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Page 1: Key pat2 3_53ps

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PAT2 . 53

1 : 4 "#

$% 56 ' 72 (*+," 17 $%) $%. 3.0 . "0 51 . +,1231%4,

g = 9.8 m/s2

h = 6.6 × 10-34 J@s

c = 3.0 × 108 m/s

kB = 1.38 × 10-23 J/K

R = 8.31 J/K.mol

NA = 6.02 × 1023 IJ,

√ = 1.414 √ = 1.732 √ = 2.236 √ = 2.646 ln 2 = 0.693

e = 1.6 x 10-19 C

G = 6.67 x 10-11 m3/(kg.s2)

= 3.14

2,"P12$%Q2%*, R

http://www.onetresult.niets.or.th/ExamGATPAT/

Page 2: Key pat2 3_53ps

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56. #R,#"R " [ 2 )*+*,

- . ./0- 1 230,45678()2-4) 2-1*6

23 = ½ (6+2)x3 + (-½ x2x1) = 11 m

- . D) 1 8 0-2 ) 60.44 (3-0)/(2-0) = 1.5 m/s2 )66782-

8 4-6 ) 60.44 (0-3)/(6-4) = -1.5 m/s2 )046782-

- . D) 160.82--45 )43)04670-)4060.*

82-4)67)82-

$% 1.

57.

#RR.\,# " [ 2 /04*I

)*+48 m1

* ∑F = ma *1 F = m1a1

F = 8m1 ---(1)

)*+48 m2

* s = ut + ½ at2

F m1

a1 = 8 m/s2

t = 2 s

s = 48 m

m2 / m1 = ? F m2 m2

u = 0 a2

Page 3: Key pat2 3_53ps

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48 = 0 + ½ a2(2)2

a2 = 24 m/s2

* ∑F = ma *1 F = m2a2

F = 24m2 ---(2)

(1) = (2) , 8m1 = 24m2

=

$% 3.

58.

#RR, .] RR,

" [ 2

)*+/04*I Q)4+-8/ *)4 4.R/+1104RR 1104RR F 67 0.5 cos30 663-R F , W = F x 0.5 cos30

W = 40 x 0.5 √

W = 17.3 J $% 2.

30° F = 40 N

0.5 m

0.5 cos30

Page 4: Key pat2 3_53ps

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59.

#RJ,]#21I4

" [ 2

/04*I

* 4-/86Q-6 E =

E = /∆/

Q8 A EA = /

∆/ ---- (1)

Q8 B EB = /

∆/ ---- (2)

(1) / (2) , = /

∆/ / /

∆/

= /

∆ / /

∆ (L0A = L0B)

=

∆ /

= 2

(

∆ /

= 2)

= 2 (EB = 2EA)

AA = 4 AB

dA2 = 4( dB

2)

dA2 = 4 dB

2

ΔL

F F

L0 A *I\ ∆

/ ∆

= 2

L0A = L0A

R81 EB = 2EA

Page 5: Key pat2 3_53ps

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dA = 2 dB $% 3.

60.

#RR.\,#

" [ 2

/04*I QR R81)4+-8/

*/42- )*+ 4R1\ 2 R 2-3\6 R81R]))) 238),0I1\67 82-R) * ∑F = ma N - W = ma N = W + ma - 1 , 2 R813 D) 1 77N 67 W *13-/674 a ^-*4_ + , - 2- 0 5 - 4 ./0- 1R))1\67 238),0I467R]))) 238),0I1\67 04]82-- 3 -)06 $% 4

N

a W

Page 6: Key pat2 3_53ps

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61.

#R#

" [ 2

)*+/04*I

*/0\R782(*Q\) 82- 1 -7867 0.4 )

663118282-8 0.4 )67 = 8 m -605-82 * v = v = !".

v = 20 m/s $% 2

62.

#RJ,]02I

" [ 2

)*+/ Q)4+-8/

L/2 W

B L/4

A L/3

W

()

12 m

()

t = 0 s

t = 0.4 s

t = 0.2 s

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)*+Q48-

∑M = W(L/2) = WL/2

∑M04 = W(L/6) = WL/6

∑M > ∑M04 6634-/Q48 - 1. D)

0- )4 ∑M04 67 WL/2 - WL/6 = WL/3 2--/Q48

- 4 ./0- ∑M04 )4367 (4/3)W(L/4) = WL/3

$% 4

63.

#RR

" [ 2

/04*I Q)4+-8/

*/Q6 --Q)Q663 1 R8163 4 411-8\-67 3λ/2 * v = f λ 340 = 400 λ λ = 0.85 m

663 3λ/2 = 3(0.85)/2 3λ/2 = 3(0.85)/2 3λ/2 = 1.275 m = 127.5 cm

f = 400 Hz

v = 340

m/s 663 1

λ/4 λ/2

663 2 663 3 663 4

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$% 2

64.

