Chapter 13 (List)

7/21/2019 Chapter 13 (List)

1/40

KABTWJS2;

OE[W

Tbhj 2ln 74

Kabptjr2;

Oest

Jxjrkesj -22

Bfswjr 2

Hevjf0-

2. X = :444t

3.

HM = 4.;m

;.

w = 34t

7.

g = :m

Wbf = g * w

X * HM

Wbf = : * 34

:444 * 4.;

Wbf = 244

2:44

Wbf = 4.4>>8

= Wbf-2(4.4>>8)

= ;.13 lr ; 75

Oest ln taj saep es ;.13 lr ; 75

Bfswjr 3

Hevjf0-

2 X (t) = 1444

3 HM (m) = 3

Etjm X(t) g (m) Gerjktelf Mlmjfts

Tlrt [tcg

[aentjg 344 7 [tcg 4 144

[aentjg 244 3 Tlrt 344 4

[aentjg 244 7 Tlrt 744 4

[aentjg :4 34 [tcg 4 2444

Wltbo >44 2144


2/40

KABTWJS2;

OE[W

Tbhj 3ln 74

Wltbo Mlmjfts = [tcg Mlmjfts - Tlrt Mlmjfts

Wltbo Mlmjfts = 2144 - >44

Wltbo Mlmjfts = 2344 [tcg

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 2344

2>444

Wbf = 4.48:4

= 7.35 [tcg

Oest ln taj saep es 7.35 tl [tcg

Bfswjr ;

Hevjf0-

2 X (t) = 24444

3 IH (m) = 8; IM (m) = 8.7

Etjm X (t) IH /g (m)

Mlmjfts

(tm)

[aep 24444 8 84444

saentjg glwf 344 24 -3444

Wltbo 24444 >1444

Nefbo IH ln vjssjo = Wltbo Mlmjfts

Wltbo Xjehat

Nefbo IH ln vjssjo = >1444

24444

Nefbo IH ln vjssjo = >.144 m


3/40

KABTWJS2;

OE[W

Tbhj ;ln 74

Nefbo HM ln vjssjo = IM - Nefbo IH ln vjssjo

Nefbo HM ln vjssjo = 8.7 - >.144

Nefbo HM ln vjssjo = 4.>44 m


Tlrt [tcg

[aentjg 344 : [tcg 4 2444

Wltbo 4 2444


Wltbo Mlmjfts = 2444 - 4


Wbf = Wltbo Mlmjfts

X * HM

Wbf = 2444

>444

Wbf = 4.2>>8

= 5.7> [tcg

Oest ln taj saep es 5.7> tl [tcg


4/40

KABTWJS2;

OE[W

Tbhj 7ln 74

Bfswjr 7

Hevjf0-

2 X (t) = 23444

3 HM (m) = 2.3


Mlmjfts

(tm)

saentjg up 244 2.: -2:4

Wltbo 4 -2:4

Kabfhj ef HM ln vjssjo = Wltbo Mlmjfts

Wltbo Xjehat

Kabfhj ef HM ln vjssjo = -2:4

23444

Kabfhj ef HM ln vjssjo = -4.42; m

Nefbo HM ln vjssjo = Efefbo HM ln vjssjo + Kabfhj ef HM

Nefbo HM ln vjssjo = 2.3 - 4.42;

Nefbo HM ln vjssjo = 2.211 m

Etjm

X(t) g (m) Mlmjfts

[aentjg 244 23 2344

Wltbo 2344

Wltbo Mlmjfts = 2344


5/40

KABTWJS2;

OE[W

Tbhj :ln 74

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 2344

273:4

Wbf = 4.4173

= 7.12

Oest ln taj saep es 7.12

Hevjf0-

2 X (t) = 23444

3

IM (m)

= :.85

; IH(m) = 7.1:


Mlmjfts

(tm)

[aep 75:4 7.1: 37448.:

Olbg :4 2.3: >3.:

Wltbo :444 37484


Wltbo Xjehat

Nefbo IH ln vjssjo = 37484:444

Nefbo IH ln vjssjo = 7.127 m


Nefbo HM ln vjssjo = :.85 - 7.127

Nefbo HM ln vjssjo = 4.58> m


6/40

KABTWJS2;

OE[W

Tbhj >ln 74

EtjmX(t) g (m) Gerjktelf Mlmjfts

Tlrt [tcg

[aentjg :4 7 Tlrt 344 4

Wltbo 344 4


Wltbo Mlmjfts = 4 - 344

Wltbo Mlmjfts = 344 Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 344

7114.4

Wbf = 4.4724

= 3.;: Tlrt

Oest ln taj saep es 3.;: tl plrt

Bfswjr >

Hevjf0-

2 X (t) = 24444

3 IM (m) = 1.3:

; IH(m) = 8.7:


