!" %R%SFNIGX%XVEZIPW%EPSRK%E%TEXL%EX%GSRWXERX%WTIIH"%%8LIVI%MW%E%GSRWXERX%RIX%JSVGI%EGXMRK%SR%XLI%SFNIGXXLEX$VIQEMRW$TIVTIRHMGYPEV$XS$XLI$HMVIGXMSR$SJ$XLI$QSXMSR2$$(IWGVMFI$XLI$TEXL$SJ$XLI$SFNIGX2

%" PMRIEV &" GMVGYPEV '" IPPMTXMGEP (" TEVEFSPMG

!" %R%SFNIGX%SJ%QEWW Q MW%SR%E%LSVM^SRXEP%VSXEXMRK%TPEXJSVQ"%%8LI%QEWW%MW%PSGEXIH%%9"!!%Q%%JVSQ%XLI

E\PI%ERH%QEOIW%SRI%VIZSPYXMSR%IZIV]%%2345%W3

!"#$$!QQ

E\PI

8LI$JVMGXMSR$JSVGI$RIIHIH$XS$OIIT$XLI$QEWW$JVSQ$WPMHMRK$MW$$45$27$$;LEX$MW$XLI

SFNIGX'W)QEWW#

%" #"$%&OK

&" #"$%OK

'" #"$%OK

(" #"$%OK

!" %R%SFNIGX%QSZIW%EX%E%GSRWXERX%WTIIH%EPSRK%E%GMVGYPEV%TEXL%EW%WLS[R"

! !

!

!

;LMGL%ZIGXSV%FIWX %VITVIWIRXW%XLI%GIRXVMTIXEP%EGGIPIVEXMSR%SJ%XLI%SFNIGX%EX%XLMW%TSMRX#

%" #

&" #

'" #

(" #

!"#"!

!" %$%"%!!$OK$TYGO$MW$EXXEGLIH$XS$E$%"3!%$OK$QEWW 1 F]$E$GSVH$XLEX$TEWWIW$XLVSYKL$E$LSPI$MR$E

JVMGXMSRPIWW+XEFPI.+EW+WLS[R1++8LI+TYGO+XVEZIPW+MR+E+GMVGYPEV+TEXL+SJ+VEHMYW+819:+Q1

1

TYGO

;LEX%MW%XLI%WTIIH%SJ%XLI%TYGO#

%" #"$%&Q(W&" #"$%&Q(W'" #"$%Q'W(" #"$%Q'W

!" %$GLMPH$MW$VMHMRK$SR$E$QIVV]3KS3VSYRH$[LMGL$MW$VSXEXMRK$EX$E$GSRWXERX$VEXI"$$;LMGL$SJ$XLI$JSPPS[MRK

HIWGVMFIW(XLI(GLMPH,W(WTIIH.(ZIPSGMX].(ERH(QEKRMXYHI(SJ(EGGIPIVEXMSR#

74))( :)03'-8= 1%+2-89())3*%'')0)6%8-32

%" GSRWXERX GSRWXERX GSRWXERX

&" GSRWXERX GLERKMRK GSRWXERX

'" GLERKMRK GSRWXERX GLERKMRK

(" GLERKMRK GLERKMRK GLERKMRK

!" %$%&&$2$GLMPH$XVEZIPW$MR$E$GMVGYPEV$TEXL$SR$E"JIVVMW"[LIIP+"";LMGL"JVII"FSH]%HMEKVEQ FIWX WLS[W%XLI

JSVGIW'[LMGL'GSYPH'EGX'SR'XLI'GLMPH'EW'WLI'TEWWIW'XLI'PS[IWX'TSMRX#

%"

*K!!!#$$!2

&"

*K!!!#$$!2

*2!!!#$$!2'"

*K!!!#$$!2

*2!!!#$$!2("

*K!!!#$$!2

*2!!!#$$!2

!"#"!

