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Wאא EFאא
١٢٢ אאאא
אאEF
١٢٢
אאאא
‐١ J
W،،אא،א
א א א אאאא א אאא،אאאאאא
אאאאאWאאאאאאא
Kאאא
א א א א א אא،אאאאאאאאאא،
א ،אאא א אאאאאאאאא
א א ،א א א אא Kאא،אא
? א א א א ? א א? ?א א אא א
אKאאאאא
אאאאאא،אאאאא
אא،אKאאא
א א א א؛ Kא
אאאא
אאEF
١٢٢
אאאא
‐٢ J
א
א א
١
אאWאא٣ א
אאWאאא٣١ א
אאWא٤٧ א
אאאWאא ٥٩
אאWאאאא ٧٥
אאאא ١١٢
א١٢٧ א
אאEF
١٢٢
אאאא
‐٣ J
א،אאא،Wא،אא
]W١٣א[،
]Wא١٩١[،אאאאאא،
K
אאאאאאא،אאאאאאאאא،
אאאאאאאאאאאKאא
אאאW،
١ J אאאK
٢ J Kאאאא
٣ J Kאא
٤ J Kאא
٥ J Kאאאא
אאאאאEאFאKEאאFאאEF
אאא،אאאאאא،אא
،אאאאא،אאאא،אאא،אאאאאאאאאאאאא
،אאאאא
אאEF
١٢٢
אאאא
‐٤ J
אא،אאא،אKאאאאא
אאאאאא،אא،א
Kאאאא
אאאא،אאא،א
א،אא،אא،אאFאאאא،EKKK،אא
Kאאאאאאא،א
Kאאאאאא
אאאאאאאאאא،אאאאאאאאאאאא
،אK
،אאאאKאאא،א
אאEF
١٢٢
אאאא
‐٥ J
אאאאאאאאאא
אאEF
١٢٢
אאאא
‐٦ J
אא אאא
Force &Linear Motion
١- ١ אIntroductionW אאאאאאא،א،
אאאאאאאאF١EK
אmechanicsאforceאmotionאאאא،א
Kאא
אאאאאW،א،אא
١-אאWאאאmicroscopicא،אאאatomsא،molecules،
אאא?אquantum mechanics?K
٢-אאאWאאאspeed of light،אאאrelativityK
F١Eא،א،אאא
Kא،אא،א
אאEF
١٢٢
אאאא
‐٧ J
אאאא،אאא،אאאא،
FאאאאWאא،E
١-אאא،אאאאKאאאא،א
٢-אאאאאא،Kא
٣-אאאאKאא
٤-אאא،אאKאאאא
٥-Kאאאא ٦-Kאאא
،אאאאאK،אא
١- ٢ אאDisplacementW ABF א א ،١-١א ،E
displacement א،אאאאאאAאBK
F א א א א א ١ EF ٢אEFא١-١אא،Edistance،
א אא א Wא א אAB א א ،A،אBאאאא،Kא
אאEF
١٢٢
אאאא
‐٨ J
אF١-١אאאאE
١- ٣ אאAverage VelocityW א אaverage velocity א)v( ،
אאאא)x(אא)t(אאWKאא
12
12
tt
xx
t
xv
(1-1)
א א א)v(א א
(x, t) ، אא א א )t,x( 22אא אא א)t,x( 11א،אאא،
Wא x = f(t) (1-2)
(x)function(t)אא،(x)אKאאאאאאvectorK
F١- ١EExample
Wאאאאאאא
x = 1t – 4t2 + t1
١ -אא)4,3,2,1(K
אאEF
١٢٢
אאאא
‐٩ J
٢ -אאאא)0t( 1 )s4t( 2 K ٣ -אאא)s2t( 1 )s4t( 2 K
אSolutionW x(1 s) = 1(1) – 4(1)2 + (1)1 = 0 -1
x(2 s) = 1(2) – 4(2)2 + (2)1 = -2 m
x(1 s) = 1(1) – 4(1)2 + (1)1 = 0
x(4 s) = 1(4) – 4(4)2 + (4)1
= 12 – 64+ 64 = 12 m
x = x(4 s) – x(0 s) -2
x = 12 m –0 = 12 m
)s/m(3s4
m12
t
xv
-3
x = x(4 s) – x(2 s) = 12 – (-2) = 14 m
t = 4 s – 2 s = 2 s
)s/m(7s2
m14
t
xv
١- ٤ אאInstantaneous VelocityW א א intanntaneous velocityא
אaverage velocity،אאאWאא
dt
dx
t
xlimv 0t
(1-3)
אאא(v)א(1-1)אאאא(x)(t)Wאא،،
F١- ٢EExample
Wא،אא x = 2 - 2t + 4t2
אאEF
١٢٢
אאאא
‐١٠ J
אא(x)א(t)Kא
אאt = 1 sK
אSolutionW
אאt = 1 sWאאא
)s/m(6
)1(82t82
)t4t22(dt
d
dt
dx)s1(v 2
١- ٥ אAccelerationW אאא)v( 1אא)v( 2
א ، א א אאaverage accelerationא)a(Wאא
t
v
tt
vva
12
12
(1-4)
אאinstantanous accelerationW
dt
dva
(1-5)
אא א א(1-1)(1-5)א א א א(v) (t) אא א א،(x) (t)،
Wאא،
F١- ٣EExample
Wאאא 2t10t50x
אא(x)א(t)א א،א(t1 = 0)،W
١ -אאKאאאא
אאEF
١٢٢
אאאא
‐١١ J
٢ -אאאt2 = 1 sK ١ -אאאt2 = 1 sK
אSolutionW ١ -אאאאאt1 = 0אt2 = 1 sK
)s/m(80)s(3
)m(240v
)s(303ttt
0)0t(x
)m(240)3(10)3(50)s3t(x
t
)0t(x)s3t(xv
12
2
٢ -אאW
)s/m(11032050v
t2050v
)t10t50(dt
dv
3t
3t
2
١ -Wאא
)s/m(20a
)t2050(dt
da
dt
dva
23t
אאאאאאאאWKאאאא،
١- ٦ אאConstant Acceleration MotionW ،אאאאא،אאאא
אאאW .consta
dt
dva o
אאEF
١٢٢
אאאא
‐١٢ J
،אא)a( oאאt
= 0K
W،א tdavd
WEFאא
.constatv
dtadv
(1-6)
אאאconst.Wאאא
const)o(av
ot
vv
o
o
א constvo
אאאא(1-5)Wאא ovtav
א)v(אאא(a)אא)v()v( oאאאא)v( o
)aa( oא(1-6)Wאא
ovtav (1-7)
Kאא
W
ovatdt
dxv
W dtvdtatdx o
אא--Wא
אאEF
١٢٢
אאאא
‐١٣ J
consttv2
tax
dtvtdtadx
o
2
1
(1-8)
Wאאאאאא
oxx
ot
Wא const)o(v)o(ax oo
Wא constxo
אא(1-7)Wאא
oo2 xtvat
2
1x
א )x( אאאאא)x()x( oאאאאא)x( oאא،Wא
tvat2
1)xx( o
2o (1-9)
א(1-7)(1-9)Wאא،
א(1-7)א(t)W
a
vvt o (1-10)
(1-9)אW
a2
vv
a2
v2vv2vv2vv
a
vvv
a
)vv2vv(
2
1
a
)vv(v
a
)vv(a
2
1)xx(
2o
2
2ooo
2o
2
2oo
2o
2
oo2
2o
o
)xx(a2vv o2o
2 (1-11)
אאEF
١٢٢
אאאא
‐١٤ J
א Wא אF١EW
W
)xx(a2)vv(
tvat2
1)xx(
atvv
o2o
2
o2
o
o
F ١- ٤EExample
، א (10 m/s)،א(50 m/s)(160 m)W
١ -Kא ٢ -אאאא(10 m/s)K ٣ -אאאא(10 m/s)K
אSolutionW ١ -א(1-11)
)s(4
s/m5
s/m)3050(
a
)vv(
a
vt
t
va
)s/m(5m)160(2
s
m)30()50(
)xx(2
vva
2o
2
222
o
2o
2
٢ -אאאא(10 m/s)W
F١Eאאאא)xx( oא)d(W،
d)xx( o K
אאEF
