Chapter 13 (List)

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W

Kabptjr ‛ 2; Oest Jxjrkesj -22

Bfswjr 2 Hevjf02. 3. ;. 7.

X = :444t HM = 4.;m w = 34t g = :m

Wbf ѳ = g * w X * HM Wbf ѳ = : * 34 :444 * 4.; Wbf ѳ = 244 2:44 Wbf ѳ = 4.4>>8 ѳ = Wbf -2(4.4>>8) ѳ = ;.13´ lr ;´ 75―

Oest ln taj saep es ;.13´ lr ;´ 75― Bfswjr 3 Hevjf02

X (t) =

3

HM (m) =

Etjm

X(t)

1444 3

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

>44

2144

Wltbo

Tbhj 2 ln 74


Wltbo Mlmjfts =

[tcg Mlmjfts - Tlrt Mlmjfts

Wltbo Mlmjfts =

2144

-

Wltbo Mlmjfts =

2344

[tcg

Wbf ѳ =

>44

Wltbo Mlmjfts X * HM 2344

Wbf ѳ =

2>444 Wbf ѳ = = ѳ =

4.48:4

7.35´

[tcg

Oest ln taj saep es 7.35´ tl [tcg

Bfswjr ; Hevjf02

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

Nefbo IH ln vjssjo =

>1444 Wltbo Mlmjfts Wltbo Xjehat


>1444 24444


>.144

m Tbhj 3 ln 74


Nefbo HM ln vjssjo =

IM - Nefbo IH ln vjssjo


8.7

-


4.>44

m

Etjm

[aentjg

X(t)

g (m)

344

>.144

Gerjktelf

:

Mlmjfts

[tcg

Wltbo Wltbo Mlmjfts =

[tcg

4

2444

4

2444


Wltbo Mlmjfts =

2444

Wltbo Mlmjfts =

2444

Wbf ѳ =

Tlrt

-

4

[tcg

Wltbo Mlmjfts X * HM

Wbf ѳ =

2444 >444

Wbf ѳ = = ѳ=

4.2>>8

5.7>´

[tcg

Oest ln taj saep es 5.7>´ tl [tcg

Tbhj ; ln 74


Bfswjr 7 Hevjf02

X (t) =

23444

3

HM (m) =

2.3

Etjm

X (t)

IH /g (m)

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 = Nefbo HM ln vjssjo =

-4.42;

m

Efefbo HM ln vjssjo + Kabfhj ef HM


2.3

-


2.211

m

4.42;

Etjm

[aentjg

X(t)

g (m)

Mlmjfts

244

23

2344


2344 2344

Tbhj 7 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wbf ѳ =


Wbf ѳ =

2344 273:4

Wbf ѳ = = ѳ=

4.4173

7.12´

Oest ln taj saep es 7.12´

Hevjf02 3

X (t) = IM (m) =

;

IH(m) =

23444 :.85 7.1:

Etjm

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

75:4

7.1:

37448.:

Olbg

:4

2.3:

>3.:

Wltbo

:444


37484 Wltbo Mlmjfts Wltbo Xjehat


37484 :444


7.127

m




:.85

-


4.58>

m

7.127

Tbhj : ln 74


Etjm X(t)

[aentjg

g (m)

:4

Gerjktelf

7

Mlmjfts

Tlrt


[tcg

344

4

344

4


Wltbo Mlmjfts =

4

Wltbo Mlmjfts =

344

Wbf ѳ =

Tlrt

-

344

Tlrt


Wbf ѳ =

344 7114.4

Wbf ѳ = =

4.4724

ѳ =

3.;:´

Tlrt

Oest ln taj saep es 3.;:´ tl plrt Bfswjr > Hevjf02

X (t) =

24444

3

IM (m) =

1.3:

;

IH(m) =

8.7:

Etjm

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

24444

8.7:

87:44

Geskabrhjg

-244

3.7:

-37:

Wltbo

5544

873:: Tbhj > ln 74



Wltbo Mlmjfts Wltbo Xjehat


873:: 5544


8.:42

m




1.3:

-


4.875

m

8.:42

Etjm X(t)

Geskabrhjg

g (m)

