�^GJAFW]=@A"Z\=YD/X � � ?:Z\G�D/XHqCK�X�DFEHq/`mAFX�W�DFP Z�K�X�_NK�X�K�Z�GJA"Z\=YX�qK�XHDFE�qF`�Z\DtL�G�KiA�OwZ�`�KxLNDFX�W�?mD�PsD/G�q[A�XH=@I�e&DFS2K�I�EHS2K�?=YX I�K�SYS@?�a}¤(E�IJ`zegD/SYKiI�EHS@A�G�WHAFe�A�qFK±5 Z\D¡� B��=2X _�A�G�Z�=@I�E�S2AFGJ<mI�A�XfW]Ki?:Z\G�D"^�P8EHX�I�Z�=2DFX AFX�W S2K�AFW�Z\D�e4E]Z\A�Z�=2DFX�?xA�X�W I�A�X�I�K�GJ?�a ¸�D"l�K�GP8G\K�h[EHK�X�I�^±GJAFW]=@A"Z\=YD/X±X�D�e�A"ZUZ\K�GQ`HD"l}=2X[Z�K�X�?UK�=2?nE�?UEVA�S2SY^±esE�IJ`{S2K�?\?nW�A�XHq/K�G\DFE�?&LNK�I�A�E�?�K�Z�`�K_�`HD�Z\D�T!W]=2?\AF?\?�D(I�=2A�Z�=2DFXCLNDFXVW(T�L�G�KiA�O(=YX�q4_HG\D]I�Ki?�?>=@?>E�?�E�A�S2SY^QA�?U=2XHqFS2K�Tk_H`HDFZ�D/XQA�LV?UD/G�_]Z\=YD/Xn_HG\D]I�Ki?�?�a

LN<Qb>`�KR_H`�D�Z�D/X�?�D�P�?�E�IJ`Q`H=Yq/`CP8G\K�h[EHK�X�I�^�GJAFW]=@A"Z\=YD/X � � � � f?UZ�G\DFXHq4K�XHD/EHqF`A�X�WnD�P Z\K�X � � _NK�X�K�Z�GJA"Z\=YX�qcK�XHD/EHqF`MZ\DcLHG\K�AFOcZ�`�K�LVD/X�WH?�D�P]DFG\q/AFXH=@I�e&D/SYKiI�EHS2K�?�=YX6I�K�S2S2?�a�¤(EVIJ`-egD/SYKiI�EHS@A�G�WHA�e�A�q/K58Z�D�¡R R��=2X�_�AFGUZ\=2I�EHS2AFGJ<MI�A�X�W]Ki?:Z\G�D"^xP8EHX�I�Z�=2DFX�AFX�WrS2K�AFW�Z�D�e4E]Z\A�Z�=2DFX�?gA�X�W�I�A�X�I�K�GJ?�a�¸�D"l�K�GP8G\K�h[EHK�X�I�^±GJAFW]=@A"Z\=YD/X±X�D�e�A"ZUZ\K�GQ`HD"l}=2X[Z�K�X�?UK�=2?nE�?UEVA�S2SY^±esE�IJ`{S2K�?\?nW�A�XHq/K�G\DFE�?&LNK�I�A�E�?�K�Z�`�KLNDFXVWQL�G�KiA�O(=YX�q4_HG\D]I�Ki?�?>=@?>E�?�E�A�S2SY^QAg?�=2XHqFS2K�Tk_H`HDFZ�DFXmA�LV?UD/G�_]Z\=YD/Xn_HG\D]I�Ki?�?�a

Ii<#��KiI�A�EV?UKM=YZ\?~I�D/SYD/G~=2?>LNK�^/DFX�WQd(=YD/SYK�Z�aWV<#��KiI�A�EV?UKM=YZ\?~I�D/SYD/G~=2?>=2X]P8GJA�G\K�WpaK*<#��KiI�A�EV?UKM=YZcD/?\I�=2SYS@A"Z\K�?>?UD�?�SYD"l~S2^C=YZB?U`VA�OFKi?�DFG\q/A�X�=2IRe&DFS2K�I�E�SYKi?�Z�D&_H=2K�I�Ki?�a

¾ ³ µgh[e4EHS�ZB¾/¾�µV��¾4� ¶ �4e&D]W]K�GJA"Z\KRZ\`H=2XHO(=YXHqVu�?UE�XHSY=2qF`[Z~K�X�K�G\qF^nAFX�Wne&D/egK�X[Z�EHe� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�]��µ�TJ� ½

½ a~�;SYKiI$Z�G\DFe�AFqFXHK�Z�=@ICGJAFW]=@A"Z\=YD/X�Z�GJA�X�?�_NDFG�Z\?gLVDFZ�`±K�XHK�G�q/^�A�X�W�egD/e&K�X[Z�EHe =YXtP,AFI�Z�a ��KiI�A�EV?UK=�Z�K�eg=YZ\?K�SYKiI$Z�G\DFe�AFqFXHK�Z�=@IwG\A/W]=2A�Z�=2DFX l~=YZ�`HD/E]Z±AFX(^ D/E]Z\?�=2WHK�K�XHK�G�q/^fG\K�?�EH_H_HS2^FoQZ�`�K�¤(EHX�esE�?UZ±I�DFX�?UZ\AFX/Z\SY^W]KiI�G\K�A/?UKR=YXnZ�D�ZJA�S�K�X�K�G\qF^�I�D/X/Z\K�X[Z�a�»{`(^CW]D(K�?�Z\`HK6¤(EHXnX�D�Z~W]K�I�G�KiAF?�KB=2XnZ\D�Z\AFS�egD/e&K�X[Z�EHe A/?�?�EHe&=2XHqZ\`�A"Zc=YZc=2?>K��HAFI$Z\SY^Q?U_H`�K�G\=2I�A�S2SY^n?�^(e&egK�Z�G\=2IMAFX�W=2?>e&D"d(=YX�qg=2X�A&?:Z\G\AF=Yq/`/Z>S2=YXHK �A[<n¯�DFe&K�X[Z�E�e =@?�A � ¦&� � � � h[E�AFX/Z\=�Z:^/a b>`HK�K�e&=YZ�=2XHq D�Pre&DFe&K�X[Z\EHe =2X�A�S2S�W]=2G�KiI$Z�=2DFXV?=@?�D�Z�G\DF_�=2I�A�S2SY^�e&K�A�XV?�Z\`HK�XHK�Z�e&D/egK�X[Z�EHe K�eg=YZUZ\K�Wf=2? � � ��� � �� � A�XVW Z�`HK{¤(EHX�· ?�Z�DFZ\A�Se&D/egK�X[Z�EHe W]D(K�?>XHDFZBIJ`�A�XHq/KFa

LN<Q¯�DFe&K�X[Z�E�e =2?wA � ¦ � � h[E�A�X[Z�=YZ:^Fa b>`HKzK�e&=�Z\=YXHq�DFP�e&DFe&K�X[Z�E�e =YX�A�S2S�W]=2G�KiI$Z�=2DFXV?=@?�D�Z�G\DF_�=2I�A�S2SY^Ce&KiA�X�?>Z\`HK6XHK�ZBe&DFe&K�X[Z\EHe}K�e&=�Z�Z�K�W�=2? � �� ��A�X�WQZ�`�K4¤(EHX�· ?~Z\D�ZJA�S�e&D/egK�X[Z�EHeWHD[Ki?>XHD�ZBIJ`VA�XHq/KFa

Ii<Q¯�DFe&K�X[Z�E�e =2?wA � ¦ � � h[E�A�X[Z�=YZ:^Fa b>`HKzK�e&=�Z\=YXHq�DFP�e&DFe&K�X[Z�E�e =YX�A�S2S�W]=2G�KiI$Z�=2DFXV?=@?�D�Z�G\DF_�=2I�A�S2SY^�e&K�A�XV?�Z\`HK�XHK�Z�e&D/egK�X[Z�EHe K�eg=YZUZ\K�Wf=2? � � ��� � �� � A�XVW Z�`HK{¤(EHX�· ?�Z�DFZ\A�Se&D/egK�X[Z�EHe W]D(K�?>XHDFZBIJ`�A�XHq/KFa

WV<Q¯�DFe&K�X[Z�E�e =@?�A � ¦&� � � � h[E�AFX/Z\=�Z:^/a b>`HK�K�e&=YZ�=2XHq D�Pre&DFe&K�X[Z\EHe =2X�A�S2S�W]=2G�KiI$Z�=2DFXV?=@?�D�Z�G\DF_�=2I�A�S2SY^Ce&KiA�X�?>Z\`HK6XHK�ZBe&DFe&K�X[Z\EHe}K�e&=�Z�Z�K�W�=2? � �� ��A�X�WQZ�`�K4¤(EHX�· ?~Z\D�ZJA�S�e&D/egK�X[Z�EHeWHD[Ki?>XHD�ZBIJ`VA�XHq/KFa

Page 158: Introductory Physics Problems David J. Jeffery Department of

� ¶ µ v�`�A�_]Zia ³ µ��;SYKiI$Z\G�D/e&AFqFXHK�Z�=@IR¿BAFW]=@A"Z\=YD/X

K*<Qb>`�K6h/E�K�?UZ�=2DFX=2?>l~G\DFXHqVajb>`HKs¤(EHXZ�DFZ\AFS�A�XHq/EHS2AFG>egD/e&K�X[Z�EHe W]D(K�?~IJ`�AFXHqFK/a

¾ ³ µgh[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�uj_NDFS@A�G\=Y��K�WnSY=2qF`[Z��¾Ha>»{`�A�Zc=2?-5,_�A�G�Z�=@A�S2S2^]<�_NDFS@A�G\=2��K�WnSY=2qF`[ZBAFX�WQI�DFe&_HS2K�Z\K�S2^n_NDFS@A�G\=Y��K�WCS2=2qF`[Z�

A[<n¸�=Yq/`[Zfl~=�Z\` Z�`�K�K�S2K�I�Z�G\=2I ��K�S@W dFKiI$Z�D/G\? _�A�G�Z�=@A�S2SY^ A�X�W I�DFe&_HS2K�Z\K�S2^ AFSY=2qFX�K�W � �� � Z�`�K_�G�D/_�A�q[A"Z�=2DFXW]=2G�KiI$Z�=2DFX�o]G�Ki?U_NK�I�Z�=2dFK�S2^Fa

LN<Q¸�=Yq/`[Z�l~=YZ�`xZ�`HK�K�SYKiI$Z\G�=@I6�VK�S@W�d/K�I$Z\DFGJ?B_VA�G�Z�=@A�S2SY^�A�XVWxI�DFe&_HS2K�Z�K�SY^�AFSY=2qFX�K�W�=2XrAQ?�=YX�qFS2K&WH=YG\K�I�Z�=2DFX���� �� ��� � ¦ ��� � � Z�D&Z\`HK-_HG\DF_�AFq/A�Z�=2DFXnW]=2G\K�I$Z\=YD/X�o]G\K�?�_VKiI$Z�=2dFK�SY^/a

Ii<Q¸�=Yq/`[Z±l~=YZ�`}Z�`HK�K�S2K�I�Z�G\=2I���K�S2W}dFKiI$Z�D/G\?�_�A�G�Z�=@A�S2S2^ A�X�W}I�DFe&_HS2K�Z\K�S2^ A�S2=Yq/XHK�W =YX�A WH=YG\K�I�Z�=2DFX � ��� �� � � �wZ�DgZ\`HK-_HG\DF_�AFq/A"Z\=YD/XQW]=2G\K�I$Z\=YD/X�o]G\K�?�_VKiI$Z�=2dFK�SY^/a

WV<Q¸�=Yq/`[ZQl~=YZ�`{Z\`HKxK�SYKiI$Z\G�=@I���K�S2W�dFK�I�Z�D/G\?�_VA�G�Z�=@A�S2SY^{A�XVW�I�D/eg_�SYK�Z�K�S2^wA�S2=Yq/XHK�W � �� � � � Z�`�K_�G�D/_�A�q[A"Z�=2DFXW]=2G�KiI$Z�=2DFX�o]G�Ki?U_NK�I�Z�=2dFK�S2^Fa

K*<Q¸�=Yq/`[Z>_VA�G�Z�=@A�S2SY^nA�Z>Z�`HK6 BDFG�Z�`�9�DFS2K�AFX�WmI�D/eg_�SYK�Z�K�S2^nA�Z�Z\`HK6 cD/GUZ\`�9�DFS2KFa

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³ µgh/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(We�A"Z\`�u�P8G\K�h[EHK�XVI�^Fo]_NK�G\=2D(W�o�9�G\DBA:KiI$Zc¤(K�A�P,A�G\K�G�Fa~9;G�D A:K�I$Z�¤(K�A�P,A�G\K�Gw58LNK�q[A�X�I�=2G\I�Af� ½F¼ ¾�osK�X�W]K�W �*< l>AF?�A�_HG�D/qFGJA�e Z�D�I�D/X�?UZ�G\E�I$Z�A�X K�XHD/G�e&DFEV?EHXVW]K�G\qFG\DFEHXVW�AFX[Z�K�X�X�AmK��(Z�K�X�W]=2XHq�D"d/K�G���¾ �¾/¾F¾jO(e �iamb>`�KC=2WHK�A�l>AF?�Z\D�E�?�KCdFK�G�^xSYD/XHq�l�A*d/K�S2K�XHqFZ�`GJAFW]=2D�l>A*dFK�?RZ\D�I�D/ege4EHXH=@I�A�Z�K�l~=YZ�`�W]K�K�_HS2^�?�EHLHe&K�G�q/K�Wr?UE�LHe�A�G\=YXHKi?�ar5,¯�DFG\K�XHDFG\e�A�SjS2K�XHqFZ�`�GJAFW]=2Dl>A*dFKi?�WHDFX�· Zc_VK�XHK�Z\G\A�Z�K-W]K�K�_HS2^n=2X[Z�D�I�D/X�W]E�I�Z�DFGJ?�SY=2OFK6?�K�A4l>A"Z�K�G�a <A[<C7kP�Z�`HK�l>A*dFK�S2K�X�q�Z�`nl�K�G�KBZ�DgLVK&��¾��R��A�G�Z�`CGJAFW]=2=�l~`�A"Z>l�DFEHS@W�Z\`HK�P8G�Kih/E�K�X�I�^gLNK���5,b>`HKMGJAFW]=2E�?�D�PZ\`HK6�;AFGUZ\`Q=@?~A�LNDFEHZ ¹F³ º�¾jO(e �±Z\`�A"Zi· ?�O(=YS2DFe&K�Z\K�GJ?>XHD�Zce&K�Z�K�GJ?�a <

LN<n»{`VA"Zcl�DFEHS@WCZ\`HK-_NK�G\=YD]WLVK �

¾ ³ µgh/P8EHS2S�¾/¾/��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�P8G\K�h[EHK�X�I�^Cl~=@W(Z\`�o���?UZ~DFGJW]K�GcAF_H_HG\D*�]=Ye�A"Z\=YD/X�]a~� _VA�G�Z�=@I�EHS@A�G-`HK�SY=2EHegTkXHK�D/X�S@AF?�K�GsK�e&=�ZJ?6S2=Yq/`[ZsA"Z ¹F³ � � ¼ XHe l~=YZ�`�Aml>A*dFK�SYK�XHq�Z\`xl~=@W(Z\`�D�Pc¾ � ¾H�i¾jXHema»{`�A�Zc=2?�Z\`HK6I�D/G�G\K�?�_NDFX�W]=2XHq4P8G�Kih[EHK�X�I�^Cl~=@W(Z�` �

¾ ³ µgh/P8EHS2S�¾/¾/�]�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u;¤(D/S2AFG~I�DFXV?:ZJA�X[Z�oH9;SYE]Z\D³ a~b>`HKzZ�DFZ\AFSS2EHe&=2XHD/?�=�Z:^�DFP�Z�`HK ¤(E�X�=@? ³ � ¼/¹ � �i¾�� !�» AFX�W�Z�`�K�e&KiA�X ¤]EHX]T!�;A�G�Z�`}W]=2?UZ\AFX�I�Kz=2?� � µ ½F¹ �x�i¾ � �VemaA[<C»{`VA"Zc=@?�Z�`HK-K�XHK�G\qF^��VE]��5,=�a KFa2oHK�X�K�G\qF^�_NK�GcEHX�=�Z~Z\=Ye&K-_NK�GcEHX�=�ZBAFG�KiA/<�A"Z~Z�`�K6�;A�G�Z�` �LN<��=2dFK�X�Z�`�Kg9;SYE]Z\DC=@?RA�Z�A�LNDFEHZRµ/¾;�~��58=�a KFa2oNµ[¾CAF?UZ�G\DFX�DFe&=2I�A�S�E�XH=�ZJ?�DFGBµ[¾&Z�=2e&K�?RZ�`�Kg¤(EHXHTk��A�G�Z�`

WH=2?UZ\AFX�I�K*<$oHl~`�A�ZcA�_H_HG\D*�]=Ye�A�Z�K�S2^�=@?>Z�`HK-K�XHK�G\qF^&�VE]�A�Z~9;SYEHZ�D �

¾ ³ µgh/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�uj_NDFS@A�G\=Y��K�WQSY=2qF`[Z>Z�GJA�XV?Ue&=@?�?�=YD/Xµ�a~� I�DFe&_HS2K�Z�K�SY^�_VD/S2AFG�=2��KiW�LNK�A�e D�P>SY=2qF`[Z-D�P�=YX[Z�K�X�?�=�Z:^��i¾j» �"e �g=@?-?UK�X[Z�Z\`HG\DFEHq/`�AFXx=@W]K�AFSj_VD/S2AFG�=2��K�G?�K�ZBA�Z~AFXAFXHqFS2KMD�P�µ ¶ �RP8G�D/e Z�`HK-_NDFS@A�G\=2��A"Z\=YD/XQW]=2G\K�I$Z\=YD/X�aA[<C»{`VA"Zc=@?�Z�`HK-=2X[Z�K�XV?U=YZ:^nDFP�Z�`�KMZ�GJA�X�?�e&=�Z�Z�K�WLNK�AFe �LN<n7kP�Z\`HK~LVKiA�e l�K�G�K~I�D/e&_HSYK�Z�K�SY^4EHXH_NDFS@A�G\=Y��K�W4l~`�A"Z�l�DFEHS@W4Z�`HK~=2X[Z�K�X�?U=YZ:^sDFPVZ\`HK~Z\G\AFX�?Ue&=YZUZ\K�WgLVKiA�e

LNK��

¾ ³ µgh/P8EHS2S�¾���¾F¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�Z\DFesLmGJA�=@W]K�Gio(G\A/WHA�G� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¼/³ �Hu ¹ µ[<

¶ a>7!Xx^FDFE�GBXHK�l A:DFL�A/?RAnqFGJA*dFK-G\DFLHLNK�G��{AF`�oVZ�DFe4L�GJA�=@W]K�G��wLNK�?�=@W]K�?cZ�`HKgXHK�I�K�?\?�AFG�^²MEHXHqnP8Ex?�O[=2S2S�AFX�WAFLH=YS2=YZ:^�Z\D�G�KiAFW�¤(EHe&K�G�=@A�X�I�EHXHK�=YP8DFG\emo�^FDFEre4E�?:Z&A�S@?UD�LNKQAFLHS2K&Z�DxWHK�Z�K�G�e&=2XHK�Z\`HKnW]=2e&K�X�?�=YD/X�?6DFPcA

Page 159: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Zia ³ µ��;SYKiI$Z�G\DFe�AFqFXHK�Z�=@IR¿cA/W]=@A"Z�=2DFX � ¶/¶

Z\DFesL�EV?U=2XHqCGJAFWHAFGs58=�a KFa2o�Z\DFesL�G\A/WHA�G$<$a>� GJAFWHAFGc_HEHS@?�Ks?UK�X[ZR?:Z\G\AF=Yq/`[ZRW]D"l~X�l~=2SYS�?UK�X/ZRL�AFIJOmA�_�AFGUZ\=2AFSG\K���KiI$Z\=YD/X�58=�a K/aYojKiIJ`HD[<-A�Z4K�dFK�G\^�=2X[Z�K�GUP,A/I�KFa�¤]A*^�GJAFWHAFGs?�_VK�K�W�=@?n�i¾ � ¾�I�e��"X�?M=YXt?UD/=YS�o>��¾ � ¶ I�e �"X�?-=2X9�K�X/Z\K�S2=2Ime�AFG�LHS2KFo~AFX�W ³ ¾�I�e �"X�?&=2X�A�=2G�58_HE]Z\G�=@Wpo>��SYZ�`(^wA�=2GJ<�a�»{`H=2S2K�?UKiA�GJIJ`H=2XHq�P8DFG�Z\`HK�S2D/?UZ���X�A�SG\K�?UZ�=2XHq�_�S2A/I�K�DFP4¡RG\A/I�DFXwZ\`HK�ºiZ�`�I�K�X/Z\EHG\^ �cv�AFG\IJ`�DFX{D�Ps��Z\`HK�XV? �{^FD/E�· d/K�`HKiA�GJW{D�Ps¡RGJAFI�D/XH=@A�XS2K�q/=2?�S2A�Z�=2DFX�D/XHKsAF?\?�EHe&K�? �w^/DFEme&K�AF?�EHG\K-Z�`�K6P8DFS2S2D"l~=YXHqQWHA"ZJA �wZ�`HG\D"l~=YX�q�DFE]ZcZ\`HKsE�XH=YX[Z\K�G\K�?UZ�=2XHqnLH=YZ\?S2=YO/K�Z�`HKMZ\G�EHK6?\I�=2K�X[Z\=2?UZ~^FDFEmA�G\KFa

�;IJ`�Dg¿~K�Z�EHG\X�b>=Ye&Ki?c�cS2DFXHq�A �HTk_ND/?�=�Z\=YD/Xm¸�=YX�K

� � 5,X�?J<�� ��T�_ND/?�=YZ�=2DFX�58eC< ¾ � � ��¾ �H� �F�

� XHDFXHK ¼ ¾ � � ¼ ¾ � ¶ ¼ ¾ � µ ¼ ¾ � ¹ X�DFXHK� � ¹ µ � ³ ½ ¾ � ¼ ½ ¾ � � �*º�¾ � ¾³ �F�F� � ¾ �F�i� � ¾µ �i�F� � º �i�]� � �

A[<C»{`VA"Zc=@?�Z�`HK6W]K�_]Z�`mZ\DgZ�`HKMZ\DF_mD�P�Z�`HKMZ\DFesL �LN<n»{`VA"Zc=@?�Z�`HK6W]K�_]Z�`mZ\DgZ�`HK-LND�Z�Z�DFe}D�P�Z�`HKMZ\DFe4L �Ii<Q£BD"l�Z\`H=2IJOA�G\KBZ\`HKM��D(DFGcAFX�WI�K�=2S2=YXHq�DFP�Z\`HKMZ�D/esL �WV<n»{`VA"ZBA�G\K�Z�`HK-`�K�=2qF`[ZcA�X�WQSYK�XHq�Z\`mD�P�`HDFS2SYD"l�_�A�G�Z~D�P�Z�`HK6W]KiA"Z\`IJ`�AFesLNK�G �K*<Q£BD"l�A�G\K6^FD/E�qFDF=2XHq&Z\DnK�?\I�AF_VK6Z�`HKgA�X�I�=YK�X/Z�`HDFG\G\DFG~^FD/E�`�A*dFK6A*l�DFO/K�X � ������ � ²MEHX�q�P8E�W]D(K�?X�D�Zcl�DFG\O�DFXLHSYD(D]W(T!W]G\=YXHO(=2XHq�?U_NK�I�Z�K�G\?�a

Page 160: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � �'14? =!1 ;75 *-H^&TN � 9S;<*IHJE

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³[¶ h[e4EHS�ZB¾/¾H�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujq/K�DFe&K�Z�G\=2I�A�S�DF_]Z\=2I�?�oHI�S2A/?�?�=@I�A�S�_�AFGUZ\=2I�SYKi?�Fac��K�DFe&K�Z\G�=@I�AFSpDF_]Z\=2I�?�Z�G\K�A"ZJ?>SY=2qF`[Z~=2Xe�AFX[^nG�Ki?U_NK�I�Z\?~AF?>=YP�SY=2qF`[ZBI�D/X�?�=2?UZ�KiWnDFP:u

A[<nAgd/K�I$Z\DFG>��K�S2W�?�aLN<QA&?\I�AFS2AFG��VK�S@WH?�aIi<QI�SYE�eg_V?~D�P�K�S2K�I$Z\G�=@I-IJ`�AFG�q/KFaWV<QI�S2A/?�?�=@I�A�S�_�AFGUZ\=2I�SYKi?�aK*<nG\K�=2X�W]K�K�Gia

¾ ³[¶ h[e4EHS�ZB¾/¾/�F¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujd"A�S2=@W]=�Z:^nD�P�qFK�D/e&K�Z�G\=@I�A�S�D/_]Z�=@I�?�]ac��K�DFe&K�Z\G�=@I�AFSpDF_]Z\=2I�?~A�_H_HS2=2K�?>l~`HK�X�u

A[< � � � ���z�-l~`HK�G\K���=@?cA�X=2G�G\K�S2K�d"A�X[Zc?�=Y��KM?\I�AFSYK/aLN< � � � � �z�-l~`HK�G\K���=@?cA�X=2G�G\K�S2K�d"A�X[Zc?�=Y��KM?\I�AFSYK/aIi< � � � � � �sl~`HK�G�K � =@?MAn?�=Y��K4?\I�A�S2K4IJ`VA�GJAFI$Z\K�G\=2?UZ�=@I-DFPjZ�`HKgDFL,A:KiI$ZJ?RD/GRAF_VK�GUZ\EHG�Ki?RAnSY=2qF`[ZMLVKiA�eK�X�I�D/EHX[Z�K�G\?�a

WV< � � � $ �Ml~`HK�G\K��}=@?~A�Xm=2G�G\K�S2K�d"AFX/Z~?�=Y��KM?\I�AFSYK/aK*< � � � ��� �sl~`HK�G�K � =@?MAn?�=Y��K4?\I�A�S2K4IJ`VA�GJAFI$Z\K�G\=2?UZ�=@I-DFPjZ�`HKgDFL,A:KiI$ZJ?RD/GRAF_VK�GUZ\EHG�Ki?RAnSY=2qF`[ZMLVKiA�eK�X�I�D/EHX[Z�K�G\?�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³[¶ h/P8EHS2S�¾/¾H��¾/¾g� ¶ ¾ge&D(WQZ\`H=YX�O[=2XHqVujG�K�P8G\A/I$Z�=2DFXnZ�`HG\DFE�qF`mA4q/S2A/?�?>_VA�XHK�Fa~9;G�D"d/K�Z\`�A"Z�A-LVKiA�e�=2X�I�=@W]K�X[Z;D/XCA-_�AFXHKcD�Ppq/S2A/?�?jK�e&K�G\qFK�?�_�A�GJA�S2SYK�S]Z�Ds=�ZJ?�DFG\=2qF=2X�A�SH_VA"Z�`�L(^&W]=@?U_HS@AFI�K�Wpa»{`�A�ZC=2?gZ\`HK�K��]_HG\K�?\?�=YD/X�P8DFG&Z\`HK�_VK�G�_NK�XVW]=2I�EHS@A�GCW]=@?:ZJA�X�I�K ��LVK�Z:l�K�K�XtZ�`HK�D/G�=2qF=2X�AFS�AFX�WtWH=2?�_HS@AFI�KiW_�A�Z�`�?RqF=2dFK�XmZ�`�A�Z��C=@?BZ�`HKg=YXVI�=@W]K�X[Z�AFXHqFS2KFo �r=2?BZ�`�KsG\K�S@A"Z�=2dFKs=YX�WHK���D�P�G\K�P8GJAFI�Z�=2DFX�58=�a KFa2oVZ\`HKs=2X�W]K���D�PG\K�P8GJAFI�Z�=2DFX�D�PRqFS@AF?\?sW]=2d(=2W]KiW�L(^�Z�`�A�ZgDFPBA�=2GJ<�o�A�X�W 0 =2?sZ�`�KnZ\`H=2IJO(XHKi?�?4D�P~Z\`HK_�A�XHK � »{`�A"Zg=2?4Z\`H=2?K��(_�G�Ki?�?�=YD/Xn=2XZ�`HK6?�e�A�S2S�A�XHq/SYK-A�_�_HG�D*�]=2e�A"Z�=2DFX � ������ � ¡BGJA*lzA&W]=@A�q/G\AFea

¾ ³[¶ h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu;�*T!WQI�DFG\XHK�G>G\K���KiI$Z�D/G�]a ��D/EQ`�A*d/K-I�DFG\XHK�G�G\K���KiI$Z\DFGia�b>`�=2?~I�DFX�?�=2?UZ\?>DFP�Z:l�D&eg=2G\G�D/G\?�A"Z�Z\AFIJ`�K�WnZ�D&K�A/IJ`nD�Z\`HK�GcA�ZcA4G\=2qF`[ZcA�XHq/SYK/a

A[<Q¤HA*^gAsLVKiA�e�D�PpS2=Yq/`/Z�P8G�D/e�=YX]�VXH=�Z:^&K�X/Z\K�GJ?jZ\`HKRI�DFG\XHK�G�G�K���K�I�Z�DFG;=YXnAs_HS@A�XHKc_NK�G\_NK�X�W]=@I�E�S2AFG;Z\D6Z�`�KZ:l�D�e&=YG\G\DFGJ?�u�=�a KFa2oHZ�`�Ks_HG\DFLHS2K�e}=2?BDFXHS2^QA�Z:l�DFTkW]=2e&K�X�?�=2DFX�AFSpDFXHK/a>b>`�K6LVKiA�e G�K���K�I�Z\? � � ¦ AFX�W4Z�`HK�X&K��]=�ZJ?jqFD/=YX�qRD �CZ�DM=2X]��XH=YZ:^4»{`VA"Z�=@?�Z�`HK>Z\D�Z\AFS�A�X�qFEHS@A�GjW]K���K�I�Z�=2DFX&D�PNZ�`HK~LNK�AFe P8G\DFe =YZ\?=2XH=YZ�=@A�S�_VA"Z�` ��5� cD�Z\K6A�XHq/EHS@A�G~W]K��VK�I$Z\=YD/Xm=2?>Z\`HKsAFXHqFS2KMLVK�Z:l�K�K�XZ�`HK-_VA"Z�`Z\`HK6LNK�A�e}l�D/EHS@Wn`�A*d/KP8D/SYS2D"l�K�W�=YP;XHDFZ6W]K���KiI$Z\K�W�A�X�W�Z�`HK&_�A�Z�`�=YZ6AFI�Z�E�AFSYS2^�W]D(K�?RP8DFS2S2D"l-as�B?�O�=�P�Z�`H=@?M=@?RX�D�Z-_VK�GUP8KiI$Z\SY^I�SYKiA�Gia <s�wqFK�XHK�GJA�S(G\K�?�EHS�Zj=@?jG\K�h[EH=2G�KiWpu�^FD/EgAFG�K � � AFSYS2D"l�KiW-Z\D6AF?\?UEHe&K�Z�`VA"Z�LNK�A�ef=2?�WHK���KiI$Z�KiWA�Z�KiAFIJ`�e&=YG\G\DFG�L(^ ½ ¾ ��a ������ � »{`VA"Z�=@?jZ\`HKMA�XHq/EHS2AFG;W]K���K�I�Z�=2DFX�DFXnK�AFIJ`�G\K��VK�I$Z\=YD/X �£cD"l{I�AFXZ\`HK�^�LNKgG�K�S2A�Z�K�W�L(^q/K�D/egK�Z�G\^��{¤(EHe�Z�`�K�?�KgAFXHqFS2K�?Re�A�O(=YX�qQ?�EHG�KsZ�`�A�Z�^/DFE�I�DFE�X/ZRZ�`HK�e =2X�Z�`�K?\A�e&K-?�K�X�?�KFu�=�a K/aYo�I�DFEHX[Z\K�GJI�S2D(IJO(l~=@?UK�DFGcI�SYD]IJO(l~=@?UK/o[L�E]ZcXHD�ZcLND�Z\`ml�A*^]?�a

Page 161: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³[¶ ��K�D/e&K�Z�G\=@I�A�S�°R_HZ�=@I�? � ¶ º

LN<Q BD"l ?�A*^�Z�`�A�Zg^/DFErZ\=Y_t^FDFE�GsI�D/G�XHK�GsG\K���KiI$Z\DFG4?�D�Z\`�A"Z4Z�`HKmI�D/G�XHK�G6=@?4A�ZsZ�`�KQLND�Z�Z�DFe AFX�WrZ�`�KG\K��VK�I$Z\DFG-=@?6?�^[e&e&K�Z\G�=@I�AFS�A�LNDFE]ZsAmd/K�G�Z�=@I�AFS�A��]=2?�a)��DFE���S2SjZ\`HKCG\K���KiI$Z�D/GMl~=�Z\`�l�A�Z�K�G6A/?�?�EHe&=2XHqZ\`HK�G\Kn=@?s?�DFe&KCK�X�W�_�AFXHK�?6Z�Dx`HDFS@WrZ�`�Knl>A"Z�K�G6=2X�a�7!X�Z\`H=@?4I�AF?�K�l~`�A"Zg=2?sZ�`HKnZ:l�DFTkWH=Ye&K�XV?U=2DFX�AFSWHK���KiI$Z�=2DFX�AFXHqFS2KgP8DFGsALNK�A�e I�D/eg=2XHq�=2X�P8G�D/e =YXH��XH=YZ:^Fo�G�K���K�I�Z�K�WxZ:l~=@I�K/o�A�XVW�WHK���KiI$Z�KiW�DFE]Z-Z\D=2X]��X�=�Z:^�� ������ � ¿~K�W]EVI�K�Z\`HK�_HG\DFLHS2K�e�Z�D�Z�`�A�ZnD�P-_�AFGUZ�5�A/<�AFX�Wwe�A�OFK�EV?UK�DFPMZ�`HK�S@A*l D�PG\K�P8GJAFI�Z�=2DFX�a

¾ ³[¶ h/P8EHS2S�¾/¾ ³ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�Z\`HK-G\AF=YX(LND"l-o(P8D]I�E�?\?U=2XHq� ª�¬"¨ �V«������V¬ ��­�� ?:ZJA"Z�=2DFXVA�G\^�_VD/=YX[Z\?

³ a ��D/E�`�A*d/KsAn?�_H`HK�G�=@I�AFS�W]G\DF_�DFP;l>A"Z�K�GRAFX�W�W]GJA*l AC`HD/G�=2��D/X[Z\A�S�A"�]=@?~Z�`�G�D/EHqF`�=YZ\?MI�K�X[Z�K�G�aM�fLNK�AFe�D�PS2=Yq/`[Z�Z\G\A*d/K�S@?�Z\DgZ�`HKMG\=Yq/`/Z~A�XVWn=@?>_�A�GJA�S2S2K�SNZ�DgZ�`�KMA��]=2?�a�7kZ~?UZ�G\=2OFK�?�Z\`HK-W]G�D/_A�Z>AFXAFXHqFS2K �4G\K�S@A"Z\=Yd/KBZ\DZ\`HKsXHD/G�e�AFS�Z�DnZ�`HKgW]G\DF_�ac7!XV?U=@W]K6Z\`HK4WHG�D/_mZ�`HK4LVKiA�e�=2?�W]K���K�I�Z�K�W�A"Z�AFX�A�XHq/SYK � � � � �>G�K�S2A�Z�=2dFK-Z\DCZ�`�KXHD/G�e�AFSpE�?U=2XHqgZ�`�K-E�?UEVA�Sp=2X�I�=@W]K�X[Z�y*G\K�P8GJAFI$Z\K�WQLVKiA�e�I�DFX(dFK�X[Z�=2DFX�?�a�¡RGJA*lzAgLH=2q�o�I�SYKiA�G~W]=@A�qFGJA�emaA[<n�R?U=2XHq qFK�DFe&K�Z\G�^ 5,KFa q�a2o4Z\`HK{=@?UD[?�I�K�S2K�?�Z�G\=2AFXHqFS2K�Z\`HK�D/G�K�eC<$o�A�X�WfZ�`�K±S@A*lc?xD�PQG\K��VK�I$Z\=YD/X AFX�WG\K�P8GJAFI�Z�=2DFX±��X�W{AFX{K��]_HG\K�?\?U=2DFXw=2XwZ�K�G�e�?CDFP���DFXHS2^�P8D/G�Z�`�K�Z�DFZ\AFSBA�XHq/EHS@A�GnW]K���K�I�Z�=2DFX � � � � D�PZ\`HKmLVKiA�e P8G\DFe =�ZJ?&=YXH=YZ�=@A�S~_VA"Z�`tP8DFGgZ\`HK�I�AF?�KQZ�`�A�ZgZ\`HKmLVKiA�e G\K��VK�I$ZJ?gDFX�I�K=2X�?�=2WHKQZ\`HK�W]G\DF_AFX�WmZ\`HK�X�K�e&K�G\qFK�?�a ������ � |�=2X�W�Z�`HKgW]K���KiI$Z\=YD/X�P8G�D/e�Z\`HK4I�EHG\G�K�X/ZR_�A"Z\`�P8DFGRK�AFIJ`�K�dFK�X/Z&58=�a K/aYoG\K�P8GJAFI�Z�=2DFXQDFG~G\K���KiI$Z�=2DFXN<�AFX�Wm?UE�e Z�`�K�?�KFa

LN<Q|�=2X�WmZ\`HKsK��(_�G�Ki?�?�=YD/XmP8DFG���Z�`�A�ZRe�A�O/K�? � � � �B?UZ\A"Z\=YD/X�A�G\^Fa~7:?cZ�`H=@?�?:ZJA"Z�=2DFXVA�G\^n_NDF=2X/ZMA�e�A"�]=2esEHeD/GBe&=2XH=Ye4EHe�DFGcX�K�=YZ�`HK�G�� cD"l���X�W�AFX�K��]_HG\K�?\?U=2DFXP8D/GcZ�`�K4?UZ\A"Z\=YD/X�A�G\^ � � � ��a ������ � ��DFE�l~=2SYSX�K�K�WQZ\`HKMP8DFG\esEHS@A

�� �?�=2X � � 5 � < $

�+ � , � �

� �� �

Ii<��=2dFK�X � � � � $�� � ¾/¾F¾[� ½ 5,A�Z�¤]b~9�<pA�X�W � � � � � � $ � � ³/³F³ 5�A"Z��F¾ ��<$o"l~`�A�Z�=2?�Z�`�K;X(EHe&K�G\=2I�A�S[?:ZJA"Z�=2DFXVA�G\^� � � � =YX�W]K�qFG\K�K�?�a��cS@?UD�l~`�A�Z~=2?-� ¼ ¾�� , � � � � a

WV<Q��Z~A�X(^&?:ZJA"Z\=YD/X�A�G\^4_NDF=2X[Z�o]W]D(K�?�AMP8EHXVI$Z�=2DFXQd"A�G\^gI�DFe&_�A�GJA"Z\=Yd/K�S2^gh[EH=@IJO(SY^gDFG�?US2D"l~S2^gl~=YZ�`nG�Ki?U_NK�I�ZZ\D�=�ZJ?~A�G\qFEHe&K�X/Z �

K*<n7kP�AsGJA�XHq/KcD�P�LVKiA�e�?�D�P�d"A�G\^(=YX�qsA�XHq/SYK�A�G\KBG\K�W]=2G\K�I$Z\K�W�=2X[Z�D&A6X�AFG�G\D"l�K�G�LNK�AFeo]l~`VA"Z�l�DFE�S2WCZ�`�A�ZLNK6I�AFSYS2K�W �

P\<m¡RK�?\I�G\=2LVK-`HD"l�Z�`HK6WHG�D/_�· ?�K.�NKiI$ZcDFXmLNK�AFe&?>DFP�S2=2qF`[Z~G�Ki?UEHSYZ\?>=2X�AgG\AF=YX(LND"l-a

Page 162: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � Q�>W;7145\@ 145\1)>�H^1

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³/¹ h[e4EHS�ZB¾/¾H�i¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�=YX[Z\K�G�P8K�G\K�X�I�K�Fa �\¸�K�Zi· ?�_HS@A*^ �]1J� D+�"����# 1 |�DFG �(�i¾F¾HoNZ\`HK�A�X�?�l�K�GR=@?�uR7kZ-`�AF_H_VK�X�?�l~`HK�X�^FD/E�e&=Y��l�A*d/K�?BD�P A:EV?:Z6A�LNDFEHZAFX[^nl�A*d/KR_H`�K�XHD/egK�X�AHa �A[<C»{`VA"Zc=@?�P8G�=@I$Z\=YD/X�o��cS2K�� �LN<n»{`VA"Zc=@?~A�I�DFX[ZJAFI$Z>P8D/G\I�KFo]�cS2K�� �Ii<n»{`VA"Zc=@?>_VD/S2AFG�=2��A�Z�=2DFX�oH�BSYK����WV<n»{`VA"Zc=@?�Z�`HK-_HG\=2egK6WH=YG\K�I�Z�=2dFKFoH�BSYK�� �K*<n»{`VA"Zc=@?>=YX[Z�K�GUP8K�G�K�X�I�K/oH�cS2K�� �

¾ ³/¹ h[e4EHS�ZB¾/¾/�F¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�?�EH_NK�G\_VD[?U=YZ�=2DFX_HG\=YX�I�=Y_�SYK�]a~b>`HK�?�EH_NK�G\_VD[?U=YZ�=2DFX�_HG\=YX�I�=Y_�SYKg=2?MXVA�e&KgP8DFGMZ�`�K4P,A/I$ZMZ�`VA"Z-l�A*d/K�?BZ�`�A�ZsA�G\Kg?�E]�CI�=2K�X[Z\SY^�?�e�A�S2S�I�A�X�LNKA/WHW]K�W�uA[<CS2=2XHK�AFG�S2^FaLN<Qh[E�A/W]GJA"Z�=@I�AFSYS2^FaIi<n=2X(dFK�G\?�K�S2^FaWV<nX�K�q/A�Z�=2dFK�SY^/aK*<Q?�=2X�I�K�G�K�SY^/a

¾ ³/¹ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj=2X[Z�K�G�P8K�G\K�XVI�KMI�G\=�Z\K�G\=YD/X³ a>7!X[Z�K�GUP8K�G�K�X�I�KgA�X�WxW]= �NGJAFI�Z�=2DFX�K.�NKiI$ZJ?�AFG�Kg?Ue�AFSYS�P8DFG-ACl>A*dFKsP8G�D/X[ZRLHG\K�AFO[=2XHqQDFL�?UZ\A/I�S2KsDFGMA�_NK�G�Z�E�G�K4D�PIJ`�AFG\A/I$Z\K�G\=2?UZ�=@IR?�=2��K ��l~`HK�X�uA[< � � � � �z�/aLN< � � � $��/aIi< � � � ���/aWV< � � �����z�/aK*< � � � �z�Fa

¾ ³/¹ h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujd(=@?U=2LHS2K�GJA�X�qFKµ�a~b>`HK-l>A*dFK�SYK�XHq�Z\`nGJA�XHq/KRDFP�`(EHe�A�Xmd(=@?U=2DFX=2?�u

A[<���¾ � µ�]¾ � º � eCaLN< ��¾ � � ��� � ¾ � eCaIi< ��¾ � µ�]¾ � º�emaWV< ��¾ � µ�]¾ � º�O(eCaK*< ��¾ � º �H� � ¶ � eCa

¾ ³/¹ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�h[E�AFX/Z\EHe K�SYKiI$Z�G\D]W]^(X�A�e&=@I�?¶ a~b>`HK-LNK�?UZ~Z�`�K�DFG\^CDFP�K�S2K�I�Z�G\DFe�A�q/XHK�Z\=2?�e O(XHD"l~X=2?