!" %$GEV$XVEZIPW$EX$E$YRMJSVQ$WTIIH$XLVSYKL$E$PIZIP$GMVGYPEV$GYVZI$MR$XLI$VSEH"$$;LMGL$SJ$XLI$JSPPS[MRK

GSVVIGXP](HIWGVMFIW(XLI(QEKRMXYHI(SJ(XLI(EGGIPIVEXMSR4(ZIPSGMX](ERH(JSVGI(EGXMRK(SR(XLI(GEV#

1%+2-89())3*%'')0)6%8-32

1%+2-89())3*:)03'-8=

1%+2-89())3**36')

%" GSRWXERX GSRWXERX GSRWXERX

&" GSRWXERX GLERKMRK GLERKMRK

'" GSRWXERX GLERKMRK GSRWXERX

(" GLERKMRK GLERKMRK GLERKMRK

!" %$WXYHIRX$TPSXW$E$KVETL$SJ$GIRXVMTIXEP$JSVGI$ *G !!ZIVWYW!XLI!WUYEVI!SJ!ZIPSGMX] Z! !!JSV!ER!SFNIGX

MR#YRMJSVQ#GMVGYPEV#QSXMSR-

Z!

;LEX%MW%XLI%WPSTI%SJ%XLMW%KVETL#

%"Q

V&"V

Q'"! !V

8!("8!

! !V

!" ;LMGL'SJ'XLI'JSPPS[MRK'HMEKVEQW'WLS[W'XLI'MRWXERXERISYW'ZIPSGMX]' Z 'ERH'GIRXVMTIXEP'JSVGI' *

JSV$ER$SFNIGX$MR$YRMJSVQ$GMVGYPEV$QSXMSR0

%"

'"

Z*

Z

*

&"

("

Z

*

Z

*

!"#"!

!"# %R&SFNIGX&XVEZIPW&[MXL&E&GSRWXERX&WTIIH&MR&E&GMVGYPEV&TEXL#&&8LI&RIX&JSVGI&SR&XLI&SFNIGX&MW

%" ^IVS"

&" XS[EVHW*XLI*GIRXVI"

'" E[E]&JVSQ&XLI&GIRXVI"

(" XERKIRX(XS(XLI(SFNIGX.W(TEXL"

!!" %$TL]WMGW$WXYHIRX$W[MRKW$E 3"4 OK TEMP$SJ$[EXIV$MR$E$ZIVXMGEP$GMVGPI$SJ$VEHMYW !"; Q"

Z

;LEX%MW%XLI%QMRMQYQ%WTIIH.%Z.%EX%XLI%XST%SJ%XLI%GMVGPI%MJ%XLI%[EXIV%MW%RSX%XS%WTMPP%JVSQ%XLI%TEMP#

%" #"$ Q W

&" #"$ Q W

'" #"$ Q W

(" #"$ Q W

!"# -R&E&TSTYPEV&EQYWIQIRX&TEVO&VMHI4&E&PEVKI&G]PMRHIV&MW&WIX&MR&VSXEXMSR#&&8LI&JPSSV&XLIR&HVSTW&E[E]

PIEZMRK(XLI(VMHIVW(WYWTIRHIH(EKEMRWX(XLI([EPP(MR(E(ZIVXMGEP(TSWMXMSR(EW(WLS[R3

6SXEXMRK(G]PMRHIV

;LMGL%SJ%XLI%JSPPS[MRK%MW%XLI%GSVVIGX%JVII0FSH]%HMEKVEQ%JSV%XLI%TIVWSR%EX%XLI%TSWMXMSR%WLS[R#

%" &" '" ("

!"#"!

!"#"!

!"# % !#% Q ''PSRK'TIRHYPYQ'VIEGLIW'E'WTIIH'SJ 6#7 Q W!!EX!XLI!FSXXSQ!SJ!MXW!W[MRK/

!"# OK

!"# Q

;LEX%MW%XLI%XIRWMSR%MR%XLI%WXVMRK%EX%XLMW%TSWMXMSR#

%" ##$2

&" #$%2

'" #$%2

(" #$%2

!"# %%%!%&''%OK%%GEV%VSYRHW%E%JPEX%GMVGYPEV%WIGXMSR%SJ%VSEH%EX &' Q W!!EW!WLS[R!MR!XLI!HMEKVEQ/

Z ! !" Q W

8LI$GSIJJMGMIRX$SJ$JVMGXMSR$FIX[IIR$XLI$GEV$XMVIW$ERH$XLI$VSEH$WYVJEGI$MW 23453$$;LEX$QMRMQYQ

JVMGXMSR(JSVGI(MW(VIUYMVIH(JSV(XLI(GEV(XS(JSPPS[(XLMW(GYVZI#

%" #"$ »!"! 2

&" #"$ »!"! 2

'" #"$ »!"! 2

(" #"$ »!"! 2

!"#"!

