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Distance and Displacement &LJ»\ 

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s = 100 km 

Ad = d f - d t = 100 - 0 = 100 km 

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s — 100 + 250 = 350 km 
A d = d f -d i = -150 - 0 = -150 km 

s = 100 + 250 + 200 = 550 km 
Ad = df — d t = 50 — 0 = 50 km 


Linear Motion Equations if ^ \ o 

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m m 

di 0 Vi 5 o, 1.5 — 2 

s s z 

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v f ~ v i + at - 5 + 1.5 t 



:( 10 sec ) jju 


df = d t + v{t + -at 2 = 5t + -(1.5 )t 2 


v f = 5 + 1.5(10) = 20 — 

1 s 

d f = 5(10) + ^ (1.5)(10) 2 = 125 m 
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dj = 125 m Vi = 20 — a =? 

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= + at : 0^ 

■•• 0 = 20 + a(15) -» a = -1.33 ^ 

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d f = 125 + 20(15) +i(-1.33)(15) 2 
••• d^- = 275 m 

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v = 5 m s' 1 v = 20 in s" 1 


+ 

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25 50 75 


100 125 150 


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175 200 225 250 275 *(n) 


v= 15 m s 1 v = 20 m s" 1 



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.-. d fl = d t + 1 7jt + - at 2 = 15t (1) 

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d t = 7000 m, 17/ = -20 — , a = 0 

s 

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m 

Vf 2 = v t + at = —20 — 

df 2 = di + 1 7jt + - at 2 

.-. d /2 = 7000 - 20t (2) 

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d/i = d /2 

15t = 7000 - 20t 


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7000 

••• t = = 200 sec. 

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••• d fl = 15 (200) = 3000 m. 


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v f = Vi + at = 20 — 

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d/ = d t + v t t + - at 2 

••d/ = 0 + (0)(20) + i(l)(20) 2 


= 200 m 



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di = 200 m , Vj = v f = 20 — , a - 0 
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df = d t + v(t + - at 2 

d f = 200 + (20) (60) + i(0)(60) 2 

= 1400 m 

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d t = 1400 777 , 77/ = 20 — , a — —2 — 

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77^- = 77j + at 

0 = 20 + (— 2)t ••. t = 10 sec 

4J 

df = d t + v ^ + - at 2 
1 

d/ = 1400 + (20)(10) + - (— 2)(10) 2 
••. df = 1500 777 



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di = 88m , Vi = 20 — , a = 0 
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1 

df-± — 88 + 20 t + — (0)t 2 
••• d A = 88 + 20 t (1) 

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d/2 = ^(1)(44) 2 = 968 m 

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Free Fall and Vertical Projectiles 

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v f = 25 - lOt (1) 

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y r = 25t — 5t 2 (2) 

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v f = 25 -10(1.5) = 10 — 

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v f = 25 — 10(3) = — 5 — 
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0 = 25 — 10 t ••• t = 2.5 sec 



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y r = 25(2.5) - 5(2. 5) 2 ••• y f = 31.25 m 

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y r = 25t - 5t 2 = 25(1) - 5(1) 2 = 20 m 

:t = 4 sec J0U3 

y r = 25t - 5 1 2 = 25(4) - 5(4) 2 = 20m 

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Vf = -lOt (1) 

1 2 

y/ = yi + ^t--at z 

••• y r = 50 - 5t 2 (2) 

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0 = 50 — 5t 2 ••• t — 3.2 sec. 

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ty = -10 t 

•■• v f = -lOt = -10(3.2) = -32 — 

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2(5) 

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l— 2 sec x 

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y / = 50-15t-5t 2 ( 2 ) 


:y f = 0 £^3 


0 = 50 — 15t — 5t‘ 




St 2 + 15t — 50 = 0 


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l— 5 sec x 

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m m 

V/ — 40 m , Vj = —8 — , g = —10 -^r 
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y fl = 40 - 8t - 5t 2 (2) 

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y f2 = 12t-5t 2 (4) 

:(4) abU*J! lSjLJ (2) ^LwJ! J 

40 — 8t — 5t 2 = 12t-5t 2 
t = 2 sec. 

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y A = 12t - 5t 2 
y/2 = 12(2) - 5(2) 2 
••• y/2 = 4 m. 

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v f2 = 12 - lot = 12 - 10(2) = -8 — 

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Graphic Representation of Average and 

Instantaneous Velocity and Acceleration 

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v = — = =10 — 

At 10-0 s 


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v ~~Kt~ 20-10 _ °7 


. Ax —150 — 100 m 

£ = - = —- — — — = -25 — 


ft = 15 sec) jJc 4c vJI 


ft = 25 sec') juc 4c*JI 


At 30 - 20 



(* *, ~£) 


: (T) J&T • 

LjU**o 

.j^bejoJI 

* /s 4Jbsc lg*d jjjJo 3-AojJI Lo .1 

? yuaJJ 4> al-~c 

(t = 7 sec) 3 (t = 3 sec) juc 2Ubw)1 .0 

kJ*lo.g9 ,JM> ^ ~4S" j>- i^Jua .£ 


u^l 

aboVt ^ \biJJ 4JI ^z ,Jjj 3JLJI 4JjLj»J3 AJbwJI JJUu (jj jojJf -4c^*J!) J^o 

i_JUI aboVI ^ ^Ljj 4if al 

X2 sec)$ (0 sec) SjZaJI ^ jaaJU tyUo ZJbvJI j$s3 -\ 
:^*<Loj Syi jJT ^ J^oJI <4JbwJI 49jXoJ — O 


~ Y . ~ 


a — 


- 6-10 

6-2 



_ 10 — (— 6 ) 
a 8-6 



: (t = 3 sec) jOcabwH 


:(t — 7 sec ) juc 


I^UJIT Oj* 4JL=» j ,jf J&6 J^" i>° 

.(2 sec) SjuJ Zcj~j ax' f^sJI Iju S 
.Lijiu (4. 5 sec) *«LiUJI j*c LLi ^J>3y 4 ~ Ijj S 

(>5 *> ( 4 — ) JJcwJI (J-aj (i^JLJI) abuV! ^ £jLj ^ ^ 

.(6 ) aJtiJf (-6™ ) ^ 

(6.5 sec) j-ic LoUJ oisy (>s 2> ( 8 ■— ) Jjjwu $bl*i U \jj cJJi jju •f 
©buV( ^ Jlj Lo ^u?s)f (jV (S yaJI © JA ^ ^> 3-0 ^bLd! (j! 4a>V) 

.(L^jo 4 cwaJI £063 yJU! 

