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/

56. #R,#"R " [ 2 !"#

""$"!" g & '&'(#)"#*+

,

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57.

#R,#"R " [ 2 '-"./(""' " #'$.+ $" .$"'$#*+))

' 50 .+ " 2.5 " $

"," u s = t

50 = (2.5)

u = 40 m/s

$% 3.

v = 0 ' , t = 2.5 s

s = 50 m

u = ?

a

58.

#RR.\,#

" [ 2

" '( A$"! "!A$- 'B# 3 #" (D!#,) B(!#,D) # &# A$"!E+(-!#,) )""! ), $% 2.

59.

#R,#"R

" [ 2

" '(

F21 F12

B A

s

u = 10 m/s

a = g

u = 10 m/s v = 10 m/s

+ !"# "" a = g

A # #","# K A $ 10 m/s $","#*+

A +# $&'( ( v2 = u2 + 2as) M*$","#

B *A+!*.+ "","(-","#K #K*) "","N

#M* ./( "" "+) ./(

($ s ) A E""B *A","N" B

$% 2.

60.

#RR.\,#

" [ 2

" '( K"#)'

'.K "$O" A$ ' " $ ∑F = ma T - f = ma T R N = ma 20 R 0.2(+40) = m(0) ( N = W = +40 a = 0 .)) = 60 N $% 3

= 0.2 f

20 N

40 N

T =20 N

N

W

61.

#RJ,]02I

" [ 2

" '( K"#)'

' A$',#K 3 +A#" mg , " FB F ', "","" ""-&'( ',' # D"# #*+ FB+ F $D"# mg $% 4

62.

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" [ 2

" '( K"#)'

+A) E$ *E T

' .K # "

) T + FB = mg

T + ρℓVg = ρVg T = (ρ - ρℓ)Vg

FB

&

mg

F

(mg) FB

T ρ , V ρℓ

$% 1

63.

#R$RQ1

" [ 2

B#(M ," v ##".' #! $' h

) v = 2gh + v √h $% 4

64.

#R",0%

" [ 2

B# O PV = nRT n R "

) "./(" P T V " V T P " V T " PV T $$[ $% 3

65.

#R,#^ 0_,0

" [ 2

"' - $$ S.H.M. $# ") T = 2ℓ

2 g ) T √ℓ +"*)D$ " #*+'$""E E"$*

$% 1

66.

#RR

" [ 2

" '( K"#)'

) so " 2 "

so = vo t ( " vo ")

so = 20x2

so = 40 m

) + [ "' ) st " 2 "

st = vt t ( " vt ")

L + (L - so) = vt t

2L - 40 = 340x2

L = 360 m $% 1

67.

#RR

" [ 2

" '( K"#)'

N1

n = 1

a = 200 m

"

λ = 630 nm

N$

" A0

N1

L = 2 m

x 2x = ?

t = 2 s

L = ?

so

vo = 20 m/s vt = 340 m/s

L - so

""# !$"K# !$ +## !$"

# "

) !$ a " = n λ ) 200x10-6 = 1x630x10

-9

x = 6.3 mm

2x = 12.6 mm $% 4

68.

#RQ`, .041a 1

" [ 2

AE(#$"(. - (

" '( K"#)'

' I = IG + IS

IS = I - IG

IS = 2.5 R 0.1

IS = 2.4 A

VS = VG (#)

ISRS = IGRG

RS = $%&%$'

RS = .

.)

RS = 83.3 Ω

$% 4

IG = 100 mA RG = 2000 Ω

RS = ?

I = 2.5 A G

IS

69.

#RQ`, b

" [ 2 .K'( )ffgA&M)#" " $"'M

$' #"A -2 )'$()")")ffg+ .)

M " )ffg F = qE M*&)M

-2 )'$() A + B + C+ D M*&)#"

A)#" *) -$" A$# 1 2 -$*)!'

# ## -2 )'$() A + B + C+ D

) W = F.s ( F s ' " ")

W = qE.s

W = 2x10-6x8x(0.03+0.03) (E" C+ D ) . F +N$ s )

W = 0.96 )'

"&(" B D ) 1 " D ) B

VB R VD = ,-+.

/

VB R VD = 01/

VB R VD = /21/

VB R VD = Ed

VB R VD = 8x0.03

VB R VD = 240 "(

$% 3

70.

#RQ`, .041a 2

" [ 2 .K'(

$"M( S )ffg IA )D# " "A A )ffgD# " "A A

, fM( ,$"A+ , B44A #*+"A )ffg IB #*+" "A B "'$"K+ )ffg"A #*+ )

& , B44B , B44A () D# " )ffg"A IB *)&"#,m#$&)# IA

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71.

