7. 3
1.
2.
3.
2
1. 2.
( 2
/10 smg )
1
2
u v
S v t t
a
2
u v
S v t t
2 v u at S v u gt
3 2
2
1
tatuS v 2
2
1
tatuS
4 2
2
1
tatvS u 2
2
1
tatvS
5 2 2
2v u aS t 2 2
2v u gh
)12(
2
1
)1()( tautStSSt
g Vector g = -10 m/s2
g g = 10 m/s2
1. 0v
1.1 t = 0v
g
1.2 t = t
t =
g
v02
1.3
g
v
h
2
2
0
1
8. 2. 2 0v
x
2.1 2 ( )
2
0
1
x
g
v
t
2.2 2 ( )
2
0
2
x
g
v
t
*
3. 2 h 2
uu
h
t
2
9. 1. (Newton's Law of Motion)
1 0F a = O 1. v = O
2. v =
2 0F
amF
3 0F
Action = Reaction
2.
2
( ) = FG
2
R
GMm
FG ----------------* G = = 6.67 x 10-11 N-m2/kg2
Fg = FG
mg = 2
R
GMm
g = 2
R
GM
-----------*
1
2
mg
mg
= 2
2
)(
R
hR
-------------* 1mg , 2mg h
3.
1. a = 0 v (N) = (mg)
2. a (N) = mg + ma
a (N) = mg - ma
3. a (N) = mg - ma
a (N) = mg + ma
4. = O
3
10. (Equilibrium)
Newton
1. F = 0 , a = 0 1. vu = 0 ( )
2. vu = ( )
2. F 0 , F= ma ( )
3. F = 0 F 0 Action = Reaction
1. F = 0 XF = 0
YF = 0
2. M = 0
Moment
M = SF = sinF S ( Scalar)
3
1. Lami’s Theorem “
Sin ”
sin
F
sin
F
sin
F 321
=
2.
2.1
1 2 3// , // , //F AB F BC F AC
AC
F
BC
F
AB
F 321
=
2F
1F
3F
A
B C
3F
2F
1F
4
11. 2.1
1F AB , 2F AC, 3F BC
BC
F
AC
F
AB
F 321
=
(Friction Force) 2
1. (Static Frictional Force = sf ) ( sf
= F )
maxsf = F = s N 0 s 1
2. (Kinetic Frictional Force = kf )
( kf = k N = )
. . .
maxs sf N = mg sin
s (mg cos ) = mg sin
s =
cosmg
sinmg
= tan
s . . .
k = tan k
k s
(Moment of Couple) ( ) 2
1
F = maxs sf mg ________ *
F]h, = mg
2h
d
*
h h
2
H
A
1F
CB
2F
3F
d
mg
H
fs N
F
h
fs
mg cosmg
mg sin
5
13. (Work)
Work = F S = F S cos (N – m = j)
Work = F S cos =
ma mg S
1 tan
Work = F S cos =
mgS
1 tan
(Energy)
1. Ep = mgh h
2. Eps = F S = SF
2
1
2 = 2
kS
2
1
( 2
kx
2
1
)
3. Ek = 2
mv
2
1
=
2m
p
2
4. , , , ,
E - E = W
( )
Power 1
P =
t
W
=
t
E
=
t
SF
= F v (
s
j
= Watt )
a
fk
a
fk
S
F F
7
14. kg m/s N s
2 Newton
F = ma
F = ma =
m v u
t
.F t = mv mu = 2 1p p
.F t p *
F t F ( 0t )
p
1
F t p
*
Vector 1h
2h
1 22 2p m gh gh
2
p = p *
kE = kE *
8
15. 1. m1 0v
m2 m1 1v
m2 2v
1v = 1 2
0
1 2
m m
m m
v *
2v = 1
0
1 2
2m
m m
v *
2. Ballastic Pendulum
m 0v
l l M
M
glgh
mM
p
v cos122
v = M
p =
M
mM =
M 2 . . .