Mlmjfts

(tm)

[aep 24444 8.7: 87:44

Geskabrhjg -244 3.7: -37:

Wltbo 5544 873::


7/40

KABTWJS2;

OE[W

Tbhj 8ln 74


Wltbo Xjehat

Nefbo IH ln vjssjo = 873::

5544

Nefbo IH ln vjssjo = 8.:42 m


Nefbo HM ln vjssjo = 1.3: - 8.:42



Tlrt [tcg

Geskabrhjg -244 > Tlrt 4 >44

Wltbo 4 >44


Wltbo Mlmjfts = >44 - 4

Wltbo Mlmjfts = >44 [tcg

Wbf = Wltbo Mlmjfts

X * HM

Wbf = >44

8734.4

Wbf = 4.4145

= 7.>3 [tcg

Oest ln taj saep es 7.>3 tl stcg


8/40

KABTWJS2;

OE[W

Tbhj 1ln 74

Bfswjr 8

Hevjf0-

2 X (t) = 24444

3

IM (m)

= 5.>

; IH(m) = 1.;


Mlmjfts

(tm)

[aep 24444 1.; 1;444

Geskabrhjg -344 24 -3444

Geskabrhjg -144 3.; -2174Geskabrhjg -:44 :.3 -3>44

Olbgs 3:4 1 3444

Olbgs 3:4 23 ;444

Wltbo 5444 12:>4


Wltbo Xjehat

Nefbo IH ln vjssjo = 12:>4

5444

Nefbo IH ln vjssjo = 5.4>3 m


Nefbo HM ln vjssjo = 5.> - 5.4>3

Nefbo HM ln vjssjo = 4.:;1 m


Tlrt [tcg

Geskabrhjg -344 : Tlrt 4 2444

Geskabrhjg -144 7 [tcg ;344 4

Geskabrhjg -:44 ; Tlrt 4 2:44

Olbgs 3:4 4 4

Olbgs 3:4 4 4

Wltbo ;344 3:44



9/40

KABTWJS2;

OE[W

Tbhj 5ln 74

Wltbo Mlmjfts = 3:44 - ;344

Wltbo Mlmjfts = 844 Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 844

7174.4

Wbf = 4.277>

= 1.3; Tlrt

Bfswjr 1

Hevjf0-

2 X (t) = 5444

3

IM (m)

= 1.5:; IH(m) = 1.;


Mlmjfts

(tm)

[aep 5444 1.; 87844

Olbgs >44 7 3744

Geskabrhjg -744 5 -;>44

[aentjg Zp 344 : 2444

[aentjgGlwf ;44 2 -;44

Wltbo 5344 87344


Wltbo Xjehat

Nefbo IH ln vjssjo = 87344

5344

Nefbo IH ln vjssjo = 1.4>: m

Oest ln saep es 1.3; Tlrt


10/40

KABTWJS2;

OE[W

Tbhj 24ln 74


Nefbo HM ln vjssjo = 1.5: - 1.4>:

Nefbo HM ln vjssjo = 4.11: m


Tlrt [tcg

Olbgs >44 ; Tlrt 2144 4

Geskabrhjg -744 : Tlrt 4 3444

[aentjg Zp 344 1 [tcg 4 2>44

[aentjg Glwf ;44 7 plrt 2344 4

4 4 4 4

Wltbo ;444 ;>44


Wltbo Mlmjfts = ;>44 - ;444

Wltbo Mlmjfts = >44 [tcg

Wbf = Wltbo Mlmjfts

X * HM

Wbf = >44

1274.4

Wbf = 4.48;8

= 7.33 [tcg

Oest ln saep es 7.33 [tcg


11/40

KABTWJS2;

OE[W

Tbhj 22ln 74

Bfswjr 5

Hevjf0-

2 X (t) = 21444

3

IM (m)

= 1.5;:

; IH(m) = 8.8:


Mlmjfts

(tm)

[aep 21444 8.8: 2;5:44

Geskabrhjg -2:44 > -5444

Olbgs :44 24 :444[aentjg Zp :44 3 2444

[aentjg

Glwf 144 3 -2>44

Wltbo 28444 2;7544


Wltbo Xjehat

Nefbo IH ln vjssjo = 2;754428444

Nefbo IH ln vjssjo = 8.5;: m


Nefbo HM ln vjssjo = 1.5;: - 8.5;:



Tlrt [tcg

Geskabrhjg -2:44 ; Tlrt 4 7:44

Olbgs :44 7 Tlrt 3444 4

[aentjg Zp :44 7 [tcg 4 3444

[aentjg Glwf 144 ; plrt 3744 4

4 4 4 4

Wltbo 7744 >:44


12/40

KABTWJS2;