-244

Gerjktelf

>

Mlmjfts

Tlrt


[tcg

4

>44

4

>44


Wltbo Mlmjfts =

>44

Wltbo Mlmjfts =

>44

Wbf ѳ =

Tlrt

-

4

[tcg


Wbf ѳ =

>44 8734.4

Wbf ѳ = =

4.4145 ѳ=

7.>3´

[tcg

Oest ln taj saep es 7.>3´ tl stcg

Tbhj 8 ln 74


Bfswjr 8

Hevjf02 3

X (t) = IM (m) =

;

IH(m) =

24444 5.> 1.;

Etjm

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

24444

1.;

1;444

Geskabrhjg

-344

24

-3444

Geskabrhjg

-144

3.;

-2174

Geskabrhjg

-:44

:.3

-3>44

Olbgs

3:4

1

3444

Olbgs

3:4

23

;444

Wltbo

5444


12:>4 Wltbo Mlmjfts Wltbo Xjehat


12:>4 5444

Nefbo IH ln vjssjo = Nefbo HM ln vjssjo =

5.4>3

m



5.>

-


4.:;1

m

5.4>3

Etjm X(t)

g (m)

Gerjktelf

Mlmjfts 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

;344

3:44


[tcg Mlmjfts - Tlrt Mlmjfts Tbhj 1 ln 74


Wltbo Mlmjfts =

3:44

Wltbo Mlmjfts =

844

-

;344

Tlrt

Wltbo Mlmjfts

Wbf ѳ =

X * HM Wbf ѳ =

844 7174.4

Wbf ѳ = =

4.277> ѳ =

1.3;´

Tlrt

Oest ln saep es 1.3;´ Tlrt

Bfswjr 1 Hevjf02 3

X (t) = IM (m) =

;

IH(m) =

5444 1.5: 1.;

Etjm

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

5444

1.;

87844

Olbgs

>44

7

3744

Geskabrhjg

-744

5

-;>44

[aentjg Zp [aentjg Glwf

344

:

2444

;44

2

-;44

Wltbo

5344




87344 5344


1.4>:

m Tbhj 5 ln 74





1.5:

-


4.11:

m

1.4>:

Etjm X(t)

g (m)

Gerjktelf

Mlmjfts 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

;444

;>44



Wltbo Mlmjfts =

;>44

Wltbo Mlmjfts =

>44

-

;444

[tcg

Wltbo Mlmjfts

Wbf ѳ =

X * HM >44

Wbf ѳ =

1274.4 Wbf ѳ = =

4.48;8 ѳ =

7.33´

[tcg

Oest ln saep es 7.33´ [tcg

Tbhj 24 ln 74


Bfswjr 5 Hevjf02 3

X (t) = IM (m) =

;

IH(m) =

21444 1.5;: 8.8:

Etjm

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

21444

8.8:

2;5:44

Geskabrhjg

-2:44

>

-5444

Olbgs

:44

24

:444

[aentjg Zp [aentjg Glwf

:44

3

2444

144

3

-2>44

Wltbo

28444


2;7544 Wltbo Mlmjfts Wltbo Xjehat


2;7544 28444

Nefbo IH ln vjssjo = Nefbo HM ln vjssjo =

8.5;:

m



1.5;:

-


2.444

m

8.5;:

Etjm X(t)

g (m)

Gerjktelf

Mlmjfts 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

7744

>:44

Wltbo

Tbhj 22 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wltbo Mlmjfts =


Wltbo Mlmjfts =

>:44

Wltbo Mlmjfts =

3244

Wbf ѳ =

-

7744

[tcg


Wbf ѳ =

3244 2>55:.4

Wbf ѳ = =

4.23;> ѳ =

8.47´

[tcg

Oest ln saep es 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 Xjehat tl cj saentjg es 237.1t

Tbhj 23 ln 74


Bfswjr 22 Hevjf02

X (t) =

7444

3

IM (m) =

24

;

IH(m) =

5

7

Efetebo Oest =

:

Nefbo HM (m)

24

T

2

Efetebo HM =

IM

-

IH

Efetebo HM =

24

-

5

Efetebo HM =

2

m

Wbfѳ = =

HH' HM Wbf 24´

=

HH' 2

4.28>m

=

HH'

Etjm X(t)

g (m)

Gerjktelf Tlrt

Mlmjfts Tlrt

[tcg

84:.;

4.4

4.4

4.4

[aep

7444

4.28>

Olbgs

2>444

;

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

84:.;

4.4



Wltbo Mlmjfts =

4

Wltbo Mlmjfts =

84:.;41

Wbf ѳ =

-

84:.;

Tlrt


Wbf ѳ =

84:.;

Tbhj 2; ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W 34444.4 Wbf ѳ = =

4.4;:; ѳ=

3.43´

Tlrt

Nefbo Oest ln saep weoo cj 3.43´ tl plrt

Bfswjr 23 Hevjf02. 3. ;. 7.