S gs
mM
p
v 2
4. M
mm
k
x
mM
p
v
5. m1 0v
m2
sinsinsin
210 ppp
2v
1m
0v 0 0u
2m
1m 2m
1v
1v
m1
0v
m2
2v
Mm
0v
Mm
0v
M
M
h
0v
9
16. m1 = m2
0
90
sinsin90sin
221101 vmvmvm
2
PROJECTILE 2
1. 0,X X Xa u v
2. g (~ + 10 m/s2
)
Projectile 4
1. 1 " "
1. cos0vux = xv
2. sin0vuy
3. t = t =
g
v
g
uy sin0
4. t = 2t =
g
v sin2 0
5.
g
v
g
u
h
y
2
sin
2
2
0
2
6.
g
v
tuS xx
2sin2
0
,
g
v
Sx
2
0
max = 450
7. tan =
xS
h4
2. 2 " " 1
1. 0vux
2. 0yu
3. gay
4.
g
h
t
2
5.
g
h
vtvSx
2
00
0v
X
Y
xS
h
h
0v
10
17. 6. = tan =
02v
gt
S
h
x
tan =
02
2
v
gh
tan2
2
tan
0v
gh
v
v
x
y
7. =
3. 3 " " Projectile 1 2
2
1. cos0vux
2. sin0vuy
3. 10 hhH
0h =
1h =
g
v
2
sin22
0
4. tvtuS xx .cos0
tY =
= tX = t
4. 4 " " Projectile
1)
= 0v
= +
cosSx sinSy 1. cos0vux
2. sin0vuy
3. t = t = tpro.
* t
xu
x
cos
cos
0v
S
t 2
0
2
1
.sin gttvy
Sx
x
y
XS
0v
0h
1h
11
18. (Circular Motion)
1. (Circular Motion)
1. (Speed = v )
2.
(Centripetal Acceleration = ca )
3.
2. (Centripetal Force= cF )
cF = 6
1.
cF = f (friction force)
2. cF = T (Tension force)
3.
cF = T sin =
mg = T cos
tan =
Rg
v2
4.
cF = N sin
mg = N cos
5.
( N = )
cF = N sin mg = N cos
6.
cF = mgh ( gh = h )
(Centripetal Acceleration = ac)
2 2
22 2 2
2
4
2 4c
v v r
a r f r rf
t r T
mg
12
19. (Centripetal Force = cF )
2 2
2 2 2
2
4
4c c
mv m r
F ma m r m rf
r T
3.
2 m1, m2
R = F F
Gm m
R
1 2
2 , G =6.67x10-11
N-m2
/Kg2
1.
2.
( )
(Torque)
= Torque = = r F = 2
mr
I = = 2
mr
= I =
L
t
( L = )
L
0 0L 1 2L L 1 1 2 2I I
“ ”
21
.
2
rK E I
13
20. = .k rE K E = 2 21 1
2 2
mv I
Simple Harmonics Motion
Simple Harmonics Motion
“ ” Simple
Harmonics Motion 3
1.
2. ( )
3. ( )
Linear Motion Angular Motion
2
u v
v 1 2
2
v
R
.S v t .t S
R
.v u a t 2 1 .t a
R
21
. .
2
S u t a t 2
1
1
. .
2
t t
2
T
21
. .
2
S v t a t 2
2
1
. .
2
t t 2 f
2 2
2v u aS
2 2
2 1 2
F ma 2
c cF ma m R 2
I mR
P mv L I
21
2
kE mv 21
.
2
rK E I
14
21. ( )
3
1 t = 0, 0
2 t = 0,
3 t = 0, ( )
1 (t=0 ), X = 0
1) tAx sin
2) tAv cos
22
xAv maxv A
3) tAa sin2
xa 2
2
maxa A
2 (t = 0 ), x = A( )
1) tAx cos
2) tAv sin
22
xAv , maxv A
3) tAa cos2
, xa 2
2
maxa A srad
T
f
t
/
2
2
A
x
15
22. Spring
SHM. 2
( )
m
1F
x
2F 1F
2F
xF
xkF
x =
xmax =
1F = k x ( ) 2F = - k x ( )
2
2F = ma = - kx
a = -
k
m
x. = - 2
x
=
T
f
m
k 2
2 T
f
m
k
1
2
Spring
Spring k
Spring
1. Spring Spring
k
k
m
m
1F2F
2k1k
2k
1k
m
m
16
23. 2 k =
ik
1
1
.......
11
1
21 kk
Spring k
Spring k
Spring k 2
Spring 2 k
2. Spring Spring Spring
Spring k * k ik
1k
m
2k
m
1k 2k
17
24. Pendulum
S.H.M. PENDULUM
(F) = - mg sin
ma = - mg sin
a = - g sin
l
x
ggx sin2
l
g2
l
g
l
g
f
T
2
2
g
l
f
T 2
1
cos1cos lllh Momentum
Ballastic Pendulum Pendulum
a Pendulum
a
l
f
T 2
1
a 4
1. ggaa 0
2. a gagagaa
3. a aggagaa
4. a = g 0a a g g g g g
T = Pendulum
mg
mgcos
mgsin
h
l
18
25. 1.