A[<v�S@AF?\?�=2I�A�S�DFGc¯�A��]l�K�SYS2=2AFXQK�SYKiI$Z\G�D]W]^(X�AFeg=@I�?�aLN<Qh[E�AFX[Z�EHe}K�S2K�I$Z\G�D]W]^(X�AFe&=2I�?�5k®��;¡M<$a

Page 163: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¹ 7!X[Z�K�GUP8K�G�K�X�I�K � ¶F½

Ii<Q£BEH^(qFK�X�?�·]_�G�=2X�I�=2_HS2KFaWV<CZ\`HK6£cE�^[q/K�X�?UT!|HG\K�?�XHK�S�_HG\=YXVI�=2_HSYK/aK*<Q²M=2GJIJ`H`HDB�~· ?~?�I�A�S@A�G�Z�`�K�DFG\^CDFP�S2=Yq/`/Zia

¾ ³/¹ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D/X�?~A�XVWnl>A*dFKRZ�GJA�=2X�?¹ aB®RE�AFX[Z�EHe e&K�IJ`VA�XH=@I�AFSV_H`�D�Z�D/X�?�DFG>I�D/`HK�G\K�X[Z>qFG\DFEH_�?;D�P�_H`HD�Z\DFX�?�58_�G�D]W]E�I�K�WnL[^C?UZ�=2esE�S2A�Z�K�WQK�e&=@?�?�=2DFX?�E�IJ`mAF?>D]I�I�EHG\?>e�A/?�?�=Yd/K�S2^�=YXmS@AF?�K�GJ?\<�I�AFXmLVK-=@W]K�X[Z\=���KiWl~=�Z\`QZ\`HK6I�S@AF?\?�=2I�A�S�uA[<Cl>A*dFK�`HD/G\?�K�?�aLN<nl>A*dFK�=2G�D/XQ`HD/G\?�K�?�aIi<nl>A*dFKMW]D/XHOFK�^(?�aWV<nl>A*dFKMIJ`�AFG�=2D�ZJ?�aK*<nl>A*dFKRZ�GJA�=2X�?�a

¾ ³/¹ h[e4EHS�ZB¾/¾[º�¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�I�DF`HK�G�K�X�I�Kº(aBv�D/`HK�G\K�X�I�K�58=2XG\K�q[A�GJW&Z�D�l>A*dFK�_H`HK�XHDFe&K�X�A/<�=@?>Z�`HK-_�G�D/_VK�GUZ:^�DFP�`�A*d(=2XHq�u

A[<CS2DFq/=2I�A�SpI�D/X�?�=2?UZ�K�X�I�^/aLN<QAgGJA�X�WHDFe _H`VAF?�K�G\K�S@A"Z\=YD/XQ=2X�?U_VAFI�KMA�XVWVy*D/G�Z\=Ye&K/aIi<QA&W]K���XH=YZ�K-_H`VAF?�K-G�K�S2A�Z�=2DFXn=2X�?U_VAFI�K-AFX�WVy*D/G�Z�=2egK/aWV<Q?UZ�=@IJO(=YX�K�?\?�aK*<nS2DFq/=2I�A�S�=2X�I�D/X�?U=@?UZ�K�XVI�^Fa

¾ ³/¹ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�uj=2XQ_�`�AF?�K¼ a>7kP�l�A*d/K�?>A�G\K�=YXm_H`�A/?UK/o(Z�`HK�^

A[<nAFG�KM=2X�I�D/`HK�G\K�X[ZiaLN<n`VA*dFK-AgXHDFX]Tk��K�G�Dg_H`�A/?UK-W]= ��K�G\K�X�I�KFaIi<n`VA*dFK-Ag��K�G\Dg_H`�AF?�K-W]= �NK�G�K�X�I�K/aWV<n`VA*dFK-Ag_VK�G�=2D]W]=2IRZ\=Ye&K�Tkd"A�G\^(=YXHq&_H`VAF?�KMWH=���K�G\K�X�I�KFaK*<n`VA*dFK-AgqFD(D]Wnl�DFG\O(=YXHq4G�K�S2A�Z�=2DFX�?�`H=2_�a

¾ ³/¹ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujI�D/eg_�SYK�Z�K6W]Ki?:Z\G�E�I�Z�=2dFKM=2X/Z\K�G�P8K�G\K�X�I�K½ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�uj��K�G\D�a �

A[<C»{`VA"Zc=@?>SYKi?�?>Z\`�A�X�oH�cS2K�� �LN<n»{`VA"Zc=@?~A�I�=2_H`HK�GioH�cS2K�� �Ii<n»{`VA"Zc=@?>DFG\K�Z�`�?�_VK�SYS2K�WQL�A/IJO[l>A�GJWH?�o]�cS2K�� �WV<n»{`VA"Zc=@?�Z�`HK-=2X[Z�K�XV?U=YZ:^nDFP�A�I�D/X�?UZ�G\E�I$Z\=Yd/KR=2X[Z�K�G�P8K�G\K�XVI�KFoH�BSYK�� �K*<n»{`VA"Zc=@?�Z�`HK-=2X[Z�K�XV?U=YZ:^nDFP�A�I�D/e&_HSYK�Z�K-W]Ki?:Z\G�E�I�Z�=2dFKM=2X/Z\K�G�P8K�G\K�X�I�KFoH�BSYK����

¾ ³/¹ h[e4EHS�ZB¾���¾/¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�Z:l�D�T!?US2=YZ�_�A�ZUZ\K�G\X��¾Ha~b>`HKMZ:l�D�T!?�SY=YZ�=2X[Z�K�GUP8K�G�K�X�I�KM_�A�ZUZ�K�G�XP8D/G~d[=@?�=YLHS2KMSY=2qF`[ZBAFX�WCP8D/G~SYD"lzDFGJW]K�GJ?�Z:^(_H=2I�A�S2SY^QA�_H_NK�AFG\?>AF?

A[<CG\DFE�qF`HS2^�K�d/K�XHS2^n?�_�AFI�K�WQLHG�=2qF`[ZcA�XVWW�A�G\O&P8G�=2XHqFKi?�aLN<nG\DFE�qF`HS2^�K�d/K�XHS2^n?�_�AFI�K�WQLHG�=2qF`[ZcA�XVWQG\K�WnP8G\=YXHq/K�?�aIi<CP8G\=2XHqFKi?>l~=�Z\`QZ\`HK-LHG\=Yq/`[Z>D/XHK�?>e4E�IJ`X�A�G\G�D"l�K�G�Z�`VA�XZ�`HK6W�A�G\O�DFXHKi?�aWV<Q�B=YG\^CG\=YX�q/?�aK*<QA&I�DFX[Z�=2X(EHDFE�?~?�_NK�I$Z\G�E�ea

¾ ³/¹ h[e4EHS�ZB¾��F�i¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�Z:l�D�T!?US2=YZ�P8D/G�e4EHS2A�F�Fa~b>`HK�P8DFG\esEHS@A>P8DFG�Z�`HK;e&A��]=Ye�A~DFP]A~Z:l�DFTk?�SY=YZ�=2X[Z�K�G�P8K�G\K�XVI�Kj_�A�ZUZ�K�G�XC58P8DFG�?US2=YZ�?UK�_�A�GJA"Z\=YD/XMD�P �[<�=2?�_HG\DFL�AFLHSY^

e&D/?UZ~K�A/?U=2SY^nG�K�egK�esLNK�G\K�W�58e�A*^(LVK-LNK�I�A�E�?�KM=�ZBI�A�XLVK-=2X�?UZ\AFX/Z\SY^QW]K�G\=Yd/K�W�<�=2XQZ�`HKMP8D/G�emuA[< ��?U=2X ��$ �ja

Page 164: Introductory Physics Problems David J. Jeffery Department of

� ¹ ¾ v�`�A�_]Zia ³F¹ 7!X[Z\K�G�P8K�G\K�X�I�K

LN< ��I�D[? ��$ � � aIi< � ��?�=YX ��$ � � aWV< ��?U=2X ��$ � � aK*<Q?�=2X ��$ �ja

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³/¹ h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�?�D]W]=YE�e�S2=YXHK/o]=YXVW]K��D�P�G�K�P8G\A/I$Z�=2DFX� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¼/¼ µVuY�i��<

�Fa~b>`HK-l>A*dFK�SYK�XHq�Z\`nDFP�Z\`HK-^FK�SYS2D"l�?�D(WH=YEHe ¡�S2=YXHKi?~=2XmAF=YG~=@?cAF_H_HG\D*�(=2e�A"Z\K�S2^C¾ � ¶�¼F½ � ena� cDFZ�KMZ\`HK-=YXVW]K��DFP�G\K�P8GJAFI�Z�=2DFXnDFP�AF=YG~A�ZB¾ ��v�A�XVW���A�Z�e}=2?M�/a ¾/¾F¾/� ½F³ 5�£ ?VT ³F¼ <$aA[<C»{`VA"Zc=@?�Z�`HKMP8G\K�h[EHK�X�I�^QD�P�Z\`H=@?~SY=2qF`[Z �LN<n»{`VA"Zc=@?>l�A*d/K�S2K�XHqFZ�`n=2XmqFS@AF?\?>l~=�Z\`m=YX�WHK��nDFP�G\K�P8GJAFI�Z�=2DFX � $ � � ¶ ���Ii<n»{`VA"Zc=@?�Z�`HK6?�_VK�K�WD�P�S2=Yq/`/Z~=2XZ�`H=@?~qFS@AF?\?�

¾ ³/¹ h/P8EHS2S�¾/¾/��¾/¾n� ¶ ¾gK�A/?U^�Z\`H=2XHO(=YXHqVujl�A*d/K�?�DFXLNK�AFIJ`� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ¼/¼ µVu ¶ 9�<

�]aBv�D/X�?U=@W]K�GBD]I�KiA�X�l>A*dFK�?cegD"d(=2XHqnA�ZRµ � ¾je��"?c=YX�I�=2WHK�X[ZRD/X�A�LNK�AFIJ`xA"ZRAFXHqFS2K6D�P�µ[¾ � Z�DCZ\`HKsX�DFG\e&AFS�Z\DZ\`HKBLNK�A/IJ`�a�5�£cK�G�KBZ�`HKBAFXHqFS2KcG\K�P8K�G\?�Z\D-Z�`�KRW]=2G�KiI$Z\=YD/X&Z�`�A�Z�l>A*dFK�?jAFG�KBegD"d(=2XHq-=2X�o/X�D�Z;Z\D-Z�`�KRA�X�qFS2Kc?UK�ZL(^Z�`HK4SY=2XHK4D�PjZ�`�K�=2G�I�G�Ki?:ZJ?�a <�¤(E�WHWHK�XHS2^mZ�`HK�^�I�G\D/?\?~=YX[Z\DQAC?�`�A�S2S2D"l�K�GcG�K�qF=2DFX�l~`HK�G�K6Z�`HKgl�A*d/K6?U_NK�KiW=@?�DFXHS2^ ³ � ¾je��"?�a � � � � 7;WHK�G\=Yd/K�W�Z\`H=@?>_HG�D/LHS2K�e�P8G\DFe £B¿�»�a]7;AF?\?�EHe&KBZ\`HK�^�O(XHD"l�l~`VA"Z�Z�`HK�^nA�G\KZJA�S2O[=2XHq�A�LNDFEHZ�aA[<n�R?�?�EHe&=2XHq�Z�`�K6S2A*l�D�PjG\K�P8GJAFI�Z�=2DFXmA�_H_HS2=2K�?~Z\DCl>A"Z�K�G~l�A*d/K�?�A:E�?UZ�A/?~=YZRW]D(K�?cZ�D�S2=Yq/`/Zio�l~`�A�ZB=@?~Z�`�KAFXHqFS2K�Z�DgZ�`�K-XHDFG\e�A�SpD�P�Z�`HK-l>A*dFKi?�=YXZ�`�K6?U`�AFSYS2D"l�K�G�l�A�Z�K�Gia ������ � ¡RG\A*lzAgWH=2AFqFGJA�ema

LN<��=2dFK~AFX4K��(_�S2AFX�A"Z\=YD/X4AF?�Z\D�l~`(^6l>A*dFKi?�DFP Z�K�XgI�DFe&K�Z�`HK~?�`HDFG\K�A�Z�A�X&A�XHq/SYK�D�PN=YX�I�=2WHK�X�I�K�DFPVXHKiA�G\SY^��K�G\D�a

¾ ³/¹ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujd"A�G\=@A"Z�=2DFXVA�S�_HG\=YX�I�=Y_�SYK� ª�¬"¨ �V«������V¬ ��­�� S2A*lzD�P�G�K���K�I�Z�=2DFXmA�X�WQS2A*lzD�P�G�K�P8G\A/I$Z�=2DFXr5�¤]XHK�S2S�· ?~S@A*lB<

³ a>7!X4Z�`HKc£BEH^(qFK�X�?:T!|HG\K�?�XHK�S/_HG\=2X�I�=2_HS2K�KiAFIJ`g_VD/=YX[ZjD�P�A�l�A*d/K�P8G\DFX[Z�AFI$ZJ?�AF?�AM?UD/EHG\I�K�S2K�Z�P8DFG�ARXHK�ltl�A*d/K�S2K�Ziab>`H=@?c_�G�=2X�I�=2_HS2K-`�AF?RA&SYDFZcD�P�Z�G\E]Z\`�=YX�=YZ�a ��E]ZRAFSYD/XHK-=�ZR=2?�X�· ZcZ�`HKsl~`HDFS2K6?:Z\DFG\^nLNK�I�A�E�?�KMP8DFGRDFXHKMZ\`H=YX�ql�KMO[X�D"l{Z�`HD[?UK-?�DFEHGJI�K�SYK�Z\?>W]D/X�· Z~GJAFW]=@A"Z\KR=@?�D�Z�G\DF_�=2I�A�S2SY^/a�7!X�I�DFG\_VD/G\A�Z�=2XHq&A�XH=@?UDFZ�G\DF_(^Fo[`HD"l�K�d/K�Gio/=@?>l�K�SYSLNK�^/DFX�WmD/EHGR?\I�D/_VK/aB�cXHDFZ�`HK�GB_HG\DFL�SYK�e}=@?B`�D"l WHD[Ki?cD/XHKsW]KiA�S�l~=YZ�`�ACI�D/X[Z�=2X[E�EHe}DFP;?UD/EHGJI�K�S2K�ZJ? ����ZZ\`H=2?>_NDF=2X[Z~l~`�A"Z>=2?~I�A�S2SYKiWnAgd"A�G\=2A�Z�=2DFX�AFSV_�G�=2X�I�=2_HS2KRl~=2S2S�I�DFe&KRZ�D&DFE�G>AF=2WQA�X�WQqF=2dFK�E�?>?�DFe&KR=2X�?�=Yq/`[Z>=YP?UZ�=2SYS�XHD�Z~Z\`HK-l~`HDFS2K-?:Z\DFG\^Fa

b>`�KQD/_]Z�=@I�AFS�d"AFG�=@A"Z\=YD/X�A�S�_HG\=YX�I�=Y_�SYKr58DFP Z�K�XwI�AFSYS2K�W�|HK�G\e�A"Zi· ?g_HG\=YXVI�=2_HSYK*<4`�AF?gA�S2DFX�q�`H=@?:Z\DFG\^�un=YZl>AF?g��GJ?UZgP8D/G�e4EHS@A"Z�KiW�L(^�£BK�G\DrD�P��BSYK��HA�X�W]G\=@At5�I�=2G\I�At� ¶ ¾�]� ¶ ¾��B¡M<�AFX�W�G\K�P8D/G�e4EHS@A"Z�KiW�L(^t9;=YK�G�G\KW]K&|HK�G�e�A�Zg5:� ¹ ¾ ¼ �N� ¹F¹[¶ <�=YXt� ¹[¶ ºm5�£ ?VT ¹ ºF<$aM»xKgl�DFX�· ZMI�DFX�?�=@W]K�GBZ�`HD[?UK&A�X[Z�=@h[EHKsd/K�GJ?U=2DFXV?c`HK�G�K/aMb>`�Ke&D]W]K�G\X�dFK�G\?�=2DFXm=2?cZ�`�A�ZR?�=Yq/XH=��NI�A�X[ZBS2=2qF`[ZBK�X�K�G\qF^Q?UZ�G\DFX�q&Z�K�XVWH?~Z\D�P8DFS2SYD"l�Z\`HK6_�A�Z�`�=2X�?U_VAFI�K6Z�`�A�ZB=2??UZ\A�Z�=2DFX�AFG�^4l~=�Z\`CG�Ki?U_NK�I�Z�Z�D4A�G\LH=�Z\G\AFG�^sd*AFG�=@A"Z\=YD/X�?j=2X�DF_]Z\=2I�A�SV_�A"Z\`�DFG;_�`�AF?�KBIJ`�AFXHqFK65,l~`H=2IJ`�=@?6A:EV?:Z~� �Z\=Ye&K�?~Z�`HK-D/_]Z�=@I�AFSp_�A"Z\`V<$a��BXD/_]Z�=@I�AFSp_�A"Z\`mSYK�XHq�Z\` � LNK�Z:l�K�K�Xm_VD/=YX[Z\? ��AFX�W � =2?

� $ � ��

� �� 5 �i<

l~`HK�G�K �;=@?�?UD/egK;_�A"Z\`sI�D(DFGJW]=2X�A"Z\K�A�X�W � 5 �i<�=@?pZ�`�K;l>A*dFK�S2K�X�q�Z�`-DFP(Z�`HK�G\A/W]=2A�Z�=2DFX6A�Z��/a�b>`HK�l�A*d/K�S2K�XHqFZ�`I�A�Xd*AFG�^nl~=�Z\` �sW]EHK�Z�D�d"AFG�^(=2XHq4=2X�W]K��QDFP�G\K�P8GJAFI�Z�=2DFX�u

� 5 �*< $ � �� � � � ��

Page 165: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¹ 7!X[Z�K�GUP8K�G�K�X�I�K � ¹ �

l~`HK�G�K � $0* � � 5 �i<�=@?�Z�`HK�=YXVW]K��CDFP�G\K�P8GJAFI$Z\=YD/X�l~`H=@IJ`Q=@?>A�S2l�A*^]?�q/G�KiA"Z\K�G�Z\`�A�Xx�Fo]K��]I�K�_]Z>=2XQA4d*A/I�EHE�ea»{`VA"Z�W]D(K�?�?UZ\A"Z\=YD/X�A�G\^Me&K�A�Xg`HK�G�K � �/E�?UZ�l~`VA"Z�=�Zje&K�AFX�?�=YX&I�AFS2I�EHSYEV?�u�Z�`HK>_�A�Z�`s=@?jI�D/X�?UZ\A�X[Z�l~=�Z\`

G\K�?�_VKiI$ZMZ�Dm�VG\?UZ-DFGJW]K�GM_NK�G�Z�EHG\L�A"Z\=YD/X�?�ag�BSYSjZ\`HK�S2=Yq/`/Z6?UZ\AFGUZJ?M=YXr_H`�A/?UKgP8G\DFe � AFX�W���D"lc?MA�S2DFXHqZ�`�K?UZ\A�Z�=2DFX�AFG�^M_�A�Z�`4P8G�D/e �tZ�D�� A�X�W4A�S2DFXHqRZ�`HD[?UK>I�D/X[Z�=2X[E�EHe D�PN_�A"Z\`�?�Z�`VA"Z�A�G\K�I�SYD[?UK�Z�DRZ�`�Kc?:ZJA"Z�=2DFXVA�G\^_�A�Z�`6l~=2S2S(AFG�G\=2dFKjl~=YZ�`6XHKiA�G\SY^�Z\`HK�?\A�e&K;_�`�AF?�KFa�b>`H=2?�S2=Yq/`/Z�l~=YS2S[=YX[Z�K�GUP8K�G�K;egD[?:Z\SY^-I�DFX�?UZ�G\E�I$Z\=Yd/K�S2^Fa�¸�=Yq/`[ZZ\`�A"ZsI�DFe&K�?-AFSYD/XHqmD�Z�`�K�G-_�A�Z�`�?Ml~=2SYS�A�G\G�=2dFKgl~=�Z\`�AQl~=@W]K�GJA�XHq/K&D�P�_�`�AF?�K�?-AFX�W�l~=YS2S;?UZ�G\DFXHq/SY^mZ\G�K�X�WZ\DnI�AFX�I�K�S�DFE]Z��w7�Z�`�=YXHOZ\`HK-Z�G\K�XVWnZ\DnI�AFX�I�K�S2A�Z�=2DFX=2?cZ�G\=2IJO(^nZ�DC?�`HD"lz=2X�qFK�XHK�GJA�S�oHLHEHZBX�A"Z\EHG\K-`�AF?~X�D_HG\DFL�SYK�e�WHDF=2XHq4=YZ�aj BD�Z�K�l�KRA�S@?�Ds`�A*d/KB_HG\=YXVI�=2_HSYKRD�P�G\K�d/K�GJ?U=2LH=2SY=YZ:^�u�Ag?:ZJA"Z\=YD/X�A�G\^4_VA"Z�`nP8G�D/e ��Z\D� =2?AFS2?�D&DFXHK�P8G\DFe � Z\D �sa

7kZ�=2?RLNK�^FD/X�W�D/EHGR?\I�D/_VK-Z\DQ?UZ�E�WH^e&K�Z�`HD]WH?BP8DFGB��X�W]=2XHqCZ\`HK4?UZ\A�Z�=2DFX�AFG�^_�A�Z�`�=2X�qFK�XHK�GJA�S�acb>`�A�Z=2X(dFDFS2dFKi?gd*AFG�=@A"Z\=YD/X�A�ScI�A�S@I�EHS2E�?�a�¤(E]�CI�K�=�Z�Z\D�?�A*^�`�K�G\KQZ\`�A"ZQ=�PM=YXVW]K��±D�P�P8G\A/I$Z�=2DFXw=@?�I�D/X�?:ZJA�X[Z�Z�`�K?UZ\A�Z�=2DFX�AFG�^�_VA"Z�`wLNK�Z:l�K�K�XtZ:l�Dr_VD/=YX[ZJ?�=2?nA�?:Z\G\AF=Yq/`/Z�S2=YX�KFa�9�K�G�`�AF_�?g=�ZQ=2?�LNK�Z�Z�K�G�Z�D�?\A*^�Z�`VA"ZCDFX�K?UZ\A�Z�=2DFX�AFG�^�_�A�Z�`m=@?~Ag?UZ�GJA�=2qF`[Z~S2=YXHK/aA[<v�D/X�?�=2W]K�G�� A�X�W ��=2XrAe&K�WH=YEHe l~=�Z\`�I�DFXV?:ZJA�X[Z-=YX�WHK��xDFP�G\K�P8GJAFI�Z�=2DFX�a�b>`HK�G�K&=@?6A`HDFG\=Y��DFX[Z\AFSe&=2G�G\DFG;LVK�SYD"lwZ\`HKB_NDF=2X[Z\?�A�X�W&Z\`HK�eg=2G\G�D/G;?UE�GUP,A/I�KBW]K���XHKi?�AFX �QA��(=@?�u�Z\`HKB_NK�G\_VK�X�W]=@I�EHS@A�G>A"�]=@?jZ\DZ\`HK ��A��]=2?>=@?~Z\`HK �QA��]=2?�a;b>`HK6_NDF=2X[Z���=@?cA"Z45�¾� � � <~AFX�W � =2?BA"Z45 0 � � <�a~°RX�K6?:ZJA"Z�=2DFXVA�G\^C_�A"Z\`LNK�Z:l�K�K�X��{A�X�W � =@?�Z�`HKR?:Z\G\AF=Yq/`/ZjS2=YX�K>Z�`�A�Z6A:DF=2X�?�Z�`�K�emajb>`H=2?�=2?jl~`(^6l~`�K�X�^FD/Eg?UZ\AFX�W&A"Z � ^/DFE?�K�K4A�?UD/EHG\I�K6A"Z �fl~`HK�X�S2D(DFO(=2XHqC?:Z\G\AF=Yq/`[ZBA"Z �sa<��E]Z�W]DFX�· ZR^/DFE�?�K�K-Z\`HK � ?�DFEHGJI�K6?�DFe&K�l~`HK�G\KK�S2?�K&=YX�Z\`H=2?sI�AF?�K�� b>`�K�eg=2G\G�D/G�A/I$Z\?sAF?MA�XrK��HI�K�S2SYK�X/Z6?\I�A�ZUZ�K�G�K�GMD�P>SY=2qF`[Z�uM=YZsW]D(K�?�X�· ZsA�L�?�DFG\L�D/GZ\G\AFX�?�eg=YZRA&S2D�Ziacv�D/X�?�=2W]K�GBA�?UZ�GJA�=2qF`[ZUTkSY=2XHK-_�A�Z�`mP8G\DFe � Z�DCZ�`HK6e&=2G�G\DFGcA�ZRA�G\LH=YZ�GJA�G\^C_ND/?�=�Z\=YD/X �AFX�W�A�X�D�Z�`�K�GB?UZ�GJA�=2qF`[ZUTkS2=YXHKM_�A�Z�`mP8G\DFe ��Z�D��Cac¤(`HD"lzZ�`�A�ZBZ\`HKs?UZ\A"Z\=YD/X�A�G\^���G�K���K�I�Z�=2DFX �&D/_]Z�=@I�AFS_VA"Z�`�=@?-Z\`HKCD/XHK�Z�`VA"Zsq/=Yd/K�?MZ\`HKnS@A*l DFP~G�K���K�I�Z�=2DFX�u � � � � $ � � � ��o�l~`HK�G\K � � � �gAFX�W � � � �xA�G\K&Z�`�KAFXHqFS2K�?�D�Pp=YXVI�=@W]K�X�I�KRAFX�W&G�K���K�I�Z�=2DFX&e&K�A/?UEHG\K�WgP8G\DFe Z�`�KcXHDFG\e�A�S]Z\D-Z�`�KBe&=YG\G\DFG;?�EHG�P,AFI�K/a ������ �¡RGJA*lzA&W]=@A�qFGJA�ema

LN<Q BD"lzl~`VA"ZBA�LNDFEHZ~Z�`HK-S@A*l�DFP�G\K�P8GJAFI�Z�=2DFX�5�¤(XHK�SYS�· ?cS@A*lB<��xv�`VA�XHq/KRZ\`HK6e&=2G�G\DFG>=2X/Z\DCA�X�W=2X[Z�K�G�P,AFI�KLNK�Z:l�K�K�X�e&K�W]=2EHe �6l~=�Z\`�=YXVW]K��mD�PjG\K�P8GJAFI$Z\=YD/X � � A�X�We&K�WH=YEHe �gl~=YZ�`�=2X�W]K��DFP�G\K�P8GJAFI�Z�=2DFX � � a¸�K�Z�� � P8D/G�� LVK-XHK�q/A�Z�=2dFKFa�¤(`�D"l�Z�`VA"Z~Z�`�K6?:ZJA"Z�=2DFXVA�G\^�DF_]Z\=2I�A�Sp_�A�Z�`m=2?�Z\`HK-DFX�KMZ�`�A�Zc^[=2K�S@WH?

� � ?�=2X�5�� � � ��< $ � � ?U=2X�5�� � � � �U< �

l~`�K�G\K � � � � � =@?RZ�`HK�AFXHqFS2KsDFP�G\K�P8GJAFI$Z\=YD/X�e&K�A/?UEHG\K�W�P8G�D/e�Z�`HKgXHDFG\e�A�S�Z�DQZ�`�K4=2X[Z�K�G�P,AFI�KFa ������ �¡RGJA*lzA&W]=@A�qFGJA�ema

� � � � b>`HK~D/_]Z�=@I�AFS]d"A�G\=2A�Z�=2DFX�AFS]_HG�=2X�I�=Y_HS2KFoF7�`HD/_VK/oF`�A/?�qF=2dFK�X&?�DFe&K>=2X�?U=2qF`[Zj=2X/Z\DMZ�`HK~_VA"Z�`V?�Z�`HG\DFE�qF`?�_�AFI�KCDFX�l~`�=2IJ`�S2=2qF`[ZsK�X�K�G\qF^��VD"lc?�u4Z�`HKi?UKQ_�A"Z\`�?sI�A�X�LNKQI�DFX�?�=@W]K�G\K�WrA�I�DFX[Z�=2X(EHEHe D�Pc?�DFEHGJI�K�SYK�Z\?�a��E]Z>XHD�Z\KB=YZ>WHD[Ki?;X�D�Z�?\A*^g`HD"l{esE�IJ`nSY=2qF`[Z�q/D(K�?�L�AFIJO(l>A�GJW4D/G;P8D/G�l>A�GJW&A"Z>K�A/IJ`C?UD/EHG\I�K�S2K�Zia�b>`HK�l>A*dFKd"A�G\=@A"Z�=2DFXVA�S"_HG\=YXVI�=2_HSYK�W]D(K�?�X�D�ZpZ�K�SYS[E�?�Z\`�A"Zia��BX�W�Z�`�K;?UD/EHGJI�K�S2K�ZJ?�A�G\KjXHDFZ�A�S2S�Z�`�K;?�AFe&KFa�b>`HK�?UD/EHG\I�K�S2K�ZJ?=2Xmd*A/I�EHE�eoV=YXZ\`HK6e&=2W�W]SYK-DFP�e&KiW]=2A�o�A�XVWA�Zc=YX[Z\K�G�P,AFI�Ki?~l~=2SYS�AFSYS�qF=2dFK-?UD/e&K�l~`�A�Z~WH=���K�G\K�X[ZcLNK�`�A*d(=2DFGiab�D-EHX�W]K�G\?UZ\AFX�WgZ�`VA"Z;LNK�`�A*d(=2DFGjD/XHK~XHK�KiWH?;AMe&D/G�KcW]K�Z\AF=YS2K�WgZ\`HK�D/G�^4D�P�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@I>GJAFW]=@A"Z\=YD/XgAFX�W=YZ\?j=2X[Z�K�G\A/I$Z�=2DFX4l~=�Z\`&e&A�ZUZ\K�Giaj°RXgZ�`�K~D�Z�`�K�Gj`�AFX�Wpo"Z\`HK~DF_]Z\=2I�A�S]d"A�G\=@A"Z�=2DFXVA�S(_HG\=YX�I�=Y_�SYKcI�A�XgLVK65�A�X�Wg`�A/?LNK�K�XV<RqFK�X�K�GJA�S2=Y��K�WmZ\DQDFZ�`HK�GRO(=2X�WH?MD�P�l�A*d/K�?�u~KFa q�a2opl�A�Z�K�G�l>A*dFK�?B7cZ\`H=YX�ONa&°RXHK4=2e&_VD/GUZJA�X[ZMK��HA�e&_HS2KDFP�AgqFK�XHK�GJA�S2=2��A"Z\=YD/XC=@?c¿~=@IJ`�A�GJWn|�K�^(XHe�A�X�· ?>P8D/G�e4EHS2A�Z�=2DFXQD�Pjh/EVA�X[Z�EHe�egKiIJ`�A�X�=2I�?�a�b>`H=@?�P8DFG\esE�S2A�Z�=2DFX=@?�K�h[EH=2d*AFSYK�X[Z�Z\DQDFZ�`HK�G-h/EVA�X[Z�EHe egKiIJ`�A�X�=2I�A�S�P8DFG\esEHS@A"Z\=YD/X�?�o�LHEHZ6=2?�L�A/?UKiW�DFXxd"A�G\=2A�Z�=2DFX�AFS�_HG\=2X�I�=2_HS2KP8D/G~e&A�ZUZ\K�Gcl>A*dFKi?�a��B?~AFXKih[EH=Yd"AFSYK�X/Z>P8D/G�e4EHS2A�Z�=2DFX�o]=YZc=2XmA&?�K�X�?�K-?�A*^]?>XHDFZ�`H=2XHq&XHK�l-oHLHE]Zc=2X�A�XHDFZ�`HK�G?�K�X�?�KM=�Zcq/=Yd/K�?>D/XHK-A4X�K�l�_VK�G\?�_VKiI$Z\=Yd/K�D/XnZ\`HK-_H`(^]?U=@I�?�a

¾ ³/¹ h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\K���KiI$Z�KiWCZ:l�D�T!?�SY=YZ~=YX[Z�K�GUP8K�G�K�X�I�Kµ�a~�BX�=2X�?:Z\G�EVI$Z�D/G5,LHE]Z&_HG\DFL�AFLHSY^rXHDFZ4^/DFEHGJ?\<s?UK�Z\?4EH_tA�Z:l�DFTk?�S2=�Zg=YX[Z�K�GUP8K�G�K�X�I�KW]K�e&D/X�?:Z\G\A�Z�=2DFX�l~=YZ�`±A¹/³ � � ¼ XHe S@AF?�K�GBA�ZRZ\`HK6P8G\DFX[ZRDFPjZ�`HKgI�S@AF?\?�a�b>`HKsS@AF?�K�GRLVKiA�e�_NDF=2X/ZJ?R?UZ�GJA�=2qF`[ZBD/E]ZM=YX[Z�DnZ�`HKgI�S@AF?\?BAFX�W_�A/?�?�K�?cZ�`HG\DFE�qF`�Z\`HKsZ:l�DQ?�S2=�ZJ?�I�G�KiA"Z\=YXHqQAC_�A�ZUZ�K�G�X�aMb>`�K4_�A�ZUZ\K�G\X�G�K���K�I�Z\?RDB��ACe&=2G�G\DFGM��¾ � ¾je�A*l>A*^P8G\DFe�Z\`HK~?US2=YZ\?jA�XVW6Z\G\A*d/K�S@?�L�A/IJOMZ�D-A�?�I�G�K�K�X4A�Z�Z�`HK�P8G\DFX[ZjD�P�Z\`HK~I�S@AF?\?�Z�`�A�Z�=@?��F� � ¾�e P8G�D/e Z�`HK~e&=2G�G\DFGia

Page 166: Introductory Physics Problems David J. Jeffery Department of

� ¹ � v�`�A�_]Zia ³F¹ 7!X[Z\K�G�P8K�G\K�X�I�K

b>`HK6Z:l�DFTk?�SY=YZBW]K�d[=@I�K/oVe&=2G�G\DFGio�AFX�Wm?�I�G�K�K�X�A�G\K6A�S2S�_NK�G\_NK�X�W]=@I�E�S2AFG~Z�D�Z\`HKsD/_]Z�=@I�AFS�A"�]=@?cKi?:ZJA�LHS2=2?�`HKiWQL(^Z\`HK-LVKiA�emaA[<n¡RGJA*l�ARWH=2AFqFGJA�e D�PHZ\`HK~?UK�Z�EH_�a�7!X�I�SYEVW]K�Z�`HK>S2D(I�A"Z\=YD/XsD�PVZ�`HK�d(=YG�Z�EVA�S(=Ye�AFqFK�D�P�Z\`HK~?�I�G�K�K�X6_VA"ZUZ\K�G\X=2XZ�`HK-G\K�q/=YD/XnLNK�`H=2X�WZ\`HK-e&=YG\G�D/G�a

LN<n»{`VA"Z�?�=2eg_�SYK6e&=2G�G\DFGR?U^(e&e&K�Z�G\^QZ�G\=2IJOmA�S2SYD"lc?c^FDFEmZ\DnA�XVA�S2^[��KMZ�`HK4=YX[Z\K�G�P8K�G\K�X�I�K6_�A"Z�Z�K�G�X�KiAF?�=YS2^�u=�a KFa2oHl~`�A"Z>Z\G�=@IJOCG\K�W]E�I�K�?�Z\`HK-_HG\DFLHS2K�e Z\DCA�XmA�S2G�KiAFW]^C?�DFS2dFKiWn_�G�D/LHSYK�e �

Ii<n7kPjZ\`HKsL�G�=2qF`[ZcP8G\=YX�qFK6e�A"�]=2e�A�DFXmZ\`HK4?\I�G\K�K�X�A�G\KsA�S2S�?�K�_�AFG\A�Z�KiWQL(^mA�LNDFE]Zg��¾ � ¾�I�emo�l~`�A�ZB=2?BZ�`�K?�S2=�ZR?�K�_VA�GJA"Z�=2DFX�W]K�Z�K�G�e&=2XHK�WmE�?�=2XHq&Z�`HK5:�i?:ZBD/G\WHK�G$<�?�e�A�S2S�AFXHqFS2K6A�_H_�G�D*�]=2e&A�Z�=2DFX � �/E�?:Z\=�P8^E�?�=YX�qZ\`HK6?�e&AFSYS�AFXHqFS2K-A�_H_�G�D*�]=2e&A�Z�=2DFXQLVDFZ�`�Ag_HG�=2DFG\=pA�X�WmAg_ND/?UZ�K�G\=2DFG\=�a

¾ ³/¹ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�?US2=Yq/`[Z�S2^nW]=@?�AFSY=2qFXHKiWQ?�S2=�ZJ?¶ a~|�DFGr?U=2e&_HSYKwW]K�dFK�S2DF_�egK�X[Z\?�l�K�EV?UE�AFSYS2^�Z�`H=2XHO�DFPCZ�`HKtZ:l�D�T!?US2=�Z�W]K�d(=@I�KwAF?xK��HAFI�Z�S2^z_NK�G\_VK�X�W]=@I�EHS@A�GZ\D�Z�`�K�DF_HZ�=@I�A�S�A"�]=@?�5,WHK���XHKiW�L(^tZ�`HKx=YX�I�DFe&=2XHq�LNK�AFe WH=YG\K�I�Z�=2DFXV<�a ��E]ZQ=2X�_NDF=2X/ZD�P-P,A/I$ZQ=2X�AFX[^EHXVW]K�G\qFGJAFW]EVA"Z�K&K��(_NK�G\=2egK�X[Z4?UEVIJ`�K��HAFI$ZsAFSY=2qFX�K�W�_HG\DFL�AFLHSY^�I�AFX�· Z6LNKCD/L]Z\AF=YXHKiWpamb>`HK�G\K�l~=YS2S�AFSYl>A*^]?LNK-?UD/egKMW]=@?�AFSY=2qFX�egK�X[Z�a ��E]Z~=�Z>Z�E�G�X�?>D/E]Z�Z�`H=@?~W]=@?�AFSY=2qFXHe&K�X/Z~W]D(K�?>X�D�Z>e&A�ZUZ\K�G>Z�D��?UZ>DFGJW]K�G>=2XQ?�e&AFSYSAFXHqFS2K�?>=2XnZ\`HK6£cE�^[q/K�X�?UT!|HG\K�?�XHK�Sp_HG\=2X�I�=2_HS2K�_�=2I�Z�EHG\KFaA[<n¡RGJA*lrAcqFD(D]W-W]=2AFqFGJA�ezl~=�Z\`4A~`HD/G�=2��D/X[Z\A�SFLVKiA�e�A�=2e&K�W-A"Z�A>Z:l�D�T!?US2=�Z�W]K�d(=@I�KB5,l~=�Z\`4?�SY=YZ�?�K�_�AFG\A�Z�=2DFX

�(<$amb>`HK�XHD/G�e�AFS�Z�DmZ�`�Kn?US2=YZsW]K�d(=@I�KC=@?6A"Z�� � � �MA�LND"dFKgZ\`HKC`HD/G�=2��D/X/ZJA�S�aCb>l�Dm_�A�Z�`�?4I�D/egKgP8G\DFe=2X]��X�=�Z:^-`HD/G�=2��D/X[Z\A�S2S2^�AFX�W6_�A/?�?�Z�`�G�D/EHqF`-Z\`HK>?US2=�ZJ?�Z�`HK�Xs`HKiAFW6D �CA"Z�AFX4AFXHqFS2K � �(AFLVD"d/K�Z�`�K�XHD/G�e�AFSZ\D&Z�`HK6WHK�d(=2I�KMZ�DCAg_NDF=2X/ZB9{A�Zc=YXH��XH=YZ:^Fa;¯�AFG�OCZ�`HKi?UKMZ:l�D&_�A"Z\`�?~DFXQZ�`�KsW]=@A�qFGJA�e AFX�Wm?U`�D"l�Z�`�KZ:l�DgZ�G\=2AFXHqFS2K�?�D/XK�=�Z\`HK�Gc?�=@W]K-D�P�?US2=�ZBWHK�d(=2I�KMe&AFG�OnDFE]Z~Z\`HK-SYK�XHq�Z\`HK�X�=YXHq&DFP�Z\`HK-LVDFZUZ\DFe _�A�Z�`�a

LN<Q¿cK�e&K�e4LVK�GMZ�`HK&_H`�A/?UK&IJ`�AFXHqFK4P8DFG�Z�GJA*dFK�SY=2XHqAQW]=@?UZ\A�XVI�K =@? � $ � o�l~`HK�G\K � $ � � � � =@?�Z�`�Kl>A*dFK�X(EHesLNK�Gia�»{`VA"Zc=@?�Z�`HK-_H`VAF?�KMWH=���K�G\K�X�I�K-LVK�Z:l�K�K�XZ�`�K-_�A"Z\`�?~W]K�?\I�G\=2LVKiWn=2Xm_�A�G�Z65,A/< �� BD�Z�K

� � $ �/, � � � ��l~`�K�G\K �&=@?>Z�`�K6A�XHq/SYKRP8G�D/e Z\`HK-`HDFG\=2��DFX[ZJA�S�a

Ii<Q¯�A�OFKnZ�`HK?Ue�AFSYS>A�XHq/SYKA�_H_�G�D*�]=2e&A�Z�=2DFX�P8DFG4Z�`�KQ_H`VAF?�KQW]= �NK�G�K�X�I�KQD�Pc_�AFGUZm58LV<4A�XVW�?U`�D"l�Z�`�A�ZZ\`HK�G�Ki?UEHSYZ>=2?;Z�`HKM?\A�e&K�A/?�Z\`HK�_H`�AF?�KRWH=���K�G\K�X�I�KBP8D/G�AFXCK��HA/I$Z�S2^&dFK�GUZ\=2I�A�S�?US2=�Z~W]K�d[=@I�KR=YXnZ�`HKM?�e&AFSYSAFXHqFS2K~A�_H_�G�D*�]=2e&A�Z�=2DFX�a�»{`�A"Z�W]D(K�?�Z\`H=@?�W]K�e&D/X�?:Z\G\A�Z�=2DFX4egKiA�X4P8DFGjEHXVW]K�G\qFGJAFW]EVA"Z�K�K��]_NK�G\=Ye&K�X[ZJ? �

WV<n»{`(^rI�AFX�· ZsZ�`HKnAFqFG\K�K�egK�X[Z6D�P~G�Ki?UE�S�ZJ?MP8DFEHXVWr=YX�_VA�G�Zn5,I�<6LVKnK��HAFI�Z�S2^�G\=Yq/`/Z6K�dFK�X�=YXrZ\`HKn?�e&AFSYSAFXHqFS2KMSY=2e&=�Z �

¾ ³/¹ h/P8EHS2S�¾/¾ ¹ �i¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�?:Z\EH_H=@WWH=2?\A�S2=Yq/XHK�W?�SY=YZ\?� ª�¬"¨ �V«������V¬ ��­�� ¤[Z�EH_�=2W�h[EHKi?:Z\=YD/X�u�eg=@?\?UKi?�Z�`HK-D/L[d(=2DFE�?�oH?�K�K-¾F¾ ¹ ¾F¾

¹ a~|�DFGr?U=2e&_HSYKwW]K�dFK�S2DF_�egK�X[Z\?�l�K�EV?UE�AFSYS2^�Z�`H=2XHO�DFPCZ�`HKtZ:l�D�T!?US2=�Z�W]K�d(=@I�KwAF?xK��HAFI�Z�S2^z_NK�G\_VK�X�W]=@I�EHS@A�GZ\D�Z�`�K�DF_HZ�=@I�A�S�A"�]=@?�5,WHK���XHKiW�L(^tZ�`HKx=YX�I�DFe&=2XHq�LNK�AFe WH=YG\K�I�Z�=2DFXV<�a ��E]ZQ=2X�_NDF=2X/ZD�P-P,A/I$ZQ=2X�AFX[^EHXVW]K�G\qFGJAFW]EVA"Z�K&K��(_NK�G\=2egK�X[Z4?UEVIJ`�K��HAFI$ZsAFSY=2qFX�K�W�_HG\DFL�AFLHSY^�I�AFX�· Z6LNKCD/L]Z\AF=YXHKiWpamb>`HK�G\K�l~=YS2S�AFSYl>A*^]?LNKC?UD/e&K&WH=2?\A�S2=Yq/XHe&K�X[Z�aCb>`�=2?6WH=2?\A�S2=Yq/XHe&K�X[ZC58=2X�Z�`HKn£BEH^(qFK�X�?:T!|HG\K�?�XHK�S�_�G�=2X�I�=2_HS2K�_H=@I$Z�E�G�K*<MA�e&DFEHX[ZJ?Z\D�Z\`HK�G\KQLNK�=2XHqrA��H�]KiW�_H`�A/?UKmW]= �NK�G�K�X�I�K � � � � LNK�Z:l�K�K�X�Z�`HKQZ:l�Dx?�SY=YZC?UD/EHG\I�K�?6P8DFG4Z�`HKm=2X/Z\K�G�P8K�G\K�X�I�K_�A�ZUZ\K�G\X�a�b>`(E�?�Z�`HK-K.�NKiI$Z\=Yd/K-_H`�AF?�K-W]= �NK�G�K�X�I�K�P8DFG~D/E]Z�q/DF=2XHq&LVKiA�e�?~A"Zc=2X]��X�=�Z:^C=@?