١٢٢
אאאא
‐١٥ J
tvat2
1xx
)s(5.6
)s/m(5
)s/m(30
a
vt
o2
o
2
٣ -Wא
)m(90
)s5.6)(s/m5(2
1x
at2
1x
0v
0x
22
2
o
o
١- ٧ אאNewton’s First LawW ،אאאאא،אאאאא
אאאאאאא،Wאאאאאא
אאאאWאאKאא
אאאWאאאא،،א
K
אreference system،،אא
אאאאאאאinertia law?אא،אאא،
K?א
אאEF
١٢٢
אאאא
‐١٦ J
אאאאאאאאאא،א
Kאא
אאאאאאאאא،א،אאא
?אאא?אאאא،אאאequilibrium conditionsא،
אאאWא،א
0F
אW vmp
)p(אmomemtum،(m)،)v(
Kא
١- ٨ אאNewton’s Second LawW אאא F
א(m)א،א)a(
،אאאKא
aF (1-
12)
Wא
.consta
F
a
F
a
F
3
3
2
2
1
1
אאא(m)א،אאאאא،אא
אאאKאא(1-12)אWא
אאEF
١٢٢
אאאא
‐١٧ J
amF
(1-13)
אאאאexternal forcesאאאא،אinternal forcesאא،
K،אאא
אא(1-13)אאאאKאא(x, y, z)אא
Wא
zz
yy
xx
amF
amF
amF
(1-14)
אא(1-14)אאא(m)אא(ax, ay, az)Kאא،
אא(1-13)אאא(SI)א،אאW
N = (1 kg)(1 m/sI2)
F ١- ٥EExample
(8 kg)،א(10 N)Wאאא،
١-אאאאא(1 N)K
٢-Kא؟אאאא
אאEF
١٢٢
אאאא
‐١٨ J
אSolutionW
F١-٢אF،E١-٥E
١-אאא)F,f( kאאא(x)W
)s/m(375.38
27a
)a(8330
fFF
2x
x
kx
٢-Wאאאאאא
)s/m(75.38
30a
)a(830
maF
2x
x
x
F ١-٦EExample
(20 kg)אאא(15 m/s)،אאאאאא(45 N)K
١-Kא؟אא
٢-Kא
٣-Kאאאא
אSolutionW
F١-١אF،E١-٦E
אאEF
١٢٢
אאאא
‐١٩ J
١-אאאא)s/m15v( o ،אא)0F( K
٢-Wאא
)s/m(25.220
45a
)a(20450
mafF
amF
2
x
xk
xx
٣-א،אאאW،א
)s(6.625.2
150
a
vvt
t
vva
o
o
א(6.6 s)K
F١-٧EExample
(9.110-11 kg)אאא،)s/m10v( 6o
א،אא(8 10-17 N)אא،א(10-8 s)אK
Kא
אSolutionW
א،אאאאאאאא،Wא،א
atvv o
אאאאא
0v
0a
oy
x
אאEF
١٢٢
אאאא
‐٢٠ J
Wא
)s/m(1079.8
10101.9
1080
tm
Fvv
m
Fa
amF
amF
5
831
17
e
yyoy
e
yy
yey
yey
١- ٩ אWeightW אweightאאאאא
)amF(
אאא،אא،אא،אא
אא،אgravetational attractionWאאא،אא
gmW
(1-15)
אאאאא(m)،א)g(
א،אא،אא)g(
)a(אאא
K
אאא(1-15)אאא(y)אאאא)j(Wאא
jgmW
(1-16)
אאאאאאאאא(y-axis)Kא،
אאEF
١٢٢
אאאא
‐٢١ J
Wאאאאא
١-Kא
٢-א(g)Kאא،
Wאא
-אאinertia massאWא،אאאאא
W،א
a
Fminertia
(1-17)
-אattraction massאאאWא،אKאא)W,W( 21
،אא)m,m( g2g1K
Wא
2
1
g2
g1
W
W
m
m
(1-18)
א،אאאאאgravitational accelerationאא
free falling acceleration(g)אאKW
)g)(m(W
)g)(m(W
22
11
(1-
19)
א(1-18)א(1-17)W
.constm
m
m
m
2
1
g2
g1
אאEF
١٢٢
אאאא
‐٢٢ J
W m mg
אאאWאאאאא
1m
m
g
, m = mg
K
١-١٠אNewton’s Third LawW אאאאא،א
אאאאאאאאאWא،אא
אא،אאKאFאא،אא١-٤אאא،E(A)
)F( AB
א(B)אא،(B)FBAFEא
(A)אאא،אאאWאא
BAAB FF
(1-20)
F١-٤אאE
Wאאא
אאEF
١٢٢
אאאא
‐٢٣ J
אאKאאאאאאאאאאintertial frames
אאKאאאאאאaction،אאאreactionK
אאאאאאאא،אאא،א،א
F١-٥KE
F١-٥אEאאא)F,F( 11 )F,F( 22
Wאא
-،אאאאאא)W(
אא،)N(
Kאא
-אאאאאאא)F(
אאא)N(K
-אאא)F(אאא
)N(K
١-١١אFrictionW )F(
،אאאאאא
אא،אאאאאאEאאFאאEאFאא
אאEF
١٢٢
אאאא
‐٢٤ J
אfriction forceאא،אאא
Kא
אאאאאאאא،א
Kא
١-Kא
٢-Kא
١-١١- ١ Wא
،אאאאאWא
-אאstatic frictional forceW אאאאאאא)F(
،אאאא static frictional force
אא)f( sא،א)f( sאא)N(
Kא،אאאא
-אאkinetic frictional forceW
אאאא)F(א،
אאאkinetic frictional forceאא)f( k،Kא
Wאאאאא
١-אאאא)F(אאא
W
sfF
(1-21)
אאEF
١٢٢
אאאא
‐٢٥ J
א)F()f( s
א،אא)f( s
א)F(
Fא،١-٦KE
٢-אא)f( s
(fs max)Wאא
Nf smaxs
(1-22)
)N(א)W(
،)( sאאcoefficient of static frictionK
F١-٦אא،אEfsfk
١-אא،אאאא)f( s
Wאאא Nf kk
(1-23)
)( kאאcoefficient of kinetic frictionK
١-١١-٢Wא
א،אאאאא،א؛אאא
אאKאא
אאEF
١٢٢
אאאא
‐٢٦ J
-EאFאאאNonfrictional incline surface motionW
Fא١-٧KE
F١-٧אE
אאא(m)א(W)،אא،()،אא(x,
y)אאאאא،א،W
١-Wא)mgW(
(g)Kא،אא
٢-אא)N(K
א)W()N(
Kאא،א
Wאאאא
אאאW Wx=W sin
Wאאא Wy = W cos
א(N)(Wy)،אאWאא
Wy + N = 0
א(Wx)אאאW،א
אאEF
١٢٢
אאאא
‐٢٧ J
Wx = mg sin () = ma
a = g sin (1-24)
אאא(1-18)אאKאאאא
F١-٨EExample
אאאאאא
F١-٧E(20 kg)אא،(45°)K
אאאא،א(g = 9.8 m/s2)
אSolutionW
אאא)(1-24W = 45°
a = g sin
= (9.8) sin (45°) = 6.91 (m/s2)
Kאא
؟אאאאWאא(1-24)K
-אFאאאEFrictional incline surface motionW
F١-٨אE
F١-٨אE
אאEF
١٢٢
אאאא
‐٢٨ J
אאא(m)א)W(،
אא()،אאא،)y,x(אאא،א
Wאא
١-Wא)mgW( K
(g)א،אאKא
٢-אא)N(K
אאא)W()N(
אאKאאאאא،א
Wx = W sin
Wy = W cos
א)N()W( y
،אאאא)W( xאא)f( kאאא
،אWאא،א
mafsinmg
mafWF
k
kxx
m
fsinmga k
(1-25)
F١-٩EExample
Fאאאאאאאא١-٨E(12 kg)אא،(20 N)אא،
אאא(10°)אא،(9.8
m/s2)K
אSolutionW
אאא(1-25)W
אאEF
١٢٢
אאאא
‐٢٩ J
= 10°
m = 12 kg
fk = 20 N
g = 9.8 (m/s2)