2.
2.1 2
-
-
2.2 2
- ,
-
2.3
- ( )
( )
- ( )
( )
- ( )
( )
3. ( phase ) X
siny x Y
3.1 Inphase 2 phase ( ) 2n rad
360n n I
3.2 Out of phase 2 phase( ) n rad
180n n
2 1 360 360 360
x t
tf
T
2 2 2
x t
tf
T
rad
2 2 2 1 1 2A B A B A Bt f f
4.
S vt v f
19
27. ( ) 8
3 10 /m s
2
1.
2.
A 2
B
C
4
1. 2. 3. 4.
1.
2.
1. 2.
1
1. (S S )
2. ( M = -1 )
3.
4. v
2
5.
S
A B C
21
28. 6.
2
2
1. 2 n
360
1n ( )
2. 2
1 2
X = 180 - 2 X
y S S f f
M
y S f S f
f = ,
1 2
1.
2.
Snail 1 2
1 1 1 2
1 2
2 2 2 1
sin
sin
v
v
( 1 2f f )
1. 1 2 1 2 1 2, v v 1 2
2. 1 2 1 2 1 2, v v 1 2
2 1 2 2
90 90
x
22
29. c
1 1
2 2
cos sin
cos sin
S
S
=
S
S
S =
S = 31 2
1 2 3
.........i
i
S SS S
1.
S f
2.
2 0 ef f 0 eL f f
3. slide S 2f S f
4. ( ) 2 f
2. 2
S 0 02f S f
eS f
3 R G Blue
R + G + B = W
R + G =
h
c
R
R
W
G
B
23
30. R + B =
G + B =
Slit (Double Slit) Grating
= sin , 0,1,2,3,......
dx
d n n
L
=
1
sin , 1,2,3,......
2
dx
d n n
L
Grating,
y
d
x
1
Single Slit
sin , 0,1,2,3,......
dx
d n n
L
( ) ( = E)
2 2
4
4
F I I
E
A R R
( / = = lx )
F = Flux ( ; lm ) = 4 I
I = ( cd )
2
cos
I
E
R
2
1 2
2 1
E R
E R
24
31. v v v ----------------*
v T T = 273 + t
1 1 1
2 2 2
273
273
v T t
v T t
1
2 1 2 1
1
,
2
t
t t
v t
v v t t t
T
t = 0 C 1 0 331.45 /tv v m s
0
0 331 0.6
2 273
t
v t
v v t ----------------------*
Sonar
2 21
( ) ( )
2
h vt l yt
2 21
( )
2
h vt L
v =
=
y = ( )
L =
1. t = S
V
1
V
1
2.
1 2
1 1
t S
v v
X
h
L
25
32. Inphase
(A) (N)
| | = d sin = n , n = 0, 1, 2, 3 -------------- ( A)
| | = d sin =
2
1
n , n = 1, 2, 3, …… ( N)
1. (Resonance) 2
1. ( 1 2 )
fn =
2 1
,
4
n
v
L
n = 1 f1
n = 2 f2 First Overtone
n = 3 f3 Second Overtone
2. ( 2 )
fn = 1 ,
2
n
v nf
L
n = 1 f1
First harmonic frequency
n = 2 f2 Second harmonic frequency
n = 3 f3 Third harmonic frequency
3. 2
fn = 1
2 2
n n T
v nf
L L
, T = (N)
= (kg/m)
2. (Beats) 2
( 7 Hz)
f = |f2 – f1| = = 1 f 7
26
33. 3. (Sound Intensity = I ) 1 .