� $ ���;?�=YX�5�� � < , � � � � l~`HK�G�K � $z��� � � =@?~Z\`HK6l>A*dFK�X[E�esLNK�GcA�XVW � ��=@?ce&K�A/?UEHG\K�WnZ:l�D�T!?US2=�ZBA��]=2?65,=�a KFa2oHP8G\DFe�Z�`HK4A"�]=2?~Z�`�A�ZB=2?_NK�G\_VK�X�W]=@I�EHS@A�G�Z�DsZ�`HKBZ:l�DFTk?�S2=�Z�WHK�d(=2I�Ki<�a�b>`�KRG\K�S@A"Z\=YD/X�D�P � ��Z�D �Q5 Z\`HKMA�XHq/SYK~P8G\DFe Z\`HKBD/_]Z�=@I�AFSNA��(=@?J<�=2?

� � $ �/, � � � � �

l~`HK�G�K � � � � ��=2?�Z\`HK6A�XHq/SYKMDFP�Z:l�D�T!?US2=YZ>A��(=@?�P8G\DFe Z\`HK-DF_]Z\=2I�A�S�A��(=@?�a

Page 167: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¹ 7!X[Z�K�GUP8K�G�K�X�I�K � ¹/³

A[<n¡RGJA*lzA&W]=@A�qFGJA�e DFP�Z\`HK6?�^(?UZ�K�emaLN<¤]DFS2dFK�P8DFG � ��aIi<Q|�DFG-Z\`HKC?�e&AFSYS�A�XHq/SYK�A�_�_HG�D*�]=2e�A"Z�=2DFX�o�W]K��VXHKCA�XrXHK�l�AFXHqFS2K � � �B5,=YXrZ\K�G\e&?MDFP~LVDFZ�`�� �;AFX�W � � � <?�E�IJ`�Z\`�A"Zgl�Kn^FDFE�`VA*dFKnA�P8DFG\esEHS@AmP8DFG � � � Z�`�A�Z4K��HA/I$Z�S2^�G�Ki?UK�esLHS2K�?6Z�`HKnP8DFG\esEHS@AmP8DFG ��=2X�Z�`�KK��HAFI$ZcAFSY=2qFXHe&K�X/ZcI�AF?�KFa

WV<n»{`(^W]DFX�· Zcl�K�K�dFK�G�l�DFG\G\^CA�LNDFE]ZcW]=@?�AFSY=2qFX�egK�X[Zc=YXEHX�W]K�G�q/G\A/W]E�A�Z�K�K��]_VK�G�=2e&K�X[Z\?�

¾ ³/¹ h/P8EHS2S�¾/¾[º"¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�|�»�£R¯ P8DFG>Z:l�D�?US2=�Zº(a~b>`HK-=2X[Z�K�X�?U=YZ:^�P8EHXVI$Z�=2DFXP8D/G>Z�`HKMP,AFGUT���K�S@WnZ:l�DFTk?�SY=YZ~=YX[Z\K�G�P8K�G\K�X�I�K�_VA"ZUZ\K�G\XQ=@?

� $wµ � � �I�D/? � 5��<

l~`HK�G�K =@?RZ�`HK�W]=@?:ZJA�X�I�KsP8G\DFe�Z\`HK�?US2=YZ\?RZ�DQZ�`HK�?\I�G\K�K�X�o � � � �4=@?RZ�`HK&=2X[Z�K�XV?U=YZ:^�_�A"Z�Z�K�G�X�P8DFG-AQ?�=2XHqFS2K=2X]��XH=YZ�K�SY^QX�A�G\G\D"l�?US2=YZ�o�AFX�W� $ �

� $ ��

�?�=2X � �

b>`HK~AFXHqFS2K ��=@?�Z\`HKcA�X�qFS2K�e&K�A/?UE�G�KiWMP8G�D/e�Z�`�K�D/_]Z�=@I�AFS]A"�]=2?�o"D�P�I�D/EHG\?�KFa�b>`HK�P8EHS2S]l~=2W(Z\`4`VA�SYPVe�A"�]=2esEHe5�|�»�£R¯�<R=2?RZ\`HKg?�_�A/I�=2XHqnLNK�Z:l�K�K�X�Z�`�KsZ:l�Dn_NDF=2X[Z\?�DFX�K�=�Z\`HK�G-?�=2WHK4DFP�A�X�=2X[Z�K�X�?U=YZ:^�_NK�A�Oml~`HK�G�K4Z�`�K`HK�=Yq/`[Zs=2?4`�AFS�PcDFP�Z\`HKn_NK�AFOr`HK�=2qF`[Z�a�¤]`HD"l�Z�`�A�Z6Z�`�KQ|�»�£B¯ P8DFG6Z\`HKQI�K�X[Z�GJA�S�LHG\=Yq/`/ZsP8G�=2XHqFKnD�P~Z�`�KZ:l�D�T!?US2=YZ~?�K�Z\EH_m=2?

� ��$ ��

A/?�?�EHe&=YX�q4Z\`HK6?�e&AFSYS�AFXHqFS2K-A�_H_�G�D*�]=2e&A�Z�=2DFXnAFX�WQZ�`�A�Z I�A�XLVKMZ\G�KiA"Z�KiWmAF?~I�D/X�?UZ\A�X[Zia

Page 168: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0���� %8*[3�5\&AH ;<*[? >

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³ º6h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�W]= ��G\A/I$Z�=2DFXmW]K���XHK�W�Fa~¡R=���GJAFI$Z\=YD/X{A�X�W±=2X/Z\K�G�P8K�G\K�X�I�K�A�G\KKi?�?�K�X[Z\=2AFSYS2^�Z�`�K�?�AFe&K_�`[^]?�=2I�A�S~_H`�K�XHD/egK�XHDFX�a�7kZC=2?nI�E�?UZ�D/e&AFG�^Z\`HDFEHq/`nZ\D�E�?�KRZ\`HKMZ�K�G�e W]= �NGJAFI�Z�=2DFXl~`HK�XZ�`�K�G\KMAFG�K/uA[<�P8K�l�?�DFE�G\I�K�?�aLN<ne�AFX[^Q?UD/EHG\I�K�?�DFG~K�dFK�XA&I�D/X[Z�=2X[E�EHe�DFP�Z�`�K�emaIi<nX�D&?�DFE�G\I�K�?�aWV<�g?�DFEHGJI�Ki?�aK*<QWH=���K�G\K�X[ZB?�DFEHGJI�Ki?�a

¾ ³ º6h[e4EHS�ZB¾/¾/�F¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj?U`VAFW]D"lc?�]a �\¸�K�Zi· ?s_HS@A*^ �]1J� D+�"����# 1 |HD/G �]��¾F¾�o�Z\`HKQAFX�?Ul�K�Gs=2?�u�� S2AFG�q/K�G�K�qF=2DFXrD�PB?UZ�G\DFX�q�58LHE]ZgXHD�ZgXHK�I�K�?\?�AFG�=2S2^I�DFe&_HS2K�Z�K*<>W]K�?UZ�G\E�I�Z�=2dFKM=YX[Z\K�G�P8K�G\K�X�I�KFa �A[<C»{`VA"Zc=@?~A�?UEHLV?:ZJA�X�I�KFoH�cS2K�� �LN<n»{`VA"Zc=@?~A�?U`�A/W]D"l-o]�cS2K�� �Ii<n»{`VA"Zc=@?~A�WHA�G\O&P8G�=2XHq/K�DFP�A4Z:l�D�T!?US2=YZ>=2X[Z�K�GUP8K�G�K�X�I�KM_�A�ZUZ�K�G�X�oH�cS2K�� �WV<n»{`VA"Zc=@?�Z�`HK-_�A�Z�`mD�P�Z�`�K6£cEHX�?�o��BSYK����K*<n»{`VA"Zc=@?�Z�`HKs¤(`VAFW]D"l-oH�BSYK����

¾ ³ º6h[e4EHS�ZB¾/¾ ³ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujD/XHK�T!?US2=YZ>_VA"ZUZ\K�G\X³ a~b>`HK-D/XHK�T!?�SY=YZcW]=���GJAFI$Z\=YD/XQ_VA"ZUZ\K�G\XQ`VAF?�u

A[<nAgLHG\D/A/Wpo]LHG\=Yq/`[Z~I�K�X[Z�GJA�SNP8G\=YX�qFKFaLN<QAgLHG\D/A/WpoHWHAFG�OCI�K�X[Z�GJA�S�P8G\=YX�qFKFaIi<CZ\`HG\K�KMLHG\D/AFWQLHG\=Yq/`[Z~I�K�X[Z�GJA�S�P8G\=2XHqFKi?�aWV<QAgX�AFG�G\D"l-o]W]=2e}I�K�X[Z�GJA�S�P8G\=YXHq/KFaK*<QAgLHG\D/A/WpoH?�`�A�q/qF^CI�K�X[Z�GJA�SNP8G�=2XHq/KFa

¾ ³ º6h[e4EHS�ZB¾/¾�µ[¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujD/XHK�T!?US2=YZ>��K�G\D/?µ�a~b>`HK>P8D/G�e4EHS@A�P8DFG�Z�`�Kc��K�G�D[?�D�PpAMDFXHK�Tk?�SY=YZ;W]= �NGJAFI�Z�=2DFX&_�A�ZUZ�K�G�X�58P8DFG;A-?�SY=YZ�D�Ppl~=@W(Z�` �]<�=@?j_HG\DFL�AFLHS2^6e&D/?UZKiAF?�=YS2^CG\K�e&K�e4LVK�G�KiWx5,e&A*^(LNKMLVKiI�A�EV?UKM=YZB?UD�?�=Ye&=2S2AFG>Z�D&Z�`�KMZ:l�DFTk?�SY=YZ>e&A��]=Ye�A4P8DFG\esEHS@A/<�=2XZ�`HKMP8D/G�emuA[<���?�=YX ��$ �jaLN<'��I�D[? ��$ � � aIi<'����?�=2X ��$ � � aWV<'��?�=YX ��$ � � aK*<Q?�=2X ��$ �ja

¾ ³ º6h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�ujK�X[d/K�S2DF_H=2XHqg_�A"Z�Z�K�G�X�?¶ a~b>`HKZ:l�D�T!?US2=YZ&=2X[Z�K�GUP8K�G�K�X�I�K_�A"Z�Z�K�G�X�5,?�S2=�ZnI�K�X[Z�K�G&?�K�_VA�GJA"Z�=2DFX �[<gl~=2S2S~LVK�K�X[d/K�S2DF_NK�WtL(^�Z�`HK�D/XHK�T!?�SY=YZW]= ��G\A/I$Z�=2DFX_�A�ZUZ�K�G�XV?>D�P�=�ZJ?>Z:l�D�?�SY=YZ\?-5,l~=2W]Z�`�?�]<�=YPA[<��'��� �Va

Page 169: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ³ º ¡B= ��G\A/I$Z�=2DFX � ¹[¶

LN<'� $ �VaIi<'� � � �VaWV<'� $�� ��aK*<'� $ ³ ��a

¾ ³ º6h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujW]= �NGJAFI�Z�=2DFXqFGJA"Z�=2XHq¹ a �\¸�K�Zi· ?�_HS2A*^ �]1\��D3�����"# 1 |�DFG �]��¾/¾Ho"Z\`HKBA�XV?Ul�K�Gj=@?�u��cX�D/_]Z�=@I�AFS�W]K�d[=@I�KRI�DFXV?U=@?:Z\=YX�q-D�P�e&AFX(^sX�AFG�G\D"lt?�SY=YZ\?5�I�A�S2S2K�WG�E�SY=2XHq/?J<�DFG>G\K���KiI$Z�=2dFKMq/G�D(D"dFKi?R5�A�S@?UD�I�A�S2SYKiWnG\EHS2=YXHq[?\<�a �A[<C»{`VA"Zc=@?~A�¯�=2IJ`�K�S@?UD/XQ=2X[Z�K�G�P8K�G\DFe&K�Z�K�Gio]�cS2K�� �LN<n»{`VA"Zc=@?~A�I�DFX(d/K�G\qF=2XHqsS2K�X�?�oH�cS2K�� �Ii<n»{`VA"Zc=@?~A�I�DFe&_�A/I$ZcW]=@?UO�oH�BSYK����WV<n»{`VA"Zc=@?~A�W]=���GJAFI$Z\=YD/XQq/G\A�Z�=2XHq�o]�BSYK����K*<n»{`VA"Zc=@?~A&S2A/?UK�G�o]�cS2K�� �

¾ ³ º6h[e4EHS�ZB¾/¾[º�¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�¿~=YZUZ\K�XH`�DFE�?�Kº(a~b>`HK6WH=���G\A/I$Z\=YD/XQq/G\A�Z�=2XHq4l>AF?~AF_H_�AFG�K�X/Z\SY^�=2X(dFK�X/Z\K�W�58XHDFZ~Z�`�A�ZBA�X(^FD/XHK�XHD�Z\=2I�K�WQesE�IJ`V<�=2Xr�*º ¼/¶ L[^�u

A[< ��K�Xm|�G\AFXHO(SY=2X�aLN<#��K�X AUA�e&=2Xmb>`�DFe&_�?�DFXr58K�X�XHDFLHS2K�WmA/?c��G\A�P�¿~EHegP8D/G\W�<�aIi<Qb>`�DFe�AF? �/K ��K�GJ?UD/X�aWV<¤HA�e}�RWHA�e�?�aK*<Q¡�A*d(=2W¿~=YZUZ\K�XH`HD/E�?�KFa

¾ ³ º6h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujE�?�KMD�PjW]= �NGJAFI�Z�=2DFXqFGJA"Z�=2XHq¼ a~b>`HK6WH=���G\A/I$Z\=YD/XQq/G\A�Z�=2XHq4=@?cAFXQ=2e&_VD/GUZJA�X[ZcW]K�d(=@I�K-=2X�u

A[<Ce&=@I�G\D/?\I�D/_[^/aLN<Q?�K�l�K�G~?�^]?:Z\K�e�?�aIi<QI�A�e&K�GJAF?�aWV<QI�DFe&_�A/I$ZcW]=@?UO]?�aK*<Q?�_NK�I$Z\G�D[?�I�DF_(^Fa

¾ ³ º6h[e4EHS�ZB¾/¾ ½ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]= ��G\A/I$Z�=2DFXqFGJA"Z\=YX�q4G\K�?�DFS2E]Z�=2DFX½ a~b>`HK-L�G�=2qF`[Z>P8G�=2XHq/K�?>D�P�A&W]=���GJAFI$Z\=YD/XmqFGJA"Z�=2XHq&W]= �NGJAFI�Z�=2DFX_�A"Z�Z�K�G\XmA�G\KFu

A[<Cd/K�G\^C`H=2qF`mA�X�WQX�AFG�G\D"l�A�XVWCZ\`H=2?BA�S2SYD"lc?�`H=2qF`ml>A*dFK�S2K�X�q�Z�`QG�Ki?UD/SYEHZ�=2DFX�aLN<nd/K�G\^CS2D"l�A�X�WLHG\D/A/WnAFX�WQZ�`H=@?cA�S2S2D"lc?�S2D"l�l>A*dFK�SYK�XHq�Z\`nG\K�?�DFS2E]Z�=2DFX�aIi<QAFG�KMK��]A/I$Z\SY^CS2=2OFK�Z:l�DFTk?�S2=�Z~LHG\=Yq/`[Z�P8G\=2XHqFKi?�aWV<QAFG�KMe&DFG\K�DFG~S2K�?\?>SY=2OFKMZ:l�D�T!?US2=YZ�LHG\=2qF`[Z>P8G�=2XHqFKi?�aK*<nd/K�G\^C`H=2qF`mA�X�WQX�AFG�G\D"l�A�XVWCZ\`H=2?BA�S2SYD"lc?�S2D"l�l>A*dFK�S2K�X�q�Z�`QG�Ki?UD/SYEHZ�=2DFX�a

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³ º6h/P8EHS2S�¾/¾F¾H�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�Fa>»rA*dFK�SYK�XHq�Z\`¾ � ¹/³F³ � e S2=Yq/`[Z>=@?>=2X�I�=@W]K�X[ZcD/XmA&?�=YX�qFS2KM?�S2=�Zia

A[<®REVA�S2=�ZJA"Z�=2dFK�SY^Q?UO/K�Z\IJ`nZ�`HK6WH=���G\A/I$Z\=YD/X_VA"ZUZ\K�G\XQ=2X[Z�K�X�?U=YZ:^nA/?~AgP8EHX�I$Z\=YD/XmD�P ��aLN<n»{`VA"ZM=2?RZ�`�KgAFX�A�S2^[Z�=@I6K��]_HG\K�?\?�=YD/X�P8DFGRZ�`HK&A�X�qFEHS@A�G�W]=���K�G\K�XVI�KgLVK�Z:l�K�K�X�Z\`HK ��Z�`�D/G\WHK�G�eg=2XH=2e�A

D/XnZ\`HK-DF_�_VD[?U=YZ�K6?�=2WHK�?>D�P�Z�`HK6I�K�X[Z�GJA�Spe�A��(=2esE�e �Ii<Qb>`�KMZ:l�Dg��GJ?:Z~D/G\W]K�G>eg=2XH=2e�A�A�G\KM?�K�_VA�GJA"Z�KiWCL(^ ³ � ¾��"aj»{`�A�Zc=2?>Z\`HK6?�SY=YZcl~=2W]Z�`�� �

Page 170: Introductory Physics Problems David J. Jeffery Department of

� ¹/¹ v�`�A�_]Zia ³ º�¡R= �NGJAFI�Z�=2DFX

¾ ³ º6h/P8EHS2S�¾/¾H��¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�?�DFEHXVWQW]= ��G\A/I$Z�=2DFX�oHI�DFXVI�K�G�Zc�� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ½ � ³ u ¹ _V<

�]a~�R?�P,AFGjAF?�_�A"Z�Z�K�G\X�?�qFDg58LHEHZ�X�D�Zj?U_NK�KiWpo"=YX[Z\K�X�?�=�Z:^/o�G\K���KiI$Z�=2DFX�o*Z�GJA�X�?�e&=2?\?U=2DFXN<�AcS2D�Z�D�PVl�A*d/K;_H`HK�XHDFX�K�e�ALNK�`�A*d/K-h/E�=�Z\K6A�S2=YO/K �wZ�`HK�^N· W?�I�A�GJI�K�S2^CA�S2SpLNK6I�A�S2S2K�WQl�A*d/KR_H`�K�XHD/egK�X�Ag=�P�Z�`�K�^QWH=2W]X�· ZiaA[<nb>`�KR?�_VK�K�WCDFP�?UD/EHX�W�=2XQAF=YG�A"Zc��¾��cA�XVW���A"Z\e�=2? ³ µ ³ eny"?c5�£B¿�»wTkµ/¾/¾/<�a�b>`�KcP8G\K�h[EHK�XVI�^&G\AFXHqFKBD�P`(EHe�AFX`�K�A�G\=2XHq4=@?cAF_H_HG\D*�(=2e�A"Z\K�S2^ ³ ¾"T ³ ¾ �¾/¾F¾�£B�s5,A&S@A�G\qFKMW]^(X�A�e&=@IMG\AFXHqFK/u;v��Bv;T ¹/¹ <$a�»{`�A�Zc=2?Z\`HK-GJA�XHq/KRDFP�`(EHe�A�X`HKiA�G\=YXHq&=2Xml�A*d/K�S2K�XHqFZ�` �

LN<n»{`VA"Zc=@?�Z�`HK-l>A*dFK�SYK�XHq�Z\`QI�D/G�G\K�?�_NDFX�W]=2XHq4Z�DCI�DFX�I�K�G�Z>� 5 # $�µFµ[¾�£c�/ujv��Bv;T ¹ ºF<��Ii<¤HA*^�?UD/e&K�DFX�Km5,l~`HD�?�`�A�S2SjLVK�XVA�e&K�S2K�?\?-`HK�G�K*<B=@?6I�S2AFG�=2XHK�Z�Z�=2XHq ��A�X(^�l�DFGJWxI�A�XrLNK�dFK�G\LNK�W � A�ZI�DFX�I�K�G�Z��tl~=�Z\`gAFe&_HSY=Y�VI�A"Z�=2DFXs=YX4DFXHK>IJ`�A�e4LVK�G�AFX�WMZ\`HK�?�DFE�X�W6l>A*dFKi?�_HG\D]W]E�I�KiW6A�G\K;_�S2AFXHK�l>A*dFKi?Z\`�A"Z&=2X/Z\K�GJI�K�_]Zg`�K�AFW]T�D/XtA�ZJA�S2S-58dFK�G�^rZJA�S2S@<4W]D(DFG4Z�`VA"Z&=2?gµ�e l~=@W]KLVK�^FDFXVW�l~`H=@IJ`�=@?&A�XHDFZ�`HK�GIJ`VA�esLNK�G&58l~=YZ�`xK�IJ`HDFT�_�G�D(D�Pjl>A�S2S2?J<>Z\`�A"Z-?UZ�G\K�Z\IJ`�K�? 0 $��i¾F¾je�?UZ�GJA�=2qF`[ZRA*l>A*^CP8G\DFe�Z\`HKgWHD[D/GcZ\DACl�AFSYS�A"ZBl~`H=@IJ`�AC?�DFS2=�ZJA�G\^x5�A�X�WmS2DFXHK�SY^H<>S2=@?:Z\K�XHK�GB=@?B?�K�A"Z\K�WmG\=Yq/`[ZRA"ZcZ\`HK4��X�W�DFGJW]K�GcW]=���GJAFI$Z\=YD/Xe&=2XH=2esEHe A�X�W�`�A*d(=2XHqQZ�G\DFEHLHS2K�`HKiA�G\=YXHq��wl~`�=2IJ`�=2?Me�A*^(LNKCA�S2SjP8DFGMZ\`HK�LVKi?:Z��w=@?sA/W A:E�?UZ�=2XHqm`HK�G`�K�A�G\=2XHqRAF=2Wpo*LHEHZ�DFP�I�D/EHG\?�K�Z\`�A"ZjW]D(K�?�XHDFZ�`HK�SY_sEHXHS2K�?\?�?�`HK�egD"d/K�?�P8G�D/e `HK�G�EHX]P8D/GUZ\EHX�A"Z\K�S2D]I�A�Z�=2DFXA�Z���egK�Z�K�G\?�P8G\DFe�Z\`HKCA"�]=@?�Z�`�A�Z6G�E�X�?MXHDFG\e�A�S�P8G\DFe�Z\`HKCW]D(DFG�Z�DmZ\`HK&l�AFSYS�Z\`�A"Zs?�`HK&=@?6?UKiA"Z\K�WA�Z ��A�X�W�o/l�DFEHS@W]X�· Z;^/DFE&O(XHD"lt=YZ�o/Z�`�KB_ND/?�K�G�DFPNZ\`H=@?;I�D/X(EHX�W]G\EHefl�DFXVW]K�GJ?jl~`�A�Z �nl�DFEHS@WgLVK/oFP8E�SYS?UZ�D/_�o]_NK�G\=YD]WpoH`VA�XHqFT�EH_�o]G�D/qFK�G>D"d/K�G>A�X�WDFEHZ�a

WV<n»{`VA"Zcl�DFEHS@W �mP8G\DFe�Z�`HK-_VA�G�Z-5�I�<�LNK-=�P�Z�`�K6W]D(DFG~l�K�G\KRD/XHSY^���e�l~=@W]K����j�]_HS@A�=2XQ^/DFEHG~A�XV?Ul�K�Gia

¾ ³ º6h/P8EHS2S�¾/¾H�F�i¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�W]=2qF=YZ\AFS�Z�K�SYK�d[=@?�=YD/X³ aBv�D/X[d/K�X[Z�=2DFXVA�S&Z�K�SYK�d(=2?�=YD/X �� � � � ¦&� � ?�=Yq/X�A�S@?�`�A*d/K�A�l�A*d/K�S2K�XHqFZ�`�D�P � ¶ ¾�I�ema ¡R=2qF=YZ\A�SZ\K�S2K�d(=2?�=2DFXmAFI�I�DFGJW]=2XHq4_�S2AFX�?-5,I�=YGJI�A���¾/¾H�*<�l~=2SYS�`�A*dFKMA&l�A*d/K�S2K�XHqFZ�`CDFP � ��¾�egemaA[<C»{=2S2S�Z�`�K6IJ`�A�XHq/K�Z�DnW]=2qF=YZ\AFSp=YXVI�G\K�AF?�KMDFGBWHK�I�G\K�A/?UKRZ�`�KsW]= �NGJAFI�Z�=2DFXmD�P�Z�K�SYK�d[=@?�=YD/Xm?�=2qFX�AFS2?>=2X[Z�D&Z�`�K?�`�A/W]D"l�G\K�qF=2DFXV?�DFP�q/K�D/egK�Z�G\=2I�A�S�DF_HZ�=@I�?� ��G�=2K���^ A:E�?:Z\=�P8^Q^FD/EHG~A�X�?�l�K�G�a

LN<¤HA*^nZ\`HK6q/AF_�D�P ¶ e LVK�Z:l�K�K�X�Z:l�D�LHEH=2S@W]=YX�q/?�A�_H_HG\D*�]=Ye�A�Z�K�?~An?U=2XHqFS2Ks?�SY=YZ �{l~`H=@IJ`mZ�`HK4_HG\DFL�AFLHSY^WHDFX�· Z�W]D dFK�G\^�l�K�S2S�LVKiI�A�EV?UKwD�PQZ�`HK�=YGr�VXH=�Z\K±Z�`H=@IJO(XHK�?\?�a |HD/GrZ�`HK{I�DFX(dFK�X/Z\=YD/X�A�SgZ\K�S2K�d(=2?�=2DFXl>A*dFK�SYK�XHq�Z\`�o�l~`VA"ZR=@?BZ�`HKgA�XHq/EHS2AFGcl~=@W(Z�`±58=2X�W]K�q/G�K�K�?J<>D�PjZ\`HK4I�K�X[Z�GJA�S�W]= �NGJAFI�Z�=2DFX�LHG\=Yq/`[ZBP8G\=YXHq/K �� � ��Z\`HKM��GJ?:Z~��K�G�D[?M58=�a K/aYoH_NDF=2X[Z\?~DFP�I�DFe&_HS2K�Z�K6WHK�?UZ�G\E�I$Z\=Yd/K�=2X[Z�K�GUP8K�G�K�X�I�K*<��

Ii<Q¿cK�_NK�A"Z�_�A�G�ZB58LV<�o(K��HI�K�_]Z;XHD"l±E�?�K>Z�`HKBWH=Yq/=�ZJA�SHZ\K�S2K�d(=@?U=2DFX&l>A*dFK�S2K�X�q�Z�`�a�v�DFE�S2W&S@AFIJO4D�PpW]=���GJAFI$Z\=YD/XLNK6Ag_HG\DFLHS2K�e P8D/GcW]=2qF=YZ\A�S�Z�K�S2K�d(=@?U=2DFX �»{`[^��

¾ ³ º6h/P8EHS2S�¾/¾/��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u>�>A�L�=YXHK�Z�· ?~_HG\=YXVI�=2_HSYKµ�ac¤]A*^r^/DFE�`�A/W�?UD/e&KnO(=YXVW�D�PRAF_VK�G\A�Z�EHG\KCLNK�^/DFX�W�l~`�=2IJ`�=@?gA�G\K�qF=2DFX�D/XHS2^�=2S2SYEHe&=2X�A"Z\K�W�L[^�Z\`HKnS2=Yq/`[ZZ\`HG�D/EHqF`QZ�`VA"ZBA�_NK�G�Z�E�G�K/aA[<)��D/E `VA*dFKtZ:l�D�e�AF?�O(?rl~`�=2IJ` LVDFZ�`�I�D"d/K�GxZ�`HK{l~`HD/SYK{AF_VK�GUZ\EHG�K/a b>`HK±��GJ?UZr=@?�I�D/e&_HSYK�Z�K�SY^Z\G\AFX�?�_�A�G\K�X[Zrl~`HK�G\K�Z\`HK�?�K�I�D/X�W =@?rDF_VAFh[EHKwA�X�W DF_�A/h[EHKwl~`HK�G\K�Z\`HK�?�K�I�D/X�W =@?�I�D/e&_HSYK�Z�K�SY^Z\G\AFX�?�_�A�G\K�X[Z�u�=�a K/aYoNZ�`�K4e�AF?�O]?BAFG�KsI�DFe&_HS2K�e&K�X[ZJA�G\^Fac»{`HK�X�Z\`HK�G\K6=@?BXHDQe�AF?�OD/XmZ�`HK&A�_NK�G�Z�E�G�K/oZ\`HK�K�S2K�I�Z�G\=2IQ��K�S2W 5�I�DFXV?U=@W]K�G\K�W±Ar?�I�A�S@A�Gg��K�S2WwAF?�AFG�K�AFSYS>Z\`HK�D�Z\`HK�GJ?&=YX±Z\`H=2?&_�G�D/LHSYK�eC<g=YX±Z�`�KLNK�^/DFX�W]T�G\K�q/=YD/Xg=@? C5 � <$a�»{`HK�X�Z�`�KB��GJ?UZ;e�AF?�O4=@?;_�E]Z�D/X&Z�`HK�A�_NK�G�Z�EHG\KFo/Z�`�KBK�S2K�I�Z�G\=2Ic��K�S@W�=2X�Z�`�KLNK�^/DFX�W]T�G\K�q/=YD/X�=2? � 5 � <$a�»{`HK�XnZ\`HK�?�K�I�DFX�WCe&A/?UOg=@?�_�E]Z�D/X�Z�`�K�AF_VK�GUZ\EHG�K/o[Z�`HK�K�S2K�I�Z�G\=2Ic��K�S@WC=2XZ\`HKgLVK�^FDFXVW(T�G\K�q/=YD/X�=2?� � 5 � <$a6�R?U=2XHqQZ�`HK&£cE�^[q/K�X�?UT!|HG\K�?�XHK�S�_HG\=YX�I�=Y_�SYK4Z�`HK�DFG\^��X�W�Z\`HKgG�K�S2A�Z�=2DFX?\A"Z\=2?U��KiW�L(^ C5 � <$o � 5 � <$o;AFX�W � 5 � <$a����]_HS2AF=YX�l~`(^rZ\`HKQG\K�S@A"Z\=YD/X�D]I�I�EHG\?�arb>`HKnG\K�S@A"Z\=YD/X�=2?q/SYD/G�=2DFEV?US2^CI�AFSYS2K�W!�>A�LH=2XHK�Zi· ?>_�G�=2X�I�=2_HS2KFa

LN<n»{`(^I�A�X�· Z �>A�LH=2XHK�Z�· ?~_HG\=YX�I�=Y_�SYKMLNK-K��HAFI�Z�S2^nI�D/G�G\K�I�Z�Ii<Qb�A�O(=2XHq �>A�LH=2XHK�Z�· ?~_HG\=YX�I�=Y_�SYK-Z\DCLNK6K��HAFI�Zcl~`�A"ZR=2?>Z\`HK6G\K�S@A"Z\=YD/XLNK�Z:l�K�K�XmZ�`HKs=YX[Z�K�X�?�=�Z\=YKi?BI�AFE�?�K�WL(^�Z\`HK&e�AF?�O(?&5,=�a KFa2o � � 5 � <�A�XVW � � 5 � <�<B=2X�AnG\K�q/=YD/X�l~`HK�G�K4Z�`�K�EHXHe�AF?�OFKiW�A�_NK�G�Z�E�G�KgqF=2dFKi?R��K�G\D

Page 171: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ³ º ¡B= ��G\A/I$Z�=2DFX � ¹ º

=2X[Z�K�X�?U=YZ:^ �N5 � <�$ ¾Hu�K/a qVaYo>ArG�K�qF=2DFXtD�P-?U`�A/W]D"l-a{»{`�A�ZQI�AFXt^/DFEw?�A*^�AFLVD/E]Z�Z�`�K�W]=���GJAFI$Z\=YD/X_VA"ZUZ\K�G\X�?~I�A/?:Z~L(^CZ\`HKMZ:l�D4e�AF?�O]?>=YXmG\K�q/=YD/X�?�D�Pj?U`�A/W]D"l-a

¾ ³ º6h/P8EHS2S�¾/¾ ³ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�ujq/^[G\=2XH=2WQLNK�K�Z\SYK� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ½ � ¹ u ³/¹ ��<

¶ a~b�G�D/_H=@I�A�SFqF^(G�=2XH=@W�LVK�K�Z�S2K�?�58l~`H=2G\SY=2qF=2q~LVK�K�Z\SYKi?\<�`�A*dFK�?\I�AFSYKi?pl~`HD/?�K�A�S2=2qFXHe&K�X[Z�e�A�O/K�?pE�_6Ac?�I�A"Z�Z�K�G\=2XHq658D/GG\K���KiI$Z\=YD/XV<�W]=���GJAFI$Z\=YD/XQq/G\A�Z�=2XHq�a�b>`HK-W]= �NGJAFI�Z�=2DFX_�A"Z�Z�K�G�XQP8G�D/e�Z�`HK-q/G\A�Z�=2XHqse�A*^nI�DFX]P8EV?UKM_HG\K�WHA�Z�D/G\?�a¤]A*^�¾ � ¶/¶F¶ � e SY=2qF`[Z-58qFG\K�K�X�SY=2qF`[Ziu�£�?VT ¶�¹ <j=2?�=2X�I�=@W]K�X[Z>XHDFG\e�A�S�Z�D6Z\`HK�LVK�K�Z�S2K�qFGJA"Z�=2XHqsAFX�WCAn��?UZ�DFGJW]K�Ge�A"�]=2esEHe�=2?c?�K�K�XA�ZBA�XmA�XHq/SYKMDFP�� ¹ �RP8G�D/e Z\`HK-XHDFG\e�A�S�aA[<C»{`VA"Zc=@?�Z�`HK-q/G\A�Z�=2XHq�?U_�A/I�=2XHq �LN<n»{`VA"ZBA�X�qFS2K�DFP�Z\`HKs�"X�WD/G\W]K�G>e&A��]=Ye4EHe �Ii<m°RGJW]=2X�A�G\=2SY^Z�`�K4q/G\A�Z�=2XHqnl~=2SYSj?\I�A�ZUZ�K�GRl~`�=�Z\KgS2=2qF`[Z�a-»{`�A�Z�l�DFE�S2W�^FDFEx?UK�K4=YP;^FD/E�_HG\DBA:KiI$Z�KiW�Z\`H=2?S2=2qF`[Z4D/X�A�?\I�G\K�K�X �}»{`�A"Zgl�D/EHS2W�^FDFEt?UK�Kn=YPc^FDFE�l�K�G�KCS2D(DFO(=2XHqxA�ZsZ�`�KQLNK�K�Z�S2K�� �B?\?UE�egKQZ�`�KLNK�K�Z�S2K-qFGJA"Z\=YXHqgl�DFG\O(?�S2=YO/K6A�X=2WHK�A�Spq/G\A�Z�=2XHq�aj¿~KiA�SpLNK�K�Z�S2K�?~e�A*^CLNK-SYKi?�?�Z\`�A�Xm=@W]K�AFSpqFGJA"Z\=YXHq[?�a

¾ ³ º6h/P8EHS2S�¾/¾�µ/¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u � T�GJA*^CW]= �NGJAFI�Z�=2DFX�o3��GJA�qFqgS@A*l� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ½ �*º]u ¶F³ ��<

¹ a ��D/Em?�`H=2XHK&� � � �� � TkG\A*^]?�DFXmA�I�G\^]?:ZJA�S�D�P�S2=�Z\`H=YE�e ��D/G�=@W]KFaA[<nb>`�Kg�"XVW�DFGJW]K�GRG�K���K�I�Z�=2DFX�D]I�I�EHGJ?BA"ZMA ��GJA�qFq�AFXHqFS2KsDFP�� ¼ ��aB»{`�A�ZR=@?cZ\`HKg=YX[Z�K�G�_�S2AFX�A�GB?�_�A/I�=2XHq=2XQ�BXHq/?UZ�G\DFe�?;P8DFG�Z�`H=@?�G�K���K�I�Z�=2DFX � ������ � ¿~KiI�AFSYSVZ�`�A�Z�Z\`HKMI�DFX(d/K�X[Z�=2DFX�=2X � T�GJA*^gWH=���G\A/I$Z\=YD/XC=2?Z\D�e&K�AF?�EHG\K�AFXHqFS2K�P8G�D/e Z�`�K6?UEHG�P,AFI�KMD�P�?\I�A�ZUZ\K�G\=YXHqVo]XHD�Z~P8G\DFe Z�`HK-XHD/G�e�AFS�A/?>=YXmd(=@?UE�AFSpDF_]Z\=2I�?�a

LN<n»{`VA"Zc=@?�Z�`HK6AFXHqFS2KMD�P�Z�`HK��i?:Z~DFGJW]K�G�G\K��VK�I$Z\=YD/XnP8D/G>Z�`HK-=2X[Z�K�G�_HS@A�XVA�G~?U_VAFI�=2XHq��

Page 172: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � U+9�1_HJ*[&AN �L1_N[&X;<*-(+*O; 6

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³/¼ h[e4EHS�ZB¾/¾F¾ ¶ ¾C�&�s�4K�A/?U^�e&K�egD/G�^�u;�MAFSY=2SYKiA�XQZ�GJA�X�?UP8DFG\e�A"Z\=YD/X�?�FaBv�S@AF?\?U=@I�AFSp cK�l>Z\DFXH=@A�XmS@A*lc?�D�P�_H`(^(?�=@I�?~A�G\K�=YXHK�GUZ\=2AFSpP8GJA�e&KM=YX(d"A�G\=2AFX[Z�EHXVW]K�Giu