OE[W

Tbhj 23ln 74


Wltbo Mlmjfts = >:44 - 7744


Wbf = Wltbo Mlmjfts

X * HM

Wbf = 3244

2>55:.4

Wbf = 4.23;>

= 8.47 [tcg

Bfswjr 24

Hevjf0-

2 X (t) = 23444

3 IM (m) = 8.:7

; IH(m) = >.1

7 Efetebo Oest = 1 T

Efetebo HM = IM - IH

Efetebo HM = 8.:7 - >.1

Efetebo HM = 4.87 m

Wbf (1) = w * g

X *HM

4.274: = w * 24

23444 * 4.87

237.1t = w

Oest ln saep es 8.47 [tcg

Xjehat tl cj saentjg es 237.1t


13/40

KABTWJS2;

OE[W

Tbhj 2;ln 74

Bfswjr 22

Hevjf0-

2 X (t) = 7444

3 IM (m) = 24

; IH(m) = 5

7 Efetebo Oest = 24 T

: Nefbo HM (m) 2


Efetebo HM = 24 - 5

Efetebo HM = 2 m

Wbf = HH'

HM

Wbf 24 = HH'

2

4.28>m = HH'


Tlrt [tcg

[aep 7444 4.28> Tlrt 84:.; 4.4

Olbgs 2>444 ; 4.4 4.4

4 4 7 Tlrt 4.4 4.4

4 4 7 [tcg 4.4 4.4

4 4 ; plrt 4.4 4.4

4 4 4.4 4.4

Wltbo 84:.; 4.4


Wltbo Mlmjfts = 4 - 84:.;

Wltbo Mlmjfts = 84:.;41 Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 84:.;


14/40

KABTWJS2;

OE[W

Tbhj 27ln 74

34444.4

Wbf = 4.4;:;

= 3.43 Tlrt

Bfswjr 23

Hevjf0-

2.

X =24444t

3.

HM = 2.:m

;.

Efetebo oest = : [tcg7. Nefbo HM = 4.:m

Wbf = HH'

HM

Wbf (:) = HH'

2.:

4.2;2m = HH'


Tlrt [tcg

[aep 24444 4.2;2 [tcg 4.4 2;23.;

Wltbo 4.4 2;23.;


Wltbo Mlmjfts = 2;23.;; - 4

Wltbo Mlmjfts = 2;23.;; [tcg

Wbf = Wltbo Mlmjfts

X * HM

Nefbo Oest ln saep weoo cj 3.43 tl plrt


15/40

KABTWJS2;

OE[W

Tbhj 2:ln 74

Wbf = 2;23.;

:444.4

Wbf = 4.3>3:

= 27.82 [tcg

Bfswjr 2;

Hevjf0-

2 X (t) = 1:443 IM (m) = 5

; IH(m) = 1.;

7 Efetebo Oest = 1.: T

: Nefbo IM (m)= 5.;


Efetebo HM = 5 - 1.;

Efetebo HM = 4.8 m

Wbf = HH'

HM

Wbf

(1.:) = HH'

4.8

4.24: = HH'


Mlmjfts

(tm)

[aep 1:44 1.; 84::4

Geskabrhjg -344 7 -144

Geskabrhjg -;44 : -2:44

Olbgs 244 3 344

[aentjg Zp 344 3 744

Wltbo 1244 >11:4

Nefbo Oest ln saep weoo cj 27.82 tl stcg


16/40

KABTWJS2;

OE[W

Tbhj 2>ln 74

Nefbo HM = Nefbo IMNefbo IH

Nefbo HM = 5.;m1.:m

Nefbo HM = 4.1m


Tlrt [tcg

[aep 1:44 4.24: Tlrt 115.3 4.4

Geskabrhjg -344 : [tcg 2444.4 4.4

Geskabrhjg -;44 3 Tlrt 4.4 >44.4

Olbgs 244 7 [tcg 4.4 744.4

[aentjg Zp 344 ; [tcg 4.4 >44.4

Wltbo 2115.3 2>44.4


Wltbo Mlmjfts = 2>44 - 2115

Wltbo Mlmjfts = 315.3;;: Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 315.3>714.4

Wbf = 4.477>

= 3.:> Tlrt

Nefbo Oest ln saep weoo cj 3.:> tl plrt


17/40

KABTWJS2;

OE[W

Tbhj 28ln 74

Bfswjr 27

Hevjf0-

2. Gespobkjmjft = 2:444t

3.

IH = 1.8m;.