( / . )
2 2
,
4
P P I
I I
A R R
2
1 2
2 1
I R
I R
--------------------*
* 0I = = 10-12
W/m2
maxI = = 1 W/m2
0
10log
I
I
( dB)
= 2 - 1 = 10 log 2
1
I
I
= 20 log 1
2
R
R
--------------*
0
10log
I
I
= 10 log
0
I
I
= 1 + 10 log n ……. I1 = I2 = I3 = I4 = ……
4. (Octave) ( ) 2 2
C ( ) = 256 Hz, C ( ) = 2 x 256 = 512 Hz
C C C f = 2fC
C 22
C
Doppler effect /
0
( )
( )
L
S
u v
f f
u v
Vector
sin =
1
v
u
S
27
34. * Supper Sonic
Ultra Sonic
Infra Sonic
(ELECTRO-STATICS)
(Coulomb's Law) Charles Augustan de Coulomb
9 2 21 2
2
9.1 10 /
kQ Q
F k N m C
r
(Electric Field)
E = = 1 (
Vector)
E =
F
q 2
kQ
r
(N/C) ...........................*
(Electric - Potential = V) 1
(Infinity)
VAB = VB - VA ------------------ * V =
kQ
r
-------------------*
Work = qV ------------------ *
(E) 2
V
E
d
-------------------*
+ + + + + + + + + + + F qE
qV
F
d
- - - - - - - - - - -
ut
vst
28
35. (Condenser Capacitor)
2 ( ) (C)
Q
C
V
--------------------------*
r kQ
C V
k r
--------------*
3
1. Q = Q1 = Q2 = Q3 = .......*
V = V1 + V2 + V3 + .......*
C =
1
1
iC
-------------*
2. Q = Q1 + Q2 + Q3 + .......*
V = V1 = V2 = V3 = .......*
C = C1 + C2 + C3 + .......*
3.
1.
Q
I
t
C/s = A ( )
2. I nevA
3.
l
R
A
3.1 1 1 1 2
2 2 2 1
R l A
R l A
3.2 1 1 2
2 2 1
R l A
R l A
( )
3.3
2 2 4
1 1 2 2
2 2 1 1
R l A r
R l A r
( )
( r = )
4.
1
S = ( - m)-1
= semen/m
5. 0 1tR R t = - (0
C)-1
6. Ohm V IR
1C 2C 3C 4C
1Q 2Q 3Q 4Q
1C
2C
3C
1Q
2Q
3Q
29
36. 7. 3
7.1 R t iR R
7.2 R
1
1t
i
R
R
2 R = 1 2
1 2
R R
R R
7.3
8. Whetstone Bridge
R5 (VC = VD)
31
2 4
RR
R R
9. y
1 3
1 2 3
x
R R
R
R R R
1 2
1 2 3
y
R R
R
R R R
2 3
1 2 3
z
R R
R
R R R
10. Y
1
x Y y z z x
z
R R R R R R
R
R
2
x Y y z z x
x
R R R R R R
R
R
3
x Y y z z x
y
R R R R R R
R
R
1R
2R
5R
3R
4R
1R 2R
3R
xR
yR
zR
1R 2R
3R
xR
yR
zR
30
37. 11.
E
I
R r
12. Cell 1 C
cell ( Volt)
13. cell cell
14. cell E
15. cell
15.1
nE
I
R nr
E
I
R
r
n
n = cell 1
a cell
2n a E
I
R nr
15.2
E
I
r
R
m
m = cell
15.3
E
I
R r
x y
, x = n, y = m
* max ,
2 2
E E
I
R r
x y
R r
x y
R
E
r
R
E
r
31
38. 16. 1
W
P
t
--------- 16.1
Work = QV --------- 16.2
Q It
Q
I
t
---------- 16.3
2
2 V
P IV I R
R
------------- 16.4
17.
= x ( )/ 103
18.
1 cal = 4.185 ( 4.2 )
2
Work QV I Rt
2
4.2 4.2
I Rt Pt
Heat Work cal
1V 2V
= 1 1
2 2
Pt P
Pt P
1P = P( 1 ) =
2
0
1
P
R
V
0P
2P = P( 2 ) =
2
0
2
P
R
V
0P
2
1 2
2 1
P V
P V
19.
19.1 P =
1 2 3
1
1 1 1
....
tP
P P P
, P =
1
1
iP
19.2 P = 1 2 3 ....tP P P P
P = iP
32
40. 1.
BF Cross Vector v B (Lorentz’s
Force)
BxvqFB
sinqvBFB
BF v B F (
F F )
2. = CF
Rm
R
mv
amF CC
2
2
----------------*
R
v
f
Tt
2
2
rad/s
3.
BF ( CF ) CB FF = 900
q
mV
BqB
mE
qB
mE
qB
p
qB
mv
R k 2122
4.