X =24444t HM = 2.:m Efetebo oest = :´ [tcg Nefbo HM = 4.:m

Wbfѳ = =

HH' HM

Wbf (:)

=

HH' 2.:

4.2;2m

=

HH'

Etjm X(t) [aep

24444

g (m)

Gerjktelf

4.2;2

Mlmjfts

[tcg



Wltbo Mlmjfts =

2;23.;;

Wltbo Mlmjfts =

2;23.;;

Wbf ѳ =

-

Tlrt

[tcg

4.4

2;23.;

4.4

2;23.;

4

[tcg


Tbhj 27 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wbf ѳ =

2;23.; :444.4

Wbf ѳ = =

4.3>3: ѳ =

27.82´

[tcg

Nefbo Oest ln saep weoo cj 27.82´ tl stcg

Bfswjr 2; Hevjf02

X (t) =

3

IM (m) =

;

IH(m) =

1.;

7

Efetebo Oest =

1.:

:

Nefbo IM (m)=

5.;

Efetebo HM =

IM

-

IH

Efetebo HM =

5

-

1.;

Efetebo HM =

4.8

Wbfѳ = =

1:44 5 T

m

HH' HM Wbf (1.:)

=

HH' 4.8

4.24:

=

HH'

Etjm

X (t)

IH /g (m)

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 Tbhj 2: ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Nefbo HM = Nefbo IM ‛ IM ‛ Nefbo Nefbo IH Nefbo HM = 5.;m ‛ 5.;m ‛ 1.:m 1.:m Nefbo HM = 4.1m

Etjm

X(t)

g (m)

Gerjktelf

Mlmjfts 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

2115.3

2>44.4



Wltbo Mlmjfts =

2>44

Wltbo Mlmjfts =

315.3;;:

Wbf ѳ =

-

2115

Tlrt


Wbf ѳ =

315.3 >714.4

Wbf ѳ = =

4.477> ѳ =

3.:>´

Tlrt

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

Tbhj 2> ln 74


Bfswjr 27 Hevjf02. 3. ;. 7. :.

Gespobkjmjft = 2:444t IH = 1.8m IM = 5.:m Efetebo Oest = 24´ Tlrt G = 23m

Efetebo HM

‛ IH = IM IM ‛ IH

Efetebo HM

= 5.:m ‛ 5.:m ‛ 1.8m 1.8m

Efetebo HM

= 4.1m

Wbfѳ

=w*g X * HM

Wbf(24´) = w * g 2:444 * 4.1

Etjm [aep Olbgs Geskabrhjg Wltbo

X (t)

Gerjktelf

2:444 +:44 -;44 2:344

Mlmjfts T (tm) 322:

[tcg Tlrt

322:

[ (tm) 3:44 2344 ;844

Wltbo mlmjfts = [tcg mlmjfts ‛ mlmjfts ‛ Tlrt Tlrt Mlmjfts Wltbo mlmjfts = ;844 ‛ ;844 ‛ 322: 322:

Wltbo mlmjfts = 2:1: tm Wltbo mlmjfts = w * g 2:1:

= w * 23

2:1: 23

=w

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

Tbhj 28 ln 74


Bfswjr 2: Hevjf02

X (t) =

3

IM (m) =

;

IH(m) =

7

Efetebo Oest =

>.:

:

Nefbo IM (m)=

5.>

Efetebo HM =

IM

-

IH

Efetebo HM =

5.1

-

5

Efetebo HM =

4.1

m

Wbfѳ = =

233:4 5.1 5 [

HH' HM Wbf (>.:)

=

HH' 4.1

4.452

=

HH'

Etjm

X (t)

IH /g (m)

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 Mlmjfts Wltbo Xjehat


221;24 2;3:4


1.535

m

Tbhj 21 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Nefbo HM = Nefbo IM ‛ IM ‛ Nefbo Nefbo IH Nefbo HM = 5.>m ‛ 5.>m ‛ 1.535m 1.535m Nefbo HM = 4.>82m