IM = 5.:m

7. Efetebo Oest = 24 Tlrt

:. G = 23m

Efetebo HM = IMIH

Efetebo HM = 5.:m1.8m

Efetebo HM = 4.1m

Wbf = w * gX * HM

Wbf(24) = w * g

2:444 * 4.1

Etjm X (t) Gerjktelf Mlmjfts

T (tm) [ (tm)

[aep 2:444 322:

Olbgs +:44 [tcg 3:44

Geskabrhjg -;44 Tlrt 2344

Wltbo 2:344 322: ;844

Wltbo mlmjfts = [tcg mlmjftsTlrt Mlmjfts

Wltbo mlmjfts = ;844322:

Wltbo mlmjfts = 2:1: tm

Wltbo mlmjfts = w * g

2:1: = w * 23

2:1: = w

23

2;3.2t =w

Xjehat ln [X tabt abs tl cj trbfsnjrrjg es 2;3.2t


18/40

KABTWJS2;

OE[W

Tbhj 21ln 74

Bfswjr 2:

Hevjf0-

2 X (t) = 233:4

3 IM (m) = 5.1

; IH(m) = 5

7 Efetebo Oest = >.: [

: Nefbo IM (m)= 5.>


Efetebo HM = 5.1 - 5

Efetebo HM = 4.1 m

Wbf = HH'

HM

Wbf (>.:) = HH'

4.1

4.452 = HH'


Mlmjfts

(tm)

[aep 233:4 5 2243:4

Olbgs 23:4 1 24444

Geskabrhjg -3:4 3 -:44

[aentjg Glwf 2>4 5 -2774

Wltbo 2;3:4 221;24


Wltbo Xjehat

Nefbo IH ln vjssjo = 221;24

2;3:4



19/40

KABTWJS2;

OE[W

Tbhj 25ln 74

Nefbo HM = Nefbo IMNefbo IH

Nefbo HM = 5.>m1.535m

Nefbo HM = 4.>82m


Tlrt [tcg

[aep 233:4 4.452 [tcg 4.4 222>.>

Olbgs 23:4 3 [tcg 4.4 3:44.4

Geskabrhjg -3:4 : [tcg 23:4.4 4.4

[aentjg 2>4 24 plrt 2>44.4 4.4

Wltbo 31:4.4 ;>2>.>


Wltbo Mlmjfts = ;>2>.:>5 - 31:4

Wltbo Mlmjfts = 8>>.:>5 [tcg

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 8>>.>

1154.4

Wbf = 4.41>3

= 7.5; [tcg

Nefbo Oest ln saep weoo cj 7.5; tl [tcg


20/40

KABTWJS2;

OE[W

Tbhj 34ln 74

Bfswjr 2>

Hevjf0-

2. X = 1444t

3.

IM = 1.>m;.

IH = 1.4m

7. IH ln kbrhl = 24m

:. Gestbfkj ln KO = 1m

>. Sjsuotbft Oest = ;

HM = IMIH

HM = 1.>m1.4m

HM =4.>m

Etjm Xjehat (t) IH (m) Mlmjfts (tm)

[aep 1444 1 >7444

Kbrhl wbsajg -x 24 -24x

Wltbo 1444-x >7444-24x

Nefbo IH ln saep = Wltbo Mlmjfts

Wltbo Xjehat

Nefbo IH ln saep = >7444-24x

1444-x

Nefbo HM ln saep = IMIH

Nefbo HM ln saep = 1.>(>7444-24x)

1444-x

Nefbo HM ln saep = 1.>(1444x)>7444 + 24x

1444-x

Nefbo HM ln saep = >11441.>x>7444 +24x

1444x

Nefbo HM ln saep = 7144 + 2.7x

1444 - x

Etjm Xjehat (t) Gestbfkj ln KLO (m) Mlmjfts (tm)

[aep 1444 4 4

Kbrhl wbsajg -x 1 1x

Wltbo 1444-x 1x

Nefbo Mlmjfts = 1x

Wbf = Wltbo MlmjftsX * HM


21/40

KABTWJS2;

OE[W

Tbhj 32ln 74

Wbf = 1x

(1444-x) * HM

Wbf(;) = 1x * (1444x)

(1444-x) * (7144 + 2.7>x)

3:2.::8 + 4.488x = 1x

3:2.::8 = 8.53;x

;2.8 t =x

Bfswjr 28

Hevjf0-

2.

X =2>444t

3.

IM = 8.:m

;. IH = >.4m

7. WTK = 3:t/km

:. Efetebo oest = ; (Tlrt)

>. Sjquerjg grbnt = 1.1m

8.

Trjsjft grbnt = 1.>m

1.