a = 12
20)30sin()8.9)(12(
= 1.2 (m/s2)
؟אאאWא(1-25)K
אאEF
١٢٢
אאאא
‐٣٠ J
א Summary
،אאאאאWאאאאאאאאא
אאא،אאאKאאWאאאאאאא
0v
K،אא
א אא א א Wא אא(m)א،א
אW،אא،אא
m
Fa
Kא،אאא
אא ? W א Wא K?א
אאא،אאאאאא،אאאאא،،אא
Kאא
א א א א א W א אKאא
a
Fm
אאEF
١٢٢
אאאא
‐٣١ J
א،אאאאאWא(W1, W2)א)m,m( g2g1W
2
1
g2
g1
W
W
m
m
، א א א א א Wא אאאאאא ،א א א،אאאKא
Wאא
Nf,fF smaxss
)( s،אאא،אאאאאא(fk)W،
Nf kk
)( kKאא
אא)a(W
)xx(a2)vv(
tvat2
1)xx(
atvv
o2o
2
o2
o
o
W
voאאWKא vKאאW
xoKאאאאW xKאאאW
tKאW aKאW
אאאאאאאאאK
אאEF
١٢٢
אאאא
‐٣٢ J
אאא Self Test Exams
אאאאאאאא،
،אאאאאאאK
אWאאא (97 kg)א
א (470 N)،אאאאאK
Fא١-٩אKE
Wאאאא אאאאא(15 m)،
K
١-אאאאא(6 m/s)،(110 g)،Fאא،אאאא١٠-
١KE
٢-Kאאאאא
Wאאאאאאאאאאאאא،
KEFא
אאEF
١٢٢
אאאא
‐٣٣ J
אא Unit One Exercises & Problems
١-١ אאא)s/m30v( o א،(20 s)א)s/m40v( אאא
Kאאאא
١-٢ א(40 m/s)אא،אאאא(-2 m/s2)WK
-Kאאאא -Kאאאאאאא
١- ١ (80 kg)א،א(6 km/h)،W
-Kאאאא
-אאא(4 s)K
١- ٤ (100 kg)אא،F١- ٩E،،אא(g = 9.8 m/s2)Kאאאא
W
-אאאא(1 m/s2)Fא،١- ٩KE
-אאא(1 m/s)K
-אאאא(1 m/s2)Fא،١-٩KE
אאEF
١٢٢
אאאא
‐٣٤ J
F١-٩אE F١-٩אE
١-٥ (16 kg)א، (40 N)אא،(4 m/s2)K
-Kא،א؟אאאא -Kאאאא
١- ٦ (15 kg)אא،(15°)Fא١-١٠אאאא،E(50 N)K،
-Kאא -אK؟
FאsfkfKE
F١- ١٠אFא،E١-٦E
אאEF
١٢٢
אאאא
‐٣٥ J
١-٧ אא)x(אא)t(W
2tt102x
)x(،)tx(W،א
١- אאא)t(א)s3t( 2 )s1t( 1 K ٢- אאאא)s3t( 2 ،)s1t( 1 K ٣- אאאא)s3t( 2 ،)s1t( 1 K
٤- אאאא)s2t( K
אאEF
١٢٢
אאאא
‐٣٦ J
אאאאאאאאאאאא
אאEF
١٢٢
אאאא
‐٣٧ J
אא אאאא
Uniform Circular Motion
٢-١W
אאאאאאאאאאאאא،
אאאאאאאKאKאאאא
אאאאאאKאאאאאאאאאא
Kא
٢-٢ אאאא :
אאאאאxאאKאא
Kאאאאאאאאאאאאא
אO F١ J٢EאKPאאאa אאאb
אאאθWאאK
אאWθ(deg)אאא K
،אאאW(rev) אאאאWא
אאEF
١٢٢
אאאא
‐٣٨ J
( 2 -1 )K1 rev =
F٢-١אE
אאאWradians KאאאFאאא١ J٢EW
אאθאs אאאθ ( مقدرة بالزاوية النصف قطرية ) ھي النسبة بينs ونصف قطر القرص
r :
( 2 - 2 ) θ =
אאs=2πr א θ=2πr/r = 2πKWאאא
(2 - 3 ) =2π rad 1 rev =
1 rad = degrees =
אאEF
١٢٢
אאאא
‐٣٩ J
א אא אא א Kא
Fא٢ J٢אאאEAא
אB אאאKאאאא
אF٢ J٢E
WאאאאאאאאאאK
‐ ( 2 - 4 )
אאאאאאאK
F٢-١EExample
Wאאאאאאא a) 28 b) rev c) 2.18 rad.
אאEF
١٢٢
אאאא
‐٤٠ J
אSolutionW
a) 28 =( 28 deg)( ) = 0.078 rev
= (28 deg) ( )= 0.49 rad
b) = ( ) ( )= 90 deg.
= ( ) ( ) = rad
c) 2.18 rad = (2.18 rad) ( )= 0.347 rev.
=(2.18 rad) ( ) = 125 deg.
F٢-٢EExample
٩٠١٥F٣ J٢EK
אאאθאאאאradiansdegreesK
אSolutionW
אF2 J2EWאאאא
radians θ =
Ws=15cm r = 90 cm
θ 0.17rad.
W
אאEF
١٢٢
אאאא
‐٤١ J
θ = 0.17rad ( ) = 9.6
אF٣ J٢E
٣ J٢Wאאא
אאאאW
אאאאאאאאאאא אאאא
Wאאא
= = ( 2 - 5 )
אאאאאאאrad/s Kא??אאאrev/m
r.p.m אrevolution per minute EFאאאאאא،א
אאEF
١٢٢
אאאא
‐٤٢ J
2π אאאאW
( 2 -6 )
fא?frequency ?אאאאאאאאאangular frequency
F٢-٣EExample
900 r.p.m
אאאאω Kאא
אSolutionW
900 =15.0
WW
ω = (15 )= 94.2
Kאאאא
٤ J٢WEאאאFאאא WאאאEאFא
אאאאאאאאא אאאאא
Wא
אאEF
١٢٢
אאאא
‐٤٣ J
= = ( 2 - 7 )
אאאא W radians per second squared
(rad/s2 ) אאאאאאאאKאאאאא
F٢-٤EExample
אאא15 rad/s 9א rad/s ٣א
אKאאאאא
אSolutionW
= = = - 2 rad/s
Kאאאאאאאאא
٥ J٢אאאאאW אאאאאאא
W
אאאאא v =vi + at ω= ωi + αt ( 2 - 8 )
∆θ=ωi t + αt2 ( 2 - 9 ) at2 x=vit + ∆
ω2=ωi2 + 2 α∆ θ v2=vi
2 + 2 a∆x ( 2 - 10 )
Kאאאאאא
אאEF
١٢٢
אאאא
‐٤٤ J
F٢-٥EExample
א3.5 rad/s2אאKאא 2 rad/s אti=0
אאאאאאאKti=0 אt=2s ) אE
אאאK ω אt=2sK
אSolutionW
JWאאθ=ωi t + αt2 ∆ : يمكن حساب الزاوية التي دارتھا العجلة
Δθ=(2rad/s)(2s)+ (3.5rad/s2)(2s)2 = 11 rad.
אאradians revolutions W Δθ= (11 rad)(1rev/2π rad) = 1.75 rev.
Jאאאאt=2s . ω= ωi + α t = 2 rad/s + (3.5 rad/s2)(2s) = 9 rad/s.
٦ J٢Wאאאאא FאאאאאEאFאאא
WEאא
אאEF
١٢٢
אאאא
‐٤٥ J
אF٤ J٢E
אPO
Vt = r ω ( 2-11)
١ J אא vt אEFr אא
אאאωאK
at= r α ( 2-12 )
٢ J אEאFאatאEFr
אאאα ويكون اتجاھھا مماسا للمسارK
ac= = r ω2 (2-13)
٣ J אאא acאאאאאא
אאא:
a = ( 2- 14 )
٤ J אאאאאאrאאא
אאא:
F٢-٦EExample
אאאאאאא31.4א rad/s 0.892s
JKאאאאאא
JKאאאאאא
Jאאאr = 4.45 cm אאאאKאא
אSolutionW
אאEF
١٢٢
אאאא
‐٤٦ J
Jאאאאאω=ωi+αt א
א0=אωit=0 W = 35.2 rad/s2=
α=
Jאא(Δθ)אאאאאאאאאt=0.892s = 0ωi Wא
Δθ=ωit + αt2 = (35.2 rad/s2)(0.829s)2 = 14 rad.