Etjm

X(t)

g (m)

Gerjktelf

Mlmjfts 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

31:4.4

;>2>.>



Wltbo Mlmjfts =

;>2>.:>5

Wltbo Mlmjfts =

8>>.:>5

Wbf ѳ =

-

31:4

[tcg


Wbf ѳ =

8>>.> 1154.4

Wbf ѳ = =

4.41>3 ѳ =

7.5;´

[tcg

Nefbo Oest ln saep weoo cj 7.5;´ tl [tcg [t cg

Tbhj 25 ln 74


Bfswjr 2> Hevjf02. 3. ;. 7. :. >.

X = 1444t IM = 1.>m IH = 1.4m IH ln kbrhl = 24m Gestbfkj ln KO = 1m Sjsuotbft Oest = ;´

HM

= IM IM ‛ IH ‛ IH

HM

= 1.>m ‛ 1.>m ‛ 1.4m 1.4m

HM

=4.>m Etjm [aep Kbrhl wbsajg Wltbo

Xjehat (t) 1444 -x 1444-x

IH (m) 1 24

Mlmjfts (tm) >7444 -24x >7444-24x

Gestbfkj ln KLO (m) 4 1

Mlmjfts (tm) 4 1x 1x

Nefbo IH ln saep = Wltbo Mlmjfts Wltbo Xjehat

Nefbo IH ln saep = >7444-24x >7444-24x 1444-x ‛ IH Nefbo HM ln saep = IM IM ‛ IH Nefbo HM ln saep = 1.> ‛ 1.> ‛ (>7444-24x) (>7444-24x) 1444-x ‛ >7444 Nefbo HM ln saep = 1.>(1444 ‛ 1.>(1444 ‛ x) x) ‛ >7444 + 24x 1444-x ‛ >7444 Nefbo HM ln saep = >1144 ‛ >1144 ‛ 1.>x 1.>x ‛ >7444 +24x 1444 ‛ 1444 ‛ x x

Nefbo HM ln saep = 7144 + 2.7x 1444 - x Etjm [aep Kbrhl wbsajg Wltbo

Xjehat (t) 1444 -x 1444-x

Nefbo Mlmjfts = 1x Wbfѳ

= Wltbo Mlmjfts X * HM Tbhj 34 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wbfѳ

= 1x (1444-x) * HM

Wbf(;´) = 1x * (1444 ‛ (1444 ‛x) x) (1444-x) * (7144 + 2.7>x) 3:2.::8 + 4.488x = 1x 3:2.::8 = 8.53;x

;2.8 t =x Xjehat ln kbrhl wbsajg es ;2.8t Bfswjr 28 Hevjf02. 3. ;. 7. :. >. 8. 1.

X =2>444t IM = 8.:m IH = >.4m WTK = 3:t/km Efetebo oest = ;´ (Tlrt) Sjquerjg grbnt = 1.1m Trjsjft grbnt = 1.>m [pbkj bvbeobcoj es :m ln kjftjr oefj lf jetajr segj

HM = IM ‛ IM ‛ IH IH HM = 8.:m ‛ 8.:m ‛ >m >m HM = 2.:m Wbf ѳ = 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 rjquerjg ‛ Efetebo ‛ Efetebo grbnt Mbxemum pjrmessecoj sefibhj = 1.1m ‛ 1.1m ‛ 1.>m 1.>m

Mbxemum pjrmessecoj sefibhj = 4.3m/34kms 4 .3m/34kms Kbrhl tl olbg = WTK * Mbxemum pjrmessecoj sefibhj

Tbhj 32 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Kbrhl tl olbg = 3: * 34kms

Kbrhl tl olbg = :44t

Etjm

X(t)

[aep Olbg Olbg

2>444 x :44-x

Wltbo

2>:44

Gestbfkj ln K.O (m)

: :

Gerjktelf

Tlrt [tcg

Mlmjfts (tm) T 23:8.1 :x

[

3:44 ‛ 3:44 ‛ :x :x

23:8.1 + :x

3:44 ‛ :x

Nlr saep tl cj uprehat Tlrt Tlrt mlmjfts = [tcg [tcg mlmjfts 23:8.1 + :x = 3:44 ‛ 3:44 ‛ :x :x 24x = 2373.3

x = 237.3t Kbrhl tl olbg ef plrt segj s egj = 237.3t Kbrhl tl olbg ef stcg segj = :44t ‛ :44t ‛ 237.3t 237.3t

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

Bfswjr 21 Hevjf02. 3. ;. 7. :. >.