[pbkj bvbeobcoj es :m ln kjftjr oefj lf jetajr segj

HM = IMIH

HM = 8.:m>m

HM = 2.:m

Wbf = w *g

X * HM

Wbf (;) = w * g

2>444 * 2.:

23:8.1tm =w * g

Efetebo trbfsvjrsj mlmjfts = 238:.1tm (Tlrt)

Mbxemum pjrmessecoj sefibhj = Grbnt rjquerjgEfetebo grbnt

Mbxemum pjrmessecoj sefibhj = 1.1m1.>m

Mbxemum pjrmessecoj sefibhj = 4.3m/34kms

Kbrhl tl olbg = WTK * Mbxemum pjrmessecoj sefibhj

Xjehat ln kbrhl wbsajg es ;2.8t


22/40

KABTWJS2;

OE[W

Tbhj 33ln 74

Kbrhl tl olbg = 3: * 34kms

Kbrhl tl olbg = :44t

Etjm X(t) Gestbfkj ln K.O (m) Gerjktelf Mlmjfts (tm)T [

[aep 2>444 23:8.1

Olbg x : Tlrt :x

Olbg :44-x : [tcg 3:44:x

Wltbo 2>:44 23:8.1 + :x 3:44:x

Nlr saep tl cj uprehat Tlrt mlmjfts = [tcg mlmjfts

23:8.1 + :x = 3:44:x

24x = 2373.3

x = 237.3t

Kbrhl tl olbg ef plrt segj = 237.3t

Kbrhl tl olbg ef stcg segj = :44t237.3t

Kbrhl tl olbg ef stcg segj = ;8:.1t

Bfswjr 21

Hevjf0-

2. X = 23444t

3. IM = 5m

;. IH = 8.3:m

7. Kbrhl tl olbg (w)=344t

:. Ajbg ln gjrreki = 37 m bclvj ijjo

>.

Lutrjbka ln wabrn = 2:m

e)

IH ln ajbg ln gjrreki = 37m

IH ln saep =-8.3:m

g = 2>.8:m

Kabfhj ef ^KH = w * g

X + w

Kabfhj ef ^KH = 344 * 2>.8:

23444 + 344


23/40

KABTWJS2;

OE[W

Tbhj 3;ln 74

Kabfhj ef ^KH = ;;:4

23344

Kabfhj ef KH = 4.38:m

Efetebo IH ln vjssjo = 8.3:mKabfhj ef ^KH =+4.38:m

Nefbo IH ln vjssjo = 8.:3:m

Nefbo HM = IMNefbo IH

Nefbo HM = 5m8.:3:m

Nefbo HM = 2.78:m

Wbf = w * g

(X + w)* HM

Wbf = 344 * 2:

(23444+344) * 2.78:

Wbf = 344 * 2:

23444 * 2.78:

Wbf = 4.2>>8

= Wbf-2

(4.2>>8)

= 5.7>

Oest es 5.7> stcg

ee)

IH ln gjki = 24m

IH ln saep =-8.3:m

g = 3.8:m


X + w

Kabfhj ef ^KH = 344 * 3.8:

23444 + 344

Kabfhj ef KH = ::4

23344



24/40

KABTWJS2;

OE[W

Tbhj 37ln 74

Efetebo IH ln vjssjo = 8.3:m

Kabfhj ef ^KH =+4.47:m

Nefbo IH ln vjssjo = 8.35:m


Nefbo HM = 5m8.35:m

Nefbo HM = 2.84:m

Wbf = w * gW

(X + w)* HM

Wbf = 344 * 8

(23444+344) * 2.84:

Wbf = 344 * 823444 * 2.84:

Wbf = 4.4>8;

= Wbf-2

(4.4>8;)

= ;.1:

Oest es ;.1: stcg

Bfswjr 25

Hevjf0-

2. X = 24444t

3. IM = 8.;m

;. IH = >.1m

7. Kbrhl tl saent (w)=244t

:.

IH ln kbrhl = 24m

>.

Ajbg ln gjrreki = 31 m bclvj ijjo

8.

IH ln Olwjr Alog = 3m

1. Efetebo oest = : Tlrt

IM = IH + HM efetebo

IMIH = HM efetebo

8.;>.1 = HM efetebo

4.:m = HM efetebo


25/40

KABTWJS2;

OE[W

Tbhj 3:ln 74

e)

Wbf = w *g

X * HM

Wbf (:) = w * g24444 *4.:

7;8.7 = w * g

Efetebo Wrbfsvjrsj Mlmjft es 7;8.7tm tl plrt


IH ln kbrhl =-24m

g = 21m

Kabfhj ef ^KH = w * gX

Kabfhj ef ^KH = 244 * 21

24444

Kabfhj ef KH = 4.21m

Efetebo IH ln vjssjo = >.1m

Kabfhj ef ^KH =+4.21m

Nefbo IH ln vjssjo = >.51m


Nefbo HM = 8.;m>.51m

Nefbo HM = 4.;3m

Wbf = w * g

X * HM

Wbf = 7;8.7

24444 * 4.;3

Wbf = 4.2;>8

= Wbf-2

(4.2;>8)

