4. F 7 ( )
ʽ ก F 7 . . 2555
ก F F F F
g = 9.8 m/s2 π = 3.14159
180 = π log10(2) = 0.3010
sin 30 = cos 60 = 1
2
sin 60 = cos 30 =
3
2
1. กF ก ก ก F ก Fm1
Fก ก g ˈ F ก F F กm2
F ก ก
1. 2.m2g (m2 − m1)g
3. 4.m2m1
m1 −m2
g
m2m1
m2 −m1
g
5. m2m1
m2 +m1
g
5
: = maΣF
=m2g (m1 + m2)a
a = m2g
m1 +m2
: = mammmm1111 Σ F
T = m1


m2g
m1 + m2


T = m2m1
m1 +m2
g
m2
m1
N
T
T
a
a
m g2
m g1
m1
m2
1

5. 2. F ก ก ( F ก กก ( F1
2
MR2)
Fก F ก ก ก F F F กMR2)
F ก ก F ก กก
F
1. 2. 3. 4.2
3
4
3
3
2
3
4
5. 1
2
1
1 : F c ˈ F ก FI = cmR2
ก =E1 E2
Mgh = 1
2
Mv2 + 1
2
Iω2
Mgh = 1
2
Mv2 + 1
2
cMR2

v
R


2
gh = 1
2
v2(1 + c)
v = 2gh
1+ c
→ v α 1
1+ c
v
v =
1+ k
1+ k
= 1 +1
1+ 1
2
= 2
3
2 :
ก =E1 E2
Mgh = 1
2
Mv2 + 1
2
Iω2
ก ก : Mgh = 1
2
Mv2 + 1
2


1
2
MR2


v2 

v ก ก = 4
3
gh = 2
3
gh (1)
ก กก : Mgh = 1
2
Mv2 + 1
2
(MR2)
v2 

v ก กก = gh (2)
(1)
(2)
:
v
v =
2
3
gh
gh
= 2
3
1
2
v
h
ω
ก กก ก ก
ก กกก ก
1
2
v
h
ω
ก ก ก ก
ก กก
ก ก
ก กก
ก กก
2

6. 3. ก 3 ก F ก F
ก F ก ก ก F F ก Fก
ก ˈ ก F F
1. F 2. F1
8
1
4
3. ˈ 4 F 4. ˈ F8
5. ˈ 8 F
3
ก
R3 αT2


R2
R1


3
= 

T2
T1


2
= 

24
3


2
= 82 = 64
R2
R1
= 4
∴ F F ก Fก ก ˈ 4 F F
4. 75 kg กก ก F F F F F ก
ก ก F ก F Fก ˈ 100 cm ก
F ˈ 150 cm
1. 245 N 2. 250 N
3. 368 N 4. 490 N
5. 735 N
1
F F F F ก R ก ก ก
F F F F ก R F
M = M O
mg100 = 2R150
75(9.8)(100) = 2R150 → R = 245 N
O
mg
2RN
100 cm
150 cm
3

7. 5. ก F ก ก ก FM1 M2
ก ก F F ก F ก ก F FM2
F ก T2
T1
1. 2.M2
M1
M1
M2
3. 4.1 +
M2
M1
1 +
M1
M2
5. 1 −
M2
M1
3
1
: = maΣF
=T2 − µm1g − µm2g (m1 + m2)a
=T2 (m1 + m2)a + (m1 + m2)µg
=T2 (m1 + m2)(a + µg) (1)
m1 : = maΣF
=T1 − µm1g m1a
=T1 m1a + µm1g
=T1 m1(a + µg) (2)
(1)
(2)
:
T2
T1
=
(m1 +m2)(a +µg)
m1(a+ µg)
=
m1 + m2
m1
2
ก F
T2
m1 +m2
=
T1
m1
→
T2
T1
=
m1 +m2
m1
M2M1
T1 T2
F F
a a
m m
T1
1 2
T2
f = m g1 1µ f = m g2 2µ
a a
m m
T1
1 2
T2
4

8. 6. F A F F กก ก Fρ
F F ก ก F กν
1. 2. 3. 4.ρAν ρAν2 ρAν3 ν
ρA
5. ν2
ρA
2
ก ΣF ⋅ t = m(v − u)
ΣF ⋅ t = ρVv
l vΣF ⋅ t = ρA
ΣF = ρA t v = ρAv2
7. F F F F F ก F
ก F F F ˈ F ก ก
F ก F ก F
ก ก ก ก
ก 1 1
318 11.2
14.5 4.0
1. ก < < 2. < < ก
3. < ก < 4. < < ก
5. < ก <
5
F M ก = M , R ก = R
ก g = GM
R2
g ก = GM
R2
g = G(318M)
(11.2R)2
= 2.54GM
R2
g = G(14.5M)
(4R)2
= 0.91GM
R2
mg < mg ก < mg
l
l
A v
ก
v
5