Jאאvt r=4.45 cm= 0.0445 m Vt= rω = (0.0445 m ) (31.4 rad/s) = 1.4 m/s
Wאאא at= rα = (0.0445 m) (35.2 rad/s2) = 1.57m/s2
F٢-٧EExample
א40m/s60m/s5sאאא400m Jא
א50m/sW
KאאאEF
KאאאEF
KאאEF
אEFKא
אSolutionW
אאאEFacא50m/sW
אאEF
١٢٢
אאאא
‐٤٧ J
ac= = = 6.25 m/s2
אאאEFω W
ω= = = 0/125 rad/s
אאEFatאEאFאאWאא
at = = = 4 m/s2
אאEFaאאאאא:
a = = = ٤٢}٧ m/s2
٧ J٢Wאאא FאEאאאFא
אאאEKEאאאFאאאאאא
אאאאmאאאac?אאא?אאאאKFCאאFאאאא
KE(2-5)
אF٥ J٢E
אאEF
١٢٢
אאאא
‐٤٨ J
אאאW
אאאאmvאr Wא
(2-15) Fc = m ac = m
אאאאאאאאאKא
F٢-٨EExample
٢٠٠א1.2m אא3rev/sאF٦ J٢EK
Wא
אFאEFאאEK
KאאEF Wא
אF٦ J٢E
אאאEF אאאα EFWאאאat= rα = 0 אא
אאאacK
אאEF
١٢٢
אאאא
‐٤٩ J
aC = = r ω2
אωאrad/s א 3rev/s = 3(2π)=6π rad/sW
aC = ( 6 rad/s )2 (1.2 m ) = 426 m/s2
אאאאאאאEFm=200g FC = m aC W
FC = m aC = (0.200 kg ) (426 m/s2 ) = 85 N
אאTKא(FC =T )
אאEF
١٢٢
אאאא
‐٥٠ J
אאא Self Test Exams
אאאאאאא،אKאא،אאאאא
אWאאא אWאא
50 revradiansא 1500rpm rad/s
48π radrevolution22rad/s rpm
72rpsrad/s 2rad/s deg/s
אאאאW 480 rpm–אאאאא30אcm
Kאא
אאאאW 25cm א120 rpmאאא660 rpm
9sאKW
אאאאEאFאEFrad/s2אEאFאEFאK
אאEF
١٢٢
אאאא
‐٥١ J
אאאאאW 30cm 8rev/sאא
א14s אאאאאאאאKK
אאאאW א1.5 kgא25cm א2rev/sאK
W אEFKאאEFאאאEFKאא
אאאאW א6rev/s א4rad/s2–אאא
אאא26rev/sKאא
W א אא א א א
א א א א א א ، א EFאK
אאEF
١٢٢
אאאא
‐٥٢ J
אאאאאאאא
אאEF
١٢٢
אאאא
‐٥٣ J
אא אא
Work & Energy
٣- ١ אIntroductionW אאאאאא
א،אאconservation of energyאאאאא،אא،
אenergy neither be created nor destroyed،Kאאא،
אאאאאאאא،،אאא
Kא
،אאאאאאאאאאאאאא
אאאא،אא،Kאאא
אאconservation of momentumKאאאאאאאאא
אאאא،אאא،אאאא،
،EFאאאאאWא
١-Kאא
אאEF
١٢٢
אאאא
‐٥٤ J
٢-אא،אאאא،Kא
٣-Kאא
٤-אאKאא
٥-Kאא
٦-Kאא
٧-אאא،אאאאאK
٨-אאאאK
٣- ٢ אWorkW אא)F(
(m)،אאא)s(
אא،אW)F(
)s(אאא،א
אאאא،אאא،אאאאאאאאא
אאFא،٣-١אKE
F٣-١אאEאאא
אאאאאאFsEW
אאEF
١٢٢
אאאא
‐٥٥ J
sFW
)cos(sFW
s.FW
(3-1)
،אאאcos (0)א،אאאא)F(
)s(Fא،٢-٢E
F٣-٢אאאאE)F(
)s(
אF cos ()אא)F( x
אאא،א(2-1)Wאא
)cos(sF)cos(FsW
(3-2)
אא)F(אא،)s(
K،(CGS)אאJouleא(SI)אאאאergeK
אJouleאאאאW(1N)א،א(1 m)W،
1 J = (1 N)(1 m) אאאא
א،electron voltאא،אאאWאא
אWא،א
J106.1
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)volt0.1)(e(eV1
19
19
אאEF
١٢٢
אאאא
‐٥٦ J
Wאאאאאאאאאא
F ٣- ١EExample
(15 kg)א(5.7 m)אFאאאא،אE(h = 2.5
m)Fא،٢-٣W،E
١-Kאאאא
٢-אאאאא)F(K
٣-אאאאאא()K؟
אSolutionW
F٣-٣אא،E٣-١
١-אאא)F(،אאא
אאא)gm()singm( K
N65m7.5
m5.2
s
m8.9)kg15(
26
)438.0(sin
438.07.5
5.2
s
hsin
s
hmgsinmgF
2
1
אאEF
١٢٢
אאאא
‐٥٧ J
٢- )cos(FsW אא()אאאא)s(
א)F(Kא
WF = (65 N)(5.7 m) cos() = 368 J
٣-אא()אאאאאsin ()א،)F(
אאsin ()אא،K
٣- ٣ אאKinetic EnergyW א،אאאא
אאאאאאאאאWא،אאא
אאאאאא،א،אא
Fא،א٣-٢KE
F٣-٢אאאאאE
א)F(אא(m)אאא،
)s(אא)W(
אא،)v( o
אאא)(vאאאא)s(
،אא،אאאאאא
Kאאאא
אאEF
١٢٢
אאאא
‐٥٨ J
אאא)amF(
א،)d.FW(
-א)F(
אא)s(א
אא-אא،אאאWאא
s)am(W
(3-3)
FaEאא(m)אאא،
א-אא-Wאא as2vv 2
o2 (3-4)
אא(2-2)אא(m)Kאא، mas2)vv(m 2
o2
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Wאא masvm)2/1(vm)2/1( 2
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אאא(2-5)W 2
f vm)2/1(K אאאWfinal kinetic energyK 2oo vm)2/1(K אאאWאinitial kinetic energyK
Wאא
(mas)אW(Fs)אWאא،אאWאאאאא
2vm)2/1(K (3-6)
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Wאאאאאאא WKK of (3-7)
אאEF
١٢٢
אאאא
‐٥٩ J
אאאאאאא،)s(
אא)F(אאK-אאwork-kinetic
energy theoremWאאאאאא، of KWK (3-8)
אאאאאאKאא،א
Wאאאא
F ٣-٢EExample
אאאאאא)J107.6( 19K
א،א)kg1011.9( 31K
אSolutionW
)s/m(102.1v
)kg1011.9(
)J107.6)(2(
m
K2v
m
K2v
vm)2/1(K
6
2
1
31
19
2
1
2
2
٢- ٤ אאGravitational Potential EnergyW ،אאא
Fא،אאא٣-٣،אEFאאא؟אאא٣-٥אKE
אאEF
١٢٢
אאאא
‐٦٠ J
F٣-٥אאEאאאא
אאא(m)Fא٣-٥אאE)y( o)y(אאאאEאאFאא
א)y( o)y(אאאא)y(W، ymgUU of (3-9)
אא(2-9)W
ygmU f אאWאfinal potential energyK
oo ygmU אאאאWinitial potential energyK
אא(3-9)W
mg yאאאאאW)y(K)y(،אKאא
Fא٣-٥אאאאE(y)אאאאאאאאאאא
אאאgravitational potential energyKא
אאEF
١٢٢
אאאא
‐٦١ J
אאאאאWא)y(אא،אאאא
Kאאאא
٢- ٥ אPowerW אאא،אאאאאאאKאאאא،
א)W(א،)W(א)t(אforce average powerא
Wא
Wא
t
WP
(3-10)
אאinstantaneous powerWא،
t
WlimP 0t
W
dt
dWP (3-11)
אאאאאאאW
)cos(Fvdt
dx)cos(FP
(3-12)
אאא(SI)א(Watt)Kאאא
s
J1W1Watt1
אאאhorse powerאWא
אאEF
١٢٢
אאאא
‐٦٢ J
1 horse power = 1 hp = 726 W
אאאא،אאאאא)F(
אא)v(א،אא
Kאאא
א،אאאאאWא
F٣-٣EExample
א(102 kg)אאא(53 m/s)،אא(2 m/s2)WK
١-Kאאא
٢-Kאאאאאא
٣-Kאאאא
٢-אאאאא،אא(t = 120 s)K
٥-אאאא(2 m/s2)K
אSolutionW
١-Wאא،אא
as2v
N204)s/m2)(kg102(
amF
2o
2
٢-
m2.702)s/m(22
)s/m53(
a2
vs
2
22o
אאEF
١٢٢
אאאא
‐٦٣ J
٣-Wאא
J1033.14
)m2.702)(N204(FdW4
٤-
W2.1194
)s30(
)J1033.14(
t
Wp
4
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N
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816
04204 2
KEאאF،אאאא
٣- ٦ אConservation of EnergyW א،،אא،
אmechanical energyאאkinetic energyאאאאgravitational potengal energyאאא،thermal energy،
אאchemical energyאא،optical energyאא،atomic
energyאאא،אאאKאא،א
Kאא
אFאא،٢א-
٢FE٢-٣،אא،،אEאא(K)א،אאא
א(m)FvEWא
2vm)2/1(K (3-13)
אאEF
١٢٢
אאאא
‐٦٤ J
אא(U)אאאאאאא،א(m)(h)א
Wא hgmU (3-14)
)g(אאgravitational accelerationK
אאspringא،(x)אequilibrium positionא،Wא
2xk)2/1(U (3-15)
(k)،،אאHock’s
lowWאא xkF
(3-16)
אאאאאא(x)אאK)x/Fk(
אאאאא
Wאא،א(N.m-1)K
،אא،אאאאאWאא
hgmvm)2/1(E 2 (3-17)
22 xk)2/1(vm)2/1(E (3-18)
،אאאאאאW
UKE EאאF (3-19)
אא(2-19)אאא،،א
אאאW،א
therEUK0 EאאF (3-20)
אאEF
١٢٢
אאאא
‐٦٥ J
W
of
of
UUU
KKK
אאאאאאאאאKאא،א
אאאאאא(2-20)אW
W...EUK ther (3-21)
אא،אאאWאא
١-Kאאאא
٢-אאאאאאאאאאא،אאא
אmass-energyWא،א 2mcE (3-22)
(E)،א(m)،א(c)אspeed of lightK
٣-אאquantized،א،אא)E( xא)E( yאא
Wא hfEE yx (3-23)
(h)Planck’s constantW
s.eV1014.4
s.J1063.6h15
34
(f)Kאאא،אא
אאEF
١٢٢
אאאא
‐٦٦ J
،אאאאאאWאא
F٢- ٢EExample
(m)א(h)،אא(v)Fאא،٣-٦KE
١-Kאאאאא
٢ -אאאאK
F٣-٦אFא،E٣-٢E
אSolutionW
،אאאאאאW
١-،אאאאWאאאאאWאאא،א
0hgmKU
٢-אא،אאWאאW،אאאא
אאEF
١٢٢
אאאא
‐٦٧ J
2omv)2/1(0KU
א،EאאFאKא
0mghmv)2/1(0 2o
א(v1)Wאאא hg2vo
אאא،אאאאWאא،אא
ax2vv 2o
2
W
vKאאאאW
ov،אאאW(x = h)Fga
EW
hg2v
hg2v0
o
2o
אא،אאאאאא،אאא،א
אאאKא
F٣-٥EExample
(2 kg)אא(300 m/s)K
١-Kאא
٢-Kאאאא
אאEF
١٢٢
אאאא
‐٦٨ J
٣-א،אאא(25
s)Kאאאא،
אSolutionW
١-אאא،אאWאא،אא
)s/m(8.9ga
gmamF2
Kאאאאאא
٢-Wאא
tgvv
tavv
o
o
א،אאא،אW
ghvaxvv
mghU
J
smkg
mvK
smv
ssmsm
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tgv
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o
22
6050
)/55)(4)(2/1(
2
1
)/(55
)(25)/(8.9)/(300
)(6.30)/(8.9
)/(300
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222
2
22
2
0
2
2
אאאא(25 s)K
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)s/m300()s/m55(
g2
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22
2o
2
אאEF
١٢٢
אאאא
‐٦٩ J
)J(173950