= 8.81

Oest es 8.81 plrt


26/40

KABTWJS2;

OE[W

Tbhj 3>ln 74

ee)

Wbf = w *g

X * HM

Wbf (:) = w * g24444 *4.:

7;8.7 = w * g


IH ln kbrhl =-24m

g = 21m


X

Kabfhj ef ^KH = 244 * 21

24444



Kabfhj ef ^KH =+4.21m



Nefbo HM = 8.;m>.51m

Nefbo HM = 4.;3m

Etjm X(t) Gestbfkj ln K.O (m) Gerjktelf Mlmjfts (tm)

T [

[aep 24444 7;8.7

[aent 244 > [tcg >44

Wltbo 24444 7;8.7 >44

Wltbo Mlmjfts = [tcg mlmjftsplrt mlmjfts

Wltbo Mlmjfts = >447;8.7

Wltbo Mlmjfts = 2>;.>tm

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 2>;.>24444 * 4.;3


27/40

KABTWJS2;

OE[W

Tbhj 38ln 74

Wbf = 4.4:22

= Wbf-2

(4.4:22)

= 3.53

Oest es 3.53 stcg

eee)

Wbf = w *g

X * HM

Wbf (:) = w * g

24444 *4.:

7;8.7 = w * g

IH ln Z.A = 24m

IH ln O.A =-3m

g = 1m


X

Kabfhj ef ^KH = 244 * 124444



Kabfhj ef ^KH =-4.41m



Nefbo HM = 8.;m

>.83m

Nefbo HM = 4.:1m


T [

[aep 24444 7;8.7

[aent 244 > [tcg >44

Wltbo 24444 7;8.7 >44

Wltbo Mlmjfts = [tcg mlmjftsplrt mlmjfts


28/40

KABTWJS2;

OE[W

Tbhj 31ln 74

Wltbo Mlmjfts = >447;8.7

Wltbo Mlmjfts = 2>;.>tm (stcg)

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 2>;.>

24444 * 4.:1

Wbf = 4.4313

= Wbf-2

(4.4313)

= 2.>2

Oest es 2.>2 stcg

Bfswjr 34

Hevjf0-

2.

X = 2;444t

3.

IM = 1.8: m

;.

IH = 1m

7.

Kbrhl tl geskabrhj (w)=2:4t:. IH ln kbrhl = 5m

>. Ajbg ln gjrreki = 33 m bclvj ijjo

8.

Efetebo oest = > [tcg


IMIH = HM efetebo

1.8:1 = HM efetebo

4.8:m = HM efetebo

e)

Wbf = w *g

X * HM

Wbf (>) = w * g

2;444 *4.8:

2437.1 = w * g


29/40

KABTWJS2;

OE[W

Tbhj 35ln 74

Efetebo Wrbfsvjrsj Mlmjft es 2437.1 tm tl stcg


IH ln kbrhl =- 5m

g = 2;m


X

Kabfhj ef ^KH = 2:4 * 2;

2;444


Efetebo IH ln vjssjo = 1m

Kabfhj ef ^KH =+4.2:m

Nefbo IH ln vjssjo = 1.2:m


Nefbo HM = 1.8: m1.2:m

Nefbo HM = 4.>m

Wbf = w * g

X * HM

Wbf = 2437.12;444 * 4.>

Wbf = 4.2;23

= Wbf-2

(4.2;23)

= 8.78

Oest es 8.78 stcg

ee)


T [

[aep 2;444 2437.1

[aent 2:4 (:+24=2:) plrt 33:4

Wltbo 24444 33:4 2437.1


30/40

KABTWJS2;

OE[W

Tbhj ;4ln 74

Wltbo Mlmjfts = Tlrt mlmjftsstcg mlmjfts

Wltbo Mlmjfts = 33:42437.1

Wltbo Mlmjfts = 233:.3tm tl Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 233:.3

2;444 * 4.>

Wbf = 4.2:82

= Wbf-2

(4.2:82)

= 1.53

Oest es 1.53 plrt

eee)

IH ln Kbrhl = 5m

IH ln saep =-1m

g = 2m

Kabfhj ef ^KH = w * gX-w

Kabfhj ef ^KH = 2:4 * 2

2;444-2:4

Kabfhj ef ^KH = 2:4 * 2

231:4



Kabfhj ef ^KH =-4.423m

Nefbo IH ln vjssjo = 8.511m


Nefbo HM = 1.8:m8.511m

Nefbo HM = 4.8>3m


31/40

KABTWJS2;

OE[W

Tbhj ;2ln 74


T [

[aep 2;444 2437.1

Geskabrhj -2:4 : Tlrt 8:4

Wltbo 231:4 8:4 2437.1

Wltbo Mlmjfts = [tcg mlmjftsTlrt mlmjfts

Wltbo Mlmjfts = 2437.1 - 8:4

Wltbo Mlmjfts = 387.1tm (plrt)

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 387.1231:4 * 4.8>3

Wbf = 4.4312

= Wbf-2

(4.4312)

= 2.>2

Oest es 2.>2 stcg

Bfswjr 32

Hevjf0-

2.