4.1 q1 = q2 m1 = m2
2
1
2
1
2
1
k
k
E
E
v
v
R
R
4.2 21 qq , 21 mm 21 vv
1
2
2
1
2
1
q
q
m
m
R
R
4.3 90090
B
( )
BxvqFB sinqvBFB
(Helix) =
qB
m
f
T
.21
1 = X = v cos T =
qB
mv cos..2
v
BF
34
41. 5.
I l
X X X X X B X BxvqFB Bx
t
l
q Bxl
t
q
x x X X BxlIF
sin... BlIF _________*
= 90 BlIF ..
6.
6.1.
6.2.
6.3. Solenoid 4
7. (H.C. Oersted )
( ) I
(A.C) B
KI
B
d
, 7
2 10 /K T m A
8.
8.1 2
d
IKI
l
F 21
_____________*
(
l
F
= 1
d = 2 )
B
I
S
1I
2I
F
F
I I
F F F
35
42. 8.2 2
d
IKI
l
F 21
___________________*
9. (Magnetic torque on a current loop)
cos.BINAMc ______________ *
BINAMc max cos = 1, = 0
10. (Induced Current)
t
BlxBA
Blv
t
x
Bl
t
Blx
(E )
I ( i )
I
iI
rR
E
I
I = I - i
I
1I
2I
F
F
SN
I I
F
F
B
g
A
B
B
v
I
I
36
43. sinBlv v B
Blv = 90
R
I
R
Blv
I
IlBF
lB
R
Blv
R
vlB
F
22
Power
RR
vlB
Fv
2222
(Transformer)
(A.C)
V N
2
1
E
E
=
2
1
N
N
---------------------- *
Power input = Power output ( Eff = 100%)
1 1 2 2I E I E
2
1
E
E
=
2
1
I
I
--------------------- *
1
2
2
1
2
1
I
I
N
N
E
E
1
2
2
1
2
1 100
XI
I
N
N
E
E
100%out
ff
IN
P
E
P
1N 2N
37
44. P
2
0
s
P
R
V
P0 =
VS =
sinme E t
sinmi I t
sinmv V t
I = I = rmsI =
I
2
m
*
V = V = rmsv =
2
Vm
*
( ) = = 2 =
2
T
= , T =
R, C L
R = R
C = =
1 1
2
cX
C fC
L = = 2LX L fL
R, C R, L R, C, L Z
1. RCL
phase V I
I V phase I phase V 900
V phase I 90o
CV
CI
LV
LI
R RI V
R
cX LX
38
45. R C LI I I I
V2
= VR
2
+ (VL - VC)2
Z = *)XX(R 2
CL
2
tan = ,L CX X
R
cos =
Z
R
2. V ( VR = VL = VC ) V
2
I =
22
R C LI I I
2
LC
22
X
V
X
V
R
V
Z
V
2
2
1 1 1 1
C LZ R X X
tan =
1 1
,
1
C LX X
R
cos =
Z
R
RCL XC = XL Z = R
1 1
2
f
LC
RCL P = IV cos , cos =
Z
R Power factor
R = O cos = O P = O
XL = XC Z = R cos =
Z
R
= 1, P = IV
R RV I
CV
LV
LX
CX
R
L CV V
RV
V
C LI I
RI
I
I
CI
R RI V
39
46. 1.
A
F
P ( 1
) P = N/m2
= Pascal (Pa) F (N)
2. P = gh ( ) P
3.
3.1
3.2
3.3
( )
4. P = Pa + Pg , Pa = P P = Pa + gh, Pg = P = gh
5.
F = PA
=
2
1
(P + P )A
F =
2
1
gh2l
* Pa Pa P = O F Pa 0
6. F = P.A =
2
1
gh2
l
7.
8. ( ) U 3
2
P = P
A
W
a
F
= a h A H
40
47. 9. (Archimedes' Principle)
(Buoyant force)
cg ”
10.
= . . . =
F
l
F l
2F l 2
11. (Stress)
A
F
(N/m2
)
12. (Strain)
= =
0L
L
13. (Elasticity)
14. (Modulus of Elasticity)
Modulus of Elasticity = Stress/ Strain
15. Young’s Modulus Modulus ( )
Y =
ll
AF
Strian
Stress
/
/
16. (Viscosity)
Stroke
41
48. 17.
1 1 2 2Av A v
Av =
pk
EE
P
V V
=
2
1
1
2
P v gh = 2 2
1 1 1 1 1 2 2 2 2 2
1 1
2 2
P v gh P v gh ----*
0
v = 2gh *
1. tmcQ
2. mLQ
3.