)m5.4437)(s/m8.9)(kg4(U
)m(5.4437h2
אא(h)אWא
)m(5.4437h
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٣- ٧ אMomentumW אאאא)v(
(m)אאא،،
Wאא vmP
(3-24)
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vdm
vmdt
d
dt
)( (3-25)
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K
אאאא)F(
(t)Wאאא
tm
Fvv
atvvm
Fa
amF
o
o
Wא
אאEF
١٢٢
אאאא
‐٧٠ J
Ftmvvm o (3-26)
אאאא)mvvm( oWא،אא، tFP
(3-27)
אאא،א)tF(
א
א،אאא)(Fאאא(t)K
F ٣-٦EExample
א)(Fא(2000 kg)،(20 m/s) (30 m/s)א(2 s)K
אSolutionW
Ns
smkgF
smkg
smsmkg
vvmvmvmPtF oo
50004
)/(102
)/(102
)/40/30)(2000(
)(
4
2
Kאאא
א(2-27)،אאKאא
cmvmP
(3-28)
(m)،א)v( cm
אcenter of
mass velocityKאאאא
٣- ٨ אConservation of MomentumW
אאEF
١٢٢
אאאא
‐٧١ J
אאאאאאא،conservative،
EF،،Wאאא،א
0Fext
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0td
vdm
td
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td
Pd
Wאא،אא ttanconsP
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אWאאא of PP0P
W of PP (3-31)
)P( o،אאא)P( fKאא
F ٣-٧EExample
(75 kg)،(39 kg)(2.3 m/s)،Kאאא،אא
אSolutionW
Wאא
WEאFא cm
אאEF
١٢٢
אאאא
‐٧٢ J
Wא mm
Wאאאא ov
Wאא cv
Wא
s/m7.6
)kg39(
)s/m3.2()kg39()kg75(
m
v)mm(vv
vmv)mm(
c
ocmc
ccocm
Wאאא
)s/m4.4(
)s/m3.2()s/m7.6(vvv o
אאEF
١٢٢
אאאא
‐٧٣ J
א Summary
אאWא)F(אא)s(
אWאאא
S.FW
אא،אאאאאאא،(1 N)א(1 m)
Kא
WאאאאWאאא
WKK of
אאאאאאאW،א
Wאאא 2f vm
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Wאאאא 2oo mv
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אWאאאWאאא
WUU of
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Wאאא hgmU f
Wאאאא oo hgmU
א)h( o)h(אאKא
אאאאאWאWא،א
E = K + U
אאEF
١٢٢
אאאא
‐٧٤ J
אאאאWW،א
K + U EאאF =0
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א Weight W Joule J
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אא Potential Energy U Joule Jאאא Initial velocity ov m/sec m/s
אא Final velocity v m/sec m/s
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١٢٢
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אאא Self Test Exams
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אWאאא (m))m2l( א
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١-אא(B)K
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אאאאW ١-אאאא(102 g)
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٢-אאאאאאאאא(1 kW)K
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א א א א א א ، א EFאK
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אא Unit Three Exercises & Problems
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٣- ٢ (10 m) א(15°)א אא א Kאאא אא
א(20 kg)K
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١-Kאאאא
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Optional Problems
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אאא אא
Fluid Fundamentals
٤- ١ אIntroductionW אאאאאאאאאאאflow ،
אאאאאאאא
אאאאאא،אאאאא
Kאא
אאאWFluid statics W
٤-٢אMass Density W אאאאא
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אא،אאאאאאF١ J٤EאאאאK
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אאEF
١٢٢
אאאא
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אאאאאאאFאאאאKא
( 4 - 1 )אאאאW אאא אא אא
א אρ
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אρ
L٣(kg/m3)א
אρ
L٣(kg/m3)
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8890 13600 אא1.98
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10500 F37°C E1060 1.25
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٤-٣אא Specific Gravity
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٤-٤אPressure W
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אF٢ J٤E אאPאאPKא
F٤-٢אE
אאאאא P0 א(gauge
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אSolutionW
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אאאאאאWאא
אEFא?אאאאאא?
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F ٤-٢EExample
אאEF
١٢٢
אאאא
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אאאאאאאr1=5cm EFא
r2=15 cm K אאאאאאאאאEF
13300NK KאאאאאאאEF
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אאאאאEFF1 W
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אאbuoyant force FB אאאאאאאא
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אP2P2A אאאאאאאאאאא
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F٤-٤אE
אאאאאאאאאאEאFאאא
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F ٤-٣EExample
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א FBWאאאא
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אρ=Wאא
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אאאאאאאאאאKאא
אאאאאא?Wאאאאאאא
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אאsteady flowאאאFאא١אEh1v1 1ρ وP1 ه ائع وكثافت ھي سرعة الم
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W
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אאא Self Test Exams
אאאא،אאאאאא،אאאK
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אא אאאא
Concepts In Heat & Temperature
٥-١ אIntroductionW אאאאאאא،אאא،א
אאאthermal energyאK،אאאאאא
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א?אאא?אאאאא؛macroscopicא،microscopicאאא،
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אאEF
١٢٢
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אא،אאא
אאאאא،אאאאthermal equilibriumK
٥-٤ אאTmeperature MeasurementW אאאא،אאאא
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אאאאliquidאsolideאgasesEאFvaporאאאאא
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١٢٢
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אאאאאאאW
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١٢٢
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אא(5-4)אאאאאא(25°C)אאא،(5-5)Kא،
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F ٥-٢EExample
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‐١٠٧ J
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W TF = 98.6°F
אא(T = 37°C)،א(98.6°F)אאא(5-5)K
F ٥-٣EExample
-אא(-71°C)א،אאK؟
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אSolutionW
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אאEF
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٥-٦ אאאאSolids Thermal ExpansionW אאאF١Eאא،
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١-אאlinear expansionK
٢-אאsurface expansionK
٣-אאvolume expansionK
אWאאא
٥-٦- ١אאLinear ExpansionW
אאאאexperimantal resultsאאWאאאאא
F١Eאאאא،
Kאא
אאEF
١٢٢
אאאא
‐١٠٩ J
١-אאאאאinitial length at room temperature،)L(K
٢-אאאא،אאאא)T( fאאאא)T(،(T)K
٣-אא،אאאאאאא?،،coefficiet of linear expansion?