Gespobkjmjft = 24444t

3. IM = 24.1m

;.

IH = 5m

7. Efetebo Oest = 24 [tcg

:. Gemjfselfs ln tbfi = 23m * 23m * 5m

SG ln NX = 2.444


IMIH = HM efetebo

24.11 = HM efetebo

2.1m = HM efetebo


32/40

KABTWJS2;

OE[W

Tbhj ;3ln 74

Gestbfkj cjtwjjf kjftjr ln hrbvety ln twl tbfis es 23m

e)

Wbf = w *g

X * HM

Wbf (24) = w * g

24444 *2.1

;28;.5 = w * g

Efetebo Wrbfsvjrsj Mlmjft es ;28;.5 tm tl stcg

Wl klrrjkt oest stcg mlmjfts = plrt mlmjfts

[tcg mlmjfts = w * g

;28;.5 = w *23

;28;.5 = w

23

3>7.:t = w

23m

H

23m 23m

5m23m

H


33/40

KABTWJS2;

OE[W

Tbhj ;;ln 74

ee

e = OC;

23

N[J = e * SG ln NX

23 * Gespobkjmjft

N[J = O * C;* SG ln NX

23 * Gespobkjmjft

N[J = 23 * (23);* 2.444

23 * 24444

N[J = 4.28;m

N[J ln 2 tbfi = 4.28;m

N[J ln 3 tbfis = 3 * 4.28;m ([emeobr ef gemjfselfs)

N[J ln 3 tbfis = 4.;7>m

Xjehat saentjg =2 * ^loumj ln tbfi * SG ln NX

;

Xjehat saentjg = 2 * O * C * A * SG ln NX

;

Xjehat saentjg = 2 * 23 * 23 * 5 * 2.444

;

23m

H

23m 23m

5m23m

H

>m

;m

;m


34/40

KABTWJS2;

OE[W

Tbhj ;7ln 74

Xjehat saentjg = 7;3t

IH ln wjehat saentjg = >m + ; m

3

IH ln wjehat saentjg = 8.:mIH tl wajrj wjehat saentjg =-2.:m

g = >m


X

Kabfhj ef ^KH = 7;3 * >

24444

Kabfhj ef KH = 4.3:5m


Kabfhj ef ^KH =-4.3:5m

IH(s) ln vjssjo = 1.872m

N[J ln 3 tbfis =+4.;7>m

IH(n) = 5.418m

Nefbo HM = IMIH (n)

Nefbo HM = 24.1m5.418m

Nefbo HM = 2.82;m

Wrbfsvjrsj mlmjfts guj tl saentefh = w * gW

Wrbfsvjrsj mlmjfts guj tl saentefh = 7;3 * 23

Wrbfsvjrsj mlmjfts guj tl saentefh = :217tm (Tlrt)

Efetebo Mlmjfts =-;28;.5 (stcg)

Fjt Mlmjfts = 3424.2 (Tlrt)

Wbf = Fjt Mlmjfts

X * HM

Wbf = 3424.2

24444 * 2.82;

Wbf = 4.228;

= Wbf-2

(4.228;)

= >.>5

Oest es >.>5 plrt


35/40

KABTWJS2;

OE[W

Tbhj ;:ln 74

Bfswjr 33

Hevjf0-

2.

Gespobkjmjft (X) = 1444t3.

Xjehat saentjg (w) = :4t

;. Wrbfsvjrsj gestbfkj = 7m

7. N[M = 232>tm

:. IM = 8m

>. IH = >.7m

N[J = N[M

Gespobkjmjft

N[J = 232>

1444

N[J = 4.2:3m

IH (s) = >.7m

N[J =+4.2:3

IH (n) = >.::3m

IM = 8m

IH (n) =->.::3m

HM (n) = 4.771m

Wbf = Wrbfsvjrsj Mlmjfts

X * HM (n)

Wbf = w * g

X * HM (n)

Wbf = :4 * 7

1444 * 4.771

Wbf = 344

;:17

= Wbf-2

(4.4::1)

= ;.25

Nefbo oest ln taj vjssjo es ;.25


36/40

KABTWJS2;

OE[W

Tbhj ;>ln 74

Bfswjr 3;

Hevjf0-

2. X =24444t

3.