!"# %%%!#&%OK%%QEWW%SR%XLI%IRH%SJ%E%WXVMRK%MW%VSXEXIH%MR%E%ZIVXMGEP%GMVGPI%SJ%VEHMYW%%9#:;%Q#

!"#$OK

V ! #$%&'Q

-J#XLI#WTIIH#SJ#XLI#QEWW#EX#XLI#XST#SJ#XLI#GMVGPI#MW##123#Q4W5#[LEX#MW#XLI#XIRWMSR#MR#XLI#WXVMRK#EX#XLMW

PSGEXMSR#

%" #"$%2

&" #$%2

'" #$%2

(" #$%2

!"# %%TIVWSR%MW%SR%E%LSVM^SRXEP%VSXEXMRK%TPEXJSVQ%EX%E%HMWXERGI%SJ%%7#8%Q%%JVSQ%MXW%GIRXVI#%%8LMW%TIVWSR

I\TIVMIRGIW)E)GIRXVMTIXEP)EGGIPIVEXMSR)SJ) /01)Q3W! !"";LEX"GIRXVMTIXEP"EGGIPIVEXMSR"MW"I\TIVMIRGIH"F]

ERSXLIV(TIVWSR([LS(MW(EX(E(HMWXERGI(SJ((012(Q((JVSQ(XLI(GIRXVI(SJ(XLI(TPEXJSVQ#

%" #"$%Q'W!

&" #"#$Q&W!

'" #"$ %Q'W!

(" #"$%Q'W!

!"# ,ERW()[LSWI)QEWW)MW))01)OK())VMHIW)SR)E)JIVVMW)[LIIP)MR)E)GMVGYPEV)TEXL)EX)GSRWXERX)WTIIH#));LIR)LI)MW

EX#XLI#XST#SJ#XLI#[LIIP+#XLI#WIEX#I\IVXW#ER#YT[EVH#JSVGI#SJ##345#2##SR#,ERW8

;LEX%MW%XLI%GIRXVMTIXEP%JSVGI%SR%,ERW%EX%XLI%XST%SJ%XLI%[LIIP#

%" #$%2

&" #$%&2

'" #$%&2

(" #$%&2

!"# %R&SFNIGX&MW&EXXEGLIH&XS&E&WXVMRK&XLEX&GER&[MXLWXERH&E&QE\MQYQ&XIRWMSR&JSVGI&SJ 9#: 2#&&8LI

SFNIGX'XVEZIPW'MR'E'GMVGYPEV'TEXL'SJ'VEHMYW' 45 64 Q'[MXL'E'TIVMSH'SJ'95: W5

QV !!"#!Q

;LEX%MW%XLI%QE\MQYQ%QEWW%SJ%XLI%SFNIGX#

%" #"$% OK

&" #"$% OK

'" #"$ OK

(" #"$ OK

!"# %%&'%OK%TMPSX%MR%E%WXYRX%TPERI%TIVJSVQW%E%ZIVXMGEP%PSST%[MXL%E%;<<%Q%VEHMYW#%%8LI%TPERI%VIEGLIW%E

WTIIH%SJ%()* Q W!EX!XLI!FSXXSQ!SJ!XLI!PSST,!!;LEX!MW!XLI!YT[EVH!JSVGI!SR!XLI!TMPSX!EX!XLI

FSXXSQ%SJ%XLI%PSST#

%" #$%&2

&" #$%&&$2

'" #$%&&$2

(" #$%&&$2

!"# 8LI'HMEKVEQ'WLS[W'E'1!'OK'GLMPH'VMHMRK'SR'E'*IVVMW'[LIIP'SJ'VEHMYW'9!'Q'ERH'TIVMSH'9;'W#

;LEX%JSVGI%+RSVQEP%JSVGI/%HSIW%XLI%WIEX%I\IVX%SR%XLI%GLMPH%EX%XLI%XST%ERH%FSXXSQ%SJ%XLI%VMHI#

V"!"$%"Q834 &38831

%" !"#2 !"#2

&" !"#$2 &'#$2

'" !"#$2 !"#$2

(" !"#$2 &'#$2

! "#!

!"# %%%"%!&&%OK%%GEV%MW%XVEZIPPMRK%EX !3 Q W!SR!E!LSVM^SRXEP!WYVJEGI!MR!E!GMVGYPEV!TEXL!SJ!VEHMYW!!23!Q5

;LEX%MW%XLI%RIX%JSVGI%EGXMRK%SR%XLMW%GEV#

%" #$2

&" #"# »"!"! 2

'" #"$ »!"! 2

(" #"$ »!"! 2

!!" %$$%&$OK$$WOEXIFSEVHIV$MW$QSZMRK$HS[R$E$VEQT$[MXL$E$$8"9$Q$$VEHMYW$SJ$GYVZEXYVI"$$%X$XLI$FSXXSQ$SJ

XLMW%VEQT%LI%VIEGLIW%E%WTIIH%SJ% /01 Q W!