A[<�Z\`HK6¸�D/G�K�X[Z���Z�GJA�X�?UP8DFG\e�A"Z\=YD/X�?�aLN<CZ\`HKs�MA�S2=2SYKiA�XQZ�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aIi<nX�D4Z\G\AFX�?UP8DFG\e&A�Z�=2DFX�?>A�ZBA�S2S�aWV<CZ\`HK6²MK�_�SYK�G�=@A�XQZ�GJA�X�?UP8DFG\e�A"Z\=YD/X�?�aK*<CZ\`HK6¯�A��(l�K�S2S2=2AFXnZ\G\AFX�?:P8D/G�e�A�Z�=2DFX�?�a

¾ ³/¼ h[e4EHS�ZB¾/¾F¾ ¹ ¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj£cK�=YXHG\=@IJ`m£BK�G�Z���]a~£BK�=2XHG�=@IJ`m£cK�G�Z��C5U� ¼[¶ º ��� ¼/½ µ[<jK��]_VK�G�=2e&K�X[Z\AFSYS2^Cd/K�G\=���KiW�Z\`HK-K��]=@?:Z\K�X�I�K-D�P:u

A[<CK�SYKiI$Z\G�D/e&AFqFXHK�Z�=@IBl>A*dFKi?�aLN<nS2=2qF`[Z�aIi<QAFXQE�_H_VK�GcS2=Ye&=YZ~Z�DCA�S2Sp_H`(^]?U=@I�AFSpdFK�SYD]I�=YZ�=2K�?�aWV<nq/G\A*d(=YZ:^FaK*<nq/G\A*d(=YZ\A�Z�=2DFX�AFSVGJAFW]=@A"Z\=YD/X�a

¾ ³/¼ h[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�W]=@?\I�D"dFK�G�^�?�_VKiI�=@A�SpG\K�S@A"Z\=Yd(=YZ:^³ a~�;=YX�?UZ�K�=YX��GJ?UZ>_�EHLHS2=2?�`HK�W`H=@?>Z\`HK�D/G�^�DFP�?�_VKiI�=@A�SpG\K�S@A"Z\=Yd(=YZ:^C=YX�u

A[<�� ½ ¾ ¶ aLN<�� ¼ º ½ aIi<�� ½/¶/¶ aWV<��"ºFº ¹ aK*<��i¾ ¹/¹ a

¾ ³/¼ h[e4EHS�ZB¾/¾H�/��¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujG\K�S@A"Z\=Yd(=YZ:^�_HG�=2X�I�=Y_HS2K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½ �"T\�/�

µ�a~�RI�I�D/G\WH=YXHqgZ\D4Z\`HK-_HG\=YXVI�=2_HSYK�5,DFG~_ND/?UZ�EHS@A"Z\Ki<�D�P�G\K�S@A"Z�=2d(=�Z:^/o[Z�`HK-S@A*lc?>D�P�_H`(^(?�=@I�?>DFGio]e&DFG\KMK��HAFI�Z�S2^Fo(Z�`�KK��(_�G�Ki?�?�=YD/X�?�D�P�_H`(^(?�=@I�A�SpS@A*lzAFG�K�Z\`HK6?�AFe&K�=2X�uA[<nAFSYS�P8GJA�e&Ki?>D�P�G�K�P8K�G\K�X�I�KFaLN<ne&D[?:Z>P8GJA�e&K�?>DFP�G\K�P8K�G�K�X�I�K/aIi<QAFSYSp=2XHK�GUZ\=2AFSpP8G\AFe&K�?M58=�a K/aYo�P8EHX�WHAFe&K�X[Z\AFSYS2^CEHX�A/I�I�K�S2K�GJA"Z�KiWCP8GJA�e&Ki?\<�D�P�G�K�P8K�G\K�X�I�KFaWV<QAFSYSpX�DFX]Tk=YX�K�G�Z�=@A�S�P8GJA�e&K�?-5,=�a KFa2o]P8EHX�W�A�e&K�X[Z\AFSYS2^QA/I�I�K�S2K�GJA"Z�KiW�P8GJA�e&K�?J<�D�P�G�K�P8K�G\K�X�I�KFaK*<nX�D4P8GJA�e&Ki?>D�P�G�K�P8K�G\K�X�I�K

¾ ³/¼ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�G�K�S2A�Z�=2d(=�Z:^C_ND/?UZ�E�S2A�Z�K¶ a �\¸�K�Zi· ?n_HS@A*^ �]1J� D+�"����# 1 |�DFG �]��¾/¾Ho�Z�`HK�A�X�?�l�K�GC=@?�u�b>`�A�ZCZ�`�K�S@A*lc?CD�P-_H`(^]?�=2I�?nA�G\K�Z\`HKx?\A�e&K�P8D/GD/L�?UK�G�d/K�GJ?;=2X�A�S2Sp=YX�K�G�Z�=@A�SpP8GJA�e&K�?�a �A[<C»{`VA"Zc=@?~��=2X�?:Z\K�=2X�· ?c?U_NK�KiWD�P�S2=2qF`[Zc_VD[?:Z\EHS@A"Z�K/oH�cS2K�� �LN<n»{`VA"Zc=@?�Z�`HK-_ND/?UZ�EHS@A"Z\K-D�P�Z�`HK-=2X(d"A�G\=2AFX�I�K�D�P�I�DF=2X�I�=2W]K�X�I�K/o��cS2K�� �

Page 173: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¼ ¤(_NK�I�=2AFS�¿~K�S@A"Z\=Yd(=YZ:^ � ¹/½

Ii<n»{`VA"Zc=@? �� ����� $ � ��NoH�BSYK����WV<n»{`VA"Zc=@?>`HDFGJ?UK-?�K�X�?�KFoH�BSYK�� �K*<n»{`VA"Zc=@?~��=2X�?:Z\K�=2X�· ?~G�K�S2A�Z�=2d(=�Z:^�_ND/?UZ�EHS@A"Z\KFo��BSYK�� �

¾ ³/¼ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�ujS2=Yq/`[Z~?�_NK�K�W_ND/?UZ�EHS@A"Z\K¹ a~b>`HK6?�_NK�K�WQD�P�S2=Yq/`/Z~=2Xmd*A/I�EHE�e�`�A/?�Z�`HK6?\A�e&KMd"A�S2EHKFoHS@A�LNK�S2K�WQL(^'*"o]=2X�A�S2S�W]=2G�KiI$Z�=2DFXV?~A�X�Wpu

A[<C=2X�?UD/e&K�=2XHK�GUZ\=2AFS�P8G\AFegKi?�aLN<n=2X�A�S2S�P8G\AFe&K�?�aIi<n=2XmXHDgP8G\AFe&K�?�aWV<n=2X�A�S2Sp=YX�K�G�Z�=@A�S�P8GJA�e&K�?�aK*<n=2XmXHD&=YX�K�G�Z�=@A�S�P8GJA�e&K�?�a

¾ ³/¼ h[e4EHS�ZB¾/¾�µ[¾F¾C�&�s�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�G�K�d(=2?�=YX�q& BK�l>Z\DFXH=@A�Xe&K�IJ`�AFXH=2I�?º(a~�;=YX�?UZ�K�=YX�· ?�Z:l�D�?U_NK�I�=2AFSpG�K�S2A�Z�=2d[=YZ:^C_ND/?UZ�EHS@A"Z\K�?>=2e&_HSY=2K�WZ\`�A"ZcI�S2A/?�?�=2I�A�S� BK�l>Z�D/XH=@A�XegKiIJ`�A�X�=2I�?

A[<CX�K�K�WHK�WXHD&G�K�d(=2?�=YD/X�aLN<nX�K�K�WHK�WG�K�d(=2?�=YD/X�aIi<nl>AF?>l~=2S@W]SY^nl~G�D/XHq&=YX�A�S2S�I�A/?UKi?�D�P�=YX[Z�K�G�Ki?:ZiaWV<nl>AF?>X�D�ZcI�D/G�G\K�I�Z�XHD"l-o]L�E]ZBl�DFEHS@WnLNK-=2XQZ\`HKMP8E]Z\EHG�K/aK*<nl>AF?~I�DFe&_HS2K�Z\K�S2^CE�?�K�S2K�?\?�a

¾ ³/¼ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�¸�DFG\K�X[Z��RZ�GJA�X�?UP8DFG\e�A"Z\=YD/X�?¼ a>7!X�?�_VKiI�=@A�SpG\K�S@A"Z�=2d(=�Z:^CZ�`HK6?�_�AFI�K�Z\=Ye&K-I�D(DFGJW]=2X�A"Z\K�?�=2XmWH=���K�G\K�X[Zc=2XHK�G�Z�=@A�S�P8GJA�e&K�?~AFG�K�G\K�S@A"Z�KiWnL(^�u

A[<�Z\`HKs�MA�S2=2SYKiA�XQZ�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�aLN<CZ\`HK6²MK�_�SYK�G�=@A�XQZ�GJA�X�?UP8DFG\e�A"Z\=YD/X�?�aIi<CZ\`HK6 cK�l>Z�D/XH=2AFXnZ\G\AFX�?UP8DFG\e&A�Z�=2DFX�?�aWV<CZ\`HK6¯�A��(l�K�S2S2=2AFXnZ\G\AFX�?:P8D/G�e�A�Z�=2DFX�?�aK*<CZ\`HK6¸�D/G�K�X[Z���Z�GJA�X�?UP8DFG\e�A"Z\=YD/X�?�a

¾ ³/¼ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujW]K�G\=2d[=2XHqgZ�`�K6¸�DFG\K�X[Z\�BZ\G\AFX�?�a½ a>7!X�W]K�G�=2d(=YXHqgZ\`HK6¸�D/G�K�X/Z\�BZ\G\AFX�?UP8DFG\e&A�Z�=2DFX�?�Z\`HK6I�D/X�W]=YZ�=2DFX=2?~=2e&_VD[?UKiWCZ\`�A"Ziu

A[<�Z\`HK-d"AFI�EHEHe�S2=2qF`[Zc?U_NK�KiWQd"AFG�=2K�?>l~=YZ�`m=2XHK�G�Z�=@A�S�P8GJA�e&KFaLN<CZ\`HK-XHD/X]T�d"A/I�EHEHe�SY=2qF`[ZB?�_VK�K�WQd*AFG�=2K�?>l~=YZ�`m=2XHK�G�Z�=@A�S�P8GJA�e&K/aIi<CZ\`HK-XHD/X]T�d"A/I�EHEHe�SY=2qF`[ZB?�_VK�K�WQ=2?~=2XHK�GUZ\=2AFS�P8G\AFegKM=2X(d*AFG�=@A�X[ZiaWV<CZ\`HK-d"AFI�EHEHe�S2=2qF`[Zc?U_NK�KiWQ=@?>=2XHK�G�Z�=@A�SpP8GJA�e&KM=2X[d"AFG�=@A�X[Z�aK*<CZ\`HK-d"AFI�EHEHe�S2=2qF`[Zc?U_NK�KiWQ=@?M��e��"?�a

¾ ³/¼ h[e4EHS�ZB¾/¾[º�¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj|�=�Z\��qFK�G\AFS2WI�D/X[Z�GJAFI$Z\=YD/X��¾Ha~b>`HKm_HG\DF_NK�G&D/GgG\K�?UZUT�P8GJA�e&KQS2K�X�q�Z�` � � _�AFG\AFSYS2K�S�Z�D�Z\`HK�W]=YG\K�I�Z�=2DFXtD�PRe&DFZ�=2DFX±D�P�AFX�D/L,A:K�I�Z&e&D"d(=2XHqG\K�S@A"Z\=Yd/KMZ�DnAFX�=YXHK�GUZ\=2AFS�P8GJA�e&K �±=@?cG\K�S@A"Z\K�WZ�DCZ�`HK6S2K�X�q�Z�` �{e&K�AF?�EHG\K�WL(^AFX�DFL�?�K�G\dFK�GcA"ZBG\K�?UZB=2X �

L(^�Z\`HK6|�=�Z\��qFK�G\AFS2WI�D/X[Z�GJAFI$Z\=YD/XCP8D/G�e4EHS2A�uA[< � $� � # � , � � aLN< � $� � � # � , � � aIi< � $� � aWV< � $�� � � � aK*< � $� �� a

¾ ³/¼ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�Z\=Ye&K6W]=2S2A�Z�=2DFXe&XHK�e&DFX�=2I�F�Fa~b>`HK-e&XHK�e&DFXH=@IRP8DFG>Z�`�KMZ�=2egK4W]=YS@A"Z\=YD/XQK.�NKiI$Zc=@?�u

A[<Ce&D"d(=2XHq�I�S2D(IJO]?�G\EHXP,AF?UZ�a

Page 174: Introductory Physics Problems David J. Jeffery Department of

�*º�¾ v�`�A�_]Zia ³F¼ ¤]_VKiI�=@A�S�¿~K�S2A�Z�=2d(=�Z:^

LN<ne&D"d(=2XHq�I�S2D(IJO]?�G\EHX�?US2D"l-aIi<ne&D"d(=2XHq�I�S2D(IJO]?>A�G\K-?:Z\DF_H_NK�W�aWV<ne&D"d(=2XHq�I�S2D(IJO]?>A�G\KMl~G�D/XHq�aK*<ne&D"d(=2XHq�I�S2D(IJO]?�G\EHXmL�AFIJO(l>A�GJWpa

¾ ³/¼ h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�Z:l~=YXV?~_�A�GJAFWHD*��i�]a>7!XZ�`�KMZ:l~=YX�?>_VA�GJAFW]D*�po[Z�`HKMZ:l~=2Xml~`HD�A�q/K�?�SYKiAF?UZ~=2?>Z\`HK-DFX�K�l~`�D�u

A[<C=@?~XHDFZcAFI�I�K�S2K�GJA"Z\K�WpaLN<n=@?~XHDFZc|�=YZ���qFK�G\AFS2WI�D/X/Z\G\A/I$Z\K�WpaIi<n=@?cA/I�I�K�SYK�G\A�Z�KiWpaWV<n=@?c|�=YZ���q/K�GJA�S@WnI�DFX[Z�GJAFI�Z�K�W�aK*<n=@?~`HK�G�e&K�Z�=@I�A�S2S2^n?UKiA�S2K�Wn=YX�AgZ�=2e&K6I�AF_�?UE�SYK/a

¾ ³/¼ h[e4EHS�ZB¾���¾/¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¯�=2XHOFD"lc?�O(=�WH=2AFqFGJA�e�?� ³ a �\¸�K�Zi· ?�_HS@A*^ �]1\��D3�����"# 1 |HDFG �]��¾F¾�o�Z\`HK&A�X�?�l�K�GR=@?�uc7kZ6I�A�X�LVK�W]=2d(=2W]KiW�=2X[Z�Dm9jAF?UZ�op|HE]Z\EHG\KFo� cD"l-opAFX�W

�;S2?�K�l~`HK�X�oHA�XVWQD/XQ=YZcl�DFG\S2W(TkS2=YXHKi?�K�dFD/SYd/KFa �A[<C»{`VA"Zc=@?~A�I�DFXHP8DFG\e&AFS�e&AF_H_H=2XHq�oH�BSYK�� �LN<n»{`VA"Zc=@?~A�|HK�^(XHe�AFXW]=@A�q/G\AFemo(�BSYK�� �Ii<n»{`VA"Zc=@?~A�¯�=YX�OFD"lc?�O[=pW]=@A�q/G\AFemo(�BSYK�� �WV<n»{`VA"Zc=@?>`H=2?UZ�D/G�^/oH�cS2K�� �K*<n»{`VA"Zc=@?>SY=YP8KFoN�cS2K�� �

¾ ³/¼ h[e4EHS�ZB¾��F�i¾F¾C�Mµ��MK�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�l�D/G�S@WQSY=2XHK��µ�a~� l�DFG\S2WQS2=YXHKM=2X�Ag¯�=YXHO/D"lc?UO(=�W]=@A�q/G\AFe =2?�u

A[<�Z\`HKMZ�GJA A:KiI$Z\DFG\^�D�PjA�XDFL,A:KiI$Z~=YX�?�_�AFI�K�Z\=Ye&KFaLN<CZ\`HKMZ�GJA A:KiI$Z\DFG\^�D�PjA�XDFL,A:KiI$Z~=YX�?�_�AFI�K-A�S2DFXHK/aIi<CZ\G\ABA:K�I�Z�DFG\^�D�PjA�XDFL3A:K�I$Z~=2XZ�=2egK6AFSYD/XHKFaWV<CZ\`HK6A�G\G\D"l{D�P�Z�=2egK/aK*<QA4Z\K�S2K�_H`HD/XHKMZ�`VA"Zc=@?~A4_VA�G�Z:^CSY=2XHKMP8D/G>Z�`HK-K�X/Z\=YG\KMl�D/G�S@W �{G�KiI�D/ege&K�X�W]K�WCP8DFG~K��(`�=YLH=YZ�=2DFX�=2?UZ\?�a

¾ ³/¼ h[e4EHS�ZB¾��i�F¾F¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu�S2=Yq/`/ZcI�DFXHK-�cS2_H`�Anv�K�X[Z\A�E�G�=� ¶ a>»�KsO(XHD"l A�S2G�KiAFW]^nZ�`�A�ZRA&Z\G�=@IJO(^n_NDFS2=�Z\=2I�A�S�?�=YZ�E�A�Z�=2DFX�l~=2SYS�A�G\=2?�K-DFX��BSY_H`VAQv�K�X[Z\AFEHG\= ¹ 58µnSY=2qF`[ZUTk^FKiA�GJ?

W]=@?UZ\A�X[Z$<�=YX�A�K�S2K�I�Z�=2DFX ³ ^/K�AFG\?�`HK�X�I�K/a�7!X&DFE�G�b�K�G�GJAFI�K�X[Z�G\=2I;l�A*^/o�l�K�Z\`HK~_NK�DF_�SYK>D�Pp�;AFGUZ\`4AFG�K>qFD/=YX�qBZ\De�A�O/K>DFEHGjd(=2K�lc?jO(XHD"l~X4Z�DMZ\`HKc�cS2_H`�Asv�K�X/ZJA�EHGJ?�a�»{`�A�Z;=2?�D/EHG�IJ`�AFX�I�K~DFPV=2X]��EHK�X�I�=2XHq-Z\`HK�=2G�W]K�I�=2?�=2DFX �A[<C7kZi· ?c_VD[?�?�=YL�SYK/u��cS2_H`�Anv�K�X[ZJA�EHG\= ³ ^FK�AFG\?>`�K�X�I�K�=@? ��� � ��� �DFE�G~SY=2qF`[ZBI�D/XHKFa�� GJAFWH=YD�?�=Yq/X�A�SpI�AFXLNKC?�K�X[Z6A�X�WxG�KiI�K�=Yd/K�W�A�X�W�Z�`HK��BSY_H`VA�v�K�X[Z\AFEHG\?�l~=2SYS�I�DFXVI�S2E�W]KgZ�`�A�Z-Z�`HK�G�K&=@?MSY=YP8K�DFEHZ�Z\`HK�G\K �AFG�q/E�A�L�SY^�=2X[Z�K�S2S2=Yq/K�X[Z�a

LN<¤]D�T!?UDVaIi<n7!e&e&K�XV?UK/u6XHD�Z\`H=2XHq�=2?6egD/G�K�IJ`HK�G�=@?�`HK�W�Z�`�AFXrEHX�AF?�OFKiW�P8D/GsAFWHd[=@I�KgP8G\DFe Z�`HD[?UK�=2X�I�D/e&_VK�Z�K�X[Z-Z\Dq/=Yd/KM=�Zia

WV<Q B=YS�uC�cS2_H`�A�v�K�X[Z\AFEHG\?sl�D/EHS@WrG\A�Z�`HK�G6Z\AFOFK�Z\`HK�=2GgD"l~X�L�AFW�A/W]d(=2I�KFo�Z�`�AFX�?�DFe&K�D/XHKCK�S@?�KF· ?6qFD(D]WA/W]d(=2I�KFu�Z�`HK�^N· G\K~_HG�K�ZUZ:^4XHDFG\e�A�S(Z�`VA"Z�l>A*^ �{K��]_HS@A�=2XH=2XHq�Z�`HK~`�DFGJ?UK/· ?�`H=2X�W&K�X�Wg=2?�AFXHD�Z\`HK�Gje�A�ZUZ�K�G�a

K*<Q B=YS�u6�cS2_H`�A�v�K�X[Z\A�E�G�= ³ ^FKiA�GJ?�`HK�X�I�K�=2? � � � ��� DFP�D/EHG-SY=2qF`[Z6I�D/XHKFaC BD�Z\`H=YX�ql�K�W]D�XHD"lI�A�Xw`�A*d/KQZ\`HK�?�SY=2qF`[Z�Ki?:Z�K.�NKiI$ZnD/XtZ\`HK�e Z�`HK�X�a��/EHe&_wEH_{A�X�WwW]D"l~X�o�?\I�G\K�AFeo>?�`HDFE]Zio�q/=Yq/qFS2K=2XHD/_H_VD/GUZ\EHXHK�SY^ �{XHD�Z\`H=YX�q&I�A�X`HK�S2_�a

¾ ³/¼ h[e4EHS�ZB¾�� ³ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�Z\=Ye&KMZ�GJA*dFK�S� ¹ a>7kP�^FD/EI�DFEHS@WCZ\G\A*d/K�S�=2X�?:ZJA�X[Z�S2^nD"d/K�G~A4��XH=YZ�K6W]=@?UZ\A�XVI�KM=YX�AFXQ=2XHK�G�Z�=@A�S�G�K�P8K�G\K�X�I�KBP8GJA�e&KFo�^FDFEI�D/EHS2W�u

A[<nWHD&AFX(^/Z\`H=2XHq�aLN<nl~G\=YZ�K�Z�`HK-q/G�KiA"Zc�ce&K�G�=@I�AFXQXHD"d/K�S�a

Page 175: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¼ ¤(_NK�I�=2AFS�¿~K�S@A"Z\=Yd(=YZ:^ �*º]�

Ii<n_�S2A*^nA&W]=@W A:K�G�=@W]E�aWV<nG\=@W]K-A&EHXH=@I�^]I�S2K-A�X�Wm?�_H=�Z~L�A/IJO(l�AFG\WH?>A�Z�Z\`HK6?\A�e&K�Z�=2egK/aK*<CZ\=Ye&KMZ\G\A*d/K�S�a

¾ ³/¼ h[e4EHS�ZB¾���µ[¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u��;=YX�?UZ�K�=YX�· ?>Kih/EVA"Z�=2DFX�*º(a~�;=YX�?UZ�K�=YX�· ?>Kih/EVA"Z�=2DFXr58D/G~e�AF?\?:TkK�XHK�G�q/^�K�h[EH=2d"A�S2K�X�I�K�Kih[E�A"Z\=YD/XV<�=2?

A[< $ �4* � aLN< $ ����* � aIi< $ ����* � aWV< $ �4*��FaK*< $ �4*���a

¾ ³/¼ h[e4EHS�ZB¾�� ¶ ¾F¾4�Q� ¶ e&D]W]K�GJA"Z\K�e&K�egD/G�^�uj��=2X�?UZ�K�=YX�· ?>K�h[E�A�Z�=2DFX=YXmq/K�XHK�G\AFS� ¼ a~�;=YX�?UZ�K�=YX�· ?>Kih/EVA"Z�=2DFX $ ��*��Fu

A[<nAF_H_HS2=YKi?>DFXHS2^�Z\D�G�Ki?:Z~e�AF?\?�aLN<QAF_H_HS2=YKi?>DFXHS2^�Z\D�K�S2K�I$Z\G�D/e�A�qFX�K�Z�=@IRG\A/W]=2A�Z�=2DFX�aIi<QAF_H_HS2=YKi?>DFXHS2^�Z\D�X[EVI�S2K�A�G>G\K�A/I$Z�=2DFXV?�aWV<n=@?~D/XHSY^nd*AFSY=@WQ=YXmXHD/X]T�=2XHK�GUZ\=2AFS�P8G\AFegKi?�aK*<n=@?4qFK�X�K�GJA�S�a��cS2S;P8D/G�e�?4D�PcK�X�K�G\qF^�`VA*dFKC=2XHK�G�Z�=@A�S�e�AF?\?�a�¿cK�?UZ4e�AF?\?6=@?s=YZ\?�K�SYPRA�?�_NK�I�=@A�S�P8DFG\e D�PK�XHK�G\qF^nSY=2OFKMK�S2K�I�Z�G\DFe�A�q/XHK�Z\=2IB��K�S2WpoHZ�`HK�G�e�A�S�o]DFG~O(=2XHK�Z\=2IMK�XHK�G\qF^/a

¾ ³/¼ h[e4EHS�ZB¾�� ¹ ¾F¾C� ³ �MK�A/?U^�e�A�Z�`�u;� $Re�I����F�6AF_H_HS2=YKiWCZ\D�K�S2K�I$Z\G�D/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T ½F³ T ³/³

� ½ a~b>`HK�e�AF?\?�DFP�A�XCK�SYKiI$Z\G�D/XC=2? ½ � � ���¾ ��� �NO(q�a�b>`HKRK�XHK�G\qF^gK�h[EH=2d"A�S2K�X[Z�DFP�Z�`�=2?�e�AF?\?�=@?>A�_H_HG\D*�]=Ye�A�Z�K�S2^�uA[<���¾ � � � ��a LN<���¾ � � �6�Va Ii< ³ �x�i¾ � � �6�Va W�< ³ ����¾ ��� 6��a Ki<�� �Va

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³/¼ h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\K�S@A"Z�=2d(=2?UZ�=@I�=2WHK�X[Z�=YZ�=2K�?�Fa~¡RD&Z�`HKMP8D/SYS2D"l~=2XHq�a

A[<Q��=2dFK�X� $ �

# � , � �

�VX�W �rA/?~A4P8EHX�I$Z\=YD/XmD�P�Z�`HK6¸�DFG\K�X[Z��RP,AFI�Z�DFG � aLN<��=2dFK�X � $ � � � � $ � � � * ��o]�VX�W �rA/?~AgP8EHX�I�Z�=2DFXmD�P � �]5 � � *�<$aIi<��=2dFK�X $ � � � *���o�?�`HD"l�Z\`�A"Z $�# � � * � � 5 � � * � < � aWV<��=2dFK�X $ � � � *���o]��XVW ��A/?~AsP8E�X�I$Z\=YD/XDFP ��]5 � � *���<$aK*<��=2dFK�XZ�`HKMG\K�?�EHS�ZcDFP�_�AFGUZ65�W�<$o���X�W ��AF?~A4P8EHX�I�Z�=2DFXmD�P�O(=YXHK�Z�=@IMK�XHK�G�q/^ � �aP\<7kP~^/DFE�O[X�D"l b�A*^(SYD/G�· ?M?UK�G�=2K�?�o�dFK�G�=YP8^�Z\`�A"Z � $ # � � �H5 � � * � <MZ�D���?UZ6DFGJW]K�G-=YX � ��]5 � � *��*<$ab>`�K���?UZ>D/G\WHK�G>K��]_HG\K�?\?U=2DFXQ=2?�oHDFP�I�D/EHGJ?UK/o(Z�`HK6I�S2A/?�?�=2I�A�Sj58=�a KFa2oHXHDFXHT�G\K�S@A"Z\=Yd(=@?:Z\=2IRG�Ki?UE�S�Z$<�G�Ki?UEHSYZ�a

¾ ³/¼ h/P8EHS2S�¾/¾/��¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu;¤[Z\A/I�^n|�=YZ���q/K�GJA�S@WQI�DFX[Z�GJAFI�Z�=2DFX�]ac¤[ZJAFI�^¡RG\AFqF=2S2A�oV9�D]I�A�Z�K�SYS2D�· ?~_HG\=2WHK4A�XVW���¾F¾/¾n°RSY^(e&_H=@I-qFD/S2W]T�e&K�W�A�S�l~=2XHXHK�G�oN=@?cL�AFG�G\K�S2SY=2XHqCAFSYD/XHqnA"Z�AG\K�S@A"Z\=Yd(=@?:Z\=2I-?�_VK�K�Wml~=YZ�`�`HK�GB_NDFS2KFa>b>`HK6_NDFS2K-=2?s� ¶ P ZcS2DFX�q�=YX�G\K�?UZBS2K�XHqFZ�`�a~¤(`HK6G\EHX�?~Z�`HG\DFEHq/`�A�L�A�G\X�i¾�P Z6SYD/XHqm=YX�G\K�?UZ-SYK�XHq�Z\`�A�X�W�D/_VK�XrA�Z6LVDFZ�`�K�X�WH?�aQ¤[Z\A/I�^�· ?-qFD/=YXHq�?�DmP,AF?UZ-Z�`�A�Z-Z�D�AFX�D/L�?�K�G\dFK�G-A�Z

Page 176: Introductory Physics Problems David J. Jeffery Department of

�*ºF� v�`�A�_]Zia ³F¼ ¤]_VKiI�=@A�S�¿~K�S2A�Z�=2d(=�Z:^

G\K�?UZc=YXZ\`HK6qFG\DFE�X�Wn=2XHK�GUZ\=2AFSpP8G\AFe&KFoH`HK�Gc_NDFS2K-=2?c|�=YZ���qFK�GJA�S@WI�DFX[Z\G\A/I$Z�KiWCZ\D�SYKi?�?~Z�`�AFX��i¾�P Z�a�b>`(E�?>Z�`�Kq/G�D/EHX�W(T�P8G\AFe&K6DFL�?�K�G\dFK�GB?�K�K�?M¤[ZJAFI�^�AFX�W�_NDFS2KsK�X[Z\=YG\K�S2^md*AFXH=@?U`x=YX[Z�DnZ�`HKgL�AFG�XmP8D/G�AnLHG�=2K�P;Z�=2egK/a ��EHZZ\Dm¤[ZJAFI�^=YZ�· ?RZ�`HKgL�AFG�X�Z\`�A"ZM=@?R|�=YZ���q/K�GJA�S@W�I�D/X[Z�GJAFI$Z\K�W�AFX�W�?�`HK4AFX�W�_NDFS2K&A�G\K6XHK�d/K�G�K�X[Z�=2G\K�S2^=2X�?�=2WHKZ\`HK-L�A�G\X�aj¿~Ki?UD/SYd/KRZ\`HK-_�AFG\A/W]D*�pa ������ � b>`�KMAFX�?�l�K�G�=@?�X�· Zcd/K�G\^CS2DFXHqVa

¾ ³/¼ h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�A�SYZ�K�G�XVA"Z�K-|�=YZ���q/K�GJA�S@WQI�DFX[Z�GJAFI�Z�=2DFX³ a~b>`HK6|�=YZ���qFK�GJA�S@WnI�DFX[Z�GJAFI�Z�=2DFXQP8DFG\esEHS@A4=2?

0 $ 0 � # � , � � l~`HK�G�K 0 � =2?RZ�`�K4_HG\DF_NK�GMS2K�XHqFZ�`xD�P;D/L,A:K�I�Z&5,=�a KFa2opSYK�XHq�Z\`xe&KiAF?�EHG�KiW�=2X�Z�`�KgG\K�?UZ�P8G\AFegK4D�P�Z\`HK&DFL,A:KiI$Z$<e&D"d(=YX�q�A"Z�?�_NK�K�W ��G�K�S2A�Z�=2dFKrZ�D�?UD/e&K�D�Z�`�K�G�=2XHK�GUZ\=2AFS6P8GJA�e&K�58S2K�Zi· ?�I�AFSYS4=�ZxZ�`HKtS2AFL P8G\AFe&Ki<�AFX�W0 =2?mZ\`HK�I�D/G�G\K�?�_NDFX�W]=2XHqtSYK�XHq�Z\`�=2XzZ�`HK�S@A�L�P8GJA�e&KFuwXHDFZ�K�Z�`HK�S2K�X�q�Z�`V?�A�G\KxLND�Z\` _�A�GJA�S2SYK�S�Z�DwZ�`�KW]=2G\K�I$Z\=YD/XrD�P>egDFZ�=2DFX�aCb>`�K&P8DFG\esEHS@Am=2?-WHK�G\=Yd/K�WxP8G�D/e�Z�`�Kn¸�D/G�K�X/Z\�gZ�GJA�X�?UP8DFG\e�A"Z�=2DFXV?�A/?�?�EHe&=2XHqZ�`�A�ZZ\`HK4e&KiAF?�EHG�K�e&K�X[ZRDFP�Z�`HKgS2D(I�A"Z\=YD/X�D�P�Z\`HKgK�X�WH?�DFPjZ�`HKgSYK�XHq�Z\`�l>AF?�?U=2esE�S�ZJA�XHK�DFE�?R=YX�Z�`HKgS@A�L�P8GJA�e&KFa��E]Z-Z\`HK�G\K�=2?sA�XHDFZ�`HK�G�l>A*^�D/XHKCI�AFXxe&K�A/?UE�G�KgZ�`�K�SYK�XHq�Z\`�DFP�Z\`HK�e&D"d(=YXHqmD/L,A:K�I�ZM=2XrZ�`�K�S2AFL�P8GJA�e&KFue&K�A/?UE�G�KMZ\`HK6Z\=Ye&K � ��5,=�a KFa2oNZ�`HK-Z\=Ye&K4=YX�Z\`HK ��SYK�XHq�Z\`P8DFG\e �CK�h[E�A�S�Z�D�*�� � <cLVK�Z:l�K�K�XmZ\`HK6P8G\DFX[ZBK�X�WDFP�Z�`HK&D/L,A:K�I�Z�_�A/?�?�=2XHqAn�H�]K�W�_VD/=YX[Z-=2X�Z�`�KgS@A�L�P8G\AFe&KgAFX�W�Z\`HKgG�KiA�G�K�X�Wx_�AF?\?�=YXHqnZ�`HK�?\A�e&Kg_VD/=YX[Z�oAFX�Wne4EHSYZ�=2_HSY^L(^�Z�`�K6?U_NK�KiWQDFP�Z\`HK-DFL,A:KiI$Zia�v�A�S2S�Z�`H=@?~S2K�XHqFZ�` 0 �*oHl~`�K�G\K

0 � $ � � � �

�R?U=2XHqtZ�`HKr¸�D/G�K�X/Z\��Z\G\AFX�?:P8D/G�e�A�Z�=2DFX�?CWHK�Z�K�G�e&=2XHK 0 ��A/?QA�P8EHX�I�Z�=2DFX�D�P 0 � a ������ � b>`HK�K�XVWH?D�PZ\`HK4D/L,A:K�I�Z�_VAF?\?U=2XHqCZ\`HK4�H�]K�W�_NDF=2X[ZMI�DFX�?UZ�=YZ�EHZ�K4Z:l�DQK�dFK�X[Z\?Rl~=�Z\`xW]= �NK�G�K�X[Z�opLHE]ZMG\K�S@A"Z�KiWpop?U_VAFI�K�Z�=2e&KI�D[D/G\WH=YX�A�Z�Ki?�a��cS@?UDVo/D/L�?�K�G\dFK�GJ?j=2XnLND�Z\`CP8GJA�e&K�?�?UK�KcZ\`HKRe&KiAF?�EHG�K�e&K�X[Z\?;`�A�_H_NK�X�=YXHq4DFXnZ�`HKRK�X�Wn_VD/=YX[Z\?DFP�Z\`HK-DFL,A:KiI$Zia�7!XZ\`HKMP8G\AFe&K�DFP�Z\`HK-DFL3A:K�I$Zio(Z�`HK-e&KiAF?�EHG�K�e&K�X[Z~K�dFK�X[Z\?~A�G\K�DFX�A�XDFL,A:KiI$ZcA"ZcG\K�?UZ�a

¾ ³/¼ h/P8EHS2S�¾/¾�µ/¾/¾ ³�¶ ¾g`�A�GJWnZ�`H=2XHO(=YX�q�u�I�D/SYS2=@W]=YX�q&?UZ\AFGc?U`�=Y_�?µ�a~|�K�W]K�G\A�Z�=2DFX�?UZ\AFG�?�`H=2_�?R�;qFG\K�q/=YD/E�?cA�XVW��j�]KiI�GJA�LHS2KsA�G\K6D/XxAC`�K�AFW]T�D/X�I�D/SYS2=2?�=2DFX�I�D/EHGJ?UK/a��;qFG\K�qF=2DFEV?~=2?e&D"d(=YX�qsA"Z�dFK�S2D]I�=YZ:^ � � $�¾ � ¹ A�X�WC���]K�I�GJA�L�SYKcA�Z�dFK�SYD]I�=�Z:^ � � $ ,c¾ � ¼ u�LVDFZ�`Cd/K�S2D]I�=YZ�=2K�?;AFG�KBG�K�S2A�Z�=2dFK~Z\DZ\`HK-e&DFG\K�TkDFG�T�S2K�?\?;=2XHK�GUZ\=2AFS�P8G\AFegKMDFP�Z\`HKs�MA�S@A"�]^FaA[<C»{`VA"Zc=@?�Z�`HK-d/K�S2D(I�=�Z:^�� �� D�Pj�j�]KiI�GJA�LHS2KR=2XQZ�`HK-=2XHK�G�Z�=@A�S�P8G\AFegKMDFP�Z�`�K6��qFG\K�q/=YD/E�?�LN<��D(D]W�?�`H=Y_����]K�I�GJA�L�SYKM`�A/?~_HG\DF_NK�GcS2K�XHqFZ�` ¶ ¾F¾jema�»{`�A"ZRAFG�K-=YZ�· ?cS2K�X�q�Z�`V?~=YXmZ\`HKg�MAFS2A��]^CP8GJA�e&K

AFX�W=YXQZ�`�K6��qFG\K�q/=YD/E�?;P8G\AFegK �Ii<n7!X�Z�`HK&�MA�S@A"�]^CP8GJA�e&Ks�;qFG\K�qF=2DFEV?~A�X�W����(KiI�GJA�LHS2K6?UZ\A�G�ZBD ��A�S2=Yq/`[ZUTk^FK�AFGcA�_�AFGUZg5:��S2^(G $ ½ � µ ¹ ¾ ��i¾ � � eC<$an£BD"lfS2DFXHq=YX � � � �tZ\=YS2SjZ�`�K�^xI�DFS2SY=@W]K&=2XxZ\`HKn�MA�S@A"�]^mP8GJA�e&K�� ������ � v�A�S@I�EHS@A"Z\KZ\`HK�=2GcG\K�S@A"Z\=Yd/KRd/K�S2D(I�=�Z:^QAF?~?�K�K�X=2XQZ\`HKs�MA�S@A"�]^&P8GJA�e&KFa

WV<n7!Xm_�AFGUZs5�I�<�oH^FD/EQD/L]Z\AF=YXHKiWmA�?UEH_NK�G\S2EHe&=YX�AFS�dFK�SYD]I�=�Z:^/o]LHE]Zc=2X�?U_NK�I�=2AFSpG�K�S2A�Z�=2d[=YZ:^Cl�K6?�A*^'*g5�?U_NK�KiWDFPjSY=2qF`[ZB=2X�d"AFI�E�EHeC<>=2?cZ�`HKsEHS�Z\=Ye�A�Z�K6_H`(^]?�=2I�A�S�?�_VK�K�Wpa ��D�Z\`mZ�`HKs_�A�G�Zs5,Ii<cA�XV?Ul�K�GcAFX�W�?�A*^(=2XHq *=@?�Z�`�KgE�S�Z\=Ye�A"Z\K�_H`(^]?U=@I�AFS�?�_NK�K�W�A�G\K&I�DFG\G\K�I$Zia4¿~Ki?UD/SYd/KsZ\`HK&_�A�GJAFWHD*��� ������ �  cDFZ�KgZ�`�Kgl�DFGJW��_H`(^]?U=@I�AFS �4LVK�P8DFG\K-?U_NK�KiWpa

K*<#��^�Z\`HK6?�=Ye&_HS2K�?UZce&K�A�XV?~I�A�S@I�E�S2A�Z�K�Z�`HKMZ\=Ye&KMZ\DCI�DFS2S2=2?�=YD/Xn=2XZ�`HK-G\K�?UZ>P8G\AFegK-DFP�Z\`HK6��q/G�K�qF=2DFE�?�aP\<m BD"l P8DFGRZ�`HK&IJ`�AFSYS2K�XHq/KFa6v�A�S@I�EHS@A"Z\K-Z�`�KsZ\=Ye&K4Z�DmI�DFS2S2=2?�=YD/X�=YX�Z�`HKgG\K�?UZBP8GJA�e&KsDFP�Z�`HK&��q/G�K�qF=2DFE�?�oEV?U=2XHq�dFK�S2D]I�=YZ�=2K�?�o;S2K�XHqFZ�`�?�o;AFX�W�Z\=Ye&Ki?gA/?gegKiAF?�EHG\K�W�=2XtZ�`HK���q/G�K�qF=2DFE�?6P8G\AFe&KFa�7:?gZ\`HK�A�X�?�l�K�GZ\`HKs?\A�e&K-AF?>Z\`�A"Zc=2Xm_�A�G�Zs58K*<�� ������ � |�=2G\?UZ�o]�VX�W��j�]K�I�G\AFLHS2KF· ?�?�_�A/I�K�Z\=Ye&K6I�D[D/G\WH=YX�A�Z�Ki?�=2XmZ�`�K�;qFG\K�q/=YD/E�?�P8GJA�e&K/a

¾ ³/¼ h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u;¤(e�A�E�q�oH|HG\D]W]D�oHAFX�WQZ�=2e&K6W]=YS@A"Z\=YD/X¶ a ��D/EAFX�Wn^/DFEHG>S2D"^/AFSV`HD/EHX�W|HG\D]W]D�A�G\KBZ\G\A*d/K�S2=YXHqsZ�`HG\DFE�qF`Q?�_�A/I�K�=YXm^FD/EHG>?:ZJA�Gc?�`H=Y_�¤(e�A�E�q�a���DFEmA�G\KS2=Ye&=YZ�KiWmZ�DCq/DF=2XHqCA"ZRSYKi?�?cZ�`�AFXmZ�`HK4EHS�Z\=Ye�A�Z�K6_H`(^]?�=2I�A�S�?�_VK�K�W * $ ��S2^[G��*^(G~D/G � $ �/o�D�P�I�DFEHGJ?UK/a ��EHZ