)( Lא،Kא
אאא،אאWא)L( fאאא)L(א(L)אאא)L(א
אא(T)W، TLL (5-6)
W
TTT
LLL
f
f
אאאא(3-7)א،א،אא،אאא
אא)( LW TLL L (5-7)
TLLL
TLLL
Lf
Lf
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אא(5-8)אאאאאאKא
א(5-7)Wאאאא
TL
LL
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אאEF
١٢٢
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אאאאא،אאאאאאK(5-9)א
אאאאאאא(SI)Wאא، 1
L KK.m
m
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F ٥-٤EExample
אcopperא(1 m)אאא،א،א(1.000019 m)אא،
)( LK
אSolutionW
אא(5-10)W
16
oL
K)1019(
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TL
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F ٥-٥EExample
אcopperא(2.5 m)אא،(15K)،אא(35K)אאא،אא،א(17.0 10-6 K-1)K
אאEF
١٢٢
אאאא
‐١١١ J
אSolutionW
אא(5-8)W L = L L T
= (17.0 10-6 K-1)(2.5 m)(35 - 15) K
= 8.5 10-4 m
L = 0.85 mm
אאא،F٥-١EKאאאא
F٥-١אא،אאאאE
(10-6/C)
אאא Substance
51 אא ice (at 0C)
29 א lead
23 א aluminum
19 אא brass
17 א copper
11 א steel
9 אא glass (ordinary)
3.2 glass (pyrex)
0.7 אא invar
0.5 אא fused quartz
אאEF
١٢٢
אאאא
‐١١٢ J
٥-٦- ٢אאSurface ExpansionW
،אאאאא،א،אאא
Kאאאאא
Wא
١-אאאAK
٢-אאאאTW، TAA (5-10)
(A)אאאאאאא(T)K،אאאאא
אאאא،אא،אW،א
A = 2L
אאא(5-10)Wאא TAA A (5-11)
Wאא،אא،אא Af – A = A A T
Af = A + A A T
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F ٥-٦EExample
אaluminum(30 cm)(50 cm)،אאא(100 K)א،אאא،
אא(23 10-6 K-1)K
אאEF
١٢٢
אאאא
‐١١٣ J
אSolutionW
אא(5-12)W A = A A T
A = 2L = (2 23 10-6 K-1)
T = 100K
A = (0.3 0.5) = 0.15 m2 = 1500 cm2
A = (46 10-6 K-1)(0.15 m2)(100K)
= 6.9 10-4 m2
= 6.9 cm2
٥-٦- ٣אאאאאThermal Expansion of Solids and LiquidsW
אאאאאאאאvolume
expansionKאאא،
אאאאאW
١-אאא)V(K
٢-אאאא(T)WK TVV (5-13)
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א(3-14)Wאא TVV V (5-14)
אאEF
١٢٢
אאאא
‐١١٤ J
VVV f
)V( fאאאאא(T)אK)(،אא Lאאאא
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W = 3L = V
Kאאאאאאא
٥- ٧ אאאאאא
The Absorption of Heat by Solids and LiquidsW ،אאאאאא
אאאאabsorption of heatK
אאאאאאא،אאאאkinetic energyאאאrandom motionא
אאmicroscopicאאאאאאאא،אאinternal energyאאא
אאאא،א،אאאא،?אא?א،אאא
(Q)א،א(Q)אKא،אאאאאאא
אא( TS ) body temperatureאאא،( TE )
environment temperatureWא،،א، TS > TE
(Q)אאאאא،אW،אאאאאא
TS < TE
אאEF
١٢٢
אאאא
‐١١٥ J
(Q)אאא،Wא،א TS = TE
(Q)Kאא،א
אאאWא(Q)אאKאאאאאאא
א،אאאאאEאFcalorieא،jouleאא،british thermal unitא،
W 1 calorie = 4.186 joule
1 btu = 1055 joule = 252.0 calorie
1 k calorie = 4186 joule = 3.969 Btu
אאאאא??אא?אאא،א،אא
Kאא،?אא
FאEאCalorieW
אאאאאאא،אאKאא
אאאאBtuW
אאאאאאpoundאאאא،אאא،א
אאאאאאא(1
nutritionists cal)אאאאאא،Wא
אאEF
١٢٢
אאאא
‐١١٦ J
٥-٧- ١אאאThe Heat CapacityW
אאאheat capacityאאא(C)אאא(Q)אאא
WKאאאא )TT(Q if (5-15)
)T( fאאאfinal temperature،)T( iאאאאinitial temperatureW،
)TT(CQ if
)TT(
QC
if (5-16)
אא(3-16)אא،(Q)אאא)TT( if אאאא(C)K
אאאאא(C)،אאא)C/cal( ،)K/cal(،)K/J(K
٥-٧- ٢אאאאThermal CapacityW
Fאאאא٣- ٨- ١אאאא،Eא،אאאא
אKאאאאא،אאאאאאאאאאheat capacity per unit massאא،
אא(c)אא،אאאא(3-16)אWאא،
)TT(mcQ if
)TT(m
Qc
if (5-17)
אאEF
١٢٢
אאאא
‐١١٧ J
אא(3-17)אאא(Q)א))TTאא(m)א if אאא(c)K
א،אאאא)C.g/cal( )K.kg/cal(א)K.g/cal(Wאאא،א،
K.kg/J.419F.lb/Btu1C.g/cal1c
٥-٧- ٣EאFאאאאMolar Heat CapacityW
אאאmolאאאאא،אאאא
אאאא(6.01023 /mol)אאatomsאא،אaluminum oxideאאmolecules،
אWאא mol/1002.6NnumberAvogadros 23
A
Fא٥-٢،אאאאאאאEWאאאאאאא،אא
(cal/mol.k)(J/mol.k)א،אF٥-٢KE
אאEF
١٢٢
אאאא
‐١١٨ J
F٥-٢א،אאאאאאאאאE
אאאאאאא Molar Heat Capacity אאאא
Thermal Capacity אאא
Characteristic א
J/mol.K J/kg.K cal/g.K א Substance
אא Elemental Solids
26.5 128 0.0305 א lead
24.8 134 0.0321 א tungsten
25.5 236 0.0564 א silver
24.5 386 0.093 א copper
24.4 900 0.215 א aluminum
Other Solids
380 0.092 אא brass
790 0.19 אא granite
840 0.20 א glass
2220 0.550 א ice (-10c)
אאLiquids
140 0.023 א mercuy
2430 0.58 א
א ethyl alcohol
3900 0.93 א seawater
4190 1.00 א water
אאEF
١٢٢
אאאא
‐١١٩ J
٥-٧- ٤אאHeat of TransformationW
אאאאאאabsorption of heat،אאאאאאאchange in temperature،
א،אאאאphase،(state)אאE،،Fconstant temperature transformationK
אאiceאאאאאאאאאKא
אא،אאאאאWא
אאאאאאא،heat of transformationאא(L)K
אא،א(m)Wאאא،
LmQ (5-18)
Wאאאאheat of vaparizationאא(LV)Kאא،
LV = 539 cal/g = 40.7 kJ/mol
= 2260 kJ/kg
אאאsolid phaseאאliquid phaseאאאheat of fusionאא(LF)W،
LF = 79.5 cal/g = 6.01 kJ/mol = 333 kJ/kg
Fא،٥-٣EאאKא
אאEF
١٢٢
אאאא
‐١٢٠ J
F٥-٣אאאאEmeltingאvaporizationא
אאאאאא
א Boiling א Melting
Substance heat of
vaporization (kJ/kg)
אא
boiling point (K)
א
heat of fusion (kJ/kg)
אא
melting
point (K)
455 20.3 58.0 14.0 אhydrogen
213 90.2 13.9 54.8 אoxygen
296 630 11.4 234 א mercury