X = 23444t IM = 5m IH = 8.3:m Kbrhl tl olbg (w)=344t Ajbg ln gjrreki = 37 m bclvj ijjo Lutrjbka ln wabrn = 2:m

e) IH ln ajbg ln gjrreki IH ln saep g→

= 37m =-8.3:m = 2>.8:m

Kabfhj ef ^KH = w * g X+w Kabfhj ef ^KH = 344 * 2>.8: 23444 + 344

Tbhj 33 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Kabfhj ef ^KH = ;;:4 23344

Kabfhj ef ^KH = 4.38:m 4.38:m Efetebo IH ln vjssjo Kabfhj ef ^KH → → Nefbo IH ln vjssjo

= 8.3:m =+4.38:m = 8.:3:m

Nefbo HM

‛ Nefbo = IM IM ‛ Nefbo IH

Nefbo HM

= 5m ‛ 5m ‛ 8.:3:m 8.:3:m

Nefbo HM

= 2.78:m

Wbfѳ

= w* g (X + w)* HM

Wbfѳ = 344 * 2: (23444+344) * 2.78: Wbfѳ

= 344 * 2: 23444 * 2.78:

Wbfѳ

= 4.2>>8

ѳ = Wbf -2 (4.2>>8) ѳ = 5.7>´

Oest es 5.7>´ stcg

ee) IH ln gjki IH ln saep g→

= 24m =-8.3:m = 3.8:m

Kabfhj ef ^KH = w * g X+w Kabfhj ef ^KH = 344 * 3.8: 23444 + 344 Kabfhj ef ^KH = ::4 23344

Kabfhj ef ^KH = 4.47:m 4.47:m

Tbhj 3; ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Efetebo IH ln vjssjo Kabfhj ef ^KH → → Nefbo IH ln vjssjo

= 8.3:m =+4.47:m = 8.35:m

Nefbo HM


Nefbo HM

= 5m ‛ 5m ‛ 8.35:m 8.35:m

Nefbo HM

= 2.84:m

Wbfѳ

= w * gW (X + w)* HM

Wbfѳ = 344 * 8 (23444+344) * 2.84: Wbfѳ

= 344 * 8 23444 * 2.84:

Wbfѳ

= 4.4>8;

ѳ = Wbf -2 (4.4>8;) ѳ = ;.1:´

Oest es ;.1:´ stcg

Bfswjr 25 Hevjf02. 3. ;. 7. :. >. 8. 1.

X = 24444t IM = 8.;m IH = >.1m Kbrhl tl saent (w)=244t IH ln kbrhl = 24m Ajbg ln gjrreki = 31 m bclvj ijjo IH ln Olwjr Alog = 3m Efetebo oest = :´ Tlrt

IM = IH + HM efetebo IM ‛ IH IM ‛ IH = HM efetebo 8.; ‛ 8.; ‛ >.1 >.1 = HM efetebo

4.:m

= HM efetebo

Tbhj 37 ln 74


e) Wbf ѳ = w *g X * HM Wbf (:´) = w * g 24444 *4.:

7;8.7

=w*g

Efetebo Wrbfsvjrsj Mlmjft es 7;8.7tm tl plrt IH ln ajbg ln gjrreki IH ln kbrhl g→

= 31m =-24m = 21m

Kabfhj ef ^KH = w * g X Kabfhj ef ^KH = 244 * 21 24444

Kabfhj ef ^KH = 4.21m Efetebo IH ln vjssjo Kabfhj ef ^KH → → Nefbo IH ln vjssjo

= >.1m =+4.21m = >.51m

Nefbo HM


Nefbo HM

= 8.;m ‛ 8.;m ‛ >.51m >.51m

Nefbo HM

= 4.;3m

Wbfѳ

= w* g X * HM

Wbfѳ

= 7;8.7 24444 * 4.;3

Wbfѳ

= 4.2;>8

ѳ = Wbf -2 (4.2;>8) ѳ = 8.81´

Oest es 8.81´ plrt

Tbhj 3: ln 74


ee) Wbf ѳ = w *g X * HM Wbf (:´) = w * g 24444 *4.:

7;8.7

=w*g

IH ln ajbg ln gjrreki IH ln kbrhl g→

= 31m =-24m = 21m

Kabfhj ef ^KH = w * g X

Kabfhj ef ^KH = 244 * 21 24444

Kabfhj ef ^KH = 4.21m Efetebo IH ln vjssjo Kabfhj ef ^KH → → Nefbo IH ln vjssjo

= >.1m =+4.21m = >.51m

Nefbo HM


Nefbo HM

= 8.;m ‛ 8.;m ‛ >.51m >.51m

Nefbo HM

= 4.;3m

Etjm

X(t)

[aep [aent

24444 244

Wltbo

24444

Gestbfkj ln K.O (m)

Gerjktelf

Mlmjfts (tm) T 7;8.7

>

[tcg

[ >44

7;8.7

>44

Wltbo Mlmjfts = [tcg mlmjfts ‛ mlmjfts ‛ plrt plrt mlmjfts Wltbo Mlmjfts = >44 ‛ >44 ‛ 7;8.7 7;8.7

Wltbo Mlmjfts = 2>;.>tm Wbfѳ

Wbfѳ Wbfѳ

= Wltbo Mlmjfts X * HM = 2>;.> 24444 * 4.;3 Tbhj 3> ln 74


Wbfѳ

= 4.4:22

ѳ = Wbf -2 (4.4:22) ѳ = 3.53´

Oest es 3.53´ stcg

eee) Wbf ѳ = w *g X * HM Wbf (:´) = w * g 24444 *4.:

7;8.7

=w*g

IH ln Z.A IH ln O.A g↛

= 24m =-3m = 1m

Kabfhj ef ^KH = w * g X Kabfhj ef ^KH = 244 * 1 24444

Kabfhj ef ^KH = 4.41m Efetebo IH ln vjssjo Kabfhj ef ^KH ↛ ↛ Nefbo IH ln vjssjo

= >.1m =-4.41m = >.83m

Nefbo HM


Nefbo HM

= 8.;m ‛ 8.;m ‛ >.83m >.83m

Nefbo HM

= 4.:1m

Etjm

X(t)

[aep [aent

24444 244

Wltbo

24444

Gestbfkj ln K.O (m)

Gerjktelf

Mlmjfts (tm) T 7;8.7

>

[tcg

[ >44

7;8.7

>44

Wltbo Mlmjfts = [tcg mlmjfts ‛ mlmjfts ‛ plrt plrt mlmjfts

Tbhj 38 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wltbo Mlmjfts = >44 ‛ >44 ‛ 7;8.7 7;8.7

Wltbo Mlmjfts = 2>;.>tm (stcg) Wbfѳ

Wbfѳ

Wbfѳ

= Wltbo Mlmjfts X * HM = 2>;.> 24444 * 4.:1 = 4.4313 -2

ѳ = Wbf (4.4313) ѳ = 2.>2´

Oest es 2.>2´ stcg

Bfswjr 34 Hevjf02. 3. ;. 7. :. >. 8.

X = 2;444t IM = 1.8: m IH = 1m Kbrhl tl geskabrhj (w)=2:4t IH ln kbrhl = 5m Ajbg ln gjrreki = 33 m bclvj ijjo Efetebo oest = >´ [tcg

IM = IH + HM efetebo IM ‛ IH IM ‛ IH = HM efetebo 1.8: ‛ 1.8: ‛ 1 1 = HM efetebo

4.8:m = HM efetebo e) Wbf ѳ = w *g X * HM Wbf (>´) = w * g 2;444 *4.8:

2437.1 = w * g

Tbhj 31 ln 74


Efetebo Wrbfsvjrsj Mlmjft es 2437.1 tm tl stcg IH ln ajbg ln gjrreki IH ln kbrhl g→