#RQ`, .041a 2

" [ 2 " '( K"#)'

")ffg ""AM*A" "A" A"-"

"* " R #""A)

E = Ir + IR

12 = 2x2 + 2R

R = 4 Ω .K")ffg $

)ffg# A v = 50 sin (100t)

$$ v = Vm sin5t ) Vm = 50 5 = 100 ".#""A XL = 5L = 100x0.04 = 4 Ω

A )ffg ""A L " R $$

L = 0.04 H , R

I = 2 A

E = 12 V

r = 2 Ω

L = 0.04 H , R

Irms = ?

V = 50 sin (100t)

"" Z = R 7 X" Z = √4 7 4 Z = 4√2 Ω

)ffgDD L

Irms = :;<=>

Irms = ?<√@>

Irms = AB√@4√2

Irms = 6.25 A

$% 2

72.

#R "

" [ 2

A = CBD n = E

FG/@

/ B A"- 2 #/ A +/ A ' 1/3 #

) IA0 = CBD

2n = 3

n = JKIJK n = E

FG/@

) JKIJK = EF

t = T JKIJK $% 2

2 :

$% 98 ' 103 (*+," 6 $%) $%. 4.0 . "0 24 . .,+,+,"cQ2%R3.2,d+, 31%.2beR f 0 2 ,14R

10,1I: b%,f 0+,14R,00,"4,1#4, 5 31%g2$eh b%,f 0+,14R,0

%"4, 5 31%g2 hR

"4,R: 1.414 × 2 = 2.828 31%i 2.83

1.414 × 3 = 4.242 31%i 4.24

9.8 × 5 = 49.0 31%i 49.00

98.

#RR.\,

" [ 2

" '( + A$"! )'

.K#"! " $

B# 2 #"

) ∑Fx = ma F R F = ma

32 cos60 + 20 R 5 = ma

32(1/2) + 20 R 5 = m(0.5)

m = 62.00 kg Ans

99.

#R,#"R0

" [ 2

" '( + A$"!)'

N

mg 32 N

20 N

5 N

60° 32 cos60 N

32 sin60 N 32 N !"#

$ "% &'

a = 0.5 m/s2

m = ?

T = ? mg

r = 0.5 m

m = 1 kg v = 3 m/s

(")* &)+

,+- ' &%#)+

$$" FC = M@N

') " T + mg = M@N

) T + 1(9.8) = I@

.O

T = 18 R 9.8

T = 8.20 N Ans

100.

#R",0%

" [ 2

" '( K+ "#)'

∆Q = ∆U + ∆W

0 = I nR∆T + ∆W

0 = I (2)(8.31)(100) + ∆W

∆W = - 2493.00 J

A$'$ 2493.00 J Ans 101.

#RR . fIc

" [ 2

E++E("E"A.#"!M*'( A

2.75 (M*-A ,E .+-.'("

Q = R +

RS

n = 2

∆T = 100 K ∆Q = 0 ∆W = ?

Q = T +

U.VO f = -2.75

E("""f 2.75 m Ans 102.

#RQ`,b

" [ 2

.K'(

#- "#" #')ffg!'

)ffg F = qE A&.#' &'(

$$" FC = M@N

') " F = M@N

qE = M@N

½ mv2 = ½ qEr

½ mv2 = ½x1x10-6x1x2

½ mv2 = 1.00x10-6 J

" ".( 1.00 J Ans 103.

#R .0

" [ 2 " '( K+ "#)'

A $D" "A#

z(. . hf

$.(' # EKmax "$

.E* )"f|(E W

hf = EKmax + W

e-

hf EKmax + W

W = 2 eV

EKmax = 9 eV

me = 0.5 MeV/c2

hf = EKmax + W

) hf = 9 + 2

hf = 11 eV

hf = mc2

) mc2 = 11

+#f$ mc = 11 eV/c

EKmax = ½ mev2

) 9 eV = ½ x0.5x106 eV/c2x v2

v2 = 36x10-6 c2

v = 6x10-3 c

+# mev = 0.5x106 eV/c2 x6x10-3 c = 3x103 eV/c

" mev / mc = 3x103 / 11

mev / mc = 272.73 Ans

$%* R PAT2 j 2552 1,2kQ2%

*,k40# "P*$% PAT2

P2 .* l I.. 0",R3%,^a2 B2S .fk1 R# "Q