#R$RQ1

" [ 2

/04*I Q)4+-8/

*]- Q68 ) = *

+, =

*+-

-

, = *

-

, = .""/0.!

0

-

, = 100 -, = 10 $% 2

65.

#R$RQ1

" [ 2

/04*I Q)4+-8/

F = 49 N . A

64 R

W = 500x9.8 N

. a

64 r

-, = ?

R

r

V

v

Page 9: Key pat2 3_53ps

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*)4 ,,Q1 (Av) --8 + 0\Ri8-8406Q4-

Q440-2- A1v1 = A2v2

1R2V = 1r2v R2V = r2v

$% 3

66.

#R",0%

" [ 2

/04*I Q)4+-8/

* ∆Q = ∆U + ∆W ∆Q = nR∆T + 0 2493 = x5x8.31x∆T ∆T = 40 (-+n/4)-RoQ )43) $% 4

67.

#R#041_Q`,

" [ 2

Q_8204 4Q4.\)] 8^6

∆Q = 2493 J

n = 5 mol

∆W = 0 ∆T = ?

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$% 1

68.

#RQ`, .041_ 2

" [ 2

/04*I Q)4+-8/

+14-0-I644 41RQ8*67 I1

*/ E = I1r + I1R

12 = I1x1 + I1x3

I1 = 3 A

+14-0-I4 41RQ8*67 I = 2 A R811RQ,,q686767 I2

* I = I1 I2

2 = 3 I2

I2 = 1 A

R82-,,q6867-4-0-I V2

* V2 = I2(R+r)

V2 = 1x4

V2 = 4 V

$% 3

R = 3 Ω

E = 12 V

r = 1 Ω

M

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69.

#RQ`, a

" [ 2 )*+/ R810682-\0-7 *15D84406I,,q-406571* C1 , C2 (= C3) ,

C4 460-67406I,,q 12 V \0-7- 1 R81- 3 *D)

0*Q-7\0-7*\+

06571* C2 R81 C3 0-67R77 R80--467 C1 R81 C4

4*4- C2 R81 C3

0- C23 = C2 + C3

C23 = 2 + 4

C23 = 6 3F

4*4-63*

0- 44

= 4 +

45 + 46

44 = +

7 +

44 =

C4 = 3F

1*634 Q4 * C = 89

Q4 = C4V4

Q4 = x 12

Q4 = 16 3C Q4 = Q1 = (Q2+ Q3) = Q4

406I-406571*R08106 * C = 89 2- V = 84

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V1 = 84

V1 = 7 ;4 ;

V1 = 4 V

V4 = 8646

V4 = 7 ;4 ;

V4 = 5.3 V

R81 V2 = V3 = 12 - (V1 + V4)

V2 = V3 = 12 - (4 + 5.3)

V2 = V3 = 2.7 V

$% 4

70.

#RQ`, .041_ 1

" [ 2

)*+/04*I _*R77Q07)*I

0*Q-7 --5 = -

-6

" =

.

0.4 = 0.4

_*7)*IQ48 441RQ8D060 20 Ω

6 V

R3=10 Ω 20 Ω

R2=2 Ω R1= 4 Ω

A R4= 5 Ω

Page 13: Key pat2 3_53ps

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40 R1 0--467 R2

404 R12 = R1 + R2

R12 = 4 + 2

R12 = 6 Ω 40 R3 0--467 R4

404 R34 = R3 + R4

R34 = 10 + 5

R34 = 15 Ω 40 R12 0-67 R34

404 -4

= -

+ -56

-4

= 7 + .

-4

= <"

R4 = "< Ω

1RQ,,q8* I

* V = IR

I = 9- 4

I = 75=

I = 1.4 A $% 1

71.

#RQ`, .041_ 2

" [ 2 )*+/04*I

VR *1 )4342-1RQ,,q* I )43 (* VR = IR)

1RQ,,q* I *1 )4342-404 Z 88 (* I = 9> )

Page 14: Key pat2 3_53ps

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84.-,,q1RQQ8674D8\40*)0n -4\ XL 88 (*

XL = ?L = 21fL) R81404 Z 88 (Z = @R B X)

$% 1

72.