.( 8 ) L5 ^- (8 ~ ) £jLjj J lj»eJ 4(7^3 

(^vo jJf — %£j«J1 ) L ^S’t*c gobgj jjbcoJf ,JXjJI : (T) u |lio • 
MT (t = 0 ) ^dJI juc .(£ ) 3 (4 ) jJ,LJ 
: JXSJf 4(x = 0) ^ 03 -©Jf jJc 

Sj« Lugiaxo Ji I&Jwjz ^J! 2 b-fjVI y-o-l .! 

t (S) 

.u5>>f 

.4^fjVf © jjfc iAaC ©jLaa) JT 4CjaiJ .0 

^ 4>Lu>JI jjacj LugJ (^gi (4^1 jV! (j«ii lugJ jj! luguguu? pISJ .! 

ii CaLwj (t = 3 sec) iAac (^ 4 ) ©jL**JI 4^lj! j^tu ) 

d — v.t 



d — 8x3 = 24 m 2 l>La) 

(t = 4 sec) j4c (F) SjLJf 

- 1 

d = -x4xl2 = 24m 2 l>L*o) 


:JSL£J\ jx> .o 

^ = 8 ™ :(4) SjL-JI 4 cj-j 

t?g = 12 :(5) 8jLy*Jf <^cjy*> 


Motion in Two Dimensions Oi**i J? Jd ° 

^ olis OwJ b 4 aJUajoJI JJLxJf ^Js>- ^ Jo^Li J3 ^ Ji ol^LwjVI (jiuu wU joXaLj 
gckua |_vQ tgjAao l 'jIT pla^wj i^qJy^aJI aJt> ^jVI glauj^cl (1 

•(V*o «g&jl t>° 3 ^ JpJ^- 

• 4JL*oJf ^9 SUswaJf (ts-^cJI 4f ’j5eJ Umi M£4i (T 

^JL: jr fiboV ( 5 ^54Vl &buVf ^ V 3 V! ,**51! (T 
2L*jf yi Ols^^XaoJf ^ 04x9 lo/ lolw (Jju JSO 4f y?sJ( oV^Uc 4 J 3 SM ^*5)! 0^3^ (^ 

.j^di 

• O^JLb^JI £r(ps^wV LgO« ^ OV^lxoJI JsUjf (0 

=0) Jfr • 

.jJiVl ^ (53°) ^ 3(^3 (30 -j-) ZJijjji Zcj**j 6 £ Os4i 
.(1.5 sec) Jjw l^cj -^3 1 ^ 93 x 1 .1 
. 8 j£J! 4JJ J*aJ £l«j1 .O 

.SjS31 4jJ I J^a^yj ^yXoJ! .£ 



~ YY ~ 


.(19 77l) Mji SjSOi loAb ^C^J! 4 ?s£q \lS y> o 

u^l 

©jjco^Vif^ai 


(y) aba! 

(x) aba! 

y* = o 

Xj = 0 

m 

v iv = Vi sin 53° = 24 — 
s 

m 

v ix = v t cos 53° = 18 — 

m 

g = -10 72 

a x = 0 

:^T _psJ! OV^Uo ^ |^*flJ! a jA j£ 

(y) aba! 

(x) aba! 

v /y = v iy - gt = 24 - lOt 

S 1 *> 

CO 

II 

£* 

II 

sT 

1 7 

y/ =yi + v iy t--gt z 

Xf = Xj + v i3C t = 18t 

y f = 24t - 5t 2 

:(1.5 sec) 8y3( 2bj*j J 


:(x) ob?!^ 

m 

v f x = v ix = 18 — 

:(y) ©b*l ^ 

m 

= 24-10(1.5) = 9 — 



ACjjJi LuLj OJU? ,^-asVl abuVI ^ jls 1©/ 

. t^w^sUj jJsS AjjmjIjH 
Ux3o..cfi 

xy = 18(1.5) = 27 m 
y f = 24(1.5) - 5(1. 5) 2 = 24.75 m 

<1 yi«? (j! £lujl SyOf J^3 •'r J 

03^-j 





Vfy = 24 - 10 1 
0 = 24- lOt 


t = 2.4 sec 

3J^Lc ^ ^JJO jJf I ,j£ 


>y = 24t — 5t 2 

y f = 24(2.4) - 5(2.4) 2 = 28.8 m 

( 2.4 sec ) ©j ^ 4Jb- jJ( kJLsi 5 j£JI (jl Lw 

^LJUj <©AoJI ©*X& (J*ii ^ ^JjoJZZmS 

<3 AoJI ^Lo ^ <Uc ( 4.8 sec) o jS31 4Jb- y ^^JbOl 


: J3^\ 


x f = 18(4.8) = 86.4 m 

MT 4 S j-03 S jjo (19 m) ^IaJjVU S^£Jf yaJ^ o 


l(olj') I^ma; 4*ii$yi 4c jimJI (jaX^w 

m 


v f x = v ix = 18 — 

:^Ia5jVI Ij^J LJ^Pa ,jdoj ^bul Lie t^?o i4.MjljJi 4Cj»Ji oLeia 




>y = 24t - 5t 2 -» 19 = 24t - 5t 2 

5t 2 - 24t + 19 = 0 :^LoJ! oaleb 3 





ty y = 24 - 10(1) = 14™ :( 1 sec) j©u 

v /y = 24-10(3.8) = —14™ :( 3.8 sec) j«j 3 

.SjSOI ~4f ijLa^db jjdJCiil 


y, 



24. 75 m 


77 YSSSSJJsssJss 7 7/ s 


'\sssss?~s//ss/sss//s 


x 


~ vt ~ 


mju* • 

(40 — ) 4Jljujl 4 c £ tbu*i (jjj 

jjw Isobo |»jia*^! ^ • J^sV! (53°) 203(^3 
JCiJb US' (B) 4kaJI jUc (96 m) L*o 

.j^btcJI 

£tbuj J£ (F) 4kaJI .1 

.JsubcJb 4o!ai£U?l 4la,pd ti^AcoJI 4 C j*j ©b«!^ jl Aco .0 

i^kXacJU 4^3 V f 


(y) abu! 

( X ) abuf 

y, = 0 

Xi = 0 

m 

v iv ~ v i sin 53° = 32 — 
y s 

m 

v ix ~ v i cos 53° = 24 — 

m 

a = ~w T2 

a x = 0 


‘.^^Sju> aS' y?J! OV^bw3 

(y) abu! 

(x) abu! 


