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ÇÔªÒ PAT2
Sk7 ph
Sk7 ph
Sk7 ph
Sk7 ph
Sk7 ph
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
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
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
(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
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
s
2h
d
s
2h
d
s =
s =
tan s = s tan = = H
D
6
(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
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
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
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
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
(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
(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
= .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
( )
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
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
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
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
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
5. การสะท้อนคลืÉน แบ่งตามลักษณะการสะท้อนได้ 2 แบบ คือ
5.1 การสะท้อนปลายปิดหรือปลายตรึงแน่น phase จะเปลีÉยนไป radS หรือ 180 องศา
5.2 การสะท้อนปลายเปิดหรือปลายอิสระ phase จะเปลีÉยนไป 0 องศา หรือ phase คงเดิมในการ
สะท้อนของคลืÉนยังคงกฎการสะท้อนไว้
6. การหักเหของคลืÉนเป็นไปตามกฎของ Snell
1 1 1 2
1 2 1 2
2 2 2 1
sin
,
sin
v
f f
v
T O K
K
T O K
v ลึก > v นํÊาตืÊน และ O ลึก > O ตืÊน
7. การแทรกสอดของคลืÉนนํÊา แบ่งได้ 2 ลักษณะคือ
7.1 Inphase แนวตรงกลางได้ 0A
หา A; ผลต่างระยะทาง , 0,1,2,3,.....n nO
หา N: ผลต่างระยะทาง
1
, 1,2,3,.....
2
n nO
§ ·
¨ ¸
© ¹
7.2 Out of phase แนวตรงกลางได้ 0N
หา N; ผลต่างระยะทาง , 0,1,2,3,.....n nO
หา A : ผลต่างระยะทาง
1
, 1,2,3,.....
2
n nO
§ ·
¨ ¸
© ¹
8. การเลีÊยวเบนผ่าน slit เดีÉยว
8.1 ถ้า d Od จะไม่เกิดแนว Node แสดงว่าการเลีÊยวเบนเด่นชัด
8.2 ถ้า d O! จะเกิดแนว Node ขึÊนรอบจุดกึÉงกลางของช่องเปิด โดยทีÉ
sin , 1,2,3,.....d n nT O ( ใช้หา Node)
20
( ) 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
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
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
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
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
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
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
* 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
(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
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
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
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
20. Diode
P-type ( 1 )
N-type
P N
I P N
P N
I
33
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
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
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
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
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
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
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
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
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
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
(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
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
(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
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
. . 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
4. 50
4 1.80
5. 360 0.8
1
1 = 1 2 = 4 3 = 4 4 = 3 5 = 1 6 = 3 7 = 3
8 = 1 9 = 3 10 = 2 11 = 2 12 = 1 13 = 4 14 = 3
15 = 2 16 = 4 17 = 2 18 = 3 19 = 2 20 = 2 21 = 4
22 = 1 23 = 3 24 = 4 25 = 2 26 = 2 27 = 1 28 = 1
29 = 4 30 = 3 31 = 1 32 = 1 33 = 1 34 = 4 35 = 3
36 = 3 37 = 3 38 = 1 39 = 1 40 = 1 41 = 3 42 = 4
43 = 2 44 = 2 45 = 4 46 = 1 47 = 3 48 = 3 49 = 4
50 = 2
2
1. 3
4
a g
2. 0.8 .m cm
3. 300 .d m
4. 45 mv
s
5. 2 288T K
1.8 m
64
Sk7 ph
Sk7 ph
Sk7 ph
Sk7 ph
Sk7 ph
Sk7 ph

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Sk7 ph

  • 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
  • 12. s 2h d s 2h d s = s = tan s = s tan = = H D 6
  • 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
  • 26. 5. การสะท้อนคลืÉน แบ่งตามลักษณะการสะท้อนได้ 2 แบบ คือ 5.1 การสะท้อนปลายปิดหรือปลายตรึงแน่น phase จะเปลีÉยนไป radS หรือ 180 องศา 5.2 การสะท้อนปลายเปิดหรือปลายอิสระ phase จะเปลีÉยนไป 0 องศา หรือ phase คงเดิมในการ สะท้อนของคลืÉนยังคงกฎการสะท้อนไว้ 6. การหักเหของคลืÉนเป็นไปตามกฎของ Snell 1 1 1 2 1 2 1 2 2 2 2 1 sin , sin v f f v T O K K T O K v ลึก > v นํÊาตืÊน และ O ลึก > O ตืÊน 7. การแทรกสอดของคลืÉนนํÊา แบ่งได้ 2 ลักษณะคือ 7.1 Inphase แนวตรงกลางได้ 0A หา A; ผลต่างระยะทาง , 0,1,2,3,.....n nO หา N: ผลต่างระยะทาง 1 , 1,2,3,..... 2 n nO § · ¨ ¸ © ¹ 7.2 Out of phase แนวตรงกลางได้ 0N หา N; ผลต่างระยะทาง , 0,1,2,3,.....n nO หา A : ผลต่างระยะทาง 1 , 1,2,3,..... 2 n nO § · ¨ ¸ © ¹ 8. การเลีÊยวเบนผ่าน slit เดีÉยว 8.1 ถ้า d Od จะไม่เกิดแนว Node แสดงว่าการเลีÊยวเบนเด่นชัด 8.2 ถ้า d O! จะเกิดแนว Node ขึÊนรอบจุดกึÉงกลางของช่องเปิด โดยทีÉ sin , 1,2,3,.....d n nT O ( ใช้หา Node) 20
  • 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
  • 39. 20. Diode P-type ( 1 ) N-type P N I P N P N I 33
  • 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
  • 70. 4. 50 4 1.80 5. 360 0.8 1 1 = 1 2 = 4 3 = 4 4 = 3 5 = 1 6 = 3 7 = 3 8 = 1 9 = 3 10 = 2 11 = 2 12 = 1 13 = 4 14 = 3 15 = 2 16 = 4 17 = 2 18 = 3 19 = 2 20 = 2 21 = 4 22 = 1 23 = 3 24 = 4 25 = 2 26 = 2 27 = 1 28 = 1 29 = 4 30 = 3 31 = 1 32 = 1 33 = 1 34 = 4 35 = 3 36 = 3 37 = 3 38 = 1 39 = 1 40 = 1 41 = 3 42 = 4 43 = 2 44 = 2 45 = 4 46 = 1 47 = 3 48 = 3 49 = 4 50 = 2 2 1. 3 4 a g 2. 0.8 .m cm 3. 300 .d m 4. 45 mv s 5. 2 288T K 1.8 m 64