#R "

" [ 2

06Q8 467-Q8/0v*1R04Q .8/0v4 6 R04Q 1 = 7 R04Q 2 = 7 R04Q 3 = 7 R04Q n = D7

*14Q64 6wI-06Q8 67*\R04Q n 2- = D7 42-,4Q64 6wI1 67 n *1,Q0446_767 7 (767Q4Q0 y = mx + c *1 E y , n E x , m E 7 R81 c = 0)

$% 2

Page 15: Key pat2 3_53ps

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2 :

$% 98 ' 103 (*+," 6 $%) $%. 4.0 . "0 24 . .,+,+,"bQ2%R3.2,c+, 31%.2adR e 0 2 ,14R

10,1I: a%,e 0+,14R,00,"4,1#4, 5 31%f2$dg a%,e 0+,14R,0

%"4, 5 31%f2 gR

"4,R: 1.414 × 2 = 2.828 31%h 2.83

1.414 × 3 = 4.242 31%h 4.24

9.8 × 5 = 49.0 31%h 49.00

Page 16: Key pat2 3_53ps

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98.

#RR.\,

" [ 2

/04*I QR6341\6760. 8/

)*+82--60.R67 23-

+60. 4*182-8

42-60.-/Qn1Q48

*1 F + f = mg sin60

F = mg sin60 f

F = mg sin60 3(mg cos60) F = 5x9.8x√

0.3(5x9.8x )

F = 35.09 N Ans +60. 4*182-3

42-60.-/Qn1Q48

*1 F = mg sin60 + f

F = mg sin60 + 3(mg cos60) F = 5x9.8x√

+ 0.3(5x9.8x )

F = 49.79 N Ans

F

f 3 = 0.3

N

mg cos60 mg

0.1 m

60°

m = 5 kg

mg sin60

Page 17: Key pat2 3_53ps

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99.

#R,#P]*Q

" [ 2

/04*I Q)4+-8/

)*+82-R) 42-8/7-8084 238 t = 2 )

* sy = uyt + ½ ayt2

0 = uyt + ½(-g)t2

t = FGH ---(1)

118/7-83Q/Q h

* vy2 = uy

2 + 2ays

0 = uy2+ 2(-g)h

uy = @2gh ---(2) R uy = @2gh * (2) 8 (1) *1 t = 2@HK

H

t = L!KH

t2 = !KH

22 = !K0.! h = 4.90 m Ans

u

θ ux uy

t = 2 s

h

Page 18: Key pat2 3_53ps

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100.

#R",0%

" [ 2

/04*I Q)4+634-8/

*]-RoQ PV = nRT

2-* V R81 n

*1 NO = N

O

""" = N"

P 2 = 256.00 kPa Ans 101.

#RR . eIb

" [ 2

/04*I Q)4+634-8/

V1

P1 = 240 kPa

T1 = 273+27 = 300 K

V2 = V1

P2 = ?

T2 = 300+20 = 320 K

s s = 20 cm

C F O

f = 8 cm

Page 19: Key pat2 3_53ps

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* P = +

Q

R ! = " +

Q

s = 13.33

s + s = 20 + 13.33 = 33.33 cm Ans 102.

#RQ`,a

" [ 2

/04*I

42-\06\84 A 67 B R016*1).1* 1*,,q4-.671*

,,q486.2- 360 4/8-47I A ^464_ 4 - B \ A 41*_ 4

- B

R11* * F = R88,

+ r 6**/I884 F = 0/ "S/!!/ "TU/</ "TU

F = 46.66 N Ans (_RD86 11*)6)

+ r 6*D)84 F = 0/ "S/!!/ "TU/</ "TU

. .

F = 40.37 N Ans

QA = 360 3C

aA = 12 cm

QB = 0

aB = 3 cm

QAB = 360 3C

F F

QA = 288 3C QB = 72 3C

r = 200 cm

Page 20: Key pat2 3_53ps

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103.

#R .0

" [ 2 /04*I Q)4+634-8/

482-7-8I = KV

*1 mv = KW v = K

W

v = / "TX/Y/ "Z[

"../ "U/"./ "TS (c = 3x108 m/s)

v = 1.8x106 m/s

* hf = EKmax + W

*1 hf = ½ mv2 + W

4x10-15x4x1015 = ½ x0.5x106x Y\ "Z[ x(1.8x10

6)2 + W

W = 7.00 eV Ans

42-8\RQ17D)81R8\-)80--818

--4 04-6I 86 868-*RQ hf

*1467 86*8IQ/Q--)80- EKmax 467

86-)80-2-,I6 W

hf = EKmax + W

e-

hf EKmax + W

W = ?

= 0.4 nm f = 4x1015 Hz

h = 4x10-15 eVs

me = 0.5 MeV/c2

Page 21: Key pat2 3_53ps

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$%* R PAT2 i 2552 1,2jQ2%

*,j40# "P*$% PAT2

P2 .* k I.. 0",R3%,l_2 B2S .ej1 R# "Q

1 R#.+,


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