2256 373 333 273 א water
858 2017 23.2 601 אlead
2336 2123 105 1235 א silver
4730 2868 207 1356 אcopper
٥-٨ אאאאאFirst Law Of ThermodynamicsW אאא،אאאאאא
א،אאאאאWא
Eint = Eint,f - Eint,i = Q - W (5-19)
Wא dEint = dQ - dW (5-20)
W
Eint،אאאאW،אאFאKEא،א
QKאאאאW
אאEF
١٢٢
אאאא
‐١٢١ J
Wא،אאאאאאאאWK،א
אאWא،א
١-אאadiabatic processesאWאא،אאאא Eint = -W (5-21)
،אאאאאW Q = 0
٢-אconstant volume processesאאאא،א،אאא
Wאא،אא Eint = Q (5-22)
W،אאאאא W = 0
٣-אאcyclic processesאא،،אאאאאאאא
Wא Q = W (5-23)
W،אאאאאא Eint = 0
٤-אאאfree expansion processesאאאאא،،אאWא
Eint = 0 (5-24)
،אאאאאאW
Q = W = 0
אאEF
١٢٢
אאאא
‐١٢٢ J
Fא،אאא٥-٤KE The Law: Eint = Q – W (Eq. 5-
23)
F٥-٤אEאאאא
א Consequences א Restrictionא Process
Eint = -W Q = 0 אadiabatic
Eint = Q W = 0 א constant volume
Q = W Eint = 0 closed cycle
Eint = 0 Q = W = 0 אאאfree expansion
F ٥- ٤EExample
אאאאאא (720 g)אא(-10C)אאאא(15C)K
אSolutionW
א،אאWא
١-אאא(-10C)(0C)K Q1 = Cice m ( Tf - Ti )
= (2220 J/kg. K)(0.720 kg)0 - (-10C)
= 15.98 kJ
٢-אא،K،אא
Q2 = LF m= (333 kJ/kg)(0.720 kg)
אאEF
١٢٢
אאאא
‐١٢٣ J
= 239.8 kJ
٣-אאאאאא(0C)(15C)K Q3 = LLiq m = ( Tf - Ti )
= (4190 J/kg. K)(0.720 kg)(15C - 0C)
= 45.25 kJ
Q = Q1 + Q2 + Q3
= 300 k
J
٥-٩ אאאThe Transfer Of HeatW א،אא
אאאאאאKאאאאWא؛אאא،
Kאא
٥-٩- ١אאאTransfer Of Heat By ConductionW
אאאאאthermal energyאאאא،אאאW،
،אאאEאFאאEאFאאאאא
אאאאאKאאאאאא،אאאאא
،א،אאאאאאאאK
אאאאrate of heat conductionאא)H( Cא(A)אאא،
א)TT( CH אאאאא،(L)Wא،
אאEF
١٢٢
אאאא
‐١٢٤ J
L
TTk
t
QH CH
CC
C
)( (5-25)
W
HCאאW Rate of heat conduction
QCאאאW Transfere thermal energy
tאאW Duration time
kCאאאW Conductivity constant
AאW Conduction area
THאאאW Hot resevoir temperature
TCאאאW Cold resevoir temperature
LאWאא Conduction path thickness
אאאאאWאKאאאא
אא(5-25)אאא)k( CאWא
אאאא)Q( Cאאאא(t)(A)אא(L)אאא،א
(T)Kאא
אאאrate of heat conductionאאאWא،א
t
QH C
C
אאEF
١٢٢
אאאא
‐١٢٥ J
אאאאthermal resistance to conductionWאא
Cther k
LR (5-26)
)R( ther،אאא(L)،אאא)k( Cאאאאאאא،،א
F٥-٥אא،E)k( Cאא(3-26)אא(5-25)W
ther
CHC R
TTAH
)( (5-27)
אאאא)R( ther،א،אאאאFא٥-٥אKE
אאEF
١٢٢
אאאא
‐١٢٦ J
F٥-٥אאאE(kC)אא
אאא(R)אאאאא R-Value
אאא
ft2.h.F/Btu(١)
Conductivity
א KC(W/m.K)
Substance
אא
אMetal
0.010 14 א stainless steel
0.0041 35 א lead
0.0006 235 א aluminum
0.00036 401 א copper
0.00034 428 א silver
אאGases
5.5 0.026 אאא air (dry)
0.96 0.15 א helium
0.80 0.18 א hydrogene
אאBuilding Materials
5.9 0.024 א polyurethane foam
3.3 0.043 rock wool
3.0 0.048 אא fiberglass
1.3 0.11 אא white pine
0.14 1.0 אא window glass
F١אKאאאאE(SI)א
אאא(0.14/k)K
אאEF
١٢٢
אאאא
‐١٢٧ J
F ٥-٨EExample
אF٥-٤E(25 cm)(90 cm2)،אאא(125°C)אא(10°C)אאאא،
אאא،אא)H( CKאא
F٥-٤אFא،E٥-٨E
אSolutionW
אאא(5-25)W
L
)TT(k
t
QH CH
CC
C
אאא(k)(401 W/m.K)K H
C = (401 W/m.k)(90 10-4 m2)(125 - 10)C/(0.25)m
= 1.66 103 J/S
٥-٩- ٢אאאTransfer of Heat by ConvectionW
אאאconvectionאאאאאא
אאאKאא
אא،אאאאKאאא
א،Wא،אאא
אאEF
١٢٢
אאאא
‐١٢٨ J
)TT(AkH iconvconv (5-28)
אאאאconvectionאWאאא(T)،אא)T( iאא
אא،אא 25.1iTT א(3-28)אא
אאאא،)TT( iK
א(3-28)אאא)k( convאWא
אא،אאאאKא
אאאאאאאאאא،אא،אא
Kאא
F ٥-٩EExample
(100 m2)א(40°C)אאאאא(22°C)אאאאאאKא(10 W/m2°C)،
Kאאא
אSolutionW Hconv. = kconv. A(T – Ti)
kconv = 10 W/m2 °C
A = 100 m2
T = 40 C
Ti = 22C
Hconv. = (10 W/m2 C)(100 m2)(40 - 22)C
אאEF
١٢٢
אאאא
‐١٢٩ J
= 18000W
٥-٩- ٣אאאTranter of Heat by RadiationW
א،אאאאאא(A)א(B)אelectromagnetic radiationאאultra violet radiationאא
אvisible light(1.0 m)(100 m)K
אאאאאא،אאא
אאאאKאאאאאאאאאאא
א(300K)،אאאאאKאאא
Kאאאאאאא
אאאgood radiatorאabsorper،אאאאאאא
black body،אאא،אKאאאא
אאאאאאאאאאאאאאKאא
W،אאאא
4ATt
QH rad
rad (5-29)
אאאאאאWא
Qrad = At T4
אאEF
١٢٢
אאאא
‐١٣٠ J
אאאאאא)T( iאאא)T(א،Wאאא
)TT(AH 44irad
א)TT( i Kאאא
א-Stefan- BoltzmanW
HradKאאאאאW
W-(5.685 10-8 Wm-2 K-4)אאאK
TKאאאאW
AKאאW
אאאWemissivityא،א(0.1)א(0.9)K
،אאאאאאאאאאאאאאאא
אאאאאאאאא،אאאאאאאאאא
(6C)אאאאאאאאאאאא،
אאאאאאאאאאאא
א،אאאKאא
אאאאאאאאא،אאאא،אא
،אWאאאא
אאEF
١٢٢
אאאא
‐١٣١ J
Wאא
i
rad
H
H (5-30)
F ٥- ١٠EExample
אאאא(80 W)،٣٠٪אאKא،א
אSolutionW
אא(3-30)W
3.0W80
W24
W24100
8030H
W80H
H
H
i
rad
i
rad
אאEF
١٢٢
אאאא
‐١٣٢ J
א Summary
אאWאא،،אאא،אאאאאא
אא،Kאאא(SI)Kא
אא،אאWאאאאא،אאאאא
אאאאאאאאאKאאאא?אא?אאאא
אאאאWאאא(A)(B)אאא(C)א،(A)אא(B)אK
Kאאאאא
אאWאאאאאא،אK
Wאא
100
273T
180
32T
100
0T KFC
אאאWאאאאWאא
L=L L T
W(L)،אאא(L)،אאא(L)،אאא(T)Kאאאא
،א Wא א אW
A=A A T
אאEF
١٢٢
אאאא
‐١٣٣ J
(A)،אאא(A)،אא،אא(A)،אאאא(T)אא
Kאא
א Wאאאאא،W
V=V V T
(V)،אאא(V)،אא(V)א،אאאא(T)،אאא
אאאKא
אא W אא א(Q)א א א)TT( if ،א،(J/C)(J/K)،
W
)TT(
QC
if
Wא אא א אא (Q) א אא(m)אא)TT( if ،(J/kg C)(J/kg K)W،
)TT(m
QC
if