= 33m =- 5m = 2;m

Kabfhj ef ^KH = w * g X Kabfhj ef ^KH = 2:4 * 2; 2;444

Kabfhj ef ^KH = 4.2:m Efetebo IH ln vjssjo Kabfhj ef ^KH → → Nefbo IH ln vjssjo

= 1m =+4.2:m = 1.2:m

Nefbo HM

= IM IM ‛ Nefbo IH ‛ Nefbo

Nefbo HM

‛ 1.2:m = 1.8: m ‛ 1.2:m

Nefbo HM

= 4.>m

Wbfѳ

= w* g X * HM

Wbfѳ

= 2437.1 2;444 * 4.>

Wbfѳ

= 4.2;23

ѳ = Wbf -2 (4.2;23) ѳ = 8.78´

Oest es 8.78´ stcg ee)

Etjm

X(t)

Gestbfkj ln K.O (m)

Gerjktelf

Mlmjfts (tm) T

[aep [aent

2;444 2:4

Wltbo

24444

(:+24=2:)

plrt

[ 2437.1

33:4

33:4

2437.1

Tbhj 35 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wltbo Mlmjfts = Tlrt mlmjfts ‛ mlmjfts ‛ stcg stcg mlmjfts Wltbo Mlmjfts = 33:4 ‛ 33:4 ‛ 2437.1 2437.1

Wltbo Mlmjfts = 233:.3tm tl Tlrt Wbfѳ

= Wltbo Mlmjfts X * HM

Wbfѳ

= 233:.3 2;444 * 4.>

Wbfѳ

= 4.2:82

ѳ = Wbf -2 (4.2:82) ѳ = 1.53´

Oest es 1.53´ plrt

eee) IH ln Kbrhl IH ln saep g↛

= 5m =-1m = 2m

Kabfhj ef ^KH = w * g X-w Kabfhj ef ^KH = 2:4 * 2 2;444-2:4 Kabfhj ef ^KH = 2:4 * 2 231:4

Kabfhj ef ^KH = 4.423m 4.423m Efetebo IH ln vjssjo Kabfhj ef ^KH ↛ ↛ Nefbo IH ln vjssjo

= 1m =-4.423m = 8.511m

Nefbo HM


Nefbo HM

= 1.8:m ‛ 1.8:m ‛ 8.511m 8.511m

Nefbo HM

= 4.8>3m

Tbhj ;4 ln 74


Etjm

X(t)

Gestbfkj ln K.O (m)

Gerjktelf

Mlmjfts (tm) T

[aep Geskabrhj

2;444 -2:4

Wltbo

231:4

:

Tlrt

[ 2437.1

8:4

8:4

2437.1

Wltbo Mlmjfts = [tcg mlmjfts ‛ mlmjfts ‛ Tlrt Tlrt mlmjfts Wltbo Mlmjfts = 2437.1 - 8:4

Wltbo Mlmjfts = 387.1tm (plrt) Wbfѳ

= Wltbo Mlmjfts X * HM

Wbfѳ Wbfѳ = 387.1 231:4 * 4.8>3 Wbfѳ

= 4.4312 -2

ѳ = Wbf (4.4312) ѳ = 2.>2´

Oest es 2.>2´ stcg

Bfswjr 32 Hevjf02. 3. ;. 7. :.

Gespobkjmjft = 24444t IM = 24.1m IH = 5m Efetebo Oest = 24´ [tcg Gemjfselfs ln tbfi = 23m * 23m * 5m

SG ln NX = 2.444

IM = IH + HM efetebo IM ‛ IH IM ‛ IH = HM efetebo 24.1 ‛ 24.1 ‛ 1 1 = HM efetebo

2.1m

= HM efetebo

Tbhj ;2 ln 74


23m

H

5m

23m

23m

H―

23m

Gestbfkj cjtwjjf kjftjr ln hrbvety ln twl tbfis es 23m e) Wbf ѳ = 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

Tbhj ;3 ln 74


ee

23m

;m 23m

H

5m

H―

>m ;m

23m

e = OC 23

23m

;

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 ; Tbhj ;; ln 74


Xjehat saentjg = 7;3t IH ln wjehat saentjg = >m + ; m 3 IH ln wjehat saentjg IH tl wajrj wjehat saentjg g↛

= 8.:m =-2.:m = >m

Kabfhj ef ^KH = w * g X Kabfhj ef ^KH = 7;3 * > 24444

Kabfhj ef ^KH = 4.3:5m 4.3:5m Efetebo IH ln vjssjo Kabfhj ef ^KH ↛ ↛ IH(s) ln vjssjo N[J ln 3 tbfis IH(n)