V/ y = v iy ~ gt = 32- 10 1 Vy x = v i3C = 24 — 

y f =yi + V iy t - ^gt 2 x f = Xi + v ix t = 24 1 


yf = 32 1 — 5t 2 

:(1?) 4k*J( J^c l^^XaoJI J^?3 uL> ULCoj (_5JaJ! 5J^bio ^ .! 

xy — 24 1 -> 96 = 24t ••• t = 4 sec 

^J^bw lJ ,ji«3*Jb3 

y r = 32t - St 2 = 32(4) - 5(4) 2 = 48 m 


W^^mWWTTTTT^^^ 


96 m 


~ Yo ~ 


:Ja3beJb pf tdxxJ M. iLSiV! ac^J! .o 

m ^ N m 

v fx = 24— ,i7 /y = 32 - 10(4) = -8- 

I4JLag«Jf jjaiJ-j b^ca 

v = V24 2 + (-8) 2 = 25.3 J 

tan 0 = — = — ••• 6 = -18.4° 


2bj! (100 m) f jJLo 

4k«sJI Ju£ Jsubu pjda^l^ . J^iVI (37°) 
4kflJ! OilT lij . JCUb UT (8 sec) jou (.4) 
(20 m) ^LaJjf (i4) 

-Jpfo 

zjijjjyi Zcj»ji ,i 
.Jj MkVf <^5^> (j£ 4»b?dU ^Vl JjuJI .o 

ici^JdoU 


(y) abu! 

(x) abuf 

y £ = 100 m 

x t = 0 

v iy = v t sin 37° 

v ix ~ v i cos 37° 

m 

a = -^ T2 

o 

II 


4 f j^di OV^lxo^ 

(y) abu! 

(x) abuf 

i7 /y = sin 37° - lOt 

Vfx = v ix = v t cos 37° 

yf = 100 + (y>i sin 37 °)t — 5t 2 

Xf = Xi + v ix t 



Xf = Vi cos 37° t 


: (yf) 2Uabw ,jdo ZJIJJjyi yJ\ uL» LXw J 

: 0' Iaj 


yy = 100 + (i7j sin 37°)t — St 2 

20 = 100 + (v i sin 37°)(8) - 5(8) 2 
m 

i7 £ = 49.8 — 

‘ s 


iJsubtlf Jju .o 


Xy = i?j cos 37° t = 49.8 cos 37° (8) 
••• %y — 318.2 m 


$ 


mM • 

Ijcj f (40 m) ©y 

4la^dUI ,j*ii .(30°) (20 — ) 

4Xj0 l5j^^ (90 m) 3iL*o jjuj 

^c_y*> . JX£ JU LuT <S j£Jf 3^si 


r//sy////////, 

.(jbjVl JguLJ l^I JJ SjXJb jJL*cVI 

: u UM 

.^b-jjlq SjSOI ^yj ^yojJI !_j1 L5 & 4ol*JI ijS^all 


(y) ©bo! 

(x) abuf 

yi = 40 m 

o 

II 

K 

m 

m 

Vi V = Vi sin 37° = 10 — 
s 

= i7j cos 30° = 17.32 — 

m 


g = -10 T2 

o 

II 

a* 


:l$J ysJ! OV^lxo^ 


~ YV ~ 


(y) abu! 

(x) abuf 

0 

1 

0 

II 

Q) 

1 

>> 

S' 

II 

S" 

m 

Vfx — v ix = 17.32 — 

1 , 

y f =yi+v iy t--gt z 

Xf = x t + v ix t = 17.32 1 

y f = 40 + lOt - 5t 2 



JLoJfcb < jiuaJJ UjL*« ( y ^IgJf IgcLujf ^Jy-w ^ o^alb SyOl ^3*23 XLc 

.l$J J^Jf JLmoI ^bosJ oj<ibJ« ^LbjV! 

y 7 = 40 + lOt - 5t 2 
0 = 40 + lOt - 5t 2 

:SjSJ ! ,J5^3 (jdoj oL^sJ 4 *x*jyJf V^lxxJI J^«3 

-(10) ± V(10) 2 - 4(— 5)(40) 

' " 2(-5) 

. t = f+ 4sec v 

l— 2 sec x 

I 4 JJ ^^XJI t gflsy I iAxa)I 3^wj 4^03 

= 17. 32t = 17. 32(4) = 69. 28 m 

d = 90 — 69.28 = 20.72 m :Sj£Jf ^jc »a« ^ 3X^3 

Ad 20.72 r „ m ^ ,, ,, 

V = M = T - = 5-2 7 :(»j!wUo) «uc^ 03XL- ^UJb3 

:(o)J& • 



.( 53 °) 203^3 ( 20 ™) aJlJCJl < xgj»j S/OJTj 
UX ( 37 °) ^3! jj j f t\s>- ©3^sS Jb-jj Igil 4^3! 

.JCiJb 


^baJjlq Ujo 


~ Y A ~ 



:Sj£V~ 4 JlJCjyi 

(y) cbuf 

(x) obcj! 

y; = o 

Xj = 0 

m 

v iv = Vi sin 53° = 16 — 
s 

m 

1% = C05 53° = 12 — 

m 

g = - 10 T2 

a x = 0 


:l$J 4 /" _psJf 

(y) &b«1 

(x) abuf 

V/ y = v iy - gt = 16 - lOt 

m 

Vfx = Vix = 12 — 

1 2 

y f = y t + v iy t - -gt z 

x^- = Xj + = 12t 

y f = 16t — 5t 2 

:c 

install Z$bd a jXJ! ^3*^3 jjjoj V3? 

Vf v 16 - lOt 

tan( - 37) %;:= 12 - - 

t = 2.5 sec. 



x f = 12t = 12(2.5) = 30 m. 

:£U?jyi 

y / = 16t - St 2 = 16(2.5) - 5(2.5) 2 

= 8.75 m. 


Newton's Laws Motion iS y* y? o 


:3JUJf £*if ‘0^5^ ^aijCLoJI JJL*oJ! £o ^^Uobw j^c 

.4a***x (JXmi 4JLjcJ1 ( 1 



ls^* £^3 (f 

II L**?» 0 LjIA>V( y»-\ ^ 

:uriw fv^J! oir lil J 

.^jbJJ j*L)_ i£j^\ ^!b fibuVI -L®j!^— S 

. jjLaJL) 4jqL^i fibuVI ^ (^c S jJ^oJI i£$aH JJ' £up-( ^ 

.t^UAT j^ a iJ 4jgL^ ^iyi aboVI ^ ^Jlc S jt-oJf i^aiiJJ u tT 

:IT _ps*o f^?sJI ijlT lij Ul .0 
.Lcj!^ If j?d1 ©bul 3 A t„ r ^>'^oJ( ©b«y! S 
. (mcC) J 4jaL^i I^JU»lq ~*£ _ps Jl abul ^ i^c SygjoJI (JT £©^-! ^ 