-
-
ab
axTRFc
100
273
80180
32
100
4. BNknR
T
VP
T
VP
2
22
1
11
5.
22
22
11
11
Tm
VP
Tm
VP
6.
22
2
11
1
T
P
T
P
7. nRTPV
TNkPV B
kENPV
3
2
kEPV
3
2
8. TkE Bk
2
3
nRTTNkE Bk
2
3
2
3
42
49. 9. nRTTNkU B
2
3
2
3
10. VPW
11. WUQ
12.
P
m
Tk
vv B
rms
332
13. T =
i
ii
n
Tn
14. Q U W WUQ ------------------*
43
50. (Sir Joseph John Thomson) ”
”( Rutherford )
Thomson
RB
v
m
q
Cathode
B
E
v
Thomson
J.J. Thomson e m
gE FF
mgqE
E
mg
q
V
mgd
Rutherford ”
”
Rutherford
1.*
2.*
1
1 H A
Z X 1
1 H
2
0nr n a
2 11
5.3 10n m
2
0n
n
r a
Z
2
11
5.3 10
n
m
Z
6
21 2.18 10
/n
v
v m s
n n
6 2
1 2.18 10 /n
Z Z
v v m s
n n
13
1
nf f
n
15
3
6.65 10
n
2
15
3
6.65 10n
Z
f
n
e 1
2n
E
E
n
2
13.6
eV
n
2
1n
Z
E E
n
=
2
13.6
Z
eV
n
+ + + + +
- - - - -
F=qE
mg
44
51. Spectrum
2 2
1 1 1
H
f i
R
n n
17
1010.1 mxRH
Spectrum H2
1. Lymam ( UV)
2,,
1
1
11
22
nIn
n
RH
2. Balmer ( )
3,,
1
2
11
22
nIn
n
RH
3. Paschen ( Infra-red)
4,,
1
3
11
22
nIn
n
RH
4. Brackett ( Infra-red)
5,,
1
4
11
22
nIn
n
RH
5. Pfund ( Infra-red)
6,,
1
5
11
22
nIn
n
RH
Franck Hertz
James Franck Gustav Ludwing Hertz
Ek (e) (e) Hg
1. Ek (e) 4.9 eV (e) (Hg
)
2. Ek (e) 4.9 eV ( ) Hg 4.9 eV
3. Franck Hertz
E (n = 1) = - 10.4 eV
E 1 (n = 2) = - 5.5 eV
E 2 (n = 3) = - 3.7 eV
4.9 eV
1.8 eV
6.7 eV
45
52. (X - rays)
Wilhelm Konard Roentgen . . 2438 X 2
1. X (Continuous X - rays)
2. X (Characteristic X – rays)
X – rays (e)
1. max
2
maxmax
2
1
)(
hfeVmvE ek
2.
mi
c
fmax
3.
EvoltV
nm
1240
)(
1240
)(
4.
OeV
hc
min
VO = (e) Cathode
VO 1.24 104
Volt
min 10-1
m 1 A
5.
m
hc
v
2
1. Hydrogen Spectrum
2. Spectrum Spectrum ( . .
)
3. . . (e)
4. (e) ( )
(Photoelectric Effect)
(e)
Photo-electron
46
53. Photoelectric effect
1. Ekmax (e) f
Ek max = eVS --------------------------*
VS = A C (e)
C A
2. Photo-electron
(e)
3. f fO Photo-electrom
fO =
Work function (e) (e)
= W = hfO
hf W Photo-electron
hf W Photo-electron
(e) Ek = hf – W
Ek = hf – W
Ek = hf – hfO ---------------------*
Ek = 2
2
1
mv eVS --------------------*
eVS = hf – W -----------------------*
VS =
e
W
f
e
h
--------------------*
Slope (m) =
e
h
Y – intercept (b) = -
e
W
Compton
E = mc2
mv
h
P
h
---------------------*
sV
f
0f
W
e
47
54. . . Bohr (e)
(L = mvr) nh (e)
(e)
(e)
2 r = n n I+
mv
h
nr2
2
h
nmvr = n
(Quantum Mechanics)
2
2
1. (Erwin Schrodinger)
2. (Werner Karl Heisenberg)
Heisenberg ( X )( p)
X
p
Heisenberg “
48
55. 1.
1.1 rays 4
2 He
1.2 rays Cathode-rays 0
1e
1.3 rays 0
0
( MeV)
( )
2.