Page 177: Introductory Physics Problems David J. Jeffery Department of

v�`�AF_]Z�a ³/¼ ¤(_NK�I�=2AFS�¿~K�S@A"Z\=Yd(=YZ:^ �*º ³

DFZ�`HK�GBZ\`�A�X�Z�`�A�Z-¤(e�AFEHqQI�A�X�q/DQA"ZMA�X(^�?U_NK�KiW�AFX�W�^/DFE�A�XVW�|HG\D]W]DQAFG�K4G�KiA�S�Z�DFE�qF`�AFX�W�I�A�X�?UZ\AFX�WAFX[^QAFI�I�K�S2K�GJA"Z\=YD/X�aA[<Q¤HA*^4|HG\D]W]DMl�AFX[Z\?�Z\DMZ�GJA*dFK�S(P8G\DFe �;AFGUZ\`sZ\Ds¤(=YG\=2E�?c5,WH=2?UZ\AFX�I�K � $ ¼ � º�S2^(GJ<�A�XVW&^FDFEgl>A�X[ZjZ�D-e�A�O/KZ\`HK�Z�G\=Y_Q=YXx�R^/K�AFG;P8D/G � � �xa]��Z>l~`VA"Z ��d"A�S2EHKMl�D/EHS@Wn¤(e�A�EHqg`�A*d/KcZ�DgqFD�� �������� � ��D/Enl~=2SYS`VA*dFK�Z�D�W]D�?�DFe&K-A�S2qFK�L�G\A�a�¿~KiI�AFSYSpZ\`HKs�MA�S@A"�]^[T�P8G\AFegKBZ�GJA*dFK�SVZ\=Ye&K6=@? � �]5 * ��<$a

LN<¤(Z�=2G�G\K�W&L(^g^FDFE�Gj��GJ?:Z�I�DFX�h[EHKi?:Z�D�P�?U_VAFI�K/oF^/DFECA�XVW�|HG\D(WHD �{l�K�SYS�|�G�D]W]Ds=2?;SYKi?�?;K�A�q/K�G��wX�D"l�l>A�X[ZZ\D�I�G�D[?�?sZ�`�KL�EHSYq/KZ�DxZ�`HKP,A�G&K�X�W�DFPBZ�`�KmWH=2?�O�D�P��MAFS2A��]^NuW]=@?:ZJA�X�I�Kx�i¾F¾�\¾F¾/¾jSY^(Gia ��E]Z�^/DFEl>A�X[Z�Z�DgSY=2dFKBZ�D&?UK�KcZ�`�K�A:D/EHG�X�K�^�· ?�K�XVWpa�»{`�A"Z>_H`(^]?U=@I�AFSVK.�NKiI$Z~e�A�OFKi?�=YZ�_ND/?\?�=YLHS2KRZ�D4?�EHG\d(=Yd/KcZ�`�KA:D/EHG\XHK�^��

Ii<Q£BD"l�e4E�IJ`�� � �xZ\`�A�XQZ�`HK6?�_NK�K�WQD�P�SY=2qF`[Z658=2XmEHXH=YZ\?~DFP *"uj=�a KFa2oH=YXQZ�K�G�e�?>DFP ��<>W]D&^/DFEXHK�KiWCZ\Dq/D�A"Z>Z�D&e�A�O/KRZ\`HK-_�AFX]T!�MAFS2A/I$Z\=2I�A:DFEHG\XHK�^CD�P���¾F¾ �¾/¾F¾jS2^(G;=2Xx�-^/K�A�G�P8DFG�� � � � ������ � ¿cK�I�AFSYSZ\`HKM��GJ?:Z~D/G\W]K�Gcb�A*^(S2DFG�K��]_�AFX�?U=2DFX

�+ � � � � � ,

�� �

l~`�=2IJ`m=@?>d*AFSY=@WQP8DFG � �����FaWV<Q£BD"lzS2DFX�q&AFG�KMKiAFIJ`mD�P�^FD/EHG>Z�`HKMZ\G�=2_�?~=2X�W]D/qg^/K�AFG\?�P8DFGR|HG\D(WHD ���BX�Wml~`(^nW]D(K�?B|HG\D(WHD�l�AFX/Z>Z\D

?UZ\A*^QA"ZB¤(=2G�=2E�?�

¾ ³/¼ h/P8EHS2S�¾/¾ ¶ �i¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu�|HG\D(WHD&AFX�WnZ�`HK-LHS@AFIJOn`HDFS2K¹ aB°RX�I�KRAFq/A�=2X�^FD/ECA�X�Wn^FD/EHG�Z\G�E�?UZ:^g`HDFEHXVWn|HG\D]W]DsAFG�KRdFD"^/AFqF=2XHq�Z�`HG\DFE�qF`Q�MAFS2A/I$Z�=@Ic?�_�AFI�KBD/XC^FD/EHG�?UZ\AFG?�`H=2_�¤]e&AFEHq�aA[<n�BX(LVK�O[X�D"l~X�?:Z;Z�D6^/DFE�o[|HG\D(WHD6`�AF?�A�X�=2XHXHK�G;S2=�P8Kc=2XCl~`H=@IJ`�`HKc=2XnI�DFe6Z\K�e&_HS@A"Z\K�?�Z\`HKBEHX�=Yd/K�GJ?UK/a�£BKA/?UO]?-`�=Ye�?�K�SYP �{?�=YXVI�K�=YZ�· ?6XHD�E�?�KnA/?UO(=2XHqm^FDFE � �U=YP;Z\`HKCq/G\A*d(=YZ\A"Z\=YD/X�A�S�P8D/G\I�K�=2?4A�S2l�A*^]?MA"Z�Z�GJAFI$Z\=Yd/KAFX�W±W]DFe&=2X�A"Z\K�?�S@A�G\qFK�Tk?\I�AFSYK?:Z\G�E�I�Z�EHG\KFo�l~`(^�W]D(K�?�X�· Z�Z�`HK�l~`HD/SYK��MAFS2A��(^�D�P�?UZ\AFG\?�I�DFS2S2AF_�?�KnZ\DP8D/G�e Am?�EH_NK�G�T�e�AF?\?�=Yd/K6LHS@AFIJO(`HDFS2K�� ���R?�?�EHe&=YX�q|�G�D]W]DmA�X�?�l�K�GJ?B`H=2e�?UK�S�P>I�D/G�G\K�I�Z�S2^Fo�l~`�A"Z-=@?�`H=2?AFX�?�l�K�G�

LN<n»{`�=YS2K |�G�D]W]D =@?zesE�?�=YX�q�or^FD/E A�G\KfW]DF=2XHq�A P8K�l I�AFS2I�EHS@A"Z�=2DFXV?�a ��D/EHGz?�_NK�K�W =2?zA S@A���^³ � ¾/¾F¾ �±��¾��pO(e��"? �wO(=2SYD/e&K�Z�K�G\?4_NK�G&?UKiI�DFXVW�e�A�G\Ox^/DFE �{G�K�S2A�Z�=2dFK&Z\D�Z�`�KQe&DFG\K�TkDFG�TkSYKi?�?M=2XHK�G�Z�=@A�SP8GJA�e&KCDFP>Z�`HKQ�MAFS2A��]^xA�XVW�¤(e�A�EHqV· ?-G\K�?UZse�AF?\?-=@?C� � ¾/¾F¾ ����¾ � O(q�a»{`�A"Zg=2?g¤(e�A�EHqV· ? � � ���� � � � � � � � ¦ O(=2XHK�Z\=2IMK�XHK�G\qF^��

Ii<mv�AFS2I�EHS@A"Z�KnZ�`HKQO(=YXHK�Z�=@ICK�XHK�G\qF^�D�PR¤(e�AFEHq�=2X�?�_VKiI�=@A�S�G�K�S2A�Z�=2d[=YZ:^Fa�¡BD(Ki?6Z\`HKQ?�_VKiI�=@A�S�G�K�S2A�Z�=2d(=2?UZ�=@II�A�S@I�EHS@A"Z\=YD/X�D�PjO(=YX�K�Z�=@I6K�XHK�G\qF^Q^(=YK�S2W�An?U=2qFXH=Y�VI�A�X[Z�S2^WH=���K�G\K�X[ZRd"AFSYEHKQ5,?\A*^¾ � � � W]= �NK�G�K�X/Z$<>P8G\DFeZ\`HK-XHD/X]T�G\K�S@A"Z\=Yd(=@?:Z\=2I�I�AFS2I�EHS@A"Z�=2DFX �

WV<#�/E�?UZ�A/?�|�G�D]W]D4=2?�LVK�qFq/=YXHqsZ�D4qFD6P8D/G�A4?U_VAFI�KBl�AFSYO�o(^FD/E�G�KiA�S2=Y��KcP8G\DFe�^FD/EHG�?�_�AFI�KRIJ`�AFGUZ;Z�`�A�Z�^/DFEAFG�K�D/X�A�?:Z\G\AF=Yq/`[ZMS2=2XHKC_�A�Z�`rP8DFG4A�LHS@AFIJO�`�DFS2K �{^FDFE�G6I�DFX[Z\G�D/S2?-AFG�K�AUAFege&KiW �{I�DFEHS@WrLNKn|HG\D]W]Dl>AF?�q/X�A*l~=YX�q4D/X?�DFe&K�d[=YZ\AFS�I�D/XHXHK�I�Z�=2DFX �wZ�`�K�e�A/?�?>DFP�Z�`�K-LHS2A/IJO�`HDFS2KM=2?M�-?�DFS@A�G�e�AF?\?-5:�-?UD/S2AFGe�A/?�?-=@?C� � ½/¼F½ ���±��¾ � � O(q[<MAFX�Wr=�Z4=2?n� � ¶ �t��¾�� �Ve A*l>A*^Fan|�G�D/e A� BK�l>Z�D/XH=@A�X�I�AFS2I�EHS@A"Z�=2DFX�A�Zl~`VA"ZsW]=@?:ZJA�X�I�K�l~=YS2S�^/DFE�G�KiAFIJ`xZ�`HKC?�_VK�K�W�D�P>S2=Yq/`/Z 1 � � �su���K�I�A�E�?�K&D�P~?U_NK�I�=2AFS;A�XVW�q/K�XHK�G\AFSG\K�S@A"Z\=Yd(=@?:Z\=2I6K ��K�I$ZJ?~Z\`H=2?RI�AFS2I�EHS2A�Z�=2DFX�=@?cXHDFZBG\K�A�S2S2^nd"A�S2=2W�oVLHEHZR=YZRW]D(K�?BSYKiAFWZ�DQ?UD/egK-=2X�?�=Yq/`[ZB=YX[Z\Dl~`VA"ZcesEV?:Z~`�AF_H_VK�X�a

K*<Qb>`�K�G\KF· ?>DFXHS2^nD/XHK�Z�`H=2XHq�S2K�P Z~Z�DCWHD �{qFK�Z>Z\`HK-S2A/?:Zcl�DFGJWpa�¤(D�l~`HK�Xm^FDFE�G>¸�DFG\K�X[Z���P,A/I$Z�D/G~G�KiAFIJ`HKi?�i¾ � � � A:E�?:ZCLNK�P8D/G�K^FD/EHGgqFGJA*d[=YZ\A�Z�=2DFX�AFS�?�`H=2K�S@W]=YX�q±5�Ax_�EHG�K_HS2D�Z�W]K�d(=@I�K*<6P,AF=YS@?&A�X�Wt^FD/EHG&A"Z�D/e�?LNK�I�DFe&Kc_NK�G\e�A�XHK�X/Z\SY^4EHX�I�D[D/_VK�G\A�Z�=2dFK��w^/DFE4?�K�XVW�AM_HG�D/_VK�G�Z�=2e&K ³ e&=YX(E]Z\Kcd(=2WHK�D-e&K�?\?�AFqFK�Z�D6AFSYS^/DFEHGBP8G�=2K�XVWH?�a �/E�?UZBP8G\DFe�?�_VKiI�=@A�S�G�K�S2A�Z�=2d(=2?UZ�=@I6_H`(^]?�=2I�?�o�`HD"l�S2DFXHqQl~=YS2S�^FDFE�GRd(=@W]K�DQegKi?�?\A�q/K6G\EHX=2X�� � � ��=2X�Z\`HK&egD/G�K�T�D/GUTkS2K�?\?~=YX�K�G�Z�=@A�S�P8G\AFe&K4DFP�Z�`HKC�MAFS2A��(^�� � � �4u���K�XHK�GJA�S�G\K�S@A"Z�=2d(=�Z:^l~=2S2S�A�S@?UD&A ��K�I�Z~Z�=2e&K6A�X�W=2XG\K�AFSY=YZ:^�^FD/EQl�DFX�· Z~LNK6A"ZBA&I�D/X�?:ZJA�X[Z~dFK�SYD]I�=YZ:^Fa

Page 178: Introductory Physics Problems David J. Jeffery Department of

�*º"µ v�`�A�_]Zia ³F¼ ¤]_VKiI�=@A�S�¿~K�S2A�Z�=2d(=�Z:^

¾ ³/¼ h/P8EHS2S�¾/¾ ¹ ¾/¾n� ³ ¾gK�A/?U^Ce�A�Z�`�u�P,A/?:Z~_HG\D�Z\DFX�?º(a~b>`HKw_HG\D�Z\DFX e�AF?\?x=2X�K�XHK�G�q/^�EHXH=YZ\?�=@? ½F³/¼ � �/ºF� ³ ��¯�K�´ D/G�A�_H_HG\D*�]=Ye�A�Z�K�S2^�����K�´4asb>`HKw_HG\D�Z\DFX?�^(X�IJ`HG\D�Z�G\DFXwA"Zm|HK�G�e&=2S2AFL{XHK�AFGv�`H=@I�A�q/D�I�AFX�AFI�I�K�S2K�GJA"Z\K�A�_HG\D�Z�D/X±Z�D�Z\D�ZJA�SBK�XHK�G\qF^�58=�a K/aYoBO[=2XHK�Z�=@IK�XHK�G\qF^�_HS2E�?~G\K�?UZ~e�AF?\?>K�XHK�G�q/^]<�DFP�A�LNDFEHZ ¶ ¾F¾���K�d�aA[<C»{`VA"Zj=2?�Z\`HK>O(=YXHK�Z�=@I�K�XHK�G�q/^-D�PHZ\`HK>_HG�DFZ�D/X6Z�D�Z\`HK~?�AFegK�DFGJW]K�G�DFPNA/I�I�E�G\A/I�^�Z�`�A�Z�Z�`HK�Z�DFZ\AFS[K�XHK�G\qF^l>AF?~h[EHDFZ�KiWCZ\D �

LN<n»{`VA"Zc=@?�Z�`HK6¸�DFG\K�X[Z���P,AFI�Z�D/G~D�P�Z\`HK-_HG\D�Z\DFX �Ii<n»{`VA"Zc=@?�Z�`HK-d/K�S2D(I�=�Z:^���DFP�Z\`HK-_HG\D�Z\DFX �

Page 179: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� � B$Da?A;7?T>�E &T>a, � &:;G;7145 � &4(T1)E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾ ³/½ h[e4EHS�ZB¾/¾H�i¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�h[E�AFX/Z\EHe e&K�IJ`VA�XH=@I�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�Fa~b>`HK-_�`[^]?�=2I�A�SNZ�`�K�DFG\^�Z\`�A"ZBW]KiA�S@?>e�A�=2XHSY^Ql~=�Z\`meg=@I�G\D/?\I�D/_H=@IB_H`�K�XHD/egK�X�Ag=2?�uA[< h[E�AFGUZ\� e&K�IJ`�AFXH=2I�?�a LV< h[E�AFG�O]? egKiIJ`�A�X�=2I�?�a I�< h[E�AFX[Z�EHe e&K�IJ`�AFXH=@I�?�aWV<>h/EVA�X[Z�EHe A:EHe&_megKiIJ`�A�X�=2I�?�a K*<>h/EVAF?�=�Tke&K�IJ`�AFXH=2I�?�a

¾ ³/½ h[e4EHS�ZB¾/¾H�/��¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�D�e&K�e&D/G�^�u;®�¯ _HG�D/L�A�L�=YS2=2?UZ�=@I� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�]a>7!X�?UZ\A�XVWHA�GJWnh[E�AFX/Z\EHe�e&KiIJ`�A�XH=@I�?�o]X�A�Z�EHG\KM=2?�P8EHXVWHA�e&K�X[ZJA�S2SY^�uA[<�EHXHS2=YO/K�S2^Fa LV<>LVA�S2SY=@?:Z\=2IFa Ii<>_HG\DFL�AFLH=YS2=@?:Z\=2IFa W�<>W]K�Z�K�G�e&=2XH=2?UZ�=@I�a Ki<~XHK�=YZ�`HK�G~�V?�`X�DFG>P8D"l~S�a

¾ ³/½ h[e4EHS�ZB¾/¾/�F¾F¾C�&���MK�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D/XQK�XHK�G\qF^³ a~b>`HK-_�`HD�Z\DFX�o(Z\`HK6h[E�A�X[Z�E�e�D�P�K�S2K�I�Z�G\DFe�A�q/XHK�Z\=2IRG\A/W]=@A"Z�=2DFX�o]`�AF? � � � �xu

A[< % # $ %, �ca LV< % � � a Ii< %, ��a W�< % � #�a Ki< % # �"a¾ ³/½ h[e4EHS�ZB¾/¾/�H��¾C�&���MK�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D/XQK�XHK�G\qF^

� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�b>`�=2?cWH=���K�GJ?�P8G�D/e}¾/¾/�]�i¾6D/XHSY^n=YX�A�XV?Ul�K�G-5,A[<$aµ�a~b>`HK-_�`HD�Z\DFX�o(Z\`HK6h[E�A�X[Z�E�e�D�P�K�S2K�I�Z�G\DFe�A�q/XHK�Z\=2IRG\A/W]=@A"Z�=2DFX�o]`�AF? � � � �xu

A[< % #�a LN< % � � a Ii<�%, �pa W�< % � #�a K*< % # � a¾ ³/½ h[e4EHS�ZB¾/¾/�/��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D/XQG\K�?UZ~e�AF?\?

� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¼ ¾"T ¶¶ a~b>`HK-G\K�?UZ~e�AF?\?>D�P�Ag_H`�D�Z�D/Xm=2?�u

A[<-Z\`HKm?�AFegKAF?sZ�`�A�Z4DFPRA�X�K�SYKiI$Z\G�D/X�a LV<C�A"Z\DFe&=2Ine�AF?\?sEHX�=�Zia I�<-X�K�q/A�Z�=2dFK/a W�<4¾HaK*<>W]K�_NK�XVWH?~DFXQP8G\K�h[EHK�XVI�^Fa

¾ ³/½ h[e4EHS�ZB¾/¾H�i¾F¾C� ³C¶ K�A/?U^�e�A�Z�`�u�K�^FK-W]K�Z�K�I�Z\AFLHSYKM_H`�D�Z�D/X�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=��>²�T:� ¼/³ T ³

¹ a~b>`HK�`(EHe�A�XCK�^FKRe&A*^gLNK�AFLHSYKBZ�D&W]K�Z\K�I�Z>A/?�S2=�Z�Z�S2KMA/?c�i¾ � ��6�gD�P�S2=Yq/`[Z�K�X�K�G\qF^Fa�£cD"l{e�AFX[^&_H`�D�Z�D/X�?�D�PP8G\K�h[EHK�X�I�^ ¶ ����¾�� ��£B�6W]D(K�?>=YZ~Z\AFOFK�Z�D�e�A�O/KMEH_ A:E�?:ZBAFLVD/E]Z>Z�`H=@?cAFegD/EHX[Z~D�P�K�XHK�G�q/^ �

A[<���¾ � �� a LV< ¶ ����¾ � � a Ii<���¾Ha W�<��/a K*< ³ a

¾ ³/½ h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj_H`�D�Z�D(K�SYKiI$Z�G\=@IRK.�NKiI$Z� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

º(a~� O/K�^C_H=2K�I�KMD�P�K�d(=2WHK�X�I�KRP8D/G>Z�`HK-l>A*dFK�T�_VA�G�Z�=@I�S2KRW]E�AFSY=YZ:^nDFP�S2=Yq/`[Zc=2?�Z\`HKFuA[<�_�`HD�Z\DFqFGJA�_�`6K ��K�I�Z�a LV<�K�S2K�I�Z�G\D(WH^[XVA�e&=2I�?�DFPV¯�A��(l�K�S2S(?UEHe&e�A�G\=2��K�W6=YX4Z�`HK�P8DFE�G�¯�A"�]l�K�SYS�· ?Kih[E�A"Z\=YD/X�?�a I�<�P8G\K�h[EHK�X�I�^nD�P�G�KiWnS2=Yq/`[Z�a�W�<�_H`�D�Z�D(K�SYKiI$Z�G\=@IRK.�NKiI$ZiajKi<�_H`HDFZ�D/e&AFqFXHK�Z�=@I�K ��K�I$Zia

Page 180: Introductory Physics Problems David J. Jeffery Department of

�*º ¹ v�`�A�_]Zia ³F½ 9;`HD�Z\DFX�?>AFX�Wm¯�A"Z�Z�K�G~»rA*dFKi?

¾ ³/½ h[e4EHS�ZB¾/¾ ³ ��¾4�Q�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�_H`HDFZ�D(K�S2K�I�Z�G\DFXK�XHK�G�q/^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¼ ¾"TJ�

¼ a~b>`HK�O[=2XHK�Z�=@I�K�XHK�G�q/^�D�PMZ\`HK�K�S2K�I�Z�G\DFX�?CK�e&=�Z�Z�KiWw=YX�Ar_H`�D�Z�D(K�SYKiI$Z�G\=@I�K ��K�I�ZQW]K�d(=@I�K�W]K�_VK�X�WH?nDFXwZ�`�KDFP�Z\`HK-SY=2qF`[Zc=2X�I�=@W]K�X/ZcD/XnZ\`HK-e&K�ZJA�S�a

A[<�=YX[Z\K�X�?�=�Z:^ LV<�P8G\K�h[EHK�XVI�^ Ii<>?U_NK�KiW W�<�G\K�?�DFX�AFX�I�K Ki<�G\K�?�DFS2dFK

¾ ³/½ h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�v�D/eg_HZ�DFXK ��K�I�Z½ a~�;=YX�?UZ�K�=YXm_HG\K�WH=2I�Z�K�WA�XVW�v�D/e&_]Z�D/XQ_HG\D"dFKiW�Z\`�A"Zc_H`�D�Z�D/X�?�u

A[<C`VA*dFKMSY=2XHKiA�G>e&DFe&K�X[Z�E�eaLN<QWHDgX�D�Zc`�A*d/KRS2=YX�K�A�G~e&D/egK�X[Z�EHemaIi<Q?�DFe&K�Z�=2egKi?>`�A*dFKMS2=YX�K�A�G~e&D/egK�X[Z�EHemaWV<nLND�Z\`m`�A*dFK-A�XVWQW]D&XHDFZc`�A*dFK�S2=YXHKiA�G~e&DFe&K�X/Z\EHe}A�Z>Z�`HK6?\A�e&K�Z�=2e&KFaK*<nX�K�=YZ�`HK�Gc`�A*dFK�XHD/G~`�A*dFK�XHD�ZcS2=2XHK�AFG~egD/e&K�X[Z�EHema

¾ ³/½ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�ujl>A*dFK�T�_�AFGUZ\=2I�SYK�W]E�AFSY=YZ:^��¾Ha~b>`HK�_�G�=2X�I�=2_HS2K&Z�`�A�Z4A�S2S�e&=@I�G\D/?\I�DF_�=2I4_H`(^]?U=@I�AFS�K�X[Z�=YZ�=2K�?6`�A*dFK&LND�Z�`�l>A*dFK&A�XVWx_VA�G�Z�=@I�S2K�_HG�D/_VK�GUZ\=YKi?M=2?

I�A�S2SYKiWCZ\`HK-l�A*d/K�Tk_�A�G�Z�=@I�S2KFuA[<>?U=2XHq/EHS2AFG�=YZ:^Fa�LV<>W]EVA�S2=�Z:^/a I�<�Z\G�=@A�S2=�Z:^/a W�<�=2X]��XH=YZ\AFSY=YZ:^Fa Ki<�X(EHSYS2=2SY=YZ:^Fa

¾ ³/½ h[e4EHS�ZB¾/¾ ¶ ��¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj¸�D/EH=2?~WHK ��G\DFq/SY=2K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

�F�Fa �\¸�K�Zi· ?R_HS@A*^��]1J� D+�"�\�"# 1 |HD/G��]��¾F¾�oHZ\`HK4AFX�?Ul�K�GR=2?�uc£cKgl>AF?~Z\`HK4��G\?UZBZ\Dn_HG\DF_ND/?�K-Z\`�A"Z�_�A�G�Z�=@I�S2K�?Rl~=�Z\`G\K�?UZ~e&A/?�?~AFS2?�D&`�AFWAgl�A*d/KRXVA"Z�E�G�K/a �»{`HD�l>AF? o��cS2K�� �

A[<Q7:?�A/AFI� BK�l>Z\DFX�5:� ¹ µ ³ �N�*ºF�/ºF< LV<!�[A�e&K�?�v�S2K�G\O�¯�A"�]l�K�S2S&5U� ¼/³ � ��� ¼ º ½ < I�<m�cS2LNK�G�Z�;=YXV?:Z\K�=2XC5:� ¼ º ½ �N� ½[¶F¶ < WV<���G\l~=2X-¤HIJ`HG��D[W]=2XHqFK�G;5:� ¼F¼ º �N� ½F¹ �*< Ki<p¸�DFEH=@?�W]K���G\DFq/SY=2Kc5:� ¼F½ � �� ½F¼ º�<

¾ ³/½ h[e4EHS�ZB¾/¾ ¶ ��¾C� ³ �MK�A/?U^�e�A�Z�`�u;WHK���G\DFq/SY=2KRl>A*dFK�SYK�XHq�Z\`QI�A�S@I�EHS@A"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¼/³ TJ�F�

�i�]a>»{`�A�Zc=2?�Z\`HK6W]K ��G\DFqFS2=2KRl>A*dFK�SYK�XHq�Z\`nD�PjA�XK�S2K�I�Z�G\DFXD�P�?U_NK�KiWx�i¾"!�e��"?�A[<�º � �[º ����¾ � � � ema LN< ¹ � ¹ � ¹ ���i¾�� � � ema I�< ½ � ��¾ ½ ����¾ ��� � ea W�< ³ � ¹ ����¾ � � � eaK*<>¾Ha

¾ ³/½ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�¤]IJ`HG��D/W]=2XHq/K�G>K�h[X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

� ³ a �\¸�K�Zi· ?�_HS@A*^ �]1\��D3�����"# 1 |HDFG �]��¾F¾�o�Z\`HK�A�X�?�l�K�GB=@?�uRb>`HKgK�h[E�A�Z�=2DFXNy"K�h[E�A"Z\=YD/X�?~Z\`�A"ZMqFD"d/K�G\X�?~Z\`HKgZ�=2e&KK�dFDFS2E]Z\=YD/XQDFP�h[E�A�X[Z\EHe�e&K�IJ`VA�XH=@I�AFS�?U^]?UZ�K�e�?>=2XZ�`HKMXHD/X]T�G\K�S@A"Z\=Yd(=@?:Z\=2IMAF_H_HG\D*�(=2e�A"Z\=YD/X�a �

»{`VA"Zc=@?Jy�A�G\K o��cS2K�� �A[<� BK�l>Z�D/X�· ?���X�W�S@A*l-o �� � ��� $ � �� LV<�¯�A"�]l�K�SYS�· ?�K�h[E�A�Z�=2DFX�? I�<x��=2X�?UZ�K�=YX�· ?���K�S@WKih[E�A"Z\=YD/X�?>D�P�qFK�X�K�GJA�SpG\K�S@A"Z�=2d(=�Z:^ W�<>¡B=2GJAFI�K�h[E�A�Z�=2DFX Ki<>¤]IJ`�G��D[W]=YX�qFK�Gi· ?�Kih[E�A"Z\=YD/X

¾ ³/½ h[e4EHS�ZB¾/¾[º�¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�®�¯ _HG\DFL�AFLH=YS2=YZ:^CW]K�X�?�=YZ:^� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

��µ�a>7!XZ�`�K6?:ZJA"Z�=@?UZ�=@I�A�Sp=2X[Z�K�G�_HG\K�ZJA"Z\=YD/XQDFP�l>A*dFKRP8EHX�I$Z\=YD/X��4o� � � �M=2?�uA[<-Am_HG\DFL�AFLH=2SY=YZ:^xW]K�X�?�=�Z:^/a LN<-Am_HG\DFL�AFLH=YS2=YZ:^xA�e&_HS2=YZ�E�W]K/a I�<&�/a WV<6¾Ha K*<MAX�K�q/A�Z�=2dFKM_HG\DFL�AFLH=2SY=YZ:^Fa

Page 181: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ³F½ 9�`HDFZ�DFXV?~A�X�W¯�A"Z�Z�K�Gc»�A*d/K�? �*º/º

¾ ³/½ h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�K� ¶ a~��?�^]?:Z\K�e =2X�Ag?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�K-l~=2SYS�u

A[<CX�D�ZcK�d/DFS2dFK�=YXZ\=Ye&KFaLN<nK�dFD/SYd/KR=2XZ�=2egK/aIi<nLND�Z\`mK�dFD/SYd/K�AFX�WXHD�Z~K�dFDFS2dFK�=2XQZ\=Ye&K/aWV<nD]I�I�AF?�=2DFX�AFSYS2^�K�d/DFS2dFK�=YXZ�=2e&KFaK*<nd(=2DFS@A"Z\KRZ\`HK6£cK�=2?�K�X(LNK�G\q&EHX�I�K�GUZJA�=2X[Z:^�_HG�=2X�I�=Y_HS2KFa

¾ ³/½ h[e4EHS�ZB¾/¾ ½ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�P8G\K�KM_�AFGUZ\=2I�SYK� ¹ a~b>`HKMP8G\K�KM_�AFGUZ\=2I�SYK-?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�K�?

A[<nI�A�XLVK-D]I�I�EH_H=2K�WL(^nAg_�AFGUZ\=2I�SYK/aLN<QI�A�XLVK-D]I�I�EH_H=2K�WL(^�Z:l�D&_�A�G�Z�=@I�S2K�?�aIi<QI�A�XHX�D�ZcAFI�Z�E�AFSYS2^CLNK-D(I�I�EH_�=YKiWQL(^nAg_�AFGUZ\=2I�SYK/aWV<QAFG�KMEHX�O[X�D"l~X�aK*<QAFG�KMXHD/G�e�AFSY=2��AFLHSYK/a

¾ ³/½ h[e4EHS�ZB¾���¾/¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�uj£cK�=2?�K�X(LNK�G\qgE�X�I�K�GUZJA�=2X/Z:^�*º(a �\¸�K�Zi· ?4_HS@A*^ �]1J� D+�"�\�"# 1 |HDFG��(�i¾F¾�o�Z\`HKQAFX�?Ul�K�G4=2?�u&7kZ&WHK�?\I�G\=YLNK�?4A�P8EHX�W�A�e&K�X[Z\AFS�S2=2eg=YZ\A�Z�=2DFX�D/X�Z�`�K

A/I�I�E�G\A/I�^�l~=YZ�`ml~`H=@IJ`l�K-I�AFXQO(XHD"lz_VD[?U=YZ�=2DFXmA�X�We&DFe&K�X/Z\EHe�?�=Ye4EHSYZ\A�X�K�DFEV?US2^Fa �A[<C»{`VA"Zc=@?~b�AFG�O/D"d(?�O(^�· ?�W]DFE�L]ZUP8EHS�Z�`HKi?U=@?�oV�cS2K�� �LN<n»{`VA"Zc=@?~¿~EHLHS2K�d�· ?cA�e4LH=Yq/EHDFEV?�_ND/?UZ�E�S2A�Z�KFoV�cS2K�� �Ii<n»{`VA"Zc=@?~²MK�S2d[=2X�· ?~d"A�q/EHKR��K�G\D�Z\`QS@A*l-oH�cS2K�� �WV<n»{`VA"Zc=@?c¤]IJ`HG��D/W]=2XHqFK�G�· ?�l~=YS@WK��]_ND/?UZ�EHS@A"Z\KFoH�cS2K�� �K*<n»{`VA"Zc=@?~£cK�=@?�K�X(LVK�G�qV· ?>E�X�I�K�GUZJA�=2X/Z:^n_HG�=2X�I�=Y_HS2KFoH�BSYK�� �

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾ ³/½ h/P8EHS2S�¾/¾�µ/¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�uj`HK�SY=2EHe�q[AF?>L�AFSYS2D(DFX�Fa ��D/E `VA*dFKwA `HK�S2=YE�e q/A/?rL�A�S2S2D[D/X A�ZrZ:^[_�=2I�A�S�G\D[D/e Z�K�e&_VK�G\A�Z�EHG\K 5 � $ ³ ¾/¾�²6<�AFX�W _HG�Ki?�?�EHG\K5U��A"Z\e $ � � ¾�� �x�i¾ � 9jA�aA[<n��?:Z\=Ye�A�Z�K�Z\`HKnA*dFK�G\AFqFK�W]K ��G\DFq/SY=2K&l�A*d/K�S2K�XHqFZ�`rD�PcA�`HK�SY=2EHe A"Z\DFe =YX�e&K�Z\K�GJ?sAFX�W��cXHq[?:Z\G�D/e�?q/=Yd/K�X�Z�`�A�ZQZ\`HKregKiA�XzO[=2XHK�Z�=@IxK�XHK�G\qF^wDFP4¯�A"�]l�K�S2SY=@A�X�q/AF?=@? � $ 5 ³ �F�F< � � ocl~`HK�G�K � $� � ³/¼ � ����¾ � � �6�-² � � =@? ��DFSYZ���e�AFXHX�· ?6I�D/X�?:ZJA�X[Z6A�X�W � =2?-=2X�²MK�S2d(=YX�a ��D/E�l~=2S2S;A�S@?UDmXHK�K�WxZ�`�KA�Z�D/eg=@I�e�A/?�?�D�P�`�K�S2=YEHemo"Z\`HK>A�esE�o�A�X�W69;S2AFX�IJO�· ?�I�D/X�?:ZJA�X[Z�u�Z�`HKi?UK>A�G\KFo*G\K�?�_VKiI$Z�=2dFK�SY^/o�� $wµ � ¾/¾/� ¹ o� � � � $ � � ¹/¹ � ����¾ � � ��O(qVoHA�X�W�% $ ¹ � ¹ � ¹ ����¾ ��� ���;?�a

LN<mv�AFS2I�EHS@A"Z�K&Z\`HK�_�AFGUZ\=2I�SYK�W]K�X�?U=YZ:^�DFP�Z\`HKCq[AF?-A�XVWx=2X(dFK�G\?�K4DFP�_VA�G�Z�=@I�S2KCW]K�X�?�=YZ:^t58=�a KFa2o�Z\`HKC?U_NK�I�=��NId/DFS2EHe&Ki<�=2Xm¯�²6¤nE�XH=�ZJ?cA�XVWn=2XZ�K�G\e�?>D�Pj�cXHq[?:Z\G�D/e�?�a

Ii<n»{`VA"ZC=@?&Z�`HK�Z:^[_�=2I�A�ScW]=@?:ZJA�X�I�K�LVK�Z:l�K�K�X±Z�`�K�A"Z\DFe�?&=YX{�BXHq/?UZ�G\DFe�?&=YPM^/DFEwI�D/X�?U=@W]K�G&Z�`HK�e A/?I�S2A/?�?�=@I�A�S�_�AFGUZ\=2I�SYKi?�a

WV<mv�AFXmZ�`HKsq/AF?cLVK-Z\G�KiA"Z\K�WmAF?cI�S2A/?�?�=@I�A�S�q/AF?cD�P�_�A�G�Z�=@I�S2K�?� ������ � ��D/E�l~=YS2S�_HG\DFLVA�LHS2^CLNK4A�L�SYKMZ\Dq/EHK�?\?�Z�`�K6I�G\=�Z\K�G\=YD/X�o(LHE]ZBS2=YO/K�S2^CXHDFZ�Z\`HKMZ�G\EHK<A:E�?UZ�=Y�VI�A"Z�=2DFXP8D/G>Z�`HK6I�G�=YZ�K�G�=2DFX�a

¾ ³/½ h/P8EHS2S�¾/¾ ¶ ¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�¿~EHZ�`HK�GUP8D/G\Wp· ?>X(E�I�S2K�EV?� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ½ ºFº]u ¹ ��9�<��cS@?�Dg=2X�h[eg_

�]a~¿~EHZ�`HK�GUP8D/G\WmW]=@?�I�D"dFK�G�KiW�Z�`�K-X[EVI�S2K�E�?~=2Xr� ½ �F��L[^QLVD/esL�AFG\WH=YXHq&e&K�ZJA�SpP8D/=YS@?~l~=YZ�`�A�S2_H`�A&_VA�G�Z�=@I�S2K�?>XHD"lO(XHD"l~XQZ�D&LNK-`HK�S2=YE�e�X(E�I�S2K�=�5�A"Z\DFe&=2IMe�A/?�?�µ � ¾F¾[� ¹ <$a��cX�A�S2_H`�Ag_�AFGUZ\=2I�SYKM`�A/?>_VD[?U=YZ�=2dFK-IJ`�AFG�q/KM�

�aj£BK

Page 182: Introductory Physics Problems David J. Jeffery Department of

�*º ¼ v�`�A�_]Zia ³F½ 9;`HD�Z\DFX�?>AFX�Wm¯�A"Z�Z�K�G~»rA*dFKi?

K��(_NK�I�Z�KiW6Z\`HK�AFSY_�`�AB_VA�G�Z�=@I�S2K�?�Z�D�_�AF?\?�G�=2qF`[Z�Z\`HG\DFEHq/`6Z�`�K;P8D/=YS@?�l~=�Z\`4D/XHSY^6?�e�A�S2S]W]K�d(=@A"Z�=2DFXV?�a�¯�D/?UZ�WH=2WpoLHEHZ�?�DFe&K�?\I�A�ZUZ\K�G\K�W-D �&ARdFK�G�^�S2AFG�q/K;A�X�qFS2K�?�a��B?�=2XHqRARI�S@AF?\?U=@I�AFSF_�AFGUZ\=2I�SYK�_H=2I�Z�EHG\K�D�P]Z�`�K�AFSY_H`VAc_�AFGUZ\=2I�SYKi?AFX�W4Z�`HK~K�X/Z\=�Z\=YKi?�Z�`HK�^sl�K�G\K~?�I�A"ZUZ\K�G\=YX�q�D �CD�P�`HKcI�AFe&K�Z\D�Z�`HKBI�DFX�I�SYEV?U=2DFXsZ�`�A�Z;A"Z�D/e�?jI�DFX[ZJA�=2XHK�W4e&D/?UZDFP�Z�`�K�=2Gje&A/?�?�AFX�Ws_ND/?�=YZ�=2dFK~IJ`�A�G\qFK�=YXV?U=@W]K~A�G�K�qF=2DFXsl~=YZ�`&AM?U=2��K~?\I�AFSYK�D�P � ��¾ � � � e $��pP8emu�Z\`H=@?>��¾ � �Z\=Ye&K�?4?Ue�AFSYS2K�G-Z\`�A�XrZ\`HKnA�Z�DFe&=@I�?U=2��K/a�5, cDFZ�K�P8e ?UZ\A�XVWH?6DF��I�=2AFSYS2^�P8D/G-P8K�esZ�D/egK�Z�K�G�o�LHE]Zg_H`(^(?�=@I�=@?:ZJ?I�A�S2SVZ\`H=@?�E�XH=�ZcAsP8K�G\e&=�a <s¿cE]Z�`HK�GUP8D/G\WQI�D/X�I�S2E�W]KiW�Z�`VA"Z>Z�`HK�G�KResE�?UZ~LVKMAgW]K�X�?�K�SY=YZUZ\SYK-I�D/G�KBZ�D&A�XnA�Z�D/euZ\`HK-X(E�I�S2K�E�?�aA[<C»{`(^�W]=2WxZ\`HKCA�S2_H`�Am_�AFGUZ\=2I�SYKi?-?�I�A"Z�Z�K�G-D ��Z�`�K�X[EVI�S2K�E�?�o�LHEHZsXHD�Z-D ��Z�`HKnK�S2K�I$Z\G�D/X�?� �������� �b>`�=YXHOW]K�XV?UK-I�D/G�K-AFX�WQWH=���E�?�K6I�S2DFE�Wpaj»{`VA"Zc=@?�Z�`HKMP8D/G\I�KMI�A�E�?�=2XHqgZ�`HK6?\I�A�ZUZ�K�G�=2XHq��

LN<n7kP�Z�`�K6A�S2_H`�Ag_�A�G�Z�=@I�S2K�?>`VA*dFK�O[=2XHK�Z�=@IMK�XHK�G�q/^º � ¶ ¯�K�dNo(l~`�A�Zc=2?�Z\`HK�=2GBW]K ��G\DFqFS2=2KRl>A*dFK�SYK�XHq�Z\` �Ii<Qb>`�K4I�S2D/?�K�?UZRAF_H_HG\D/AFIJ`mDFPjZ�`HK&A�S2_H`�A�_VA�G�Z�=@I�S2K�?~Z\DCZ\`HK4X(E�I�SYK�E�?cl>AF?BD�P�D/G\W]K�G ³ ¾�P8emac»xD/EHS@W�Z�`�Kl>A*dFKBX�A"Z\EHG�KBD�P�Z\`HKRAFSY_H`VA6_�AFGUZ\=2I�SYKi?�`�A*d/Kc`�AFWnA�X(^&K ��K�I$Z �� cDFZ�KBZ�`HKRl�A*d/K�Tk_�A�G�Z�=@I�S2KcW]E�AFSY=YZ:^&l�A/?X�D�ZcK�d/K�Xm?UEV?U_NK�I�Z�K�WQP8D/G>Z�`HK-e�AF?\?�=Yd/KR_�AFGUZ\=2I�SYKi?>=YXr� ½ �F�/a

¾ ³/½ h/P8EHS2S�¾/¾ ¹ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�I�D/e&_HSYK��nX(EHesLNK�GJ?� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT ½ ºFº]u ¹/¹ ��<

³ a~��I�DFe&_HS2K��nX(EHe4LVK�G�&=2?cWHK���XHKiWL[^��$ � � � �

l~`HK�G�K���A�X�W �CA�G\KBG\K�AFS�X[E�esLNK�GJ?�AFX�W � $ + ,-��=2?�=2e�A�qF=2X�AFG�^/a�b>`HKMG\K�AFSV_�AFGUZ>D�P �g=2? � $�¿~K � ��!�AFX�WZ\`HK-=Ye�AFqF=2X�A�G\^�_�A�G�Z~=2?�� ${7!e � ��!�b>`�K6I�DFe&_HS2K��I�DFXBA:EHq/A�Z�KMD�P �&=2?cWHK���XHKiWL[^

� � $ �1, � � �

A[<C»{`VA"Zc=@? � � � �LN<Q9;G�D"d/KcZ\`�A"Z

5 � � � � <� $�� �� �

�� �

Ii<Q9;G�D"d/KcZ\`�A"Z � �� �

�$ �

� � �

WV<Q9;G�D"d/KcZ\`�A"Z � � �� � ��$ � ��� ��

¾ ³/½ h/P8EHS2S�¾/¾[º"¾/¾g� ¶ ¾ge&D(WHK�GJA"Z�K�Z\`H=YX�O[=2XHqVu;¤]IJ`HG��D/W]=2XHqFK�G>K�h[X�aµ�a~¡RD&Z�`HKMP8D/SYS2D"l~=2XHq�a

A[<C´jK�G�=YP8^CZ\`�A"Z~Z\`HKMP8EHS2SpZ�=2e&K�T!W]K�_NK�XVW]K�X[Zcl>A*dFKRP8EHX�I$Z\=YD/X

�g5�� � < $��R5��<�� � � � ����

G\K�WHE�I�Ki?�Z�`HKMP8EHS2SpZ\=Ye&K�T!W]K�_VK�X�W]K�X[Z�¤HIJ`HG��D[W]=2XHqFK�G�Kih/EVA"Z�=2DFX

, %, �� �

� � �� � �

� �n5��< � $ �3%, � �

� �Z\D&Z�`HKMZ\=Ye&K�T�=2X�W]K�_VK�X�W]K�X[ZR¤]IJ`�G��D[W]=YX�qFK�G>Kih/EVA"Z�=2DFX

, %, �� �

� ���� � �

� �C5��<�� $ ��

Page 183: Introductory Physics Problems David J. Jeffery Department of

v�`�A�_HZ�a ³F½ 9�`HDFZ�DFXV?~A�X�W¯�A"Z�Z�K�Gc»�A*d/K�? �*º ½

P8D/G>Z�`HK6?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�Ki? �BaLN<Q|�DFG � $�¾m58=�a K/aYo]Z\`HKMP8G\K�KM_�A�G�Z�=@I�S2K-?U^]?UZ�K�e�<�oHdFK�G�=YP8^�Z\`�A"Z

��$�� � �

AFG�K�Z\`HK-EHXHXHD/G�e�AFSY=2��KiWn?UZ\A"Z\=YD/X�A�G\^n?UZ\A�Z�K�?�o]l~`HK�G�K

� $ �� � �

%, � �

»{`(^I�A�X�· Z>Z�`�K�?�K6?:ZJA"Z�Ki?>LVK-X�DFG\e&AFSY=2��KiW �Ii<Qb>`�K-=YX]�VXH=�Z\K6?�h[E�AFG�K�l�K�S2S�`�AF?