. j^aU 4jgL^ Uixg-lg ^£**> 1 y ! fibuVI ^ ^ Lc 8 y^oJ! (£yi)l ,jr ^o^-f v'' 

.,J!^*J! ^ o^JlxoJI oL*?sJ l^juu ^jo OV^bwJI 4»jj! (1 
.aA> tjf ft 3 ^JbeJI oAfe (,>»«> ^yo ^3X0 fUguM Ci\S" I^J (0 

KDJ^ • 

(V z&ui ^gLc £ 3 * 33 ^ (100 kg) 4 jJjS* (u**^ 

LX J^sSM ^0 (37°) 433 1 j (F) 83 a? 4x3^ 

^^(3 iJUC^V! JUbw jlT !i! . jcau 

:JWJc (0.4) 3 (0.5) La 
. 4f j^di |^?sJI CLjqj i^w^u (F) ^XaJI 83 HJ 4oJI ,^*331 .1 

.JIX^V! 835 <(F = 500 N) OolT !ij .0 

. ,*■*!! 4bwJI 4 (F = 1150 N) Ooir lit .£ 

^F 

4 ^ 33^1 |^?tJI ^^JL; Sjj^oJ! jA) J 

:0l9 Jw |^J i^scJt LJ 3 tfts— j jJf ^^JL: 

I^^asVf &buVI ^ ^ 3 *JI £ 3 ^X 0 


wmw/mmmwm 



F x - F cos 37° - f s = 0 


~ r * ~ 


F x — F cos 37° — g s N = 0 (1) 


F y = N — F sin 37° — mg = 0 
N = F sin 37° + mg (2) 

:(1) (Ai ) 4rfu9 


F cos 37° — g s (F sin 37° + mg) = 0 
F cos 37° - (0.5) (F sin 37° + (100)(10)) = 0 
F cos 37° - 0.3F - 500 = 0 
0.5 F = 500 F = 1000 N 

:(1) ^J^lxoJI ^g9 0^5*^ .o 

F cos 37° — f s = 0 
••• / s = (500)cos 37° = 399.3 Af 

3^0 iJ jjdo £6*3(3 ^£t> 

N = F sin 37° + mg = (1150)sm37° + 1000 
••• JV = 1692 /V 


F cos 37° — fa = ma 


F cos 37° 


/fc 


a = 


(1150 cos37°) - [(0.4)(1692)] 
100 


2.4 m/s 2 




JjU 03 (m — 10 kg) 


(F) S 3 S OjJ? tit . JCiJb ur <(0. 4) y* (53°) ^ 3 ! jj 



4,JjU)JI ^3^**1) 
^glc ^^5^ *^yy?w (F) ©3^0 4 <u 9 Jil .1 

. jawSu jyjiyi 

wl^j (F) S 3 .aU 4cwJ ^£* 2,91 .O 


~ n ~ 


.(0.35) JOC^V! Jobwj t (F = 150 iV) OolT !i! ^1 aUc .£ 


-hjjM t| _UUJI 4JI^- :^o 3Ia>Ma 

jjpwJi L.jjXj 

b^VQ-c (v) j,qJ?«Jlq oda^j Ujlam fx) 

.<ulc 

3JbsJI © jjb ^ ^^JL: .1 

.j^btoJI JXiJI ^ 

:(x) sbof 

F + f s — mg sin 53° — 0 
F = mg sin 53° — g s N 
F = 100 sin 53° - (0.4)iV (1) 

:(v) abul 

N — mg cos 53° = 0 

N = 100 cos 53° (2) 

:(1) ^ (iV) 4<u9 

F = 100 sin 53° - (0.4)(100 cos 53°) 

F = 55.79 N 




JjCi J! ^ 4JbsJI ©AgJ i£$sl I >ktla?w .o 


:(x) ©bol 

F — f s — mg sin 53° = 
F - f s + mg sin 53° 
F = g s N + mg sin 53' 


~ n ~ 


F = (0.4)iV + 100 sin 53° (1) 

:(V) sbol 

N = 100 cos 53° (2) 

: (1) 4J^lxoJI ^ ( N ) ioJj 
F = (0.4)(100 cos 53°) + 100 sin 53° 

F = 104 N 



:f*) obol 

F — f k — mg sin 53° = ma 


F — g k N — mg sin 53° = ma 
F - g k N - mg sin 53° 


150 - (0.35)N — 100 sin 53° 
' 10 


N = 100 cos 53° 


■( 2 ) 


150 - (0.35)(100 cos 53° ) - 100 sin 53° m 

a = — = 4.9 — tt 

10 s 2 



: (jl Uu 


:oi! 


(m 2 = 3 kg) 3 (m ± = 9 kg) jlo~^ 

Ua gzbuJ\ U^yj ^ L5 i3£*Jf 


~ rr ~ 


^ C)/\ ( 37 °) 4 * 3 ! j <wu (F) 033 (°- 4 ) 3 (°- 5 ) 

.JCiJb UT J3VI 

. 4 /" ^Jb l^*j> ( f ) 4 <u 9 ^^all .1 

:^l t (F = 75 N) OJir !i! .0 
.plkJf 4 Jbsc .1 

.(T)-kupdl .r 

u^l 

JT Sji^l ^3^! JJbsi; (*3*^ J 
.^ 53^1 oiA* ^*i? 3 J j 3 btoJI 



: J 3 ^f i^wj’dU 2 u*Jb 

l(x) obol 


F cos 37 ° — T — f sl = 0 
F cos37 ° -T-n s N = 0 




Ai = 90 -F sin 37 ° ( 2 ) 

:( 1 ) 4 J^lxoJI ^ (Ai) 4 <yi ,ji« 3 AJb 3 


F cos 37 ° - T - ( 0 . 5)(90 - F sin 37 °) = 0 
F cos 37 ° - T - 45 + 0.3 F = 0 


1.1 F — 7 — 45 = 0 ( 3 ) 


:(V) sbul 


T = f S 2 

= n s N = ( 0 . 5 )Ai 


:(V) sbul 


~ ?i ~ 


N = m 2 g = 30 N 



7 = (0.5)(30) = 15 N 

:S y^cJI uL^l (3) 4J^buJI ^ JwJ! cai ^ 

1.1 F - (15) - 45 = 0 ••• F = 54.5 N 

— ^TjpeJI ^JLc py<*geJI L 'jaio LoJoc JwJI Sai 3ia>Mo 

^ jylH Sai i^aLi y — (f)^JjpeJI ^ U/~ 

:(F = 75 Ai) 03 ^ Ua*c .0 



:^*5eJI 4Jbsc . 1 


jjXJa '4«LJI jjXj 


:ol ,j<a« ^0 

: J3V1 f^-^dU 


F cos 37° — T — f kl = 

F cos37° — T — g k N = m-^a (4) 