V ! !"# Q

Z ! !" # Q W

;LEX%YT[EVH%JSVGI%EGXW%SR%XLI%WOEXIFSEVHIV%EX%XLI%FSXXSQ%SJ%XLI%VEQT#

%" #"$ »!"! 2

&" #"$ »!"! 2

'" #"$ »!"! 2

(" #"#»!"! 2

!"# %%WTEGI%WXEXMSR%LEW%ER%SYXIV%VEHMYW%SJ%%456%Q#%%8LI%WXEXMSR%VSXEXIW%WS%XLEX%XLI%SGGYTERXW%EX%<%EX

XLI$SYXIV$[EPP$I\TIVMIRGI$ER$EGGIPIVEXMSR$SJ 123 Q W! !"";LEX"EGGIPIVEXMSR"[MPP"XLI"SGGYTERXW"EX

="I\TIVMIRGI"EX"XLI""-.."Q""VEHMYW#

Z

%" #"$ Q W!

&" #"$ Q W!

'" #"$ Q W!

(" #$ Q W!

!"#"!

!"#"!

!"# %%FEPP%EXXEGLIH%XS%E%WXVMRK%MW%W[YRK%MR%E%LSVM^SRXEP%GMVGPI#

-

--

---

-:

:MI[%JVSQ%%FSZI

;LMGL%TEXL%[MPP%XLI%FEPP%JSPPS[%EX%XLI%MRWXERX%XLI%WXVMRK%FVIEOW#

%" -

&" --

'" ---

(" -:

!"# %%XIWX%XYFI%VSXEXIW%MR%E%GIRXVMJYKI%[MXL%E%TIVMSH%SJ 7#!8 »!"! " W "##8LI#FSXXSQ#SJ#XLI#XIWX#XYFI

XVEZIPW(MR(E(GMVGYPEV(TEXL(SJ(VEHMYW(23452 Q 3

7MHI%: MI[

!"#$! Q

8ST$:MI[

!"#$!Q

;LEX%MW%XLI%GIRXVMTIXEP%JSVGI%I\IVXIH%SR%E 2344 »!"! " OK#EQSIFE#EX#XLI#FSXXSQ#SJ#XLI#XYFI#

%" #"$% »!"! " 2

&" #"$% »!"! " 2

'" #"$$ »!"! " 2

(" #"$$»!"! 2

!"#$"!

!"# %R&SFNIGX&EXXEGLIH&XS&E&VSXEXMRK&XEFPI&MW&QSZMRK&MR&E&GMVGYPEV&TEXL&[MXL&E&GSRWXERX&WTIIH#

;LMGL%MW%XLI%GSVVIGX%JVII%FSH]%HMEKVEQ%JSV%XLI%SFNIGX#

%" &" '" ("