� $� ¾ P8D/Gc¾� �$� � ) �P8D/G � �±¾&A�XVW � � �Na

´jK�G�=YP8^CZ\`�A"Z��$

� �� ?�=YX�5 � �N<

AFG�K�Z\`HK-XHDFG\e�A�S2=Y��K�WQ?UD/SYE]Z\=YD/X�?>l~=YZ�`mLVD/EHX�WHAFG�^QI�DFXVW]=�Z\=YD/X�? �R5�¾/< $��R5 �(< ${¾Ha��BS2?�D�?U`�D"l�Z�`VA"Z

� $ � �� AFX�W $ %, �

��� � � � � � � � �

¾ ³/½ h/P8EHS2S�¾[��¾F¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u�I�DFe&_HS2K�Z�K6?�K�ZcDFP�?UZ\A�Z�K�?� ª�¬"¨ �V«������V¬ ��­�� � qFD(D]WQIJ`�AFSYS2K�X�qFKMh/E�K�?UZ�=2DFX�u�?\A*dFKRP8DFG>Z\K�?UZ\?

¶ a>7kZB`VAF?>LNK�K�X�e�A�Z�`HK�e&A�Z�=@I�AFSYS2^Q?�`HD"l~XQZ�`�A�ZcZ�`HK6?�K�ZRD�Pj?:ZJA"Z�=2DFXVA�G\^n?:ZJA"Z\K-l�A*d/KBP8EHXVI$Z�=2DFXV?~P8DFGcA�?�^]?:Z\K�eI�DFX�?UZ�=YZ�E]Z\K~A ¦ � � ��� � � Cu"=�a KFa2oFA�X(^MP8EHXVI$Z�=2DFX4Z�`VA"Z�DFLNK�^]?�Z�`HK~?\A�e&K�LNDFE�X�WHA�G\^6I�D/X�W]=YZ�=2DFX�?�A/?Z\`HKB?UZ\A"Z\=YD/X�A�G\^s?UZ\A�Z�K~l>A*dFK�P8EHX�I�Z�=2DFX�?�I�A�X&LNKcK��]_�AFX�W]K�W&A/?�AMSY=2XHKiA�G;I�DFesL�=YX�A�Z�=2DFXgD�P�Z�`�D/?�Kc?:ZJA"Z�=2DFXVA�G\^?UZ\A�Z�K�l�A*d/KjP8EHX�I�Z�=2DFX�?�a�|�DFG�K��HA�e&_HS2K�?\A*^ �x=@?�ABq/K�XHK�G\AFSFl>A*dFKjP8EHXVI$Z�=2DFX&A�XVW � � � � A�G\K�?�K�Z�D�PN?:ZJA"Z�=2DFXVA�G\^?UZ\A�Z�K6l>A*dFK�P8EHX�I�Z�=2DFX�?BDFGcK�=Yq/K�X]P8E�X�I$Z\=YD/X�?>P8DFG�?U`�DFG�Z�ujZ\`HKsI�E�G�S2^QL�G\A/IJOFK�ZJ?>=Ye&_HS2^m?UK�ZBD�P:a>b>`HK�X�l�K6I�AFXK��(_VA�X�W �wZ�`(E�?

��$ -�

� � � �

l~`HK�G�KsZ�`HK&?�EHe�=YXxqFK�XHK�GJA�S�I�DFE�S2W�LVKgD"dFK�GB=2X]��XH=YZ�K�SY^�e�A�X(^mK�=2qFK�X]P8EHX�I�Z�=2DFX�?�A�XVW � � =@?MA�X�K��]_�A�X�?�=2DFXI�D[K��CI�=2K�X[Zcl~`H=@IJ`e�A*^C=2XmqFK�XHK�GJA�S�LNKsI�D/eg_�SYK���aj7kZc=@?cAFS2?�DgZ�G\EHK�Z�`�A�ZcZ�`HK-K�=Yq/K�X]P8E�X�I$Z\=YD/X�?cI�AFXAFSYl>A*^]?LNK � � � � � � ��� � � ��� ���aHb>`�=2?>e&K�AFX�?>Z\`�A"Z

� � �� � � � � $ � � � l~`HK�G�KMl~`HK�G�K�Z\`HK-=YX[Z\K�qFGJA�Sp=@?>D"dFK�G~A�S2S�?U_�A/I�K-A�XVW

� � � $ � � �P8DFG�� $ � )¾ �P8DFG�� �$ �

=@?>Z�`�K6²MG�D/XHK�IJO"A�G>W]K�S�ZJAsP8E�X�I$Z\=YD/X�a;¸�K�Z~E�?cAF?\?�EHe&KRZ\`�A"Z � � � � =@?>DFG�Z�`HD/XHDFG\e�A�S2=Y��K�WpaA[<Q¤]`HD"l�Z\`�A"Z

� � $�� � �� � � � �

Page 184: Introductory Physics Problems David J. Jeffery Department of

� ¼ ¾ v�`�A�_]Zia ³F½ 9;`HD�Z\DFX�?>AFX�Wm¯�A"Z�Z�K�G~»rA*dFKi?

LN<��=2dFK�XZ�`�A�Z � ��� � � $ �

5,=�a KFa2o �{=@?>XHDFG\e�A�S2=Y��K�W�<�oH?U`�D"l�Z�`VA"Z -�

� � � � � $ �

l~`�K�G\K�� � � � � $�� �� � � aIi<Qb>`�KMZ�=2egK�T�=2X�W]K�_VK�X�W]K�X/ZR¤HIJ`HG��D[W]=2XHqFK�G�Kih[E�A"Z\=YD/XnP8D/G~DFEHGc?�^]?:Z\K�e�I�A�XmLVK-l~G\=YZUZ�K�X

� � � $ � � �

l~`�K�G\K�� =2? I�A�S2SYKiW Z�`HK�£RA�e&=2S�Z\DFXH=@A�X D/_VK�G\A�Z�DFG�D/G A:E�?UZ � � � ��� � ��� � �ra�|HD/G DFX�KWH=Ye&K�XV?U=2DFX�AFS�?U^]?UZ�K�e&?

� $�, %, ����

� �� � �

� �n5�N< �b>`�KM£RA�e&=2S�Z\DFXH=@A�XmAFI�Z�=2XHq&DFXQZ�`HK-K�=Yq/K�X]P8EHXVI$Z�=2DFX � � IJ`�A�X�qFK�?�=YZc=YX[Z\Dg=YZ\?�K�SYP�Z\=Ye&Ki? � a� cD�Z\K � =2?A:EV?:ZBA ¦ � � � � �� ���4�� ��AFX�WQI�A�XLVKMZJA�O/K�XDFE]Z~D�PjA�X(^�=2X[Z�K�q/G\AFS�aj BD"l�=YZ~Z�EHG\X�?>DFEHZZ\`�A"Z�Z�`�K�e&KiA�XCK�XHK�G\qF^ � � � �6D�P�As?�^(?UZ�K�e l~=�Z\`�� A�X�Wnl�A*d/K~P8EHX�I�Z�=2DFX �t`�A/?�A4d"A�S2EHKBq/=Yd/K�XCL(^

� � � � $ � ��� � � � �

¤]`HD"l�Z\`�A"Z � � � � $ -

� � � � � �AFS2?�D�a�|HD/GRXHDQqFD(D]W�G\K�AF?�DFX�e&KiA�X�d"A�S2EHKi?B=2Xxh[E�AFX/Z\EHe�e&K�IJ`�AFXH=2I�?RAFG�K4I�A�S2S2K�W�K��(_NK�I�Z�=2DFX�d"AFSYEHKi?�a¤]D � � � � =2?~Z�`HK-K��(_NK�I�Z\A�Z�=2DFXd*AFSYE�K-D�P�Z\`HK6£BAFe&=YSYZ�D/XH=2AFX�a

¾ ³/½ h/P8EHS2S�¾ ³ ¾F¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�u��;=YX�?UZ�K�=YX�o�¿~EHX(^FD/X¹ a �J��D(WW]D(K�?cXHD�Z~_HS@A*^nW]=@I�K � ����=2X�?:Z\K�=2X�aj¡B=@?\I�E�?\?�a

Page 185: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� o � ?A5<1 � e�? dS; � &X;G;71)5 � &4(T1)E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾�µ[¾4h[e4EHS�ZB¾/¾H�i¾F¾C�&���MK�A/?U^�e&K�egD/G�^�uj=2X]��XH=YZ�K6?\h[E�A�G\K�l�K�SYS�Fa>7!X�h[E�A�X[Z\EHe e&K�IJ`�AFXH=@I�?�o(Z�`HK-=2X]��XH=YZ�K4?�h[E�AFG�K�l�K�SYS�I�A�XLVK-G\K�q[A�GJW]K�WQAF?�Z\`HK-_HG\D�Z�DFZ:^(_VKMD�P:u

A[<nAFSYSpLNDFE�X�Wm?U^]?UZ�K�e�?�aLN<QAFSYSpE�X[LNDFE�X�Wm?U^]?UZ�K�e�?�aIi<nLND�Z\`mLVD/EHX�WmA�X�WEHX(LNDFEHXVWQ?�^]?:Z\K�e�?�aWV<nX�K�=YZ�`HK�GcLVD/EHX�WXHD/G�E�X[LNDFE�X�Wm?U^]?UZ�K�e�?�aK*<Q9;G�D/e&K�Z�`�K�E�?>EHX(LNDFEHXVWpa

¾�µ[¾4h[e4EHS�ZB¾/¾/�F¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�ujLNDFEHXVWHA�G\^CI�D/X�W]=YZ�=2DFX�?�]a~¯�K�K�Z\=YXHq&Z\`HK-LNDFEHX�W�A�G\^CI�DFXVW]=�Z\=YD/X�?~DFP�h[E�A�X[Z\EHe�e&K�IJ`VA�XH=@I�AFSNLNDFE�X�Wm?U^]?UZ�K�e�?>=2e&_VD[?UKi?�u

A[<n£BK�=@?UK�X(LVK�G�qV· ?>EHXVI�K�G�Z\AF=YX[Z:^�_HG\=2X�I�=2_HS2KFaLN<¤HIJ`HG��D[W]=2XHqFK�G�· ?�K�h[E�A"Z\=YD/X�aIi<Qh[E�AFX[Z�=2��A"Z\=YD/X�aWV<QAgd/K�I$Z\DFG~_ND�Z\K�X[Z�=@A�S�aK*<QA4Z\=Ye&K�T!W]K�_VK�X�W]K�X[ZB_ND�Z\K�X[Z�=@A�S�a

¾�µ[¾4h[e4EHS�ZB¾/¾ ³ ¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uje�AFI�G�D&?�^(?UZ�K�e =2XmA&?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�K³ a~���]I�K�_]Z�P8DFG~I�K�G�Z\A�=2Xn?�_VKiI�=@A�SpI�A/?UKi?R5�?UE�_VK�G\I�DFX�W]EVI$Z�D/G\?�o(?UEH_NK�G���EH=@WH?�oHA�X�W#��D/?�K�T!��=2X�?:Z\K�=2XnI�D/X�W]K�X�?�A�Z�Ki?\<�oXHD&e�AFI�G�D[?�I�DF_H=@I�?U^]?UZ�K�e}I�A�XLNK-=YX�AHuA[<Ce&=Y�]K�Wm?:ZJA"Z\KFaLN<nd"A/?:Z\SY^Ce&=Y�]K�Wm?:ZJA"Z\KFaIi<QI�S2A/?�?�=@I�A�Sp?UZ\A�Z�KFaWV<Q?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�K/aK*<Q?UZ\A�Z�KMD�P�Z�`�K-EHXH=2DFX�a

¾�µ[¾4h[e4EHS�ZB¾/¾�µ[¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�Z\G\AFX�?U=YZ�=2DFXV?µ�a~b�G\AFX�?�=�Z\=YD/X�?BLNK�Z:l�K�K�X�?UZ\A"Z\=YD/X�A�G\^m?:ZJA"Z�Ki?&5,?�DFe&K�Z\=Ye&K�?�o�LHE]Z-AFI�Z�E�AFSYS2^mG\AFG�K�SY^/oNI�A�S2SYKiW�h[E�A�X[Z\EHe A:EHe&_�?\<AFG�K/uA[<CD/XHS2^nI�D/SYS2=2?�=2DFX�AFS�aLN<nLND�Z\`�I�DFS2S2=2?�=YD/X�A�SpAFX�WG\A/W]=2A�Z�=2dFK/aIi<nD/XHS2^CG\A/W]=@A"Z�=2dFK/aWV<nX�K�=YZ�`HK�GBI�D/SYS2=2?�=2DFX�AFSNX�DFG~GJAFW]=@A"Z\=Yd/KFaK*<nD/XHS2^�I�DFS2SY=@?U=2DFXVA�S6Z\D�`H=2qF`HK�G�K�XHK�G\qF^ ?:ZJA"Z\=YD/X�A�G\^z?UZ\A�Z�K�?xA�X�W D/XHS2^zGJAFW]=@A"Z\=Yd/K�Z�D�SYD"l�K�G�K�XHK�G\qF^?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�Ki?�a

¾�µ[¾4h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�S2A/?UK�G\?�o]?:Z\=Ye4EHS@A"Z�KiWK�e&=2?\?�=YD/X¶ a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�uj7kZc=@?�Z�`HK-LVAF?�=2?�P8D/G~S2A/?UK�G\?>A�XVWQe�A/?UK�G\?�a �

A[<C»{`VA"ZB?�_VD/X/ZJA�XHK�DFE�?�GJAFW]=@A"Z\=Yd/KMK�e&=2?\?�=YD/X�oH�cS2K�� �LN<n»{`VA"ZBW]Ki?UEHSYZ�D/G�^nG\A/W]=2A�Z�=2dFK�K�e&=@?�?�=YD/X�oH�cS2K�� �

Page 186: Introductory Physics Problems David J. Jeffery Department of

� ¼ � v�`�A�_]Ziajµ/¾ ¯�DFG\KM�BLVD/E]ZB¯�A�ZUZ�K�G~»�A*d/K�?

Ii<n»{`VA"ZB?UZ�=2esEHS@A"Z\K�WG\A/W]=@A"Z�=2dFK�K�e&=@?�?�=2DFX�oH�BSYK����WV<n»{`VA"Z~Z�`�K-S2A/?UK�G�P8D/G\I�KFoH�BSYK����K*<n»{`VA"Z~Z�`�K-S2A/?UK�G�_ND�Z\K�X[Z�=@A�S�o��BSYK����

¾�µ[¾4h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u�I�DFX[Z�=2X(EHEHe DFP�EHX(LNDFEHXVW?UZ\A�Z�Ki?¹ a~��ZcK�XHK�G\qF=2K�?�`H=2qF`HK�G>Z�`�AFXZ�`HK-LNDFEHXVW?UZ\A�Z�=2DFX�AFG�^C?UZ\A�Z�Ki?�Z�`HK�G�K/u

A[<nAFG�KMLNK�Z:l�K�K�XQD/XHK-A�X�Wm?�K�dFK�G\AFSNZ�K�XV?>D�P�EHX(LVD/EHX�Wm?:ZJA"Z\K�?�aLN<QAFG�KMD/XHSY^CZ:l�D&EHX(LNDFEHX�Wm?UZ\A�Z�K�?�aIi<n=@?cA&?�=YXHq/SYKMEHX(LNDFEHXVW?UZ\A�Z�K/aWV<QAFG�KMXHD�?UZ\A�Z�K�?�aK*<n=@?cA&I�D/X[Z�=2X[E�EHe D�P�EHX(LNDFEHX�Wm?UZ\A�Z�K�?�a

¾�µ[¾4h[e4EHS�ZB¾/¾[º�¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�Z�EHX�XHK�S2=YX�qº(a �\¸�K�Zi· ?M_�S2A*^ �]1J� D+�"����# 1 |HDFG �]��¾/¾HoNZ�`HK�AFX�?Ul�K�GM=@?�u-b>`H=@?MK ��K�I�Z-D(I�I�EHGJ?�LVKiI�AFE�?UK&l>A*dFKsP8EHX�I$Z\=YD/X�?-I�AFXK��[Z\K�X�W�5,=YXCAFX&K��]_VD/XHK�X[Z\=2AFSYS2^4W]KiI�G\K�A/?U=2XHqMl�A*^4A�S2LVK�=�Z$<�=YX[Z\DMZ�`HKBI�S2A/?�?�=@I�A�S2S2^-P8DFG\LH=@WHW]K�X�G\K�q/=YD/X�u�=�a K/aYo/Z�`�KG\K�q/=YD/Xnl~`HK�G�K-A�I�S@AF?\?�=2I�A�S�_�A�G�Z�=@I�S2KMl�D/EHS@Wn`�A*d/KRX�K�q/A�Z�=2dFKMO(=YX�K�Z�=@IMK�X�K�G\qF^Fa �A[<C»{`VA"Zc=@?~?:Z\=Ye4EHS2A�Z�KiWQGJAFWH=2A�Z�=2dFK�K�e&=2?\?�=YD/X�oH�cS2K�� �LN<n»{`VA"Zc=@?~h/EVA�X[Z�EHe}e&K�IJ`�AFXH=2I�A�S�Z\EHXHXHK�SY=2XHq�oV�cS2K�� �Ii<n»{`VA"Zc=@?~h/EVA�X[Z�=2��A�Z�=2DFX�oH�BSYK����WV<n»{`VA"Zc=@?~?U^(e&e&K�Z�G\=2��A"Z\=YD/X�oH�cS2K�� �K*<n»{`VA"Zc=@?>XHDFG\e�A�S2=Y�iA"Z�=2DFX�oH�cS2K�� �

¾�µ[¾4h[e4EHS�ZB¾/¾ ¼ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�uj`(^]W]G\DFqFK�XQA�Z�DFemo��"T�LND]W]^¼ a~b>`HK-`(^]W]G\DFq/K�XQA�Z�D/e =2?�Z\`HK6?�=Ye&_HS2K�?UZcD�PjA�S2SpXHK�EHZ�GJA�S�A"Z\DFe�?>LNK�I�AFE�?�KFu

A[<C=YZc=@?cA��*TkLVD]W]^n?�^]?:Z\K�emaLN<n=YZc=@?cA ³ TkLVD]W]^n?�^]?:Z\K�emaIi<n=YZc`�A/?>XHD&K�S2K�I$Z\G�D/X�?�aWV<n=YZc`�A/?>e&AFX(^CK�S2K�I�Z�G\DFX�?�aK*<n=YZc=@?>Z�`HK-e&D[?:ZcA�L�EHX�WHAFX/Z~K�SYK�egK�X[Zc=YXZ�`�K-EHXH=2dFK�GJ?�KFa

¾�µ[¾4h[e4EHS�ZB¾/¾ ½ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u ��DF`HGcA�Z�DFe½ a �\¸�K�Zi· ?C_HS2A*^ �(1J��D3�����"# 1 |HD/G �(�i¾F¾Ho;Z�`HK�AFX�?�l�K�G�=2?�u�b>`H=@?�e&D]W]K�ScDFPMAFX{A"Z�D/e =@?�D�PM`H=@?:Z\DFG\=2I�A�ScAFX�W_NK�WHAFqFD/qF=@I�A�Sp=2X[Z�K�G�Ki?:Zio�LHE]Z�=�ZR=2?BD�PjXHDCE�?�K6=2X�e&D(WHK�G\X�_HG\A/I$Z\=2I�A�S�I�A�S@I�EHS@A"Z\=YD/X�?cA�XVWP8G�D/e�Z\`HK6e&D]W]K�G\X?UZ\AFX�W]_NDF=2X/Zc=@?>_HG\DFL�AFLHS2^Ce&=2?�SYKiAFW]=2XHq&GJA"Z�`�K�G�Z�`�AFXm=YX�?�=2qF`[ZUTkqF=2d(=YXHqVa �A[<C»{`VA"Zc=@?c¤(`HG��D/W]=2XHqFK�G�· ?�e&D(WHK�S�DFP�Z\`HK-`(^(WHG�D/qFK�XA"Z\DFemoH�cS2K�� �LN<n»{`VA"Z~Z�`�K6b>`HDFe�AF?UT!|HK�G\e&=�egD]W]K�S�D�PjAge�A�X(^CK�S2K�I�Z�G\DFXmA"Z\DFemoH�cS2K�� �Ii<n»{`VA"Zc=@? ��D/`HGi· ?>e&D]W]K�S�D�P�Z\`HK-`(^]W]G�D/qFK�XQA"Z\DFemoH�cS2K�� �WV<n»{`VA"Zc=@?�Z�`HK-S2=2h[EH=@WmW]G\DF_egD]W]K�S�D�P�Z�`�K6A"Z�D/emoH�cS2K�� �K*<n»{`VA"Zc=@?>egD]W]K�S�`(^]W]G�D/qFK�XQA"Z\DFe DFP�¸�K�E�I�=Y_�_VD[?~A�X�Wm¡RK�e&D]I�G\=�Z\D/?�· ?MoH�BSYK����

¾�µ[¾4h[e4EHS�ZB¾��F�i¾F¾C�&� ¶ K�A/?U^�e&K�egD/G�^�u;��G\K�K�OnA"Z\DFe&=2?UZ\?��¾Ha~b>`HK&A"Z\DFe&=@I-Z�`�K�DFG\^l�A/?c��GJ?UZR_HG\DF_ND/?�K�WmL(^Z�`HK&A�XVI�=2K�X[ZM��G\K�K�O(?�¸�K�E�I�=2_H_ND/?g5 ¶ Z�`xI�K�X[Z�E�G�^ �cv><cAFX�W

¡RK�e&D]I�G\=�Z\D/?C5 ¶ Z\`rZ�D�µ�Z\`�I�K�X/Z\EHG\^ �cvRu�`HKCG\K�_�E]Z�KiW]SY^�S2=Yd/K�WxZ�D�LNK���¾/¾/<�aQb>`HK�Z\K�G\e A�Z�DFe&D[?-e&K�A�XV?EHXVI�E]Ziu�KFa q�a2o]Z�`�K-qFGJAF?\?>=2?~A�Z�DFe&D[?�a�b>`HK6A�Z�D/eg=@?UZ\?c?UZ\AFGUZ\K�WnP8G�D/e}Ag_H`H=2SYD[?UD/_H`H=@I�AFSp_VD[?U=YZ�=2DFXZ�`VA"Z~Z�`�K�G\K`�A/WxZ�D�LNKn?UD/e&K�Z�`�=YXHqmZ\D�qF=2dFKC?UZ\AFLH=YS2=YZ:^�Z�D�XVA"Z�E�G�K/u6DFL(d(=YD/E�?�SY^�Z\`HK�e�AFI�G�D[?�I�DF_H=@Igl�D/G�S@W�l>AF?�P8E�SYS�D�PIJ`�AFXHqFK/upZ�`�K�G\K�P8DFG\K;l~`VA"Zjl�A/?�=2e&_VK�G�=@?�`�A�LHS2K>DFG�EHX�I�E]Z\AFLHSYK��{A�Z�D/e&? �{esE�?UZ�LNK>LVK�SYD"l�_VK�G\I�K�_]Z\=YD/X�a�b>`�Ke&D]W]K�G\XCh[E�A�X[Z\EHefZ\`HK�D/G�^&W]D(K�?;=YXVW]K�KiW�LVKiA�G�D/E]Z�?�DFe&KcDFP�Z�`HK�=YG;Z�`H=2XHO(=YX�q�aj¯�=@I�G\D/?\I�DF_�=2I>_�AFGUZ\=2I�SYKi?�I�AFXLNK4I�G�KiA"Z�KiWmA�X�W�W]Ki?:Z\G�D"^/K�WpoVD�P�I�D/EHGJ?UK/o�LHE]ZRZ�`HKsegK�esLNK�GJ?cDFP;A�I�S@AF?\?BA�G\K-esEVIJ`�egD/G�Ks=2W]K�X[Z�=@I�A�S�Z�`�AFXe�AFI�G�D[?�I�DF_H=@I-D/L,A:K�I�Z\?MI�AFX�K�d/K�G�LVK/ucP8EHXVWHA�e&K�X[ZJA�Sj_�AFGUZ\=2I�SYKi?BS2=YO/K4K�SYKiI$Z\G�D/X�?RAFX�W�h[E�AFG�O]?�A�G\K6Z\`HDFEHq/`[ZZ\D-LVKBAFL�?�DFS2E]Z�K�SY^4=2W]K�X[Z�=@I�A�S�a�b>`[EV?�Z�`HKcP8DFG\e&?�_�A�G�Z�=@I�S2K�?jI�A�XgZ\AFOFKcA�G\K~A�_H_VA�G\K�X[Z�S2^sK�Z�K�G\X�AFS�u�AM`[^]W]G\DFq/K�XA�Z�DFe Z�D]WHA*^C=@?>Z�`�K6?�AFegKM=2XnZ\`HK�D/G�^QAF?>DFX�KMA�ZBA�X(^�Z\=Ye&K-=2XE�XH=Yd/K�GJ?�AFS�`H=2?UZ�D/G�^/a

Page 187: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Ziajµ/¾ ¯�D/G�K-�BLVD/E]ZB¯�A"Z�Z�K�Gc»�A*d/K�? � ¼/³

b>`�K�A�Z�DFe&=@?:ZJ?CZ\G�=2K�W�Z�Dtl�D/G�O±DFE]Z�A�X�A"Z\DFe&=2I�EHX�W]K�G\?UZ\AFX�W]=2XHq�DFPsK��]=@?:Z\K�X�I�K�=2X�q/K�XHK�G\AFS�a�|HD/G=2X�?UZ\A�XVI�KCZ\`HK�^�I�DFX�?UZ�G\E�I�Z�K�W�AxI�D/?�egD/SYD/qF^xE�?U=2XHqrA"Z\DFe�?6Z\`�A"Z&LNK�A�GJ?s?�DFe&KQG�Ki?UK�esLHS@A�X�I�KCZ\D�e&D]W]K�G\XK�Z�K�G\X�AFSj=YX]�NA"Z�=2DFXVA�G\^�I�D/?�e&DFS2DFq/^=2Xrl~`H=@IJ`�Z\`HK�G\K�A�G\K4=2X]��XH=YZ�K�SY^xe�A�X(^�EHXH=2dFK�G\?�K�?RZ\`�A"ZsAFG�KgLVD/G�X�DFEHZDFP�_HG�=2e&DFGJW]=@A�S�?�_�A/I�K�T�Z�=2e&K6P8D[A�e�A�X�W�_VK�G�`�AF_�?RG�K�Z�EHG\X�Z�DnZ�`�A�Z �wP8D/AFe�Z�DCP8D[A�emaM�cX]P8D/GUZ\EHX�A"Z\K�S2^FoNZ�`�KA�Z�DFe&=@?:ZJ?�q/D�Z;D �D/X&Z�`HKRl~G�D/XHqMP8D(D�Z�D/X�Z�`�KR?�`�A�_NKcD�PpZ\`HKR��A�G�Z�`�u�Z�`HK�^&l�K�G�KB?UZ�=2S2SH�VA�Z��;AFGUZ\`HK�GJ?jl~`HK�XZ\`HK6G\DFEHX�Wm��A�G�Z�`Z�`HK�DFG\^Cl>AF?~LNK�=2XHqCKi?:ZJA�LHS2=2?�`HKiWpa>®REH=YZ�KsDFL(d(=YD/E�?US2^�Z\D�E�?�o�Z�`HK4A"Z�D/e&=2?UZ\?~l�K�G\KML�AFWHSY^XHD/X]TkK��]_VK�G�=2e&K�X[Z\AFS�a~¯�EVIJ`�D�PjZ�`�K�=2GcZ�`�=YXHO(=2XHqnI�A�X�LNK4I�AFSYS2K�WmGJA"Z\=YD/X�A�S�es^[Z�`�acb�DnACWHK�qFG\K�KMZ\`HK�^ml�K�G\KS2E�IJO(^C=2X`VA�_H_NK�XH=2XHq&Z\DgLNK6A"Z�Z�GJAFI�Z�K�WnZ�DCAFXQKi?�?�K�X[Z\=2AFSYS2^�G�=2qF`[Z~=@W]K�A�a

b>`�K�A"Z\DFe&=@?:ZJ?�l�K�G\K�K�d/K�X[Z�EVA�S2SY^M?:Z\=Yq/e�A"Z�=2��KiW6AF?�A"Z\`HK�=@?UZ\?�upZ�`HK�^-W]=2WsXHD�Z�W]K�X(^�Z�`VA"Z�q/D]WH?�K��]=2?UZ�o*LHE]ZW]=@W]X�· ZjSYKiA*dFK�A�X(^[Z�`H=2XHqcP8D/G�Z\`HK>qFD]WH?�Z�DMW]D�a�b>`H=@?�e�A*^-`�A*d/K;LNK�K�X6Z�`�K�=2G�WHD"l~X]P,A�S2S�a�b>`HK�egD/G�K�DFG�Z�`�D(WHD*�AFX�Wn_NDF_�EHS2AFG>_H`H=2SYD[?UD/_H`H=2K�?�D�P�9�S@A"Z�DVoH�cG\=2?UZ�DFZ�S2KFo]A�XVWCZ\`HKs¤[Z�D/=2I�?�G�K9A:K�I$Z\K�WA"Z\DFe&=2?�e _HG\DFLVA�LHS2^Fo]A�e&D/XHqDFZ�`HK�G>Z�`H=2XHq/?�o(P8DFG~=YZ\?~?�K�K�e&=YXHq�A�Z�`HK�=2?�ema�v�`�G�=@?:Z\=2AFXH=YZ:^�P8DFS2SYD"l�K�WQ?UE�=�Z~=2XQZ\`H=@?>G�K�q/A�GJWpa�b>`HK-l~G\=�Z\=YXHq[?�D�PZ\`HK4A�Z�DFe&=@?:ZJ?BD/XHS2^K��]=2?UZB=2X�P8GJA�qFe&K�X/ZJ? ��A�XVW�¡BK�egD]I�G�=YZ�D[?B?�K�K�e�?BZ�DC`VA*dFK6LNK�K�XxAF?cP,A�e&DFEV?RA/?B9�S@A"Z\D=2X�`H=@?BWHA*^/a>b>`�Ks��_H=@I�E�G�KiA�Xm_H`H=2SYD[?UD/_H`HK�G\?~A/W]DF_]Z\K�W�A�Z�DFe&=@?UemoVLHE]Z�AFS2?�DC?�E,�NK�G�KiWZ�`HK4?:Z\=Yq/e&A�Z�=2��A�Z�=2DFXA/?�A�Z�`HK�=2?UZ\? ��A�X�WxA�S@?UD`HK�WHDFXH=@?:ZJ?Ml~`HDmA�G\KFopD�P>I�D/EHG\?�KFoNZ\`HK&l�D/G\?UZ�a ��E]ZMZ\`HKCA"Z\DFe�=@W]K�AQSY=2XHq/K�G\K�W�D/XZ\`HG�D/EHqF`nZ�`HK-I�K�X[Z�EHG\=2K�?�u�¸�K�E�I�=Y_H_ND/?~AFX�Wn¡RK�e&D]I�G\=YZ�E�?�oH��_H=@I�E�G�E�?�o]¸�E�I�G�K�Z�=2E�?M58`H=@?~?�EHG�d(=2d(=YXHq4_VD(K�e��41R1��$�]3 �&�"���]�%���C>� � �"���]��1 !NK��]_VD/EHX�WH?>A"Z\DFe&=@?UeC<$oH�MA/?�?�K�X�WH=�5U�*ºiZ\`nI�K�X[Z�EHG\^H<$o] cK�l>Z�DFX�oH¡RAFS�Z\DFX�u�Z�`�KIJ`�AF=YXQ=2?�EHX(LHG\DFO/K�X�u�=YZ>=@?>XHDFZ�Z\G�EHK�Z\`�A"Z>e&D(WHK�G\XA�Z�DFe&=@?Ue `VAF?�XHDg`H=2?UZ�D/G�=@I�AFSVD/G>K�?\?UK�X/Z\=2AFSpI�DFX�XHK�I�Z�=2DFXZ\DCA�X�I�=YK�X/ZcA�Z�DFe&=@?Uema

�tqFD(D]W6A/I�I�D/EHX[Z�DFPVA�X�I�=YK�X[Z�A"Z\DFe&=@?Ue�I�AFXsLNK;P8D/EHX�Ws=YXg¡RA*d(=@W6|HEHG\S2K�^�· ? ��'H1��>��1J1�� ���")J3��"02�%$F+@)$�,)$a BD"l-o]l~=�Z\`HDFEHZcG�KiI�EHG\G�=2XHq4Z�D&Z\`HKMZ�D/_QDFP�Z\`H=2?c_HG�KiA�e4LHSYK/o]A"Z�D/e&=2?�e�l>AF?�=2X[d/K�X[Z�KiWn=2X�u

A[<�Z\`HK-K�AFG�S2^�� ½ Z�`mI�K�X[Z�EHG\^FaLN<CZ\`HK��*º*Z�`mI�K�X/Z\EHG\^CL(^�MAF?\?�K�X�W]=�aIi<CZ\`HK���¾�Z�`mI�K�X/Z\EHG\^n�B¡4aWV<CZ\`HK ¶ Z\`�I�K�X[Z\EHG�^Q�B¡4aK*<CZ\`HK ¶ Z\`�I�K�X[Z\EHG�^#�~vRa

¾�µ[¾4h[e4EHS�ZB¾��i�F¾F¾C�&�-µ&K�A/?U^�e&K�egD/G�^�uj`(^]W]G\DFqFK�XH=@IBK�XHK�G\qF^&P8D/G�e4EHS2A�F�Fa~b>`HKMP8D/G�e4EHS@A

�$�, �� � � * � � ���

�� �

q/=Yd/K�?�Z�`HK-e�AF=YXmK�X�K�G\qF^�S2K�dFK�S2?>DFP:uA[<C_ND/?�=YZ�G\DFXH=2EHemaLN<ne�AFqFXHKi?U=2EHe�W]K�LVD/G�=@W]K/aIi<CZ\`HK-`(^]W]G�D/qFK�Xne&DFS2K�I�EHSYK/aWV<CZ\`HK-`(^]W]G�D/qFK�XH=2I�A"Z\DFemaK*<CZ\`HK-=2X]��XH=YZ�K6?\h[E�A�G\KMl�K�SYS�a

¾�µ[¾4h[e4EHS�ZB¾�� ³ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�uj`(^]W]G\DFqFK�Xnl>A*dFKBP8EHX�I$Z\=YD/X�?�i�]a~b>`HK-`(^]W]G\DFq/K�Xnl>A*dFKRP8EHX�I�Z�=2DFX�?BI�DFX[ZJA�=2XQAgP,AFI�Z�D/G�Z\`�A"ZBI�A�E�?�K�?�Z\`HK�e�Z�DVu

A[<C=2X�I�G�KiAF?�KRK��(_NDFX�K�X[Z�=@A�S2SY^nl~=�Z\`GJAFWH=YE�?�aLN<QWHK�I�G\K�A/?UK�K��]_NDFXHK�X[Z�=@A�S2SY^Cl~=YZ�`mGJAFW]=2E�?�aIi<n=2X�I�G�KiAF?�KRS2DFq[A�G\=�Z\`He&=2I�A�S2SY^�l~=YZ�`mGJAFW]=2E�?�aWV<n=2X�I�G�KiAF?�K�h[E�A/W]G\A�Z�=@I�AFSYS2^�l~=�Z\`�G\A/W]=2E�?�aK*<n=2X�I�G�KiAF?�KRS2=YX�K�A�G\S2^Cl~=�Z\`ml�A*d/K�S2K�XHqFZ�`�a

¾�µ[¾4h[e4EHS�ZB¾���µ[¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�X(E�I�S2K�E�?� ³ a �\¸�K�Zi· ?;_HS@A*^ �]1J� D+�"����# 1 |HDFG �(��¾/¾Ho"Z\`HKBAFX�?Ul�K�G;=2?�u�b>`�=2?;LVD/EHX�W�h[E�A�X[Z\EHe e&KiIJ`�A�XH=@I�AFS�?�^(?UZ�K�e I�DFX�?�=@?:ZJ?

DFP�_HG\D�Z\DFX�?>AFX�WXHK�E]Z\G�D/X�?>`HK�S2WnZ�D/qFK�Z\`HK�G~L(^�Z\`HK6?UZ�G\DFXHq&X(E�I�S2K�AFG�P8DFGJI�KFa �

Page 188: Introductory Physics Problems David J. Jeffery Department of

� ¼ µ v�`�A�_]Ziajµ/¾ ¯�DFG\KM�BLVD/E]ZB¯�A�ZUZ�K�G~»�A*d/K�?