;(iV) S^aJI 4 jojJ ^M^ej c _ s — a fjJf fibuVI 

Af = 90 - 75 sin 37° = 44.86 Af 

:(4) ^ l^Lc 

(75) cos37° -T- (0.4)(44.86) = 9 a 
59.9-7-17.94 = 9a 
41.96 - 7 = 9 a (5) 


-UwJba 


T-fk 2 = m 2 d 

7 = m 2 a + [i k N ^ 7 = 3a + (0.4)(30) 

7 = 3a + 12 (6) 

:(5) ^ (6) jyiJ! S^s ,ji«^Jb 

41.96 -(3a + 12) = 9a 



9a + 3a = 41.96 -12 


~ ro _ 


:(6) ^ :jyiJ( ©^5 .f 

T = 3a- 12 = 3(2.5) + 12 /. T = 19.5 N 

WJ** 

(m 2 = 2 kg) 3 (77^ = 5 kg) oLws- 


^JUlxc . Jsu^u lug^axo |jl^3Jj* 

(t 71 2 = 2 kg) j-j l5 T_ J5SJI3 

(0. 6) 3 (0. 7 ) Ua £tk*J! J-J3 

. jcau ur 


iJy (jl JJj ( 7712) l> ^lc IgJA; jj£w ( f ) 4 <u 9 .f 

.(F = 70 N) ByyoJI B^aJ I (J3X2 Ua*£ ^Jbccg jJUf &3i .0 


Oe*^ |^*> c _ s JLc S .1 
.j 3 bwJ! JXiJ! 

py^^gcJb UjI^ I Jo I ydl ,yi ^gJJt I Afe ^ 

. 4 Ubo ! ( jJbuJI 


T — m 1 g = 0 
.-. T = 50 N 

T + fs-F =0 


: J 3 VI ,^-lc iyyfJI ^ 3 *JI 

(^JL: oyyaJi ^ 3^(3 
:Uil 


T + f s -F =0 ^F = 7 + /7 s yV 
••• F = 50 + (0.7 )N (1) 


N = m 2 g =20 N 


1^3 Li Zj^yojd! S^aJi :L*>!j 


~ n ~ 


:( 1 ) ^ Ig^c 

••• F = 50 + (0.7) (20) = 64 iV 

iJjCiJb U if 4f j?d1 abw! jjl9 (F = 70 N) UAb .o 



iJjlxcJf 4**Jb 

T — m 1 g = m ± a 
T = 5a + 50 (1) 

F — T — g k N — m 2 a (2) 


:( 1 ) S 59 ( j£ ( 2 ) ^ (jiu^Jb^ 

70 - (5a + 50) - (0.6)(20) = 2a a = 1.14 ^ 

s z 

:( 1 ) 4J^lxoJI ^ 0 ^ 5 *^ <lsu3sJJ ^ bX^Jf S 39 4<u9 


••• T = 5(1.14) + 50 



T = 55.7 N 

:(e) J& • 

(m 2 = 10 kg) 3 (m x = 3 kg) jU-^> 

. |a j5Cl}b l^T -ktbu Lc^axo ijMj&c 
bjXo jelliuJf (J-ol^o ,Ji! 3A lc 

!? 

,^-lc 4su> J/' ^ JJUf ^39 J^joj 

.^LJI ^ (■***> J^" 

^^JL: |^> ,jr <2&U! ^ LuT 


.aAa>- 


~ rv ~ 


: JjVl J&t 
— ( 1 ) 


T ± = m 1 g = 30 N 


T 2 =fs 

T 2 = g s N = g s m 2 g = ju s (100) 
(2) 

*^bLT ^ ol^?sio JJbw) £3*23*^ ^ 

C^tPy ‘J^bJI JXiJf ^ JwiJI ^cai oI^cmo JJbci dil£ob t^+ijJudl 
.oM*M oJ&> £^0 3iaii<L}1 VI 31wi (J3O 

l^^-asVl abuV! ^ ^3®}! 

T 3 sin S3 — T 2 = 0 -> 7 2 = T 3 sin S3 (3) 

jJI fibuVI ^ ^3^! 


T 3 cos 53 — T ± = 0 -» T 3 — - 


30 


- = 49.85 AT 


cos 53 cos 53 
:(3) 4blxoJ! ^9 ( T 3 ) 4©J j£ ^ 3*^3 

r 2 = ( 49.85) sin 53 = 39.81 N 

:(2) 4J^lxoJI ^ (T'2) i<u 9 ,j£ <4*03 

(39.81) 


Ms = - 


100 


-= 0.4 


Ols ( 0.4) Js! JUC^V! Jobw 2 UJ v^olT li! 4if 

.(j! jJVI ^LJb^ Jpjiyw 



: 0)J^ • 

oUbw (m 2 — 6 kg) 3 ( 7 % — 10 kg) 

I® Usui I 4 JL?c£ ^*^1 .JiCiJb LuT pLJLo S ^335 jxj 

..ku^dl ^9 JwJI 03 9 t^Uj^3 


~ va ~ 


Jj*** 1 J3V! f&**£*Jt OM J^b> <J*> 

. JjCiJI ^£. 4^33^) 4T _pJ! ©bcil 

: J 5 Vl f^JU 2L*Jb 

m 1 g — T — m-^a -> T = 100 — 10 a (1) 

i^UJf fv»^3 

T — m 2 g = m 2 a -> T = 6 a + 60 (2) 

jJ-yd^lxoJ! (J^l LS^* -bu2s)f *X£JI 035 (Jl Lw 

: (2) 3 (1) 


100 — 10 a = 6 a + 60 


.-. a = 2.5- 


IhXwJf O 33 Ulw3d iS^l ^ 

7 = 6 (2.5) + 60 = 75 N. 

lOU^ 

(m 2 = 5 kg) 3 (m x = 3 kg) oU-^> 

©33 .(jJU! ^Ic ^jL: 3 m? 3^3 la^u Lug<3u^j 

UT (20°) 2 ^ 3 ! jj (m 2 ) Cj/\ (F = 10 N) 

.J£i)b 

l®f .? 

!?(Ja*StI 

^3 JwJ! ©333 i&llaJf 4Jbec .0 





!!!! 3 ^d jjlT (jL**?sJ! (jb ,JX£JI ^ lo 03 ^ ^ •! 