!"# %%%&'%OK%%WXYHIRX%MW%MR%E%GEV%XVEZIPPMRK%EX% !' Q W!!SR!E!LMPP!SJ!VEHMYW!!--.!Q0!!;LIR!XLI!GEV!MW!EX

XLI$XST$SJ$XLI$LMPP*$[LEX$YT[EVH$JSVGI$HSIW$XLI$WIEX$I\IVX$SR$XLI$WXYHIRX#

%" #$%&2

&" #$%&2

'" #$%&2

(" #$%&2

!"# %%%&!''%OK%%GEV%GER%XVEZIP%[MXLSYX%WPMTTMRK%EX%E%QE\MQYQ%WTIIH%SJ !" Q W!!MR!E!GMVGYPEV!TEXL

SJ#VEHMYW##*+#Q##SR#E#HV]#LSVM^SRXEP#WYVJEGI5##;LIR#MX#VEMRW7#XLI#GSIJJMGMIRX#SJ#JVMGXMSR#MW#VIHYGIH

XS#SRI#LEPJ#MXW#SVMKMREP#ZEPYI0##;LEX#MW#XLI#QE\MQYQ#WTIIH#YRHIV#XLMW#[IX#GSRHMXMSR#

%" #"$ Q W

&" #$ Q W

'" #$ Q W

(" #$ Q W

!"# %%FYW%SJ%[IMKLX *K !MW!QSZMRK!EX!E!GSRWXERX!WTIIH!SZIV!E!LMPP!ERH!HMT!XLEX!LEZI!XLI!WEQI!VEHMYW!SJ

GYVZEXYVI(Z

Z

;LIR%XLI%FYW%MW%TEWWMRK%SZIV%XLI%GVIWX%SJ%XLI%LMPP4%XLI%VSEH%I\IVXW%E%RSVQEP%JSVGI%SR%XLI%FYW%IUYEP%XS

XLVII%UYEVXIVW%SJ%XLI%FYW-W%[IMKLX% !! *K !"";LEX"MW"XLI"RSVQEP"JSVGI"XLI"VSEH"I\IVXW"SR"XLI"FYW"[LIR

XLI$FYW$MW$TEWWMRK$XLVSYKL$XLI$FSXXSQ$SJ$XLI$HMT#

%"!

!*K

&"!

!*K

'"!

!*K

("!

!*K

!"##"!

!"# 8LI'HMEKVEQ'WLS[W'ER'SFNIGX'SJ'QEWW'!#"'OK'XVEZIPPMRK'MR'E'GMVGYPEV'TEXL'SJ'VEHMYW'<#='Q'[LMPI

WYWTIRHIH'F]'E'TMIGI'SJ'WXVMRK'SJ'PIRKXL'456'Q5'';LEX'MW'XLI'GIRXVMTIXEP'JSVGI'SR'XLI'QEWW#

%" #$%2

&" #$%2

'" #$%2

(" #$%2

!"!

!"#$Q

956phpk - 2 - May 1, 1996

1. The diagram shows a toy plane flying in a circle of radius 1.20 m, supported by a string which makesan angle of 28° with the vertical. The tension in the string is 1.80 N.

28°

1.20 m

a) What is the mass of the plane? (3 marks)

F T = 1.80 N

F c

F g

28°

Fg = FT cos 28°

= 1.59 N ← 2 marks

m = 1.599.8

= 0.16 kg ← 1 mark

956phpk - 3 - May 1, 1996

b) How long does the plane take to complete one orbit? (4 marks)

FC = FT sin 28°

= 0.845 N ←2 marks

m4π2rT2 = 0.845

T = 0.16 × 4π2 ×1.200.845

= 3.00 s ←2 marks

966phpk - 4 - September 18, 1996

2. A 35 kg child rides a ferris wheel of radius 12 m. The child moves in a vertical circle at aconstant speed and completes one rotation every 9.0 s.

12 m

a) As the child travels over the top, what is the magnitude of the force that the seat exerts on thechild? (5 marks)

FN

Fg

Fnet = Fg − FN

Fc = Fg − FN ← 2 marks

FN = Fg − Fc

= mg − m4π 2rT 2

= 35( ) 9.8( ) −35( ) 4π 2( ) 12( )

9.0( )2 ← 2 marks

= 343 − 205

FN = 138 N ← 1 mark

b) How does the magnitude of the child’s acceleration at the top of the ride compare to heracceleration at the bottom?

The child’s acceleration at the top is: (circle one) (1 mark)

i) less than at the bottom.ii) greater than at the bottom.iii) the same as at the bottom.

Explain your choice using principles of physics. (3 marks)

Since this child is moving in uniform circular motion her net force must be a constant centripetalforce. The magnitude of the acceleration must therefore be constant.

978phpk - 5 - October 27, 1997

3. A 3.5 kg object is suspended by a string and moves in a horizontal circle of radius 0.60 m. Thetension in the string is 36 N.

string

r = 0.60 m

3.5 kg

18°

a) What is the magnitude of the net force on the object? (3 marks)

FT

Fg

18°FT Fg

Fnet

sin18° = FnetFT

Fnet = FT sin18°

= 36( )sin18°

Fnet = 11 N ← 3 marks

b) What is the period of revolution of the object? (4 marks)

Fnet =m4π2rT 2

← 2 marks

T 2 = m4π2rFnet

← 1 mark

=3.5( ) 4π2( ) 0.60( )

11

T = 2.7 s ← 1 mark

986phk - 6 - July 24, 1998

4. A 6.1 kg object on the end of a massless connecting rod moves in uniform circular motion ina vertical circle with radius 1.2 m . The period of revolution is 0.80 s .