A[<C»{`VA"Zc=@?~A�Xm=YXH��XH=YZ�K6?\h/EVA�G\KRl�K�S2S�oV�cS2K�� �LN<n»{`VA"Zc=@?~Ag��XH=YZ�K6?\h/EVA�G\KRl�K�S2S�oV�cS2K�� �Ii<n»{`VA"Zc=@?~Ag��XH=YZ�K6?\h/EVA�G\=2?�`nl�K�S2S�oV�cS2K�� �WV<n»{`VA"Zc=@?~A�X�A"Z\DFemoH�cS2K�� �K*<n»{`VA"Zc=@?~A&X[EVI�S2K�E�?�oH�cS2K�� �

¾�µ[¾4h[e4EHS�ZB¾���µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�I�A�E�?\A�S2=�Z:^/o(G�K�S2A�Z�=2d[=YZ:^��µ�a~�;=YX�?UZ�K�=YXmG\EHS2K�WQDFE]Z~P,A/?:Z\K�G>Z�`VA�XSY=2qF`[ZB?�=Yq/X�A�S2=YX�q4LNK�I�A�E�?�KFu

A[<C=YZcl�DFEHS@WQI�A�E�?�KM=YG\G\K�?�DFS2d*AFLHS2K�I�A�E�?\A�S2=�Z:^�_VA�GJAFW]D*�]K�?�aLN<n=YZcl�DFEHS@WnX�D�ZBI�AFE�?�K�=2G\G�Ki?UD/SYd"A�L�SYK�I�A�EV?�AFSY=YZ:^C_�AFG\A/W]D*�]K�?�aIi<n=YZcS2K�WQZ�D&=2G�G\K�?�DFS2d"A�LHS2KR_VA�GJAFW]D*�]K�?�=2Xmh[E�AFX[Z�EHe}egKiIJ`�A�X�=2I�?�aWV<n=YZcl�DFEHS@WQWHK�?UZ�G\D"^�Z�`HK-E�XH=Yd/K�GJ?UK/aK*<n=YZc`�A/WQLNK�K�XmK��]_VK�G�=2e&K�X[Z\AFSYS2^Cd/K�G\=���KiWpa

¾�µ[¾4h[e4EHS�ZB¾�� ¶ ¾F¾C�&� ³ K�A/?U^�e&K�egD/G�^�u���9;¿�_VA�GJAFW]D*�� ¶ a~b>`HK��;=YX�?UZ�K�=YXHTk9�D]W]D/S2?�O(^/T!¿~D[?UK�X�5,�;9�¿B<s_�A�GJAFW]D*��l>AF?g_HG\DF_ND/?�K�W�Z�D�?U`�D"l Z�`�A�Z�DFGJW]=YXVA�G\^rh[E�AFX[Z�EHe

e&K�IJ`VA�XH=@I�?>=2e&_HSY=2K�Wm?�EH_NK�G\SYEHe&=2X�A�S�?U=2qFX�AFSY=2XHq&A�X�WnZ�`�K�G\K�P8DFG\KMl�A/?�uA[<Ce&D/G�KMDFG~S2K�?\?~I�D/G�G\K�I�Z�aLN<QAFL�?�DFS2E]Z�K�SY^nI�DFG\G�KiI$ZiaIi<QWHK�P8K�I�Z�=2dFK/aWV<nl~G\DFX�q4=2X�A�S2S�=�ZJ?>_HG\K�W]=@I$Z\=YD/X�?�aK*<nX�K�dFK�G~l~G�D/XHqg=YXm=YZ\?~_HG\K�WH=2I�Z�=2DFX�?�a

¾�µ[¾4h[e4EHS�ZB¾�� ¹ ¾F¾C�Mµ ³ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u ��K�S2S�· ?>Z�`�K�DFG\K�e� ¹ a �\¸�K�Zi· ?;_HS@A*^ �]1J� D+�"����# 1 |HD/G �(�i¾F¾HoFZ�`HKRA�X�?�l�K�G�=@?�ujb>`H=@?jZ\`HK�D/G�K�e 5,=�P�=YZ�=@?�=2X�W]K�K�W�=2XHK�?\I�AF_�A�L�SY^gI�DFG\G\K�I$Z$<

AFX�W�Z\`HK�?�EHL�?�K�h[EHK�X[Z�K��]_NK�G\=Ye&K�X/ZJ?mDFXzZ�`HK�K.�NKiI$ZmZ�`�KrZ�`HK�DFG\K�e W]KiA�SYZ�l~=�Z\` ?�`HD"l Z�`�A�Z�h[E�AFX[Z�EHee&K�IJ`VA�XH=@I�AFS�?U=2qFX�AFSY=2XHqgK��HI�K�K�WH?�Z\`HK6?�_VK�K�WD�P�SY=2qF`[Z�a �A[<C»{`VA"Zc=@?~¡RAFG�O�· ?�Z�`HK�DFG\K�emoH�cS2K�� �LN<n»{`VA"Zc=@?~¯�=2WHXH=Yq/`[Z�· ?>Z�`HK�DFG\K�emoH�cS2K�� �Ii<n»{`VA"Zc=@? ��K�SYS�· ?>Z�`HK�DFG\K�emoH�cS2K�� �WV<n»{`VA"Zc=@? ��D(D/ON· ?�Z�`�K�DFG\K�emoH�BSYK����K*<n»{`VA"Zc=@?Bv�A�X�W]S2KF· ?>Z\`HK�D/G�K�eoH�BSYK�� �

�Fd�NIN j��'>�E�� 145LB$5<?Te�N-1)= E

¾�µ[¾4h/P8EHS2S�¾/¾H��¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\K�A�SpK��]_VD/XHK�XHK�X[Z>K��]_VD/XHK�X[Z�=@A�S@?�FaBv�D/X�?U=@W]K�G>Z�`HKMZ\=Ye&K�Tk=2X�W]K�_NK�XVW]K�X[ZR¤]IJ`HG��D/WH=YXHq/K�G>K�h[E�A�Z�=2DFX

, %, ����

� � �� � �

� � ��$ ��

l~=YZ�` ��I�D/X�?UZ\A�X[ZcA�XVW � ��aA[<C´jK�G�=YP8^CZ\`�A"Z~Z\`HK-K��]_NDFXHK�X[Z�=@A�S�?�DFS2E]Z�=2DFX�?

��$�����

?\A"Z\=2?UP8^Q¤]IJ`�G��D[W]=YX�qFK�Gi· ?�Kih[E�A"Z\=YD/XQl~`HK�X

$� � �r5 ��, s<

%, � �

Page 189: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Ziajµ/¾ ¯�D/G�K-�BLVD/E]ZB¯�A"Z�Z�K�Gc»�A*d/K�? � ¼[¶

LN<mv�AFXgZ�`HKRG�KiA�S]K��]_NDFXHK�X[Z;K��]_NDFXHK�X/Z\=2AFS�?�DFS2E]Z�=2DFX�?�LVK~Z\`HKB?�DFS2E]Z�=2DFXV?�P8DFG;AsI�DFe&_HS2K�Z\K~l�A*d/K�P8EHX�I$Z\=YD/X �»{`(^QDFG>l~`(^nXHDFZ�

Ii<m°BP�l~`�A�Z>EV?UK6AFG�KRZ�`HK-G\K�AFSpK��]_NDFXHK�X/Z~K��(_NDFX�K�X[Z�=@A�S�?�DFS2E]Z�=2DFXV?�a

¾�µ[¾4h/P8EHS2S�¾/¾/��¾/¾ ³�¶ ¾4Z�D/EHqF`QZ�`H=2XHO(=2XHq�ujLND*�h[E�AFX/Z\=Y�iA"Z\=YD/X� ª�¬"¨ �V«������V¬ ��­��  cK�KiWH?>Z\DgLNKM��XH=@?�`HK�Wpuj7�XHK�K�WQZ�D&EHX�WHK�GJ?:ZJA�X�W

�]a~b>`HKx?:ZJA"Z�=@?UZ�=@I�A�SRe&K�IJ`�AFXH=2I�?&Z�G\K�A�Z�e&K�X[ZnDFP-q/AF?�K�?�5,A�XVW{h/EVAF?�=�Tkq/A/?UKi?�u�=�a K/aYo>Z\`H=2XHq/?CZ�`�A�ZQA�G\X�· ZnG�KiA�S2SY^q[AF?�K�?�o�LHE]Z>A�G\KcA�e&K�X�AFLHS2K~Z�DsAFX�A�S2DFq/DFE�?�P8D/G�e�AFSY=@?UeC<�DFP Z�K�X�LVK�qF=2X�?�l~=YZ�`��VX�W]=2XHq-Z�`�KR?UZ\A"Z\=YD/X�A�G\^4?UZ\A�Z�Ki?DFP�A-G�KiI$ZJA�XHq/EHS2AFG�LND*�gl~=YZ�`Q��K�G\D-_ND�Z�K�X[Z�=@A�S�58DFG�I�D/X�?:ZJA�X[Z;_ND�Z\K�X[Z�=@A�S <j=2X�?�=2W]KR=�Z~A�XVW&_VK�G�=2D]W]=2IBLVD/EHX�WHAFG�^I�DFX�W]=YZ�=2DFXV?�a�b>`H=@?MLVD*��h/EVA�X[Z�=2��A�Z�=2DFX�qF=2dFK�?�q/D[D]WxG�Ki?UE�S�ZJ?MK�dFK�Xxl~`�K�X�XHD�Z\`H=YX�q�SY=2OFK�ALVD*�x=2?-AFG�D/EHX�WZ\D&I�DFX[Z\AF=YXQZ�`�K�q[AF?�ajb>`HK-?U=2e&_HSYKMG\K�A/?UD/Xn=@?�Z�`�A�Z~P8DFG~AgS2AFG�q/KRLND*�po]=YX[Z�K�G�=2DFG>LNK�`�A*d(=2DFG�esE�?UZcLNK�e&D[?:Z\SY^EHXVA ��K�I$Z\K�W�L(^gl~`�A"Z�=2?�DFEHZ\?�=2W]KcZ�`HKRLVD*�&K�d/K�XC=YP�=�ZJ?�A:EV?:Z�egD/G�KBq/AF?�u�?�D6^/DFECI�AFXCA�S2l�A*^]?j=2e�A�q/=YXHKRA-LH=2qLND*�Q58DFP�I�DFX�?UZ\AFX[Z�=2X[Z�K�G�=2DFG�_ND�Z�K�X[Z�=@A�S <�W]G\A*l~X4=YX�?�DFe&K>esE�IJ`gLH=2qFq/K�GjG\K�qF=2DFX4D�PNq/AF?~58Z�`�A�Z�e�A*^6XHD�Zj`�A*d/KI�DFX�?UZ\AFX/Z�_VDFZ�K�X/Z\=2AFS�LNK�`VA*d[=2DFG$<$aMb>`HKgE�?�KsD�P�_VK�G�=2D]W]=2IsLVD/EHX�WHAFG�^�I�DFX�W]=YZ�=2DFXV?B=@?R?�=2eg=2S@A�G\SY^me&D�Z\=Yd"A"Z\K�Wpab>`HKRLVD/EHX�WHAFG�^gI�D/X�W]=YZ�=2DFX�?;D�P�G\K�A�SVI�DFX[ZJA�=2XHK�G�e&A*^4LVKRdFK�G�^&I�D/eg_�SYK���u�KFa q�a2o/LNDFE�X�WHA�G\^&I�DFXVW]=�Z\=YD/X�?�DFP�AAUAFG�oFZ�`HKB?�=@W]K�?;D�Ppe&K�Z\AFS�?�S2AFL�5 P8DFG�A�X�K�S2K�I�Z�G\DFX&q/A/?j=2X�?U=@W]KBAMe&K�Z\A�S <$o[DFG;XHD�Z\`H=YX�q6A"Z�AFSYS�P8DFG;AFX�=Ye�A�q/=YX�K�WLND*�gK�esLNK�WHWHK�W�=2XCA-LH=2qFq/K�G�G\K�q/=YD/XgDFPpq/AF?�a ��EHZ;=�PpZ\`HKBLND*�&=2?;S2AFG�q/K~K�XHD/EHqF`gZ�`�KBLNDFEHX�W�A�G\^gI�DFX�W]=YZ�=2DFXV??�`HDFE�S2WnXHD�Z~A ��K�I�Z�Z\`HKR=2X[Z�K�G�=2DFG�esE�IJ`�a�b>`(E�?�_NK�G\=YD]W]=@IBLNDFE�X�WHA�G\^�I�D/X�W]=YZ�=2DFX�?>A�G\KRA/?;q/D(D(WnA4IJ`HD/=2I�KRA/?AFX[^mDFZ�`HK�G�AFX�W�Z\`HK�^�AFG�Ks?�=2eg_�SYK4Z�DE�?�KFas°BP�I�D/EHGJ?UK/oV=YP;^FD/E�G\K�A�S2S2^`VA*dFK4AQ?Ue�AFSYS�I�D/X/ZJA�=2XHK�G�=2Xx?�DFe&K?�K�X�?�KFo(Z\`HK6AFI�Z�E�AFS�?U=2��K6AFX�WQLVD/EHX�WHAFG�^nI�DFX�WH=�Z\=YD/X�?>D�P�Z�`HK6I�DFX[Z\AF=YXHK�G~e&=Yq/`/Z~LNK�I�DFe&K-=Ye&_NDFG�Z\AFX/ZiaA[<

¾�µ[¾4h/P8EHS2S�¾/¾ ³ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�ujG\K�I�D/=YS2=2XHq4`(^]W]G\DFq/K�XQA�Z�D/e� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT\�i¾F¾Fµ�u µ[��9�<

³ a~�w`(^]W]G\DFqFK�XsA"Z\DFefA�Z�� � zK�e&=YZ\?jAM¸�^ ��_�`HD�Z\DFX�u�=�a KFa2o/A�_H`HDFZ�D/XsP8G\DFefARZ\G\AFX�?U=YZ�=2DFXsP8G�D/e�Z�`�K � $��Z\D&Z�`HK � $��MS2K�dFK�S�a�¿cK�I�AFSYS�Z\`HK-`(^]W]G�D/qFK�XH=2I�A"Z\DFe K�XHK�G\qF^�S2K�d/K�S�P8D/G�e4EHS2A

$�, �� ��* � � � � �� �

$�, �� � � � �� �

l~`HK�G�K � � � $�� ³ � ¹ K�´4o �x=@?�Z�`HK-_�G�=2X�I�=2_�AFS�h/EVA�X[Z�EHe}X(EHesLNK�GioHA�X�W � =@?>Z�`�K-X[EVI�S2K�A�G~IJ`�AFG�q/KFaA[<C»{`VA"Z4=@?sZ�`HKQK�XHK�G�q/^�AFX�W�l>A*dFK�S2K�X�q�Z�`rDFP~Z�`HKQK�e&=�Z�Z�KiW�_H`HDFZ�D/X � £B7: BbMuj� E�?�K�P8E�S�X(EHe4LVK�G4=2X?�E�IJ`mI�AFS2I�EHS2A�Z�=2DFX�?>=@?%�* $ �i� ³F½/¼ K�´BT ��sa

LN<Q�R?�?�EHe&=2XHqmZ�`�A�ZMZ�`HK�`(^]W]G\DFqFK�XxA�Z�DFe I�A�XrLNK&Z�G\K�A�Z�K�W�AF?-AmI�S2A/?�?�=2I�A�S�opXHDFXHT�G\K�S@A"Z\=Yd(=@?:Z\=2Ig_�AFGUZ\=2I�SYK/o�VX�WxAFX�K��]_HG\K�?\?�=YD/X�P8DFG�=�ZJ?�G�KiI�DF=2S�O[=2XHK�Z�=@I4K�XHK�G\qF^m=2X�Z\K�G\e&?�DFPjZ�`HK&K�X�K�G\qF^Z�`HKg_H`HDFZ�D/XxA�XVW�Z�`�KG\K�?UZ4e�A/?�?sD�P~Z�`�KQ`(^]W]G\DFqFK�X�A"Z�D/ema ������ � »{`�A"Z&I�D/X�?UK�G�d"A�Z�=2DFX�S@A*l�I�A�X�LNKmA�_H_HS2=2K�WrZ\D�Z�`�K?�^]?:Z\K�ema

Ii<n»{`VA"Z-=2?�Z\`HK&G�KiI�D/=YS�O(=YX�K�Z�=@IgK�XHK�G�q/^�D�P�Z�`HK&`(^]W]G�D/qFK�XxA"Z\DFemas»{`�K�G\Kge4E�?UZ�Z\`H=@?MO[=2XHK�Z�=@I4K�XHK�G\qF^`VA*dFKMI�DFe&KRP8G�D/e �m£cD"lzWHD[Ki?�Z�`H=@?>O(=YXHK�Z�=@I�K�XHK�G�q/^CI�DFe&_�AFG�KRZ�D4Z�`�K�_�`HD�Z\DFX�· ?>K�XHK�G�q/^�A�X�WnZ�DgZ�`�KZ\`HK�G\e�A�SpO(=2XHK�Z\=2IMK�XHK�G\qF^CDFP�AFXmA�Z�D/e�A"Z ³ ¾/¾�² ��»{`�A�Zc=2?>Z\`HK6?�_VK�K�WD�P�Z�`HK-G\K�I�DF=2SY=2XHqg`[^]W]G\DFq/K�X �»�K�G\K�l�K�A:E�?:Z\=��VK�Wr=2XxZ\G�KiA"Z\=YXHqZ\`H=2?sG�KiI�D/=YSjXHD/X]TkG�K�S2A�Z�=2d[=@?UZ�=@I�A�S2S2^ � ������ � ��DFEre&=Yq/`[Z-��X�W�Z�`�KP8D/SYS2D"l~=2XHq�I�DFXV?:ZJA�X[Z\?&`HK�SY_HP8EHS�u

�$�� � ¹ ¾[���{��¾ � � #"o * $ � � ½F½/¼ �{��¾ pe��"?�o � � � � $�� � ¾F¾(º ½ º(o

� � � � $ � � ¹/¹ �x�i¾�� � � o � � � � * � $ ½/³ � � ¶ �x�i¾ ! K�´soHA�XVW � $�¾ � ¼F¹ �"º�����¾ � � K�´�² � � � a

¾�µ[¾4h/P8EHS2S�¾/¾ ¶ ¾/¾g� ³ ¾ge&D(WHK�GJA"Z�KMe�A"Z\`�u�£�A"Z\DFe GJAFWH=2AFSp_HG�D/L�A�L�=YS2=�Z:^� ª�¬"¨ �V«������V¬ ��­�� 5,£B¿�»wT\�i¾F¾ ¶ u ¶F¶ 9�<

µ�a~b>`HK&q/G�D/EHX�W�?UZ\A�Z�K&D�P�Z�`HK�`(^]W]G\DFq/K�X�A�Z�DFe `�AF?-AQ=2?�D�Z\G�D/_H=@Isl>A*dFK4P8EHX�I�Z�=2DFX�uM=�a K/aYo�=�Z-`�A/?MXHD�A�XHq/EHS2AFGW]K�_VK�X�W]K�X�I�K/a�b>`H=2?cl�A*d/KBP8EHXVI$Z�=2DFX�58Z�=2egK�T�=2X�W]K�_VK�X�W]K�X/ZRdFK�GJ?�=YD/XV<�=@?

�R5 < $�

+ µ���

� � � � � ��� ��

Page 190: Introductory Physics Problems David J. Jeffery Department of

� ¼/¹ v�`�A�_]Ziajµ/¾ ¯�DFG\KM�BLVD/E]ZB¯�A�ZUZ�K�G~»�A*d/K�?

l~`HK�G�K � $ ¾ � ¶ � ½ �� =@?&Z�`HK/��D/`HG�G\A/W]=2E�?�azb>`HK�G\A/W]=@A�S~_HG\DFL�AFLH=2SY=YZ:^�W]K�X�?U=YZ:^z5,=�a KFa2o>Z�`�K�_HG�D/L�A�L�=YS2=�Z:^W]K�X�?�=�Z:^C=2X[Z�K�qFGJA"Z�KiWnD"d/K�G~A�S2S�?�DFS2=2WA�XHq/SYK�Z\=Ye&K�? �*<�=@?

�N5 < $�� �&� � � � � $ µ �

� � � � � � �� �

b>`HK-_�G�D/L�A�LH=2S2=�Z:^�DFP���XVW]=YX�q&Z�`HK-K�SYKiI$Z�G\DFXQ=YX�A&?�_H`HK�G\=@I�A�S�?�`HK�SYS�DFP�Z\`H=2IJO(XHKi?�? � =2?�Z\`HK�X

��� $ µ �� � � � � � �

� � �

A[<C»{`VA"Zc=@?�Z�`HK-e&D/?UZc_HG\DFL�AFLHS2KRGJAFW]=2E�? P8DFG>��XVW]=YX�q4Z\`HK-K�S2K�I�Z�G\DFX�aLN<n´jK�G�=YP8^�Z\`�A"Z�Z\`HK�qFG\DFE�X�Wt?UZ\A�Z�Kml>A*dFKQP8EHX�I$Z\=YD/Xw=2?�X�DFG\e&AFSY=2��KiWpa ������ � ��DFEwe&=2qF`[Z���X�WtZ�`�K

P,A/I$Z\DFG\=2AFSN=2X[Z�K�qFGJA�SpE�?�K�P8EHS�u� 1 $ � +

��� � � � � � �

Ii<Q�R?�?�EHe&K�Z\`�A"Z6D/EHG6l>A*dFKgP8EHX�I�Z�=2DFX�=@?sAFI�I�EHGJA"Z\K&G�=2qF`[ZsW]D"l~X�Z�D $ ¾�a�5�b>`H=@?6I�AFX�· Z4LVKCK��HAFI$Z\SY^Z\G�E�K&?�=2X�I�KgZ�`�Kg_ND�Z\K�X[Z�=@A�Sje4E�?UZ-IJ`VA�XHq/K6P8G\DFe AQ_VD/=YX[Z6IJ`�AFG�q/KsP8D/G�e�l~`HK�XxD/XHK&=2?�d/K�G\^�I�S2D/?�KsZ\DZ\`HK�_HG�DFZ�D/XCDFG�K ��K�I$Z\=Yd/K�S2^�=YXV?U=@W]KBDFP�=YZ�a <s»{`VA"Z�=@?�Z�`HK�_HG\DFL�AFLH=2SY=YZ:^4DFP���X�WH=YXHqsZ�`HK�K�S2K�I�Z�G\DFXC=2X�?�=2WHKZ\`HK�X(E�I�S2K�AFG-G�K�qF=2DFX � £B^]W]G�D/qFK�X�o�D�P>I�D/EHG\?�KFo�`�AF?-ALNDFG\=YXHqmD/XHK�_HG\D�Z�D/XxX(E�I�SYK�E�?�ag»�KCI�AFX�Z\A�O/KZ\`HKgDFE]Z\K�GBGJAFWH=YE�?RD�PjZ\`HKgX[EVI�S2K�E�?BZ�DQLVK&A�_HG\D�Z\DFX�· ?BG\e�?BGJAFWH=YE�?BD�P $ ¼ ���i¾�� ! ��6a ������ � 7kZ?�K�K�e�?R_NK�G�P8K�I�Z�S2^�G�KiAF?�DFX�AFLHS2K6Z�De�A�O/K4AQ��K�G\D�Z\`�D/G\W]K�GRK��]_�A�X�?�=2DFX�DFP�Z�`HK&K��(_NDFX�K�X[Z�=@A�S�P,AFI�Z�DFGM=2XZ\`HK-_HG\DFL�AFLH=2SY=YZ:^nW]K�X�?U=YZ:^Fa

Page 191: Introductory Physics Problems David J. Jeffery Department of

¥ DS&A9S;J0�� p �Zd�HJN[1)&:5LB$DW6FEGHJ*-E

� d�NO;<*[9fN-1Jj ¥ Da? *-H^1�B 5\?AefN[1_= E

¾�µ ³ h[e4EHS�ZB¾/¾H�i¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u�¿~EHZ�`HK�GUP8D/G\WA"Z\DFe� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�"µ ½ TJ�

�Fa>7!XZ�`�K6¿~E]Z�`�K�G�P8DFGJWne&D]W]K�S�D�P�Z\`HK6A"Z\DFemo]Z\`HK-_VD[?U=YZ�=2dFK-IJ`�AFG�q/KR=@?�uA[<?U_HG\K�A/W{Z\`HG�D/EHqF`�DFE]ZZ�`HK�A�Z�DFema LV<I�D/X�I�K�X[Z�GJA"Z�KiW�=2X�A±?�e&AFSYS6I�K�X[Z�GJA�SMI�D/G�KrI�AFSYS2K�W�Z�`�KX(E�I�SYK�E�?�a Ii<�D/E]Z\?�=@W]K�Z�`HK>A"Z\DFe�=2XgARX(E�I�S2K�E�?�a W�<�A"Z�Z�`HK�LND�ZUZ\DFe DFPHZ�`�K>A�Z�D/e�=YXgABX(E�I�SYK�E�?�aK*<�XHD�Zc_�G�Ki?UK�X/Zia

¾�µ ³ h[e4EHS�ZB¾/¾/�F¾F¾C�Mµ ¶ K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujA"Z\DFe&=2I�X(EHe4LVK�G� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�"µ ½ T ³

�]a �\¸�K�Zi· ?>_�S2A*^��]1J� D+�"�\�"# 1 |�DFG �(�i¾F¾�o/Z\`HK6A�XV?Ul�K�G>=@?�uj7kZc=@?�Z�`HK6A�Z�D/eg=@I�X(EHesLNK�GcDFP�AFXQK�SYK�egK�X[Z�a �»{`�A�ZBA�G\K�Z�`HK-X(EHe4LVK�G~D�P =YXZ�`�K-X[EVI�S2K�E�?�oH�cS2K�� �

A[<�Z�G\=2AFXHqFS2K�? LN<�=2?�D�Z\DF_NK�? Ii<�XHK�E]Z\G�D/X�? W�<�K�S2K�I�Z�G\DFX�? K*<�_HG\D�Z�D/X�?

¾�µ ³ h[e4EHS�ZB¾/¾/�H��¾C�&�s�4e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�G\K�AFWH=YXHqgX(E�I�S2=@W]K6?U^(e4LVD/S2?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ��T ¶

³ a~£BD"l�e�A�X(^CXHK�E]Z�G\DFXV?~A�G\KRZ\`HK�G\KM=YX !� ¸�=�o � �! vRo � �� � 9�o�AFX�W # ��� ?�G�aA[< ³ o ¹ o�� ¶ oNA�X�Wµ(º]a LN< ³ o�º(o�� ¹ o�AFX�Wmµ(º]a Ii< ¹ o�� ³ o ³ �/o�A�X�W ½ µ�a W�< ½ o�� ½ oHµ ¹ o�AFX�W� ¶ �/a K*<>¾Hop�Fo��HoHA�X�W ³ a

¾�µ ³ h[e4EHS�ZB¾/¾�µ[¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�Z\`HG�K�KMG\A/W]=2A�Z�=2DFXQ_�A�G�Z�=@I�S2K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=

µ�a>»{`�A�ZBA�G\K�Z�`HG\K�KMO(=YXVWH?~D�P�X(E�I�S2K�AFG~G\A/W]=2A�Z�=2DFX��U_�AFGUZ\=2I�SYKi? � �A[<�A�S2_H`�A�o�LVK�Z\A�oFq/AFe&e&A�a LN<jA�S2_H`�A�o�LVK�Z\A�oFDFe&K�q/AHa I�<�AFSY_�`�AHo/_�?U=�o�D/egK�q/A�a W�<jLVK�Z\AHo_V?U=�oHDFe&K�q/AHa K*<>�cS2_H`HK�Gio+��K�`[Z\KFo��MA�e&D"l-a

¾�µ ³ h[e4EHS�ZB¾/¾�µV��¾C�&� ³ K�A/?U^�e&K�egD/G�^�u�AFSY_H`VA4_VA�G�Z�=@I�S2K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:�"µ ½ T ¹

¶ a~�BXmAFSY_�`�Ag_�A�G�Z�=@I�S2KM=2?cA�uA[<�_VD[?U=YZ�G\DFX&D/GjK�S2K�I$Z\G�D/X�a LV<�`HK�SY=2EHegT ³ X[EVI�S2K�E�?�a I�<�`HK�SY=2EHegT�µ-X(E�I�SYK�E�?�a W�<�q/AFege�A�TGJA*^Fa K*<�XHK�EHZ�G\=YXHDVa

¾�µ ³ h[e4EHS�ZB¾/¾�µ(��¾C�&�-µ&K�A/?U^�e&K�egD/G�^�u�AFSY_H`VA4_VA�G�Z�=@I�S2KMIJ`VA�XHq/K�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ��TJ�F�

¹ a>»{`HK�X�A�X�A�S2_H`�Ag_�AFGUZ\=2I�SYKM=@?>K�e&=�Z�Z�KiWpo]Z�`�K6A"Z�D/e&=2IMX(EHe4LVK�GcA�X�WQe�AF?\?>X[E�esLNK�GcDFP�AgX(E�I�S2K�E�?�uA[< AFG�K�EHXVIJ`�A�XHq/K�Wpa LV< LVKiI�DFe&K K�h[E�A�S�a I�< =2X�I�G�KiAF?�K L(^ � AFX�W µ�o G�Ki?U_NK�I�Z�=2dFK�SY^/aWV<>W]K�I�G�KiAF?�KRL(^�gAFX�WnµVoHG\K�?�_VKiI$Z�=2dFK�SY^/a K*<�LVDFZ�`�W]KiI�G\K�AF?�K�L[^�]a

¾�µ ³ h[e4EHS�ZB¾/¾�µ ¶ ¾4�Q�-µ&e&D]W]K�GJA"Z\K�e&K�egD/G�^�u�X(E�I�S2K�D/X�?~A"P Z\K�GcW]KiI�A*^

Page 192: Introductory Physics Problems David J. Jeffery Department of

� ¼/¼ v�`�A�_]Ziajµ��f BE�I�S2K�AFGc9�`(^]?�I�=2?

� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"TJ�i�º(a~�cP Z�K�G6AGJAFW]=2D/A/I$Z\=Yd/K4W]KiI�A*^mZ�`�KgX(EHe4LVK�GMD�P�X(E�I�SYK�DFX�?�=2X�Z�`HK&X(E�I�S2K�EV?M=2? Z�`�K�DFG\=Yq/=YX�AFSX(EHe4LVK�G�a

A[<�AFSYl>A*^]?�K�h[E�AFS�Z\D LN<;AFSYl>A*^]?je&DFG\KcZ�`VA�X Ii<�X�K�dFK�G;S2K�?\?�Z\`�A�X W�<;XHK�d/K�G�egD/G�KBZ�`�AFXK*<>A�S2l�A*^]?�S2K�?\?�Z�`�AFX

¾�µ ³ h[e4EHS�ZB¾/¾�µ ¹ ¾ ³�¶ �sZ�D/EHqF`QZ�`�=YXHO(=2XHq�ujE�G\AFXH=YE�e�W]K�I�A*^�Z�D�S2K�A/W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ �*T ¶

¼ a~�BG\AFXH=YE�e4T:� ³[¶ 5 � � �# � �R<4W]KiI�A*^]?-K�d/K�X[Z�EVA�S2SY^�Z�D�A�?UZ\A�L�SYKQSYKiAFW�=@?UDFZ�D/_VKCL(^rK�e&=YZUZ\=YXHq�ºmAFSY_H`VA�_�AFGUZ\=2I�SYKi?AFX�Wµ�K�S2K�I$Z\G�D/X�?-58=�a KFa2oHµ�XHK�q[A"Z\=Yd/K�LNK�ZJA&_�A�G�Z�=@I�S2K�?J<$a�b>`HK-_HG\D(I�K�?\?>qFD(K�?�Z\`HG\DFEHq/`=2X[Z�K�G�e&K�WH=2A�Z�K-?:ZJA�q/K�?�a»{`�A�Zc=2?�Z\`HK-X(E�I�S2=@W]K6?U^(e4LVD/SpD�P�Z�`HK-G\K�?�EHSYZ�=2XHq&X[EVI�S2K�E�?�

A[< � � ��� 9;L�a LV< � � � � 9�L�a Ii< � � � 9;L�a W�< � � � � 9�L�a Ki< � � � � �6a

¾�µ ³ h[e4EHS�ZB¾/¾ ¶ ¾F¾C�Mµn�4K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�`�A�SYP TkSY=YP8K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"TJ��µ

½ a �\¸�K�Zi· ?B_HS@A*^��]1J� D+�"����# 1 |�DFG��]��¾/¾Ho]Z\`HK4AFX�?Ul�K�GB=2?�u~b>`HK6Z\=Ye&K6P8D/GRA�`VA�SYP�D�P�A�e�AFI�G�D[?�I�DF_H=@I-?�AFe&_HSYKsD�PAgGJAFW]=2D/A/I$Z�=2dFKM?�_VKiI�=2K�?�Z�DCWHK�I�A*^/a �»{`�A�Zc=2? oH�BSYK����

A[<>h[E�A�G�Z�K�GUTkSY=YP8K LV<�`�AFS�P TkSY=YP8K Ii<�`�A�SYP T�Z\=Ye&K WV<�`�A�SY��=2XHq Ki<�`�AFS�PjW]D/XHK

¾�µ ³ h[e4EHS�ZB¾/¾ ¶ ��¾C� ¶�¶ K�A/?U^&Z\`H=2XHO(=YXHqVu;W]KiW]E�I�=2XHq�Ag`�A�SYP TkSY=YP8K� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ �*TUº

��¾Ha~�BXG\K�WH=YD[AFI$Z\=Yd/KR=@?�D�Z�D/_VK-?\A�e&_HS2KMD�P>��¾F¾�qs=@?Rº ¶�� W]K�I�A*^FK�WQA"P Z\K�G-��¾g^/K�A�GJ?�a�7kZi· ?~`VA�SYP T�S2=�P8K-e4E�?UZ>LNKFuA[<���¾4^FKiA�GJ?�a LV<c�F¾s^/K�AFG\?�a I�<cº ¶ ^/K�A�GJ?�a WV<~�s^/K�AFG\?�a Ki< ¶ ^FKiA�GJ?�a

¾�µ ³ h[e4EHS�ZB¾/¾ ¹ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�¯�K�´ W]K��VXHK�W� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"TJ�*º

�F�Fa~b>`HK-e&K�q/A"TkK�S2K�I�Z�G\DFX]TkdFD/S�Z�5,¯�K�´�<>=@?~A&EHXH=YZcD�P:uA[<�K�XHK�G�q/^Fa LV<�e&DFe&K�X/Z\EHema I�<>IJ`�AFG�q/KFa W�<�G�K�Z�G\K�A�Z�a Ki<>W]K�L�AFI�SYK/a

¾�µ ³ h[e4EHS�ZB¾/¾ ¹ ��¾4� ³�³ e&D]W]K�GJA"Z\K�e�A�Z�`�ujLH=2X�W]=2XHq�K�XHK�G\qF^�DFP�£BK�Tkµ� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ �*TJ� ¶

�i�]a~b>`HK�e�A/?�?MDFP � � £cK�=@?-µ � ¾F¾[� ¹ E�opl~`�K�G\K � =@?MZ\`HKCA"Z\DFe&=2Ige�AF?\?-EHX�=�Zian¿~K�I�A�S2S�Z�`�A�ZC��E $ ½F³ � � ¶ ¯�K�´4oZ\`�A"ZRA&`(^]W]G\DFq/K�XmA"Z�D/e�`�A/?~e�AF?\?M� � ¾F¾(º ¼ E�oHAFX�WXHK�EHZ�G\DFXm`�AF?ce&A/?�?6� � ¾F¾ ¼ º�E�aj»{`�A�ZB=@?>Z�`HKsLH=YXVW]=YX�qK�XHK�G\qF^6AFX�W6LH=2X�W]=2XHqMK�X�K�G\qF^-_NK�G�X(E�I�S2K�D/X4DFP � � £BK>=YX4Z�`�A�ZjDFGJW]K�G�AF?\?UE�eg=2XHq�DFXHK>?UZ\A�G�Z\?�l~=YZ�`��R`[^]W]G\DFq/K�XX(E�I�SYK�=�A�X�Wm�4XHK�EHZ�G\DFX�?�

A[< ½/³ � � ¶ ¯�K�´ A�X�W � ³F³ ¯�K�´-y*X(E�I�S2K�D/X�a LN<µ � ¾/¾/� ¹ EQAFX�Wr� � ¾F¾(º ¼ ENy"X(E�I�S2K�D/X�a I�<c� ¼ � ³ ¯�K�´ AFX�W�º � ¾ ¼ ¯�K�´-y*X(E�I�S2K�D/X�a W�<Rº � ¾ ¼ ¯�K�´AFX�W�� ¼ � ³ ¯�K�´My"X(E�I�S2K�D/X�a K*<�� � ¾�¯�K�´ AFX�W¾�¯�K�´-y*X(E�I�SYK�DFX�a

¾�µ ³ h[e4EHS�ZB¾/¾[º�¾F¾4�4µ ¶ e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�X[EVI�S2K�A�G~L�=YX�WH=YXHq�K�XHK�G\qF^�e�A��(=2esE�e� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"TJ� ½

� ³ a~b>`HK-X(E�I�SYKiA�G>LH=2X�W]=2XHq�K�X�K�G\qF^�_NK�GcX(E�I�SYK�DFX=2?~q/G�KiA"Z\K�?UZ�P8D/G~X[EVI�S2K�=pD�P:uA[<�G�KiW]E�I�K�We�AF?\?�a LV<>XHD�e�A/?�?�a Ii<�SYKiAF?UZce�AF?\?�a W�<>q/G�KiA"Z�Ki?:Z~e�AF?\?�a K*<>e�AF?\?>XHK�AFG=2G\DFXr58=�a K/aYoH=2G\DFX_VKiA�OCX(E�I�SYK�=@<�a

¾�µ ³ h[e4EHS�ZB¾/¾[º]��¾4�4µ ³ e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�egD[?:ZB?UZ\AFLHS2K�X(E�I�SYK�E�?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ��TJ�*º�LHEHZc7$· d/K-`�AFWnZ�D�I�D/G�G\K�I�Z>Z�`HK6h[EHKi?:Z\=YD/X�a

Page 193: Introductory Physics Problems David J. Jeffery Department of

v�`VA�_]Ziajµ��f BE�I�S2K�AFGc9�`(^]?�I�=2? � ¼/½

��µ�a �\¸�K�Zi· ?�_�S2A*^ �]1J� D+�"����# 1 |HDFG �]��¾/¾Ho*Z�`�K>AFX�?�l�K�G�=@?�u���K�I�A�E�?�K�=YZ�=@?�`�AF?�Z\`HK ³ GJWsq/G�KiA"Z�LH=YXVW]=YX�q�K�XHK�G\qF^-_NK�GX(E�I�SYK�DFX-A�e&DFX�qc?:ZJA�LHS2KjX(E�I�S2K�=�o*=�Z�=@?�A~d/K�G\^ce&D/?UZ�?UZ\A�L�SYKjX(E�I�SYK�E�?�=2XMZ�K�G�G\K�?UZ�G\=2AFS�A�X�W�e�A�X(^�AF?UZ�G\DF_H`(^]?U=@I�AFSK�X[d(=2G�D/XHe&K�X[Z\?�a �»{`�A�Zc=2? oH�BSYK����

A[< � � �# � � LV< � � £ Ii< � !� ! |HK W�< � �! v Ki<�Z\`HK-L�A�G\KMXHK�EHZ�G\DFX

¾�µ/µgh[e4EHS�ZB¾/¾[ºF��¾C�&���MK�A/?U^�e&K�egD/G�^�ujK��(DFZ�`HK�G�e&=@IcP8EV?U=2DFX�A�XVWC�V?\?�=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ �*TJ� ½

� ¶ a~���(DFZ�`HK�G�e&=@IRP8E�?U=2DFXmA�XVWn�N?�?�=YD/XQ_�G�D]I�Ki?�?�K�?>AFG�K�_VD[?�?�=2LHSYKMLNK�I�A�E�?�K-X(E�I�S2K�=p`�A*d/KFuA[<nWH=���K�G\K�X[Z�LH=2X�W]=2XHqtK�XHK�G\qF=2K�?Q_NK�GmX(E�I�S2K�D/X�a LV<�Z\`HK�?�AFe&KxLH=2X�W]=2XHq±K�XHK�G�q/^w_VK�G�X[EVI�S2K�DFX�aIi<�e�AF?\?�a W�<�XHD�e�AF?\?�a K*<�XHK�E]Z\G�D/X�?�a

¾�µ/µgh[e4EHS�ZB¾/¾ ¼ ¾F¾C�&�s�4K�A/?U^�e&K�egD/G�^�u��V?\?�=YD/XW]K���XHKiW� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"T:��¾

� ¹ a~b>`HK~?�_HS2=�Z�Z�=2XHq-D�P�ARX(E�I�SYK�E�?�=2X/Z\D�Z:l�DMDFG�e&DFG\K>S2AFG�q/K�P8GJA�q/egK�X[Z\?�_HS2E�?�_ND/?\?U=2LHS2^6D�Z\`HK�G�?�e�A�S2SYK�G�K�e&=2?\?U=2DFXV?=@?cI�AFSYS2K�W�u

A[<�P8E�?�=YD/X�a LV<��V?\?U=2DFX�a Ii<�LVK�Z\A�W]KiI�A*^/a W�<>A&IJ`�A�=2XQG\K�A/I$Z\=YD/X�a K*<�X(E�I�S2K�A�Z�=2DFX�a

¾�µ/µgh[e4EHS�ZB¾/¾ ¼ ��¾C�Mµ�µ&K�A/?U^CWHK�W]E�I�Z�DFT�e&K�e&D/G�^�ujIJ`�A�=2XG�KiAFI$Z\=YD/X� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"T:�]�

�*º(a �\¸�K�Zi· ?�_HS@A*^ �]1J� D+�"����# 1 |HDFG �]��¾F¾�oFZ\`HK-A�X�?�l�K�G�=2?�u�7!XnZ\`H=2?�X(E�I�SYKiA�G>_HG\D(I�K�?\?�o[XHK�E]Z�G\DFX�?�K�eg=YZUZ\K�WmW]EHG\=2XHq�V?\?�=YD/XQ=2X�W]E�I�KMP8EHG�Z�`HK�G>�V?�?�=2DFX�?�a �»{`�A�Zc=2?~A o��BSYK����

A[<�q/AFege�A�T�GJA*^-W]K�I�A*^ LV<�LNK�ZJA-W]K�I�A*^ I�<�P8EV?U=2DFX&G\K�AFI�Z�=2DFX W�<jIJ`VA�=2X4G\K�A/I$Z�=2DFX K*<IJ`VA�=2XQq[A�XHq&G\K�AFI�Z�=2DFX

¾�µ/µgh[e4EHS�ZB¾/¾ ¼/³ ¾4�4µ ³ e&D]W]K�GJA"Z\KMWHK�W]E�I�Z�DFT�e&K�e&D/G�^�u�_HSYEHZ�DFX�=YEHe G\K�AFI�Z�D/G\?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ �*T:� ³

� ¼ a ��K�?�=@W]K�?�EHGJA�XH=2EHegT:� ³/¶ 5 � � �# � �R<�o]DFXHK�I�A�XA�S@?UDgE�?�KBZ\`H=@?�=@?�D�Z�D/_VK�=2Xn�V?\?�=YD/XCG�KiAFI�Z�DFGJ?;AFX�Wn�V?�?�=2DFXCLNDFe4L�?�aA[<�W]K�E]Z�K�G�=2EHe 5 � � £R<$a LV<�Z�G\=�Z\=YE�e 5 � � £�<$a I�<�_HSYEHZ�DFX�=YEHegT:� ³/½ 5 � � ## � 9�EV<�a W�<m=2G�D/X]T ¶�¹5 � !� ! |HK*<$a Ki<�`�K�S2=YEHegTkµ�5 � � £cKi<

¾�µ/µgh[e4EHS�ZB¾/¾ ¼ µ/¾C�&� ¶ K�A/?U^�e&K�egD/G�^�ujG\K�A/I$Z�D/G�e�A/?�?>S2D/?\?� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶F³ TJ�*º

� ½ a~�}X(E�I�S2K�AFG4G\K�A/I$Z�D/Gsq/K�XHK�G\A�Z�K�?n� � ¾;��» D�PR_VD"l�K�Gia��BLVD/E]Z�`HD"l esEVIJ`�e�AF?\?4W]D(Ki?4=YZ&SYD[?UKQ_VK�G&W�A*^ ������� � ¿cK�I�AFSYS $ �4*���a

A[<���¾���O[qVa LV<���¾ � � O(qVa I�<R��¾ # O(q�a W�<��i¾�� O[q K*<���¾ ����O(q�a