9. 8. 50 kg 5.0 m 5.0 s F ก
ก F ก F 20%
F F ก F F ก
1. 98 J/s 2. 392 J/s 3. 490 J/s 4. 1960 J/s
5. 2450 J/s
2
Q = 80% p F FE
Q = 80
100
mgh
=Q
t
80
100
mgh
t =
80
100
(50)(9.8)(5)
5
= 392 J
s
∴ ก F F ก = 392 J
s
9. F ( ก x) F F
F ก F ˈ ก ก F F
+x F ก F ก ก F F
t = 0 F ˈ กt = T1
1. 2.1
3
T1
1
2
T1
3. 4.2
2
T1
2 − 2
2
T1
5. 2 + 2
2
T1
4
กก Fก F F
F ก(a) = v − t = −
V0
T1
: S = Fก กt = 0 − t =
T0
2
1
2
t = 0 − t =
T0
2
S = 1
2


1
2
V0T
 = 1
4
V0t
ก S = ut + 1
2
gt2
=1
4
V0T1 V0t + 1
2

−
V0
T1

 t2
V0
T1
6

10. F ก4T1
F =T1
2
4T1t − 2t2
= 02t2 − 4T1t + T1
2
t =
− (−4T1) ± (−4T1 )2 − 4(2)(T1
2
)
2(2)
=
4T1 ± 8T1
2
4
= 4T1 ±2 2 T1
4
=



2± 2
2


 T1
F t = 


2− 2
2


 T1
10. F F F ก
F F F ก กก F ก F F
ก F F ก
1. 2. 3. 1 4. 21
4
1
2
5. 4
2
ก r = mv
qB
v B r α m
q
rα
rp
= 

mα
mp




qp
qα

 = 

4
1




1
2

 = 2
7

11. 11. F F ก 300 N/m 50.0 cm
1.00 kg F F F ก ก ก
10.0 cm F F F
1. 46.5 cm 2. 50.0 cm 3. 55.3 cm 4. 60.0 cm
5. 65.3 cm
3
=E1 E2
= mgh1
2
kx2
=1
2
(300)(0.1)2 1(9.8)h
h = 0.153 m = 15.3 cm
∴ F = 40 cm + 15.3 cm
= 55.3 cm
m
h
10 cm
40 cm
50 cm
(1)
(2)
8

12. 12. F F F920 kg/m3
F F F ˈ F F1030 kg/m3
1. 11% 2. 21% 3. 50% 4. 79%
5. 89%
1
=
= mgFB
V g = V gρ ρ
ก ˈ =V
V
ρ
ρ
F V = Vρ
ρ
= = 0.89 V

920
1030

 V
= 89% V
∴ = 11%
13. F F ʽ F (double slit) F F ʽ
0.03 mm F F ʽ F F F ก ก ˈ 1.5 m ก F F
F F ก ก ก ก ˈ 5.0 cm
1. 250 nm 2. 400 nm 3. 500 nm 4. 667 nm
5. 1000 nm
3
F 2 ก ก F F
=dx
L
n λ
=(0.03×10−3)(5× 10−2)
1.5
2 λ
=λ 500 × 10−9m = 500 nm
mg FB
x A2
L
0
9

13. 14. F F F ˂ F ก F
F F ก ก F F F F F F
ก ˂ ก F F ก F F g ก
1. 0.5g 2. 1.0g 3. 1.5g 4. 2.0g
5. 4.0g
4
ก e F
qE = mg
ก ˂
ก = maΣF
qE + mg = ma
mg + mg = ma
a = 2g
15. ˂ F ก F F 6Ω
1. 6 W 2. 18 W
3. 24 W 4. 36 W
5. 54 W
1
ก กก F VOLT
F F ก F F 6 V6 Ω
P6Ω = V2
R
= 62
6
= 6 W
qE
mg
E e
qE mg
E
E
e
12V
2Ω
6Ω
3Ω
12 V
6 V 6 V
2Ω
6Ω
3Ω
= 2Ω
6
2+1
10

14. 16. F ก F 8.0 m F F 85 dB
F F F ก F 80 m F ˈ ก dB
1. 65 dB 2. 75 dB 3. 83 dB 4. 95 dB
5. 105 dB
1
ก β1 − β2 = 10 log
I2
I1
= 10 log 