Wאאאאאאאאאאאאא(W)אאא،(Q)א،
אא (Eint) אא ،KW
Eint = Q - W
(Q)،אאאאאאאא Kאא א א אא (W)א
Kא،אא
אאEF
١٢٢
אאאא
‐١٣٤ J
אאWאאא،אאאW،Wאאא
EאF L
)TT(kH CH
cC
EאF )TT(AkH iconvconv
EאF 4rad ATH
אאאאאאF١E
אא אא א
אא temperatureT K
Celsius scaleTC C
Fahrenheit scaleTF F
אא linear expansion coefficientL 1K
אא surface expansion coefficientA = 2L 1K
אא volume expansion coefficientV = 3L V =
1K
אאא thermal energyQ J
אאא heat copacityC K/J
אאאא heat capacity per unit massc K.kg/J
Avogadro’s numberNA mol/1002.6 23
א heat of transformationL kg/J
אאאא HC W
אאאא kC K.m/W
אאא RC )Btu/F.h.ft( 2
אא Hconv W
F١Eאא،אאא،Kא
אאEF
١٢٢
אאאא
‐١٣٥ J
אא Kconv Cm/W 2
אא Hrad W
אא 42 KWm
אאEF
١٢٢
אאאא
‐١٣٦ J
אאא Self Test Exam
אאאאאאאא،אאאאאא،א
Kא
אWאאא אmercury(0.1 liter)אא(10°C)אא(35°C)،אאא،
א(1810-5 K-1)K
אWאאא אsteel(130 cm)(1.1 mm)،
אא(101°C)א،אא(20°C)K
אאאא،אאאאא(11.010-6 K-1)K
Wא אא א א אא א א א א א ، א
EFאK
אאEF
١٢٢
אאאא
‐١٣٧ J
אא Unit Five Exercises & Problems
٥-١ Wאאאאא
١KKאא
٢KKאא
٣KKאא
٥-٢ אאא(32C)(20 cm)،אאאא(50C)K
٥-٣ א،אאא(2.725 cm)אא(0C)אאא(100C)K
٥-٤ א(10 cm)אא،אא،(0C)(100C)K
٥-٥ א(100 cm3)אאא،(22C)،אאאא(28C)א
WאאK؟5.1א 10-4 /C
٥-٦ (a)(b)(A = ab)،א()אאא،(T)אאא،
(a)،(b)Wאאא،אא A = 2 A T
Wאאא
ab
ba
אאEF
١٢٢
אאאא
‐١٣٨ J
אא،אאאWא،K
٥-٧ אKאאEאאFאאאאא،אאאאא
()אאאא(T)אWא T
()Kאא
K؟אאא
٥-٨ אא--אא(130 g)אאא،(15C)א،אאא
W (236 J/kg. K)
٥-٩ (200 W)،(100 g)אאאאאא،א
אאאאא(23C)א،אאWאאאא(4100 J/kg. K)K
٥-١٠ א(1500 kg)،א(90 km/h)א،א(80 m)אאא،Kאאא
٥-١١ black body(50 cm2)א،(1000C)،אאא(30 s)K
W-5.67 10-8 W.m-2. K-4
אאאW(5-29)K
אאEF
١٢٢
אאאא
‐١٣٩ J
FאEAppendix אאאPhysical Constants
א אאא אאabsolute zero temperature K0 C15.273
אאא
acceleration due to gravity at sea level (Washington d. c.)
2s/m801.9
Avogadro’s number ON mole/particles10022.6 23
א charge of an electron e C106022.1 19
constant in Coulomb’s K 229 kg/m.N10988.8
אא gravitational constant G 2211 kg/m.N10673.6
א mass of an electron em kg10109.9 31
א mass of a proton pm kg10673.1 27
Planck’s constant h s.eV10136.4
Hz/J10626.615
34
א speed of light in a vacuum c )exact(s/m1099792458.2 8
א mass of neutron nm kg1067492.1 27
אאpermittivity of space o m/F1085.8 12
אאpermeability constant o A/m.T104 7
אConversion Factors ١אאatomic mass unit = 227 c/MeV5.931kg10661.1
١electronvolt = J10602.1 19
١Joule = m.N1
١Joule = C.V1
١coulomb = )unitseargchelementary(10242.6 18
אאEF
١٢٢
אאאא
‐١٤٠ J
FאEAppendix
אאאMathematical SignsW ؛
א١٠Arithmatic Power ofW
abba
baba
baba
1010
1010/10
101010
אAlgebraW الكسورFractions:
bd
bcad
d
c
b
a
bc
ad
d
cb
a
bd
ac
d
c
b
a
cd
b
dc
b
c
ab
c
ba
:جذرا المعادلة التربيعية
א0cbxax2 ،a2
ac4bbx
2 K
א0x2x2 ، 2xK
אאEF
١٢٢
אאאא
‐١٤١ J
אTrigonometryW تعاريف الدوال المثلثيةDefinitions of trigonometnc Functions:
אאאinverse functionsFאWEsinu F،uEusinarcF،-١uEusin 1WאאאאKucosarc،utanarcKא
y
x
tan
1ctn
x
y
cos
sintan
x
r
cos
1sec
r
xcos
y
r
sin
1csc
r
ysin
خواص بسيطةSimple Properties:
tan)(tancos)(cossin)(sin
ctntan
1
2tansin
2coscos
2sin
tan)(tancos)(cossin)(sin
אאEF
١٢٢
אאאא
‐١٤٢ J
خواص مثلثProperties of a triangle:
sin
c
sin
b
sin
a
cosab2bac
cosca2acb
cosbc2cba
222
222
222
2
W222 cba
الدوال المثلثيةTrigonometric functions:
אאEF
١٢٢
אאאא
‐١٤٣ J
אאאאאאאKא
אאאWא
tan)(tan
cos)(cos
sin)(sin
Wאא
tan)(tan
cos)(cos
sin)(sin
Wאאאאא
tan)(tan
cos)(cos
sin)(sin
Wאא،א
tan
1ctn
cos
1sec
sin
1csc
אאEF
١٢٢
אאאא
‐١٤٤ J
FאE
Appen
dix
אאEF
١٢٢
אאאא
‐١٤٥ J
EFאAppendix אאא
אאאא אWאאא
אא،אאאא
א،W NKאאאW gmKאW
Wאאא
61.0
61.0
)s/m8.9)(kg79(
N470
N
f
Nf
k
2k
k
kk
אWאאא אאK
אאאאאא،
אאEF
١٢٢
אאאא
‐١٤٦ J
Wא
amfk
Wאא
12.0
)s/m8.9)(kg11.0(
N13.0
mg
f
gmf
gmN
0gmN
Nf
N13.0f
N13.0)kg11.0)(s/m2.1(f
s/m2.1)m15(2
)s/m6(
x2
va
0v
xa2vv
k
2k
k
kk
kk
k
2k
222
o
f
2o
2f
אאEF
١٢٢
אאאא
‐١٤٧ J
אאאא אWאאא
א 314 rad 157rad/s
24 rev 210rev/min
425rad/s 114.6deg/s
אאאאW 50.3rad/s , 15.1 m/s
אאאאW 6.28 rad/s2EF157 cm/s
אאאאאW 56 rev , 110 m
אאאאW EF3.1 m/sEF39 m/s2EF59 N
אאאאW 502 rev , 31.4s
אאEF
١٢٢
אאאא
‐١٤٨ J
אאאא אWאאא
١-א(A)א،אא،אאW
)732.12(mgmghU A
Wא 0mv)2/1(K 2
oA
)v( 2oKא
א)B(Wאא0UB א،)0h( א)B(Wאא،
2B vm)2/1(K
אאאאאא،
Wאאאא،אאא
s/m2287v
mv)2/1()m267.0)(s/m8.9(m
KU
0KUW
B
2B
2
אא)B(K
אאEF
١٢٢
אאאא
‐١٤٩ J
٢-אא)C(אאאא)B()C(W
0v0mvm)2/1(0
KU
)0h(0U
0W
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אא The References
אאאThe Arabic ReferencesW
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אאאThe English ReferencesW
אא א Fundamentals of physicsJohn Willey
College PhysicsAddison Electric Devices and CircuitsMc Graw
ElectronicsMc Graw Electronic Devices and Circuits Mc Graw