JT ©y^oJI ^isVl JJbb 
‘d)J 3^ ^*^3* t gfe 4^©t«<j 1 yJ( ©3^1 !(jllj) |^«*»|dU 4 mmJ(j 

m 1 g sin 30 = 15 iV 

«UaSVl ©3©) I 4 4 ^?s*J' ^yjf ©3^)1 (Jjl 9 (in 2) Lot 

F cos 20 = 9.4 W 




. Vf ^6 jjlflJji**! ijL) J-9 si 4io 3 

Jf JJL?bJ O-y’w (<&?LJf 4JLtoVl ^ of^ls^dl ( j«ai ^Jl iJjJI caia 4JbwJI uL^i .o 

.(7 1 = 12.7 N ta = 0.66 m/ 5 2 :2ub-V!) .& ,^-JL: (**£>■ 



^^30 [■slia.JJ 4ojMJI o^sJi yw->l 

^dxS^\ £*©^ 5 ) (Ffc = 0.3) (jlf* !i! 2 UjO 

3 (m A = 6 kg) fL^Vl Jtfj 
•(m 8 = 2 kg) 
U*>! 

.j 3 btoJ( JX^Jf ^ 4^?^ (U**^ S ygjoJI 


'. (i4) 4 *M*aJU 

F-T~f kl -f k2 = 0 
F-T- g k ( m A g + m B g) - g k (m B g) = 0 
F — T — 0.3(60 + 20) - 0.3(20) = 0 
F-T - 30 = 0 (1) 

'.(B) 4^~Jba 

T = f k 2 = ft(m Bfl ) = 0.3(20) = 6 N 

:(1) ^IxcJf ^ J-iJ! 4a*3 J£ 

F = T + 30 = 6 + 30 = 36 N. 





, glc (ttl — 2 kg) 4 jSjS~ 

JoUo . JCiJU ur (M = 4 kg) 4JUT 
<(F fe = 0.2) jdsu/V! ^TpsJt JOC^V! 
:4JL> jr ^jMJ! (F) S^f 2uJ 


- i * ~ 


,^-30 J 

.(a — 2 m/s 2 ) 4Jbt« .o 
(F = 36JV .o 4 F = 20 JV J :2bb-VI) 





jM^c (m 2 = 8 kg) 3 (m-L - 4 kg) jU-^> 
JJLo ^3 (jAyjMJ (jlflJj-03 >ku?o Lo^axo 
U*wo JUC^Vf JUbw .( 30 °) 4*3! jj 

£da*JI jJ*^3 

.Jsu^cJI ^ JuUI ©3 53 ^UsuM 4Jbsc 



(T = 


T = 5.84 JV 4 a = 1.4 ™ :2ub-V!) 

uxu^ • 

(m 2 = 8 kg) 3 (mi = 4 kg) jlw- 

3Jw*to0 U^« h xo (jVL^uUi 

Li* ^jdjLog QmJU)! 

.JjCiJU 

.4a*2cJf ^9 JUJI ©393 |»UaJI 4JbsC 

.25 JV < a = 2.45 g- : 2 bb-y!) 


:(1) ^_yoJ • 



(m x = 2 kg) ^am+s* £3*233 ^bwJf ,J£iJf 
.kujju U^flxo jjJLaio (m 2 = 4 kg) 3 
(m 2 ) .jjJLol jj*c3-i?3^3 

(0 = 25 °) 4)3 ! jj JJLo c _ s JLc ^3-i?3^ 

433! j £**333 (F = 26 ) ©39 4 Jlc ji’333 
.(JjLJI (Xo (a = 15 °) 


Ol 1 CQ 

EM 6 




• 4sui?dl ^ JwiJI oa.Sa 4Jbsc 

(F = 2.74JV , a = 1.37 ~ AWI) 



: (°) 04^ • 

^istyj t J.C £3*33.0 (771 = 2.1 kg) 4*JUJ”” 
kj! (F x = 5 iV) S3S 4-dc o y \ ;,jJLof 
(F 2 = 7 N) I ©333 <(0! = 40°) 

. JiCSJb UT (0 2 = 25°) 


.j^o-^dl 4Jbsc J 
^IsuJi l$> £ 3 } ^J 1 4j^ajc^JI S^-aJI .o 

(iV = 0.26 JV <a = 4.84 ™ $ub-V1) 



: 0) • 

3>f -Jsu^ 4 Jomi1^j Jjlxc (m^ = 1 kg') 

4 jj( jj ,JjU (j-JUl ^da*o (^Ic £3*33^ (777.2 = 2 kg) 
S3S3 flbJf 2Ubac . j3 bwjf JXiJU ur (0 = 20°) 
.Isuid! ^ JwJ! 

(F = 4.4iV 4 a = 5.6 ^ :2bb-VI) 


: ( V ) * 


£3^3-0 (m B = 3 kg) p»*=r ^ 



I^mTu ,kw?w ,J^**3 ,jJL>! ^daw ^glc 

(m c = 1 kg) fv-jpdl .J>1« (m^ = 2 kg) 
S3S l&gJ*?3 (tub) £3*33 * 

.fUaJ!2U»: .? 


.U* jjA^Jsdl i 0 n c) 3 ( m B) J-rf J^slxo .O 

( /* s = 0.33 4 a = 3.33 ^ AWI) 


~ £Y ~ 


Kjj£>\jS\ o 


Uniform Circular Motion 

:^JU)f of^la^l jLceVI ^ (3jj3f Jjf j5>dU 4 aLcuJI ^Jsw ^w> wULbu jLc 

.|^**3s)l ^^Ic ojgjoJI 2^3 0 

4g2e^oJ! 4*J>^o jT yJf ^ei 4g2s*oJf ^^aJI jL*cf £o kjT jaJI £M>4 (V 

,(mff) _J IgJL^ 4 JLi / j^JI jc fju« 

.jLal J kjL** IgJbol^ (jJ>j (j!) j^di obdi ^^i/l jJT ^o^-l (f 

P)Jfr * 

ls® 0^J3^ ^LaJj (HjSIjJI y> l^sl jl?! jjjJo v^*?w j3^ (0- 8 m) Lac 


2LJLUf 

.(— j— ) Sj^-^j 4j^I jJ! l^c j»j .! 
.LaaJ! oLa^L ^ £<u 4bii jLc 4Ja^dl 4Cj*JI .0 
.L a aJJ >Vf cijiaJf JuC 4Ja5»dl 4Cj*JI 