IM = 8.1m;.

IH = 8.48:m

7. SG ln ANL = 4.5:

:. Gemjfselfs ln jbka tbfi = 2:m * 23m * 3m

>. Fl ; stcg nefbo slufgefh = 2.3m

ANL klfsumjg = O * C * (Aslufgefh ) * SG ln leo

ANL klfsumjg = 2: * 23 * 4.1 * 4.5:

ANL klfsumjg = 2;>.1t

IH ln saep = 8.48:m

IH ln ANL klfsumjg =-2.>m

g = :.78:m

Kabfhj ef KH = w * g

X - w

Kabfhj ef KH = 2;>.1 * :.78:

244442;>.1

Kabfhj ef ^KH = 871.51

51>;.3

Kabfhj ef KH = 4.48>m

3m

23m

2:m

3m

23m

2:m

2.3m

4.1m

HH'


37/40

KABTWJS2;

OE[W

Tbhj ;8ln 74

Efetebo IH = 8.48:m

Kabfhj ef ^KH =+4.48>m

Nefbo IH (s) = 8.2:2m

e = OC;

23

N[J = e * SG ln ANL

23 * Gespobkjmjft

N[J = O * C;* SG ln ANL

23 * Gespobkjmjft

N[J = 2: * (23);* 4.5:

23 * 24444

N[J = 2: * 23 * 23 * 23 * 4.5:23 * 24444

N[J = 4.341m

IH (s) = 8.2:2m

N[J =+4.341

IH (n) = 8.;:5m

IM = 8.1m

IH (n) =-8.;:5m

HM (n) = 4.772m


X * HM (n)

Wbf = w * g

X * HM (n)

Wbf = 2;>.1 * >

24444 * 4.772

Wbf =134.1

7724

= Wbf-2

(4.2118)

= 24.>5

Nefbo oest ln taj vjssjo es 24.>5 tl Tlrt


38/40

KABTWJS2;

OE[W

Tbhj ;1ln 74

Bfswjr 37

Hevjf0-

2 X (t) = 5444

3 IM (m) = 1.43

; IH(m) = 8.:

EtjmX (t) IH /g (m)

Mlmjfts

(tm)

[aep 5444 8.: >8:44

Olbgs 3:4 23 ;444

Olbgs 2444 ; ;444

Geskabrhjg -3:4 1 -3444

N[M 2344

Wltbo 24444 83844


Wltbo Xjehat

Nefbo IH ln vjssjo = 83844

24444



Nefbo HM ln vjssjo = 1.43 - 8.384

Nefbo HM ln vjssjo = 4.8:4 m

Etjm

X(t) g (m) Gerjktelf MlmjftsTlrt [tcg

[aep 5444 4.444 4 4.4 4.4

Olbgs 3:4 ; [tcg 4.4 8:4.4

Olbgs 2444 2 Tlrt 2444.4 4.4

Geskabrhjg -3:4 3 [tcg :44.4 4.4

[aents 244 ; [tcg 4.4 ;44.4

Wltbo 2:44.4 24:4.4



39/40

KABTWJS2;

OE[W

Tbhj ;5ln 74

Wltbo Mlmjfts = 24:4 - 2:44

Wltbo Mlmjfts = 7:4 Tlrt

Wbf = Wltbo Mlmjfts

X * HM

Wbf = 7:4.4

8:44.4

Wbf = 4.4>44

= ;.7; Tlrt

Bfswjr 3:

Hevjf0-

2. Gespobkjmjft (X) = 27444t

3.

IM = 5m

;.

IH = 8.1m

7. N[M = 3244tm

:.

Efetebo Oest = 1 Tlrt>. Wrbfsvjrsj gestbfkj = 24m

N[J = N[M

Gespobkjmjft

N[J = 3244

27444

N[J = 4.2:m

IH (s) = 8.1mN[J =+4.2:

IH (n) = 8.5:m

IM = 5m

IH (n) =-8.5:m

HM (n) = 2.4:m


X * HM (n)

Wbf(1) = w * gX * HM (n)

Nefbo Oest ln saep weoo cj ;.7; tl Tlrt


40/40

KABTWJS2;

OE[W

34>> = w *g

Wl klrrjkt taj oest Tlrt Mlmjfts = [tbrclbrg Mlmjfts

34>> = w * Wrbfsvjrsj gestbfkj

34>> = w * 24

34>> = w

24

34>.>t = w

Xjehat tl trbfsnjr es 34>.>t

-l4l-

Documents

Chapter 13 (List)