2.1 ( A )
dN
A N
dt
0
t
A A e 2 2
t
n T
o
A
A
0A 0t
A t t
e = 2.718
= (DecayConstant)( )
1
2.2 0
t
N N e
0
2 2
t
n T
N
N
0N = 0t
N = t t
2.3 0
t
M M e
0
2 2
t
n T
M
M
0M 0t
M t t
2.4 1
2
ln 2 0.693
T
1
2
T =
49
56. 3.
A = B
A A B BN N
4. Mass-spectrograph
4.1
P kE E
21
2
qV mv
2qV
v
m
4.2 E BF F
E
v
B
4.3 B CF F
2
2
mv
qvB
R
1 2RB B q
m
E
5.
1
3
0R R A 15
0 1.2 10R m
1
3
1 1
2 2
R A
R A
6.
2
E mc hf 1 931u MeV
7.
7.1
( Atomic mass 230 ) 2
7.2 Atomic
mass ( )
EF
2B
1B
BF
50
57. g = 9.80 m/s2
e = 1.60 10-19
C c = 3.0 108
m/s
G = 6.67 10-11
Nm2
/kg2
h = 6.6 10-34
J.s
R = 8.31 J/mol.K kB = 1.38 10-23
J/K
kE =
O4
1
= 8.99 109
N.m2
/C2
O = 8.85 10-12
F/m
NA = 6.0 1023
/mol 1 u = 930 MeV
me = 9.11 10-31
kg mp = 1.67 10-27
kg
log 2 = 0.301 log 3 = 0.477
In 2 = 0.693 In 10 = 2.303
= 3.1415 2
= 9.870
= 1000 kg/m3
0 C = 331 m/s
1 = 1.013 105
Pa
1 50 3.0
1. a 45
1
g
a2
1 2.
a
g2
1
3.
g
a2
1 4.
a
g2
1
51
58. 2. 2 10
4 2
2
1. 90 J 2. 72 J
3. 36 J 4. 18 J
3. 2 2 13 6
13
1. 1.33 m 2. 1.00 m
3. 0.75 m 4. 0.67 m
4. v t
4.5
1. 1.0 s 2. 2.0 s
3. 3.0 s 4. 4.0 s
5. 100 50
30
12
1. 2.4 m/s 2. 7.2 m/s
3. 9.6 m/s 4. 14.4 m/s
6. 245 m
45
1. 49 2. 98
3. 176 4. 245
t(s)
/v m s
1 2 3 4
1
2
3
4
52
59. 7.
0.25 /
0.75 /
1. 4: 3 2. 3: 2
3. 3 :1 4. 1 : 3
8. M R 2
MR
5
2
2.8
1. 6.3 m/s
2. 7.4 m/s
3. 9.0 m/s
4. 12 m/s
9. A B B A B
50 N A B
A 3 B
1. 8.3 2. 33
3. 75 4. 300
10. . . .
.
3
2
kg/m3
( )
2.8
.
.
53
60. 1. 1500 2. 1800
3. 2300 4. 3000
11. 1.8 1.2 1.0
9.0
1010
1. 6 N 2. 60 N
3. 600 N 4. 6,000 N
12. M m k
m
M
1. 4 2. 2
3.
2
1
4.
4
1
13. A
1. A
4
1
2. A
2
1
3. A
4
3
4. A
2
3
14. k1 k2 m
d k1
M
g
= T
k
m
k
=
2
T
1k 2k
m
54
61. 1. d
k
k
2
1 2. d
k
k
1
2
3. d
kk
k
21
2 4. d
kk
k
21
1
15. 0.5 2.20
2.64
1. 220 m/s 2. 440 m/s
3. 550 m/s 4. 1100 m/s
16. O
5 2
3 O
1. 1 cm 2. 2 cm
3. 3 cm 4. 4 cm
17. 3.14
80
1. 25 m 2. 50 m
3. 100 m 4. 180 m
18. 1
9.5 26.7
1. 321 2. 331
3. 344 4. 354
l
55
62. 19. 6.0
7.2
1. 0.8 Hz 2. 2.5 Hz
3. 3.3 Hz 4. 4.3 Hz
20. 2 1
10 /
( = 350 / )
1. m
175
165
2. m
165
175
3. m
175
185
4. m
185
175
21.
30 2
1.
3
1
arcsin
2.
3
1
arctan
3.