= 5m =-4.3:5m = 1.872m =+4.;7>m = 5.418m

Nefbo HM

= IM IM ‛ IH (n) ‛ IH

Nefbo HM

= 24.1m ‛ 24.1m ‛ 5.418m 5.418m

Nefbo HM

= 2.82;m

Wrbfsvjrsj mlmjfts guj tl saentefh = w * g W 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) Wbfѳ

Wbfѳ

Wbfѳ

= Fjt Mlmjfts X * HM = 3424.2 24444 * 2.82; = 4.228;

ѳ = Wbf -2 (4.228;) ѳ = >.>5´

Oest es >.>5´ plrt

Tbhj ;7 ln 74


Bfswjr 33 Hevjf02. 3. ;. 7. :. >.

Gespobkjmjft (X) = 1444t Xjehat saentjg (w) = :4t Wrbfsvjrsj gestbfkj = 7m 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 Wbfѳ = Wrbfsvjrsj Mlmjfts X * HM (n) Wbfѳ = w * g X * HM (n) Wbfѳ = :4 * 7 1444 * 4.771 Wbfѳ = 344 ;:17 -2

ѳ

= Wbf (4.4::1)

ѳ

= ;.25´

Nefbo oest ln taj vjssjo es ;.25´

Tbhj ;: ln 74


Bfswjr 3; Hevjf02. 3. ;. 7. :. >.

X =24444t IM = 8.1m IH = 8.48:m SG ln ANL = 4.5: Gemjfselfs ln jbka tbfi = 2:m * 23m * 3m Fl ; stcg nefbo slufgefh = 2.3m

2:m

2:m 23m

23m

4.1m 3m

3m

2.3m

HH'

ANL klfsumjg = O * C * (A ‛ (A ‛ slufgefh slufgefh ) * SG ln leo ANL klfsumjg = 2: * 23 * 4.1 * 4.5:

ANL klfsumjg = 2;>.1t IH ln saep IH ln ANL klfsumjg g→

= 8.48:m =-2.>m = :.78:m

Kabfhj ef ^KH = w * g X-w Kabfhj ef ^KH = 2;>.1 * :.78: 24444 ‛ 24444 ‛ 2;>.1 2;>.1 Kabfhj ef ^KH = 871.51 51>;.3

Kabfhj ef ^KH = 4.48>m 4.48>m

Tbhj ;> ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W 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 Wbfѳ = Wrbfsvjrsj Mlmjfts Ml mjfts X * HM (n) Wbfѳ = w * g X * HM (n) Wbfѳ = 2;>.1 * > 24444 * 4.772 Wbfѳ = 134.1 7724 -2

ѳ

= Wbf (4.2118)

ѳ

= 24.>5´

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

Tbhj ;8 ln 74


Bfswjr 37 Hevjf02

X (t) =

5444

3

IM (m) =

1.43

;

IH(m) =

8.:

X (t)

IH /g (m)

Mlmjfts (tm)

[aep

5444

8.:

>8:44

Olbgs

3:4

23

;444

Olbgs

2444

;

;444

Geskabrhjg

-3:4

1

-3444

Etjm

N[M

Wltbo

2344

24444




83844 24444


8.384

m




1.43

-


4.8:4

m

8.384 8 .384

Etjm X(t)

g (m)

Gerjktelf

Mlmjfts Tlrt

[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

2:44.4

24:4.4



Tbhj ;1 ln 74

KABTWJS ‛ KABTWJS ‛ 2; 2; OE[W Wltbo Mlmjfts =

24:4

Wltbo Mlmjfts =

7:4

Wbf ѳ =

-

2:44

Tlrt


Wbf ѳ =

7:4.4 8:44.4

Wbf ѳ = =

4.4>44 ѳ =

;.7;´

Tlrt

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

Bfswjr 3: Hevjf02. 3. ;. 7. :. >.

Gespobkjmjft (X) = 27444t IM = 5m IH = 8.1m 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) = 8.1m N[J =+4.2: IH (n) = 8.5:m IM = 5m IH (n) =-8.5:m HM (n) = 2.4:m Wbfѳ = Wrbfsvjrsj Mlmjfts X * HM (n) Wbf(1´) = w * g X * HM (n) Tbhj ;5 ln 74


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-

Tbhj 74 ln 74

Chapter 13 (List)

Recommend Documents