:<ji! ‘(2 rad) (jl lw .1 


rev 27 t rad rad 

a) = 2 = 2 = 12.6 

s s s 

:(r = 0.4 m) jLc 4*kisJf ^c^-J! .0 

v = oj.r = (12.6)(0.4) = 5.04 — 
s 

:(r — 0.8 m) jLc kkid! ~Ac.yJ\ .g 

v = o).r = (12.6X0.8) = 10.08- 
s 


jjc l&Juu JmJJ 6 ZhJai ^JaiJf 3cj*JI ,JLcJ! ^ 4a>MJ 
4jjI jJI %Cj«J1 loJL* jT 



~ tr ~ 




4 c (r = 45 cm) l& oi*cj 5 yo 
^ 1 ^ 5 ^- t-aJ .(6 — ) IAjIj^o 2 uj 0 4j^lj 

IgxkvL*) 43L*cJI U . JXiJb LX 4c>lgj 

? ijl^j oMj Jju 

u*n 

ojCJi 43 bd Jb^JI 

v = o).r = (6) (0.45) = 2.7 — 
s 

4C j**» wll jXa (SyCJf 43 1> ^glc <0(3 453 ^ 3cja*i ^C^Lj' oA& 

lg*LiLw 43UJI (J^Xam) I 3L03 (Jrf^sJb ,J*£&0 4j 3X I 

s = v.t = (2.7) (3) = 8.1 m 




=(HJfr * 

>>T J-^o ( r i = 10 cm) ^jCji 
LX ^^Llbw (»l)> (r 2 = 30 cm) 

jJU?SM ^3! jJ! ^£yJ\ OiX lij . JXiJb 

^i^ijJi 4c^**J! — 1.2 — ) 


.y'Vi 


Sja 3 ^ 45? *^wj> (j^yi jjc 4flLbw ^IjJI 3c^*JI ijO ^tbl3 

.4clbtO U (3 J (j^C * jojf £0*0J W) 4 aLj 

(jls <L 4Xoj Sys ^ 4 Ljw> 4p-lj! ^jupSM (jtfjflJ I ^3b- OjIa !ij ‘JXJ 3 
J^fl-uAi ^ 0 ^X 3 5 jZaJI aA& ^gS 4^-f jV! jjwfli ^IsuLai (^LUaoJ! pf j^sJI 


~ a ~ 


4Ja5jsJ! ijJJjJ ' 3 ZJz&dl 4>!jV! (Jb Luo yf*$\ ^ ^ 

: ijU^Xam) ^iJJ 

Vl = ^2 

a ) 1 r 1 = o) 2 r 2 

o>iri (1-2)(0.1) n , rad 

" 2 ~ = ^r = °- 4 — 


=(*)Jfr 

(i = 1 . 5 m) 4)3^ (m = 2 kg) Jsuj 

LuT (37°) Su^lj ^L ^«3 4*j0 2 ic 4*ii9! Sj3!^ ^ j 3 i -M 

4 Cj^ij -kugd| ^ Jy^JI oui .JJCiJb 

=J*» 

Ij^bwJI |-^wj jJI ^^JL: 5 ^ 93 ^) |^«*9sJ( HygjoJI ^S^aJi 

'.^ijf' j*>J1 ^3^1 

v 2 

T sin 37° = m— (1) 

:^^ 3 -urJI ^£ 3 *)! 

T cos 37° - mg = 0 -> T = — — ^— = 25 N 

w cos 37° 

i^ljJ! pJli i^JLUJ! ,jtfuLa> ^3 

r 

sin 37° =- -» r = 1. sin 37° = 0.9 m 

lAxxH Icy J! ib«V (1) IfebuJI ^ ( T ) 3 (r) pJ 







(r)(Tsin 37°) (0.9) (2 5. sin 37°) 


= 2.6 


~ to ~ 





.( r = 30 ni) a jh>3 ^ 8jLw 

^Lj oljl^V! ^^CJf JUC^VI Jobw 

jLJU ~4£y*i (>5 & U .JXiJb (jU s = 0.8 ) 

5 jbu*Jf JpLJ! a&m (j! ^^a^s-LoJI ^ 8 

• Ifelc 



u^l 

tjl 0*^3 833 3 Jbs)l &A& ^ 4 jjT yjl 83a/! 

: JVjiVf ^3 JL: f^aJ! 


fs = m— -> (1 S N = mgg 


:l^3 


= V (30)(0.8)(10) = 15.5 m/s 


lOU^ 

4iyjw> Zbuii Iwb ( ^L) LS jf3^i**iV! jIJmJI j 3^J y>3 

Wl .(M e = 5.98 xlO 24 /c^V^/V!Sji3!aJUr)^!3^V!4ai- L5 k 

g cL^ a JI jaJLU ^ 3! jJ! .1 



M' 


.©jljwC jiaS .O 

4aC ;j*j 

U*j| 

31«JI ,j*kfli J 533 ^gilo ^gcU^aJI j^fl/l (Jl Lw .! 

^> 3 ! jJI 4 £j-JI jj-ii LugJ I j^9 ilwli 

8^(3 8j3^ ^5? 2U3! jJI j*J1 




~ £1 ~ 


1 rev 2n rad 
1 day ~ 24(3600) s 


7.27xl0 -5 


rad 

s 


o^X:* ls^ ©3*JI O' J££J1 O* •‘t* 


M F m 

G ~ L 2~ 

r 2 



:^53LJ 4 j y" jjcJI S3&M (jls ijibd) 


-> G 


M e m 

~V 2 ~ 


= mo) 2 r 


( 1 ) 


•X vQ i^vQ jfiXOf jja9 1 a^\ \r 3 4JUT ITU *, 




:(1) 3J,abw>Jf ^ jAi/l 2uur LikX?«3 


(e.eyxio-^xs.gsxio 24 ) 


'j 


(7.27xl0 -5 ) 2 


= 4.23 xl0 7 m = 4.23xl0 4 km 


fdsut jj£ jmJI f (j^X^yj ^UJb^ 4 (6380 km) Ljjoj ypjVf y^il 

. (36000 km) J^/VI 
‘.^gC lOaM 3JsOsJI 

v = 0 jr = (7.27xl0 -5 )(4.22xl0 7 ) = 3072 — 

s 


Simple Harmonic Motion 


jI^aw 4^-fjJ ft? (80 cm) 4)3!? .kuOu J«^o (15 kg) -^uJUT 

.£t> jLj Oy y 4jly! <033^ j£ (15 cm) 
$(15 cm) <o!jf jO: J 3JOJ! ^yJf ^3! jlf ^ Lo .f 
.^J3 iAmJJ lSj3^ t -o 



4>1jV! <^,^.0 jJf Vaj Zcjm J ig ^-IjV! OV^lxo ^f\ .£ 


.t^Xjb-j .(0.6 sec ) Juu J^JudJ 


u^l 


0 = - = — = 0.1875 rad = 10.7° .? 