R1
R2


2
85 − β2 = 10 log 

80
8


2
85 − β2 = 10 log 102 = 10(2)log 10 = 20
β2 = 65 dB
17. ʽ F F ก กF500 cm3
F F2.0 × 106 Pa
F ก F ก ˂ ก ก ˂ 15 V F ก F
ก ˈ 10 s กF ˈ 1.1 × 107 Pa
F F F F F
1. 2. 3. 4.3
11
Ω 1
3
Ω 1
2
Ω 3Ω
5. 10
3
Ω
2
ก = ( = 0)∆Q ∆U + ∆W ∆W = 0 ∆V
E ˂ = 3
2
∆PV
=V2
R
t 3
2
V∆P
R = 2
3
⋅ V2t
V∆P
= 2
3
⋅
(15)2(10)
(500× 10−6)(1.1× 107 −2 ×106)
= 1
3
Ω
R = 8 m2
R
=80m
1
= 85 dB1β
= ?2β
1
2
F
0
11

15. 18. F ก ก ก F กกF 10.5 cm
F ก ก F ก F ˈ
44.5 cm ก ก F ก F ก ก F F ก
F ก F ก 340 m/s F ˈ F
1. 250 Hz 2. 500 Hz 3. 764 Hz 4. 810 Hz
5. 1000 Hz
2
ก F Fก F F
ก λ
2
= 44.5 − 10.5 cm
λ
2
= 34 cm = 0.34 m
λ = 0.68 m
ก v = fλ → f = v
λ
= 340
0.68
= 500 Hz
19. F 2.0 cm F F ก ก F 1.0 m F
F F ก F ก F ก F
ก
1. F , 100 cm 2. F F , 100 cm
3. F , 200 cm 4. F F , 200 cm
5. F F , 400 cm
2
F F F F
ก F F ก ก F 1 m
F F F
F F ก F ก F F 1 m
กก F F ˈ ก ก ก ก
F = ก = 1 m = 100 cm
10.5 cm
44.5 cm2
λ
S = 1 m'
12

16. 20. F R ก ก C F ก Fก F ก ˂
Fก ˂ F F t F ˈω
F ก F ˂ AI0sin ωt
1. 2.ωCl0sin ωt ωCI0sin 
ωt + π
2


3. 4.l
ωC
I0sin ωt 1
ωC
I0sin 
ωt + π
2


5. 1
ωC
I0sin 
ωt − π
2


5
Vm = ImXC = I0
1
ωC
ก ก C I V I L
F FIC VC
π
2
rad
VC = Vmsin(ωt − π
2
)
VC = 1
ωC
I0sin(ωt − π
2
)
21. ก A F ˈ 100 F
ก B A ˈ T B ˈ 2T
ก F ก A ก B F ก
1. 2. 3. 4.(2 log102)T (2 log210)T 4T
0.693
(4 log102)T
5. (4 log210)T
5
ก F = =NA NB
t
2T
log102 log 102
= =N0
2
t
2T
100N0
2
t
T
t
2T
log 2 2 log 10
= t =2
t
T 100(2
t
2T ) 2(2T)
log10
log 2
= 100 t =2
t
2T (4 log210)T
=log 2
t
2T log 100
ω
A
R
ωI sin t0
~ C
~
A
I sin t0 ω
13

17. 22. F ก ˈ 24 cm F ก F 0.002 s
ก F ก F ˈ ก
F ก
1. 10 m/s 2. 15 m/s 3. 20 m/s 4. 60 m/s
5. 120 m/s
3
ก F ก P → Q
=tPQ
2
3


T
4

 = T
6
= 0.002 sT
6
T = 0.012 s
ก v = λ
T
F v = 0.24
0.012
= 20 m/s
∴ F ก = 20 m/s
23. F F ˈ F ก ˂ F ก ก F ก
ก
1. ก 2. ก F
3. 4.
5.
2
x - rays ˈ F ก ˂ ก
x F ก F F ก F ก กλ
F ก ˂
P(t = 0s)
3060
A
2
A
2
A Q
14

18. 24. F ก ก
n = 3 n = 1 ก F ˂ ( F F )
F
1. 12.1 eV 2. 24.2 eV
3. 1.5 eV 4. 12.1 eV
5. 24.2 eV
5
En =
E1
n2
= −13.6
n2
eV Epn = 2En
n = 3 E3 = − 1.51 eV , Ep3 = 2(−1.51) = − 3.02 eV
n = 2 E2 = − 3.4 eV , Ep2 = 2(−3.4) = − 6.8 eV
n = 1 E1 = − 13.6 eV , Ep1 = 2(−13.6) = − 27.2 eV
∴ ก ก n = 3 n = 1
ก F ˂ = 27.2 − 3.02 = 24.18 eV
≈ 24.2 eV
15

19. 25. F F ก ˈ x F ก ˈ 3 F
F F F ก ˈ ก Fx
2
1. F 2. 6 F3
2
3. F 4. 3 F3
2
5. 6 F
4
F F ก = x F ก m = + 3
F F F F ˈ F
ก m = f
S −f
+3 = f
x −f
= f3x − 3f
f = 3x
4
x
2
F m =
f
S −f
=
3x
4
x
2
− 3x
4
=
3x
4
−x
4
= − 3
∴ F F ก ˈ 3 Fx
2
16