¾�µ/µgh[e4EHS�ZB¾/¾ ½ ¾F¾C�&���MK�A/?U^�e&K�egD/G�^�u�P8E�?�=2DFXG�KiAFI$Z\DFG�P8EHK�S� ª�¬"¨ �V«������V¬ ��­�� _H`(^(?\I�=�² ��T:� ¶ ¾"T:� ³

��¾Ha~|�DFG>P8EHK�S�o]P8EV?U=2DFXmG\K�AFI�Z�D/G\?�l~=YS2S�_HG\DFLVA�LHS2^CE�?�KA[< ��£z5�W]K�EHZ�K�G\=2EHeC<�AFX�W � £z58Z�G\=�Z\=YE�e�<�a LV< �$£�58D/G\W]=2X�AFG�^M`(^]W]G�D/qFK�XV<$a I�< � � � ��58E�G\AFXH=YE�e4T� ³/¶ <$a W�< � � #i9�Er58_HS2E]Z�D/XH=2EHegT!� ³F½ <�a Ki<�q[AF?�DFS2=YXHK/a

Page 194: Introductory Physics Problems David J. Jeffery Department of

� 9�9�1)>�,�* � p QR>2;75<?+,�d�H ;7?T576/B$D26FEG*IHJE ���Wda&X;<*[? > UFDS1)14;

� �Vª�«�� b>`H=@?;Kih[E�A"Z\=YD/Xn?U`�K�K�Z�=2?�=2X/Z\K�X�WHK�W&P8D/G�?UZ�E�W]K�X[Z\?�l~G�=YZ�=2XHq6Z\K�?UZ\?�DFG�G�K�d[=2K�l~=2XHq6e�A�Z�K�G\=@A�S�a�b>`HK�G�K�P8DFG\Kc=YZ=@?>XHK�=YZ�`HK�G~=YX[Z\K�X�W]KiWQZ�D&LVK-I�DFe&_HS2K�Z�K-X�DFG~I�D/eg_�SYK�Z�K�S2^CK��(_�SY=@I�=YZ�a�b>`HK�G�K-AFG�KRP8K�l�K�Gc?�^(esLNDFS@?;Z\`�A�Xd"A�G\=2AFLHS2K�?�oA�XVWQ?�D�?UD/egK-?�^(esLNDFS@?>esE�?UZcLVK-EV?UKiWnP8D/GcW]= �NK�G�K�X/Z>Z\`H=YX�q/?�u�I�DFX[Z\K��(Z~esE�?UZBW]=@?:Z\=YXHq/EH=@?U`�a

Page 195: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z � ½ �

��� ���-������� ������c��/�&��� �����j�� ������Q c������ ������������������

b>`HKMK�h[E�A�Z�=2DFX�?~AFG�K�e&XHK�e&D/XH=2IFa;¤[Z�EVW]K�X[Z\?~AFG�KMK��(_NK�I�Z�KiWCZ\DgE�X�W]K�GJ?UZ\A�XVWn`HD"l�Z�D&=2X/Z\K�G\_HG\K�Z~A�X�WQE�?�KRZ\`HK�ema�B?�E�AFSYS2^Fo]XHD/X]TkdFK�I�Z�D/G�P8D/G�e�?>`�A*d/KMLVK�K�Xm_HG\K�?�K�X[Z�KiWpu�=�a KFa2o]P8DFG\e�?~?UE�=�ZJA�LHS2K�P8DFG~DFX�K�T!W]=Ye&K�X�?U=2DFXVA�Spe&D�Z\=YD/X�a

� � «�� � «[ª�¬ �

� � � � $���� � � � � $ � � � ��� ��${µ�� � � ��� � $ µ³ � �

� � ���« � ¨]ª ��/­

� $ � � � ��� � $ ��� ��� , � � � � � � � �

� ����� � $ � �� � �2, � � � � � � ���

Z\=Ye&K $ �BegD/EHX[Zv�DFX�?UZ\AFX/Zc¿cA�Z�K � � � � � � � � ��� � � $ � �

³ � ����¨ � ��/­

� � ��� $ ��� ��  �{¾ � �/� ¶ S2L � � � � � � � � ��� � � $ � � �

� $ � �

µ � ¬"¨ ���8ª �

� $ � � � � � �

� ��$ � � � � � � � � � � $� ���

� � � � � � � $ � � ���

� $ ¹ � ¹ º*µ(������¾ � � � ¯�²6¤CE�XH=�ZJ?65,I�=YGJI�A��F¾F¾/�/< $ ½ � ¼ ¾je��"? � 58S@A"Z�=YZ�EVW]K-G\AFXHqFK � ½ � º ¼ ¾ ³ ¾� ½ � ¼F³ �F��e���? � � v��Bv;TUº���!2<

¶ ��«[¬ � �t¨3��� � �V¬ �

� $ � � ����$���  ��e � $ �� � $ �

� � � � � �� ��� � � ��$ � �

$ �4* � � � � � $ ��� � � � * � � � � � � � � � $ � � # �-,w5 � ��*�< �

¹ §�«[¬ � ��� ����¨ � ��F­4¨3��� � ���V¨+��"�

� � � � � � � � � $ � � � � � � �� � �/º ³ � � ¶ � � � � � � � ��� � � $ ½¶

� � � � � � �� � ³ � � � $ � � � � � ��� � � �

� $ �

�� $ �

�� $ � � � $ � � � � � � � � � �� � ��� � ��� � � � $ � � � � $ ���� � � � � � �

� ��� � � � � � � $ � � � � � � ����� $�� � �

� $�� ,� ��� � �

�� � �

º� �,«��ª�¬ �� �,ª �t¨3��� � ¨ � ��«[ª �,­ �

� $ � � � � � ���

� $ ¼ � ½/½ ����¾ #  �e � �/v ��$ � � ¹ ¾/�]�"ºFº ³F³ ����¾ � � # v

Page 196: Introductory Physics Problems David J. Jeffery Department of

� ½ � �c_H_NK�X�WH=����f7!X[Z�G\D]W]E�I$Z\DFG\^C9�`(^]?U=@I�?~��h[E�A"Z\=YD/X¤(`HK�K�Z

�>AFe&_VK�G�K65��R< $�� I�DFE�SYD/esLm5�v><?�K�I�DFX�Wm5�?\<

�~dFDFSYZc58´M< $�� A:DFE�SYK65�[<I�DFEHS2DFe4Lm5kv>< �~D/`He}5 �~< $�� dFD/S�Zc5,´�<

AFeg_NK�G\K65,��<- � � � � � � $ - � � � � � � � $ � � � $ � �

¼ � ¨ �V«(­

� $ # � � $ � ��# ���� $ � �

�$ � �

�#�$ �

� � �

� � � � � � � ��� � � � � � $ ³ µ ³ e��"? � � � � � � ��� � � � � � $ ³/³ ��e���?

½ � �����«[¨H¬ � § ��­ �F­�

�� ��5 � < $ � �

� � � ������� ��AFesE $ ½/³ � � µ ½ µ/¾Fµ ³ ¯�K�´

�i¾ � ��¨3��ª � � � «�*§�¨3����/­

% $ ¹ � ¹ � ¹ ¾ ¹/½F³ ����¾ ��� � �;? � � $ ½ � ��¾ ½/³F¼ � ¹ ����¾ ��� � O(q $�% # � $ %�$ %

� �

� � � � � � � � � � � � � � $�% #�,� � � $ � %���

� �

� ��/� �Q­�ª�¬ � � � � �

� $ � � � $�º(� � ����O(e��"?¯�_�I 5�I�=2G\I�A&�F¾F¾Fµ[<

�*� � «�� � «[ª�¬ ��/¨ � ��¬ � � ��¨H«

� � � � $�� � � � � � $ � � � ��� � $wµ�� � � ��� � $ µ³ � �

� ³ ¬ ����� � � � «/ª�¬ � �V¬ � ���,¨H«

� $&%cI�D/? � � $"%B?U=2X � I�D/? � � $ �� �Y� � I�D/?�5�� �/<"! ?U=2X � ��$ �

� �Y� ,�I�D/?�5�� �[<"!?�=YX�5�� �/< $z�j?�=YX�5 �/<]I�D/?i5��/<

?�=2X�5 � �� < $�?�=YX�5 �]<]I�D[?�5 � < � I�D/?�5 �]<]?�=YX�5 � < I�D/?�5 � �� < $�I�D[?�5 �(<HI�D/?�5 � < ,�?�=YX�5 �]<]?�=YX�5 � <

��µ �n©�©�¬ � � � ¨]ª � � � �V¬ � ���,¨H«

� #� �

��4#� �

�� , � � � � � u�5� �����i<

Page 197: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z � ½/³

?U=2X � � � Z\A�X � � � I�D[? � ��� , �� � � AFSYS�P8D/G � �����

� ¶ � ��¨3��¬"¨]ª � �V¬ � ���,¨

7kP ¾�$�� � � ��� � � * Z�`HK�X � $ , � � + � � ,�µ � *��� $ , �

�!� �� � �

�!� � � , *�

� ¹ � «��ª ��¬ ��¬ � � ��¨H«

�� � �� $ 5 � � ��� � � � �� � � � ��� � < �� � �� $"� � I�D[?���$"� � � � � � � � � � � � � �

�* $ �� � �� $0� � ?�=YX�5��/< �* $�5 ��� � � , � � � � � � � � , � ��� � �� �!� � , � � ����<

�"º � ���;«[¬"«���ª ��¨]ª � � �w¨3��� � ��ª�«��V¬"¨]ª � � � ��¬ � � ��¨H«

�N5� � <� �

$ � � � � � K��HI�K�_HZ�P8D/G � $�¾�) �N5� � <� �

$�¾ � � S2X�5 �N<4!� �

$ ��

� ��

#�5 �N<�� � $ ��5�N<*� �� $ ��5 � < , ��5 �]< l~`�K�G\K � ��5��<� �

$ #�5�N<

� � � � ��$ � � � �� � � K��]I�K�_]Z~P8D/G � $ ,-� ) � �

�� � $�SYX�5 �N<

� ¼ � ��« ��� � � « ��­ � � ��¨ � � ���« � ¨Hª ��/­

� ����$ � �� � � $ � �

� � � � ��$ � �� � � $ � �

� � $ � � �� � �

� $ � � � � � � $ � � � � � � ��� � � �

� $ � � � �� 5 � � ��� < � � � $ � �� � �!�N5 �1, � � < $ ½ � ¼ e��"? �

� � $ �1, � � � � � � � � � $ � , � � � � � � � � $0�

� ½ � � � ¨3��� §�¬*«(« ��� � � « ��­ � � ��¨ � � ����« � ¨]ª �F­�� � «���«[¬"¨ �

�� ����$ ���� � �� $ � �

� � �� ����$ ����� � �� $ � ��

� � $ ��� �� � �

�� � � � � � � � ��� � � $ � �5 , � < ��� � � � � � � ��� ��� $ � �

Page 198: Introductory Physics Problems David J. Jeffery Department of

� ½ µ �c_H_NK�X�WH=����f7!X[Z�G\D]W]E�I$Z\DFG\^C9�`(^]?U=@I�?~��h[E�A"Z\=YD/X¤(`HK�K�Z

�F¾ � ¬ ����«�Fª ����« � �Vª � � �

� $ ���� � � � $ � � ��� � � � � ,

�� � � ���

� � $ � � I�D[? � � �� � $ � � ?U=2X �

� $ ����� �$ �� � I�D[? �

� $ � � � �~ZJA�X �/, � � � � �� I�D[? � �

� � � � ���� $ � �� ?�=YX ��I�D/? �

�������$ � � � � �� ?�=YX � ��

��� � $ Z\A�X�� � # ZJA�X � �/,r� �5 � , � � < �H5 � �� I�D/? � �/<

��H5 � �� I�D[? � �[<$ � �� ?�=2X ��I�D/? �

�� �

�� , � p5� , � � <

� �� ?�=YX � �����5� $ � � < $

� � �� ?U=2X ��I�D[? �

$ � �� ?�=YX�5�� �/<

� � � � ���� � ��� � $ ��µ � ����H5� $ � � < $

� ��

��5�� $�¾/< $ � � �

� �H5 � � , �]<

� 5���$�¾/< $� ��5� � , �H<

�H� � «[¬ � ¨H­ ���¦ ��¨H­i­ �F¨ � � «�*§�¨3����/­

�� � ��� $ � �� �� � ���$ , �� � � $ � $ ½ � ¼ e ��? � � $�, � �

� � � � � � � � ${eg=2X�� � � ���� � � � � � � � � � � � ����*! � � � � � � � � �����$ � � � � � � � � � � � � � � ��� � � $ � � � ����� � � ���

� � � ��� � � � ��� $ � $

� �� � � � � �

�� � � � � � $ � $

� �� � $

� � �� � �

���� � � � � � � ��� � � $ � �5 , � < �� � � � � � � � ��� � � $ �

� �5 , � <

�/� � �V¬ �t¨3��� ��«[¬ � �

� � $ �� � � � � $�� �� � � � �� $ �� � � � � � � � � � � � ��� $ �� � �

� $ � �� � � ���

�$ �� � � $ �� � ��

�� ��$�� � � � � ��� � � � � � ��� � � � � �� � � � � � � � � � $�, � � ��� ��� � � � � �� � � � � � � � � � � $ � � � � � � ��� � � � � �� � � � �

Page 199: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z � ½[¶

� $ , � �� �

�� $�,���� � $ �� � � � � $ � �

� ³ � ��­�ªi« � ­ � � � ¨]¬*ª �� �,«(­

� � � $ ��� � � �

� � � � � �$ � ��� � � ��� � � � � ��� �

� � � � ���� � � $

��� ��5 � < � � �� � � � � �

�� � ��� � � � $ � �� � �

�� $ � �� �� ����� $ �� ��� �

�� � ���2� � � $ �� �� � � � ���� �

� �� $ �� ����� � � � T � � � � � � � � � � � � 5 �� � � � � � � � � � � ��, �� < � �� � $ �� � ��� � � � T � � � � � � � � � � � � �� � � � � �

� �

� $ � � � � ��� ���� � SYX � � �� � G\D]IJOFK�Z>=2XQP8G\K�K-?�_�AFI�K

��µ ¦ � ������­ � � ��­

�� $ � ���

���

��&5 � <�� � �� ����$

��� � �� � � � �� � � $ �� � � � �� � � �� � � $ �� � � �� �

� � � � ���

� � � � � � ��$�� � � � ��� � � � ��$� � � , � �� � � � � � � � � �

� � � �� � � � � � � � � � � � � ��$�, � � � � �

��T!W4�;S2A/?:Z\=2I>�j�]_HG\K�?\?�=YD/X�?

� � � � � � � ��� � � � � � ��� � � $ �

³ � +� � � ��5 � <�� � � � � � � ��� � � � � ����� � � $ � � �

� ¶ � ��ªi¨]ª � � �

��$ �

� $ � �

� � $ �

� $ � � �� � � $ � �

� � $ �

# $ �

��� � $ # � � $ � ��

� $ � � � � � ��$ � � � � � � ��� � � � ��$ � � � �

� 5 � � � ��< � � � $ � �� � � ��5��/, � � <

�� $ � � �� �� � ��� $ � ��� �

���$ � � ��

� $ ��?U=2X�� � ����� $ � � � $ ���

� $ -�

� � �� � � � � $�� � �� � � � � � � � T �� � � $ � �� � � � � � � � �

Page 200: Introductory Physics Problems David J. Jeffery Department of

� ½/¹ �c_H_NK�X�WH=����f7!X[Z�G\D]W]E�I$Z\DFG\^C9�`(^]?U=@I�?~��h[E�A"Z\=YD/X¤(`HK�K�Z

� $ �?�=2X �� � ���H5 � � <

�� � � � $ �� � � � �� � � � ��� $ �� � � � � � � �� � � � $ �

� � � � � �� ��� � � � $ � � � � $� �

� �� � � � $ � ����� $�� ������� � � � � $�, � $�, � � � � � $ � � � � � � ��� � � � � �� � � � �

� ¹ � ª�¨]ª �� �� ��� ��� � ¬ ��� � ��� � � � � � «���­ � � ��­

¾�$ � XHK�Z � $ - � � ¾�$ � XHK�Z � $ - � � ¾�$ � X�K�Z $ - �

�[º � ¬"¨ ���8ª �

� $ ¹ � ¹ º"µ/¾(º�����¾ � � � e � O[q � � ? � � 5���¾/¾/�sG�Ki?UEHSYZJ< �� � � � � $� � � � � ����

5 , � ��� <

�# � $ ��� �

5 , � <�

�# � � � �� $ ,~µ�� ���

� $ , � � � � � ���

� $ , ���

� � � � � � � $ � � ���

� � � � � � $� ���

� � $� µ�� ���� � � � $

� � �+ ��� � � � � � �

� � $ �� � � $ �

� � $zv�D/X�?:ZJA�X[Z

� ¼ � �����­

� $ � �� �

� $ � � � $ � � � � �� � � � ���

9jA/?�I�A�S�· ?�_HG\=YX�I�=Y_�SYK � $ � � � � , � �5 � , � � � � < � � $�� � � � ��BG\IJ`H=2e&K�W]Ki?>_HG\=YX�I�=Y_�SYK � � ��� � $ � ��� � � � � � $ � � � � � � � � � ��� � �

K�h[E�A�Z�=2DFXD�PjI�D/X/Z\=YX(EH=YZ:^�P8D/G~=2W]KiA�S���E�=2W � � $ � � $zv�DFX�?UZ\AFX/Z��K�G�XHD/EHS2SY=�· ?�Kih/EVA"Z�=2DFX � � �

� � � � � � � $�v�DFXV?:ZJA�X[Z

� ½ � � � © �,« � ¨]¬ � � ��� � ­ 7��� �,¨]ª ��¬

� $ # � � � $�� �# � $ , � � � $ �� � � � ��5 � < $ , �

���5 � < $ , � � ��5 � <

Page 201: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z � ½ º

��$� �

�� $���� � �

���5 � < $ ��I�D/?�5 � � < � ?�=YX�5 � � <

� � � � � � ����$ �� � � ����� $

�� � � ����� $

�� � � � �

�� � � �

� $z� �� �

� 0 � $�� �� 0

³ ¾ � ¨ �V«(­

� � �� � �

$ �� �

� � �� � � � $

� � �

�� $ #�5��� � � < � $ �������?�=2X� ��5��� � � <4!�$ �������?�=YX�5 � ��� � � <

9�K�G\=2D(W $ �# � $ � ��

� $ # � $ �

���� � �����

� $z� �������?�=YX�5 � �N<HI�D/?i5 � � < � $ �

� ��� � $ ��

� � $ � ��

# $ ��

� �

� $� � � �

� � ��� � � $ ��?U=2X�5��[< �� � �

� � � $ �;?�=YX�5��/<

� $ �

µ�� �� $f5:�i¾�W3�>< �SYD/q � �

� � �# $ �

µ � u � $ � ³ ¶ ��� � # � � � � � � $ # �� , � � � � � � � � � �

³ � §�«[¬ � ��� ����¨ � ��F­

�� $ � � � �[º ³ � � ¶ ² � � $ � � ¼ � � � ³ � � � � $ � � � � � � $ � � � �

� $ ³ �

� $ ��* � � $ ��*�5 � � , �� < � $ -

� � * �(5 � � , ����"<

� $�� ���

� � � � � $ ���&, � � � $ � ��� , � � �

� ��� � � $�, � ��

� �� ��� � � � � � $ � � �

� �� � � � � � � � � � � $ � � �� �� � � ��$ ¶�� ¹ º�����¾ � »�e � � ² � �

Page 202: Introductory Physics Problems David J. Jeffery Department of

� ½/¼ �c_H_NK�X�WH=����f7!X[Z�G\D]W]E�I$Z\DFG\^C9�`(^]?U=@I�?~��h[E�A"Z\=YD/X¤(`HK�K�Z

� � $ � � � $�� � � � $ ¼ � ³ � ��e&DFS � � ² � � � $�� � ³/¼ �x�i¾ � � � � �"²

� � � � ����� � ����� $ � � � SYX�5 � � � � � < $ #� � �

� $ � � � �� � $ #

� � ��� $ � � � �

��� � $zv�D/X�?:ZJA�X[Z � $ � �

� �$ � � � �

� �$�� � �#

¾�$�� $f5 � � , � �J< , � ��$ �� �

$ � , � �� �

� $� �� �

$�� , �� �

� � � � � � � $ �-,� �

��

� � � � � � � $� �

��

$�� , � � � � � � � � � � � � � � � � � � � � � � $ �

��� $�� ��� � $�� �

���� ��� $ � �xSYX

� � � ��� �

� � � � � �� � � �

³ �� �,«��ª�¬ �V­�ª�¨]ª ��/­

�$�� � ¹ ¾[������¾ � � # v � � $ ½ � ��¾ ½ ����¾ ��� � O(q

� � $ ¼ � ¼/¶ µ ����¾ � ��� v � �H5, ~Tke � < � ��¾ � � � � $ �µ�� � �

$ ¼ � ½F½ ����¾ #  ~Tke � �Fv � ����¾ � �

�� � � � � $��� � � � ���� �

� ��� ��� $ � � �C5 � < $

���

�� $

µ�� � ��

�� � � �� $ � � � �

� �

� $ �

� ��� �� $ �� � � � $ , �� � �

��� $ ��� � � � $�, � ��

� � � �� � $ ���

� $ � -

� �

�� $ � � � �

� $ ,�� �

� $ �

�� $ � � �

�� � � � � � � � � $ -

� ��

� � � � � � � $ -�

�� �

��$ � �� � $ �

� � � � � � � � � � � � � � � $ � �� � � � � � ���� � � � ��� � � � � � � ��� $ � �����

� � � � �� $ � � � �

� �

³/³ ¦ ��¬i¬"«���ªC¨3����¦&�8¬ ����8ªi­

Page 203: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z � ½/½

� $ � �� � � $�� �� � � �� � $ �� �� $ � � �� � � � � � �� $ � � � $ � �

� $ � � � ��

� $ ��

� $ � � � $ � �� � $ � � � $ � � � $ ����

¾�$� � � �-�

� � ¾�$� � � �-�

� � � � � � � � � � $ -�

� ��

� � � � ��� � � � $ -�

�� �

� $�� � � $ � � � � � � � ���� �

� � ��� � � $ � ��� ��� �/� ,

�� � ��� �

³ µ�� ¨ � ��«[ª �� ��« ���­g¨3��� �V¬ F«(­

� � $wµ�� ����¾ � � b�T�e���� �pZ\K�?�S2A&5�bc< $ �i¾ � q/AFE�?\?~5��-<

�� $ � �� � �� �� � $� � �0 � ��� � � � � � � � � ��$ � �

��� � � � � � � � � � ��$ ����

# � � � � � � � � � $ ������ � � $ � � �

����� $�� � � �� � $ �� � �� � $�, �� � ��

� �� $ � �µ��� � ���� � �

� � � � � $ � � ����

� � � � $ � � � �µ��

�� � � � � $ � � 0 � � � �� �

� � � � �

� � ��� � � � � � $ � � � � � � � � � � � $ � � � ����

�� � � � ��

� � � � $ � � � � ��H5 � � � � � < � � � ��

�� � � � � � � $ � � ��� �.� �

��� � � ���$ � � � ��� $��

� � � ��� � � � � ��� � � �� �2� � � $

�� � � ���$�, � ���

� � $�, �� � � � � � ��� � � � � � �� � � ��

��$ ���

�� � ��� � � � � ��$ � � � � � � ��� � � � � � � � ��$ �

���� � � � $ �

� � � � � � $ � �� � �

³[¶ �(� �5� ¦ � ��� ¦ ¦&�8¬ ����8ªi­�¨3��� � �8ªi«[¬ ��¨]ª ������¦ ��¬*¬"« ��ª

� � $ �

�� $ � � � �

��F� ,

�� � ����� � � $� � � � � �����

Page 204: Introductory Physics Problems David J. Jeffery Department of

��¾/¾ �c_H_NK�X�WH=����f7!X[Z�G\D]W]E�I$Z\DFG\^C9�`(^]?U=@I�?~��h[E�A"Z\=YD/X¤(`HK�K�Z

� $ �+ � � � �����$ � ����

� � � � � � � � ,±� �H5 � � � <"! �³/¹ �,«��ª�¬ � � ¨ � ��«[ª �� � ¨ �V«(­C¨3��� � ¨3���,¨Hª � � �

* $�� � ½/½ º ½ �"µ ¶�¼ �r��¾ � ³ � ¾F¾ ����¾ e��"? 9�K�G\=YD]W $ �# * $ # � $ �

�� $ � �

�* $ �

+ � � � �

� $ � � ?�=2X�5 � ��,� � < �� $ �� � ?U=2X�5 � �1,� � < �

$ �*

� � � � � � � � $ �� �� �� $ � �� � � � � � � � � $ �

µ�� �

� ��� ��� � � $�µ�� ��� $�?�=YX�� � � � �

� � � � � ��

� ��� � � ��

� � $ � � � �NI�D[? � � � � � � � ��

� � � T � ��� � � ��

� � $ �� � � � �

³ º � «�� � «[ª�¬ ��/¨ � � ©�ª ��F­

� � � � $ � � � � � � ?�=YX�� � $ � � ?U=2X � � � ��� � � � � � � � � $�?U=2X � �� � �� � �

� $ *� � �

�$ � �� � � � �

�# $ � �

��

$ *� �� � � � �

³/¼ � ��ªi«[¬�k«[¬"«���/«�¨3��� � � ��¬"¨3�ª � � �

�*T!?US2=�Z � � $ �;?�=YX � ���� � $ µ�� � �

I�D/? � 5���< � $ ��

�?�=YX �

?�=YX�qFS2K�T!?US2=�Z � � $���?U=2X���

� � � � $ � � �?�=YX � 5���<� �

� $ ��

�?�=YX��

q/G\A�Z�=2XHq � � $ �;?�=YX � ���� � TkGJA*^ � � $�����?U=2X � ����

³/½ � ©;«� ��¨ � � «��,¨]ª �����8ª �

* $�� � ½/½ º ½ �"µ ¶�¼ ����¾ e��"?���� � ½F½F¼ ����¾ e ��? � ³ ����¾ e��"?�����SY^(G��*^(G � �pP Z��*X�?

� $ � * � $ �# � , � � � 5 �������i< $ � � �

� � � � $0* �

�MAFSY=2SYKiA�Xmb�GJA�XV?:P8D/G�e�A"Z\=YD/X�? ¸�D/G�K�X[Z��-b�GJA�XV?:P8D/G�e�A"Z\=YD/X�?� ��$ ��, � � � � $ � 5��, � ��<

Page 205: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y��� 7!X[Z�G\D(WHE�I$Z\DFG\^C9�`(^]?U=@I�?~��h/EVA"Z�=2DFXm¤(`HK�K�Z ��¾��

� � $ � � � $ �� � $"� � � $"�� � $ � � ��$ � 5���, � �N<� �� ��� $ � � ��� , � � �� ��� $ � � ��� , �

� , � � � ���0 $ 0 � � � � � � # � , � � � � � � � � � � $ � � # � , � �

� � $ � � � � � � � � � � � � ��

$ � �� � � ��� � � � , � �� � � � � � $ � � � � � ��� � � � � � �

$ � �� � � ��� �� � , � �� � � � ��� � ��� $wZJA�X � � 5 ��<

� $ � � � � $ � � $ � � � * � � $ � � * � $ � � $ � � � * � $ �4* �

$ ��* � $ # 5 ��*�< � � 5 � � * � < � � $ , � $ # 5 ��*�< � � 5 � � * � < � , � � * � $ 5 � ,±�i< � � * �

# $ # � � � � � � � � , �� � � P8DFGc?�DFE�G\I�K�AFX�WmW]K�Z\K�I$Z\DFGc?�K�_�AFG\A�Z�=2XHq #�5 � ���z�i< $ # � � � � � � � � , � � �

� � � �# � � � � � $ # � � � � � � # � , � � # � � � � � 5 � �����*< $ # � � � � � � � � , �

� � � �µ[¾ � ��¨3��ª � � � «�*§�¨3����/­

%, $ %� � $&% # � $ %

�$ %, � � � $ %

��* 5U� ,�I�D/? �/<

, %, ����

� ���� � �

� � � $ �3%, � �

� � , %, �� �

� ���� � �

� � ��$ � �g5 � � < $ �R5 �N<�� � � � � %,

� � � � �%,� � +

� +� � � � � � $ �

�$�, �� � � * � � ���

�� �

$ , � � � � �� �

� � ��$�� ³ � ¹ ¾ ¶F¹F½/¼ ��K�´ � $ ��

µ�� � � %, * $ �� ³ º � ¾ ³[¶�½F¼/½/¶

��� � � � ${¾ � ¶ � ½ �"ºFº���µ ½ ����¾ � � � $�¾ � ¶ � ½ �"ºFºF�"µ ½ ��

� �� ��$ � � ¹F¹ ¾ ¶ µ/¾/� �m��¾ � � � O[q $ ½/³ � � µ ½ µ ³ �j¯�K�´ � � $ ½ � �i¾ ½F³/¼F½ º �m��¾ ��� � O(q $�¾ � ¶ ��¾ ½F½F½/½ ¾ ¹ ¯�K�´

� � $ � � ¹ ºF� ¹ � ³ ���x�i¾ � � � O(q $ ½F³F¼ � �[º�� ³ ��¯�K�´ ��$�� � ¹ º*µ ½ � ¼F¹ ����¾ � � � O(q $ ½/³F½ � ¶�¹[¶�¹/³ ¯�K�´

Page 206: Introductory Physics Problems David J. Jeffery Department of

� 9�9�1)>�,�* � n � &:efN-1Z?A@CQ�>W;714cT5<&ANIE ` �C;<H:0

� �Vª�«�� b>`HK�G\KsAFG�KMXHDCq/E�A�GJA�X[Z\K�K�?>DFP�A/I�I�EHG\A/I�^Ql~=�Z\`mZ�`HKi?UK6=2X[Z�K�qFGJA�S@?�o]K�Z\I�a>7>=2X�I�S2E�W]Ks?�DFe&K6W]K�G�=2d"A"Z\=Yd/K�?cA�ZZ�`�K6?:ZJA�G�Z�o]LHE]Z~Z\`HK�^A�G\K-?UE�IJ`mAge&=YXHD/GcI�D/eg_NDFX�K�X[Z~Z�`�A�Z>Z�`HK�^QW]D�XHDFZ~egK�G�=YZBA&IJ`�A�X�qFK�=YXZ�=YZ�S2KFa

� � � «[¬ ���H¨]ª ���V«(­

5:�*< �� �?U=2X � � � $

�+ � , � �

� �� �

P8D/Gc?U=2X � � ��� , ��

����

5��/< �� �I�D/? � � � $

,-�+ � , � �

� �� �

P8DFGcI�D[? � � � � ¾� � !

� � �����ª � � ��­��� ��ªi¨3��������� � � � ���

5:�*< � � �� � � ��� $

������������������ �����������������

�+ � � ZJA�X � �

��� �

� � � �±¾&A�XVW � �w¾�)�

� + ,� � S2X� � + � , + , �� + � � + , � � � �±¾&A�XVW � �w¾�)

�� + ,� � S2X�� + � � � + ,�

+ � , � + ,��� �'�±¾&A�XVW � �w¾�), �� � � ${¾�)

�� � $�¾

5��/< � � �5 � � � ��� < � $ �

� ��

5 � � � ��� < � �� �

�+ � � Z\AFX � �

��� �

� � � �t¾&A�XVW � �±¾

5 ³ < � � �+ � � � �� $ �

+ ,� ?�=YX � ���� , �

� � $ , �+ ,� I�D/? � �

��� , �

� � ���t¾

� �����ª � � ��­��� ��ªi¨3��������� � � � ��� � � *

5:�*< � � �5 � � � ��� � � *�< � � � $ , �H5��!� � �� <

5 � � ,xµ � *�< + � � � ��� � � *

� �����ª � � ��­��� ��ªi¨3��������� ?U=2X�5 � ��<

Page 207: Introductory Physics Problems David J. Jeffery Department of

�c_H_NK�X�WH=���� b�A�LHS2KMD�P�7!X[Z�K�q/G\AFS2?�o]�jZJI�a ��¾ ³

5:�*< � ?�=YX � 5 � ��<�� � $ , �� I�D[?�5 � ��< ��³ � I�D/? � 5 � ��<

5��/< � ?�=YX � 5 � ��<�� � $ , �¶ � ?�=YX � 5 � ��<]I�D[?�5 � ��< �

µ� ¶ � I�D/? � 5 � �N< ,

µ¶ � I�D/?i5 � ��<

5 ³ < � ?�=YX � 5 � �N<�� � $�, ��.� ?�=YX � � � 5 � �N<]I�D/?i5 � �N<

��,t��� ?U=2X � � � 5 � ��<�� �

��� � � �V«[¬"­�« ¬ ����� � � � «[ª�¬ �� ����Fª � � ��­

5:�*< � ?�=YX � � 5 � ��<�� � $ �R?U=2X � � 5 � �N< � �� # � , � � � �

5��/< � I�D[? � � 5 � ��<�� � $ �RI�D/? � � 5 � �N<$, �� # � , � � � �

� � � ���N« � ¬"¨3�Q¨3��� ¬ ����� � � � «/ª�¬ �� �����ª � � ��­

5:�*< � �B?�=YX�5 � �N<�� ��$ �� � ?U=2X�5 � ��< ,

�� I�D[?�5 � ��<

5��/< � � � ?U=2X�5 � ��<�� � $ , � �� I�D[?�5 � ��< � � �� � ?�=YX�5 � �N< �

�� � I�D[?�5 � ��<

5 ³ < � �BI�D/?i5 � �N<�� � $ �� � I�D[?�5 � ��< ,

�� ?U=2X�5 � ��<

58µ(< � � � ?�=YX�5 � �N<�� ��$ � �� ?�=2X�5 � �N< � � �

� � I�D[?�5 � ��< ,�� � ?�=2X�5 � �N<

��� � ¨ ��­i­ ��¨3� ����Fª � � �{¨3��� ¨3�ª ��¬ �,¨ � � ��ª�«���¬"¨ �

5:�*< ��5��< $ �� + ��� K��]_

� , 5 � , � <��� � �

� ?UZ\AFX�WHA�GJW�P8D/G�e

5��/< � +� +

�� 2 � � � �

3� � � ��$

� �� � � �

Page 208: Introductory Physics Problems David J. Jeffery Department of

��¾Fµ �c_H_NK�X�WH=���� b�A�LHS2KMD�P�7!X/Z\K�q/G\AFS2?�o]�jZ\IFa

5 ³ < � +� +

� ��� 2 � � � �

3� � � ��$ + �

��

5 � � � � < � � �

58µ(< � 1 $ � +�

�� � � � � �

5 ¶ < ¾ 1 $ � � 1 $ � � , �� � 1 $ + � 5 �/,±�i< 1 $ � 1�

5 ¹ < �5 � �N< $�� �

��� � � � � � $ � 1 ��� ,

�� �

�-./ ��

.0�1 �

5�ºF< p5,¾� �N< $�� ,�� �

5 ¼ < �5U� ��< $�� ,�� � 5U� � ��<

5 ½ < p5��� ��< $�� � � ,�� � � � � � � �

� � � � �

Page 209: Introductory Physics Problems David J. Jeffery Department of

� 9�9�1)>�,�* � � � d�NO;<*-9�N-1Jj ¥ DS? *-H^1�B$5<?AefN-1)= �'>�E�� 1)5 � &Ae�N-1)E

� �Vª�«�� |HD/GRZ\`HD/?�Kgl~`HDn�VX�W�?\I�AFX/Z\G�D/X�?BP8G�Kih/E�K�X[Z�S2^�=YXVAFI�I�EHGJA"Z�KgA�X�W�_HG\K�P8K�G�Z\DQ`�A*d/K6Z\`HK�=2GMD"l~X�Z\AFLHS2KgAFX�We�A�G\O(=YXHq�Z�K�e&_HS@A"Z\KFo~Z\`HKxP8DFS2SYD"l~=2XHq�AFG�K�_�G�D"d(=@W]K�Wpaf7�qFD�ZnZ�`HKxZ�K�eg_�S2A�Z�K�Z\G�=@IJOtP8G�D/e  BK�=2S�£BE,�pAFIJOFK�GQA�Z�cX�=Yd/K�GJ?U=YZ:^�D�P6°RO[S@A�`�DFe�AHa{°RXHK A:EV?:ZC_HE�X�IJ`HK�?&D/E]Z&Z�`HKmG\=Yq/`[Z&AFX�?Ul�K�G&_HS@AFI�K�?gDFXwA�XwA�XV?Ul�K�G4Z\AFLHSYK�AFX�WD"dFK�G�S@A*^]?;=YZcDFXm?UZ�E�W]K�X[ZBA�X�?�l�K�G�Z\A�L�SYKi?~A�X�Wmh[EH=@IJO[S2^C=@W]K�X[Z\=���Ki?~A�X�We�A�G\O]?�Z�`HK-l~G\DFXHq�AFX�?Ul�K�GJ?

� ����� �R��� ��� ��� F�&��� ����� � �$��� � ��� � ������ ��� �������j�������

A L I W K A L I W K�Fa ° ° ° ° ° ¹ a ° ° ° ° °�]a ° ° ° ° ° º(a ° ° ° ° °³ a ° ° ° ° ° ¼ a ° ° ° ° °µ�a ° ° ° ° ° ½ a ° ° ° ° °¶ a ° ° ° ° ° �i¾Ha ° ° ° ° °

Page 210: Introductory Physics Problems David J. Jeffery Department of

��¾ ¹ �c_H_NK�X�WH=�� ³ ¯�EHSYZ�=2_HS2K�TUv�`HDF=@I�K-9;G�D/LHSYK�e��cXV?Ul�K�Gcb�A�LHS2K�?

� ����� �R��� ��� ��� F�&��� ����� � �$��� � ��� � ������ ��� �������j�������

A L I W K A L I W K�/a ° ° ° ° ° �/�Fa ° ° ° ° °�Ha ° ° ° ° ° �*�]a ° ° ° ° °³ a ° ° ° ° ° � ³ a ° ° ° ° °µVa ° ° ° ° ° ��µ�a ° ° ° ° °¶ a ° ° ° ° ° � ¶ a ° ° ° ° °¹ a ° ° ° ° ° � ¹ a ° ° ° ° °º]a ° ° ° ° ° �"º(a ° ° ° ° °¼ a ° ° ° ° ° � ¼ a ° ° ° ° °½ a ° ° ° ° ° � ½ a ° ° ° ° °��¾�a ° ° ° ° ° �F¾Ha ° ° ° ° °

Page 211: Introductory Physics Problems David J. Jeffery Department of

�B_H_VK�X�W]=Y� ³ ¯�EHSYZ�=2_HSYK�T:v�`�DF=@I�K69�G\DFL�SYK�e �cX�?�l�K�Gcb�AFLHS2K�? ��¾(º

� ����� �R��� ��� ��� F�&��� ����� � �$��� � ��� � ������ ��� �������j�������

A L I W K A L I W K�/a ° ° ° ° ° � ¹ a ° ° ° ° °�Ha ° ° ° ° ° �"º(a ° ° ° ° °³ a ° ° ° ° ° � ¼ a ° ° ° ° °µVa ° ° ° ° ° � ½ a ° ° ° ° °¶ a ° ° ° ° ° �F¾Ha ° ° ° ° °¹ a ° ° ° ° ° �H�Fa ° ° ° ° °º]a ° ° ° ° ° �/�]a ° ° ° ° °¼ a ° ° ° ° ° � ³ a ° ° ° ° °½ a ° ° ° ° ° ��µ�a ° ° ° ° °��¾�a ° ° ° ° ° � ¶ a ° ° ° ° °�F�/a ° ° ° ° ° � ¹ a ° ° ° ° °�i�Ha ° ° ° ° ° �[º(a ° ° ° ° °� ³ a ° ° ° ° ° � ¼ a ° ° ° ° °��µVa ° ° ° ° ° � ½ a ° ° ° ° °� ¶ a ° ° ° ° ° ³ ¾Ha ° ° ° ° °

Page 212: Introductory Physics Problems David J. Jeffery Department of

��¾ ¼ �c_H_NK�X�WH=�� ³ ¯�EHSYZ�=2_HS2K�TUv�`HDF=@I�K-9;G�D/LHSYK�e��cXV?Ul�K�Gcb�A�LHS2K�?

� � � ���

� ����� �R��� ��� ��� F�&��� ����� � �$��� � ��� � ������ ��� �������j�������

A L I W K A L I W K�/a ° ° ° ° ° � ¹ a ° ° ° ° °�Ha ° ° ° ° ° �[º(a ° ° ° ° °³ a ° ° ° ° ° � ¼ a ° ° ° ° °µVa ° ° ° ° ° � ½ a ° ° ° ° °¶ a ° ° ° ° ° ³ ¾Ha ° ° ° ° °¹ a ° ° ° ° ° ³ �Fa ° ° ° ° °º]a ° ° ° ° ° ³ �]a ° ° ° ° °¼ a ° ° ° ° ° ³/³ a ° ° ° ° °½ a ° ° ° ° ° ³ µ�a ° ° ° ° °��¾�a ° ° ° ° ° ³[¶ a ° ° ° ° °�F�/a ° ° ° ° ° ³/¹ a ° ° ° ° °�i�Ha ° ° ° ° ° ³ º(a ° ° ° ° °� ³ a ° ° ° ° ° ³/¼ a ° ° ° ° °��µVa ° ° ° ° ° ³/½ a ° ° ° ° °� ¶ a ° ° ° ° ° µ[¾Ha ° ° ° ° °� ¹ a ° ° ° ° ° µV�Fa ° ° ° ° °�*º]a ° ° ° ° ° µ(�]a ° ° ° ° °� ¼ a ° ° ° ° ° µ ³ a ° ° ° ° °� ½ a ° ° ° ° ° µ/µ�a ° ° ° ° °��¾�a ° ° ° ° ° µ ¶ a ° ° ° ° °�]�/a ° ° ° ° ° µ ¹ a ° ° ° ° °�F�Ha ° ° ° ° ° µ]º(a ° ° ° ° °� ³ a ° ° ° ° ° µ ¼ a ° ° ° ° °�"µVa ° ° ° ° ° µ ½ a ° ° ° ° °� ¶ a ° ° ° ° ° ¶ ¾Ha ° ° ° ° °