J 0.8 


(J- 0 ^ 

1.78 sec. 

/ = 1=0.56 Hz. :^l 

^f) ( o>) toV^lxoJI 4 jL& pu\JI (J^i 

a) = 2nf = 2n (0.56) = 3.52 ^ 
:2b-!jV!^bw 

d = A cos (w t) = 0.15 cos (3.52 t) 

Urad ^gj ^ 4*~jbcJl 2jyi ^3 : (0-6 sec) jju 03J03 

d — 0.15 cos (3.52 x 0.6) = —0.08 m 

.(j! jJV ! In JU i^JLJI p js sJI ^ ^iu fJJ&l ijb ^ju 4JLJI SjUiV! 

llcjjJi ^^Ixo 

v = -coA sin ( o) t) = -(3.52)(0.15)sm(3.52 t) 

••• v = —0.528 sin( 3.52 t) 

:(0.6 sec) jju J 3 *uJ! 05^ 



</ 


'll 



7 " 


V 

y 



••• 1 ; = -0.528 sm(3.52 x 0.6) = -0.45 — 
s 

3^si 2LT ' j> abol jj! 4c j*JJ 4 JUI SjLiV! 

|^*psJ( £$30 £s*? 3 > ^bwJf .^LJ! ab«V( 

.(^jJ!-^!jV!)^b^ 


T/4 T/2 3T/4 T 


~ £A ~ 


(DJ& 


^ J5VI 2b-!j! ,j*o 3iL*©Jf ±ju so ^kib 0*?u j& 4 su«j J 3 J-b 

:^«*>! .(0.252 sec) 

.IsuSsJI J3I? .o 


u^l 


o- 0 ^ 1 (g) 0^ j*^ (0.252 sec) jojJf J 


1 1 

t — —T -> 0.252 = — 7 ••• 7 = 2.016 sec 


:>kuOsJ! J3I? .o 


„ 0 i , T 2 g (2.016) 2 (10) ^ no 

7 = 2n — -> l=—— = — — = 1.03 m 

g An 2 An 2 


UT) Jfr> 

.x = 0.24 sin (12 1) :49M*Jf ,ji«to OO* (60 g) |^> 

10 4 JbwJ(j 2b-!jV! :lgJ 03^ Ls^i^f ^Jwoj Vf .! 

.(x = 0.028 m ) jOc 4 cj-j .0 
.(l? = 1.5 j) <UCj*J O3X5 Ua-Lc .£- 


7 = ^ = ^= 0.524 sec. :& 3 jJ 1 j*jS1 ^*6 J 
oUT ^ 1 n OsOaJ! < 1— 1 jiai!) jj! JJV! <023* ^ 4 *T _j> I Jo <j! Uo 

•J 3 ^ O^ 

:^S? SjjJJ! J3V! £jjJ! ^ ^fjf j^-sasf 



~ n ~ 


t = -T = -(0.524) = 0.131 sec. 

4 4 

17 — OjA — (( t = 0) i A*C 4 Cj*j L I g 

(12)(0.24) = 2.88 j 

:( t = 0.131 sec) J 3 Vl 4Jbsc Uf 

a = -oj 2 A = — (12) 2 (0.24) = -34.56^ 

s z 

Vyi <(x = 0.028 m ) £S 3 »oJ! ^ 4*9 ^aJI j)f .o 

.rad ,_J 4**>beJI 


x = 0.24 sin (12t) Lw 

0.028 = 0.24 sin (12 1) -> sin (12t) = 0.117 

, sin -1 (0.117) 

12 t = sin -1 (0.117) -» t = ^ = 9.77 x 10“ 3 sec 

! lAfe A*c 4c j*J! (J^X**o <twca 

17 = coTL cos (12 1) = 2.88 cos(12 x 9.77 x 10“ 3 ) = 2.86 — 

s 

3J^lxo ,Jd0 Jit 

17 = coA cos (12 1) -» 1.5 = 2.88 cos (12 t) 

cos (12t) = 0.52 -* 12 t = cos -1 (0.52) 
cos _1 (0.52) 


12 


- = 0.085 sec 


I jJ ! I Afc Ax; 4x9^o <J^X**; 4*o^ 


x = 0.24 sin (12t) = 0.24 sin (12 x 0.085) = 0.2 m 


=(*) Jfr 

[x = sin (cot) ] :*9MxJf ^*4° ( m = 0.5 kg) 

4*c (x = + 0.2 m) 4£>(j! OolT (t — 0.1 sec) a*c .(/c = 50 N /m) 4J Jy* 

.(17 = +0.5-) 

v s' 



.4*Jf 


S (v = - 0.5 — ) 4Zc j-^3 (x = + 0.2 m) 2b»!j! ^3X1*, 2Lioj Sys ^ .o 

[k l~50 rad 

(o= — = — - = 10 

Jm J 0.5 s 

:4>( jV ! 3J^Uo ^ 4 xmJ1 uL» jjXw 

x = /I sin (cut) -» + 0.2 = /I sin (10 x 0.1) 

+0.2 

71 = — — — — — - = 0.24 m. 


sin (10 x 0.1) 


co A. 

0 

-ioA 




■Jr 


0.5 


T/4 T/2 3T/4 T 

(\ A OjSLiJl 


T — 2n /— = 2n — — 0.63 sec. 


Uju£ (v = — 0.5 j-) axc^ (x = + 0.2 m) aj3^ 
.^Vl 4 Jj3^ ja> ^ttl! <^yi ^ 03XJ 

4J .J3J& >_X) b (m — 30 g) 


T/4 T/2 3T/4 T 

4Jbccg 4c_yj .(12 cm) 2L>!j! j* <^uTy> I Ju < (fc = 1.4 N /m) 

liJlsJI gSlpdl 

(x = - 4 cm) .? 
(x = 8 cm) .0 

(v = -0.61- , a = -3.74™ .0 < v = -0.77- , a = -1.87™ J :2bb-VI) 


* L o 

(r) • 

(e) ar^J! ov^bw • 

( 1 ♦) olS^AaoJf^ j^di • 

(U) 2UbuJ( 3 2u: r J(3 4^!jMJ^U( • 

(n) • 

(fA) ATysdU • 

(£f) 4 cJ£UacJI AT • 

(n) ar^j! • 

(of) ^SrljJoJIf j^LaqJI • 



~ oy _ 


1 . Harris Benson, University Physics, Revised Edition, 
John wiley and Sons. 


2 . Lecture Notes, Department of Physics, Sultan Qaboos 
University, 2014 . 


3 . Peter J. Noland, Fundamentals of College Physics, 
Second Edition, Wm. C Brown Publishers.