13
1
arcsin
4.
13
1
arctan
22. A B 1.0 4.0
A 2
B 4 (
)
300
56
63. 1. 0 2. 3
3. 12 4. 30
23. m
1. m 2. (m – 1)
3. (m + 1) 4. m2
24. A 1.50 500
B ŜŝŘ
B
1. 1.35 2. 1.45
3. 1.54 4. 1.67
25. 70.0
a 40.0
řŘ.Ř
1. 8.0 cm 2. 18.7 cm
3. 26.7 cm 4. 34.7 cm
26. 30,000 50 0
333
4.2 .
1. 100
2. 60
3. 20
4. 0
57
64. 27. C a
C b
1. 1
sin sina b
2. sin sina b
3. sin
sin
b
a
4. sin
sin
a
b
28. 1
5 Hz 7 23
25
1. 170 Hz 2. 150 Hz
3. 120 Hz 4. 110 Hz
29. 90
70
1. 77% 2. 70%
3. 20% 4. 1%
30. 500
30
1. 333 nm 2. 353 nm
3. 707 nm 4. 750 nm
31. 20
5
1
1. 16 cm 2. 24 cm
3. 80 cm 4. 120 cm
32. 80
1.5
58
65. 1. 53 cm
2. 80 cm
3. 120 cm
4. 125 cm
33. 293
15
1
75
343
1. 34 J 2. 47 J
3. 72 J 4. 117 J
34. A 2
B
1. 2 10-6
J
2. 3 10-6
J
3. 4 10-6
J
4. 6 10-6
J
35. 10 1
5
1. 0 V 2. 9 103
V
3. 9 104
V 4. 1.8 105
V
36. 200 20
220
10
A 1 F
B 3 F
59
66. 1. 4,840 W 2. 220 W
3. 48.4 W 4. 22.0 W
37. XY X vx = 4 x 105
/
Y vy = 3 x 105
/
0.5 Z
1. 2.4 x 10– 14
N 2. 3.2 x 10– 14
N
3. 4.0 x 10– 14
N 4. 8.0 x 10– 13
N
38. B
m
I
1. 2IB 2. IB
3. 2mg 4. mg
39. m e R
B
1.
m
ReB2
2.
m
eBR2
3.
m
BRe2
4.
m
eBR
40. C
L RMS
g
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
I
I
B
0 sinV
C
60
67. 1.
L
)LC1(
2
V
2
0 2.
C
)LC1(
2
V
2
0
3.
)LC1(
L
V 20 4.
)LC1(
C
V 20
41. Q A, B, C D
R
1. 0 2.
0
Q
R
3.
0
Q
R
4.
04
Q
R
42.
1. I1 – I2 + I3 = 0
2. E – I1R1 – I2 (R2 + r) = 0
3. I2R2 + I3R3 = 0
4. E – I1 (R1 + r) – I3R3 = 0
43.
1. 2.
3. 4.
44. 2.0 300
1. 1.2 eV 2. 2.1 eV
3. 4.2 eV 4. 6.1 eV
45. n
2
13.6
nE
n
2
1
D
Q
CA
B
Q
Q
QO
R
1R
1I
2I
2R
3I
3R
rE
_
61
68. 1. 3.40 10-8
kg.m/s 2. 4.89 10-10
kg.m/s
3. 1.63 10-18
kg.m/s 4. 5.44 10-27
kg.m/s
46.
1. 2.
3. 4.
47. –226
1,620 200 4,860
–226
1. 67 g 2. 50 g
3. 25 g 4. 20 g
48. A A0 B
B0 A a B b
1. 0 0A B
a b
2. 0 0A B
b a
3. 0 0ln A ln B
a b
4. 0 0ln A ln B
b a
49. 2 2 3
1 1 2 3.3H H He X MeV
X
1. 2.
3. 4.
50. SP 32
16
32
15
uuSuP 00054.0,9833.31,9841.31 32
16
32
15
9 x 10-31
Kg 1 eV = 1.6 x 10-19
J, 1 u = 930 MeV
(Relativistic effect)
62
69. 1. 2.2 x 106
m/s 2. 2.9 x 105
m/s
3. 2.3 x 105
m/s 4. 3 x 105
m/s
2 5 6
1. m 2 40 30
50 30
m
g
2. m q V = 2,000
6
5 10v / 0.1B T
3. 600
1
4.0
m
50
40 30
m
q
V B
63