1.2 m

6.1 kg

constant v

connecting rod

a) Draw and label a free body diagram for the object at the bottom of the circular path. (2 marks)

Fg

T

2 marks←

b) Calculate the tension in the connecting rod at this position. (5 marks)

Fnet = ma

T − Fg = m 4π2

T 2r

T − mg = m 4π2

T 2r

← 2 marks

T − 6.1 kg ⋅9.8 m s2 = 6.1 kg ⋅ 4π2 ⋅1.2 m0.80 s( )2

T − 60 N = 452 N

← 2 marks

T = 510 N ← 1 mark

0206phk - 7 - July 23, 2002

5. A space station of radius 90 m is rotating to simulate a gravitational field.

v90 m

a) What is the period of the space station’s rotation so that a 70 kg astronaut will experiencea normal force by the outer wall equal to 60% of his weight on the surface of the earth?

(5 marks)

Fnet = mac

0.60 mg = m 4π2

T 2 R

T 2 = 4π2 90( )0.60 9.8( )

T = 25 s

← 1 mark

⎫

⎬⎪⎪

⎭⎪⎪

← 3 marks

← 1 mark

b) What would be the effect experienced by the astronaut if the space station rotated faster sothat the period of rotation was decreased? Explain your predicted effect. (4 marks)

The period is decreased and therefore the centripetal force increases ( Fc ∝ 1T 2 ). Since the

centripetal force is only provided by the normal force, the normal force on the astronaut

increases ( FN is perceived as weight.)

- 8 -

6. A 85 kg acrobat supported by a 6.0 m rope swings along a circular path from rest at position X as shown below. The rope hangs from the end of a uniform boom of mass 54 kg. Find the tensionforce as the acrobat passes the lowest point, position Y. (9 marks)

6.0 mHinge

Cable

32

320

°X

6.0 m

Y

2.0 m

( )( )marks2

sm8.100.68.92gh2v

mv21mgh

COE

2

���

���

�

===

=

T

Fg

Fc

( )marks3

N25000.68.108.985

rvgmT

rmvmgFFT

FBD

FBD

22

2

cg

���

���

�

=��⌅

���⇤

�+=��

⌅

���⇤

�+=

+=+=

( )( ) ( )( ) ( )( )( )( )( ) ( )( )( ) ( )( )( )

marksT

TWT

cable

cableboomrope

ccwcw

30.432sin0.38.9540.62500

0.432sin0.30.60

0

��

���

=+

=+

t=t ��

} markNTcable 11082.7 3·=

7. A racetrack surface has the shape of an inverted cone on which cars race in horizontal circles. For a steady speed of 29 m/s, to what distance d should a driver take her car, if she wishes to stay on a circular path without friction? (9 marks)

420420

d

- 9 -

Fc

FN

Fg

( )( )

marks2m130d

d95

dr48sin

marks2m95r

298.9r48tan

marks3vrg

rmvmg

FF

48cosF48sinF

marks2F48cosF

F48sinF

0

20

22C

g0

N

0N

C0

N

g0

N

��

���

=

==

��

���

=

=

���

���

�

===

��

���

=

=

006phk - 10 - July 20, 2000

8. A mass is suspended by a string attached to a spring scale that initially reads 14 N as shown inDiagram 1.

Rope

Spring scale

Q

F = 14 N

The mass is pulled to the side and then released as shown in Diagram 2.

F = ?

Rope

Spring scale

Q

As the mass passes point Q, how will the reading on the spring scale compare to the previousvalue of 14 N? Using principles of physics, explain your answer. (4 marks)

The reading will be greater than 14 N. by mv2

r

← 1 mark

Initially, the net force is zero, so the spring scale reads the weight of the mass. Whenmoving, there is a net (centripetal) force provided by the spring scale (tension in the rope)which exceeds the weight (force of gravity) of the mass so that the mass goes in a verticalcircle. ← 3 marks

0306phk - 11 - July 17, 2003

FRc µ

ÊËÁ

ˆ¯˜

1

9. During a roller coaster ride, the riders move through two loops, the second being one-half theradius of the first. The riders, however, travel at the same speed at the top of each of these twoloops.

v

FN

FN

12 R

R v

Using principles of physics, explain why the riders would experience a greater normal force atthe top of the second smaller loop than at the top of the first larger loop. (4 marks)

The centripetal force is the sum of the normal force and the force of gravity on the riders

(1 mark). Since the radius decreases while the velocity does not change in the smaller loop

the centripetal force must increase (2 marks). The normal force must increase to

provide a greater centripetal force as force of gravity remains constant (1 mark).