() 72 (PAT 2) 7 .. 2553 08.30 - 11.30 . -................................................................. ...................................... ................................................................. ............................................ 1. 2 : 1 : 4 2 : 2. - 3. - 2B 5. 2B () 6. 7. 1 4 2 R 1 4 2 3 2
Key pat2 1_53ps
Jul 07, 2015
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72 (PAT 2) #$ 7 # %. . 2553 )* 08.30 - 11.30 .
/$-0*................................................................. )*1#$$......................................
#$................................................................. 2............................................
34 1. 12)56 2 : #$ 1 : 5 4 )*/ #$ 2 :
2. 3 92)1#/$-0* )*1#$$ #$*:2 912
3. 92)1#/$-0* #$ #$ 2 )*1#$$*:#$
259:3 %2;:)*1#$$*: 23
) 2B )*19* 92)*1#$)1#
5. 9 92923) 2B :*)*/ /
9:392)= (2:) 9*:12#3#$>2/
):#$0)%#3)#
2)*/ )563#$>2 923#;
22)5*#$)*/9 2*:9*)*/) 92:
3)# *2?:*)*/9
6. 2312*::3?2
7. A0B92C>2)12?2 )*
1 4 2 R
1 4 2 3
2
#$ 1 : 5 4 )*/ DE
12 56 F 72 (?3 17 12) 12*: 3.0 : 51 : 392
g = 9.8 m/s2
h = 6.6 × 10-34 JPs
c = 3.0 × 108 m/s
kB = 1.38 × 10-23 J/K
R = 8.31 J/K.mol
NA = 6.02 × 1023 0X
√ = 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
56. D31)# 4 )56>5 9)* 5 # )#92#$#:?
) 1. 1 2 2. 2 3 3. 3 4 4. )/$)*/$#$ 4# !"# #$%&##'( )($%&##'($)!"$ (t
= 0) ! "/ 01"2 (t = 5) ! $#4)$%&#"$5('#$%&# "/ 06
'#'($
1 2 3 4 5
31)#, X ())
4
)*, t (#) 0
3 2 1
-1 -2 -3
#$ 1
#$ 2
#$ 3
#$ 4
4
0
3 2 1
-1 -2 -3
#$ 1 #:? 4 m 1;
#$ 2 #:? 2 m *
#$ 3 #:? 2 m 1;
#$ 4 #:? 3 m *
31)#, X ())
5 '('' ("'/#"8#)
12 4.
12 9(: $'!) 56 '()(#' 4!#! 5 !" ($< 2.) 57. 0)*/$#$)56)22)D a)$2)*/$#$?)=2 20 )/#
::#$0)*/$A29)* 4 # )56 #$)
Tips
s !" #$%& $
$ (m)
#!*% ! % ! " *%#+ $ (m)
B
s1
s2
s3 A
s1 , s2 , s3
1& s2 !!
1 2
!# ($/!"2)
2 t (!")
-2 3 4
4
1. 47 2. 69 3. 92 4. 94 )/$)*/$#$ 4# $4!#!!'$0)!(!##$'! &(##)$
4!# !%!'5C(#)'/#&
1"24!#! t = 0 s D# t = 1 s !'$0)!(!# a = 2 m/s2 !6!$ u = 20 m/s
&!6!! t = 1 s v1 = u + at
v1 = 20 + 2(1) = 22 m/s
&(#4!#/ s1 = (u + v1)/2 t
s1 = (20 + 22)/2 (1)
s1 = 21 m
1"24!#! t = 1 s D# t = 2 s !'$0)!(!# a = 0 m/s2 #!!6!#$'! v1= 22
m/s
&(#4!#/ s2 = v1t
s2 = 22 (1)
s2 = 22 m
1"24!#! t = 2 s D# t = 3 s !'$0)!(!# a = 4 m/s2 !6!$ v2 = v1 = 22 m/s
&!6!! t = 3 s v3 = v2 + at
v3 = 22 + 4(1) = 26 m/s
&(#4!#/ s3 = (v2 + v3)/2 t
s3 = (22 + 26)/2 (1)
s3 = 24 m
1"24!#! t = 3 s D# t = 4 s !'$0)!(!# a = -2 m/s2 !6!$ v3 = 26 m/s
&!6!! t = 4 s v4 = v3 + at
v4 = 26 + -2(1) = 24 m/s
&(#4!#/ s4 = (v3 + v4)/2 t
s4 = (26 + 24)/2 (1)
s4 = 25 m
(#)4!# 4 !" s = s1 + s2 + s3 + s4
s = 21 + 22 + 24 + 25
s = 92 m 12 3.
12 !'$0)5C $#!(!#$ 9("$)!6!$ 10 $/!" <#4!#!)5C 4 4!#'#5 4!#!!'$0)(#'
Tips
&!2 !3 4 u / 7$ t 4
v / # s !% ! #
!!! 2% $ a = 4 !% ! #$
#
- !!3 2* >$ >2! ?3>4@& #%>% #
#$%*
- 4 $+2" ! ! s = vt
a =
1. v = u + at
2. s = t 3. s = ut + at
2
4. v2 = u2 + 2as
u a
tv
1 2
!# ($/!"2)
2 t (!")
-2 3 4
A
B
C D
1. A B 2. A C 3. A , B C 2. A , B , C D ($< 3.)
58. 0 2 2 #*A) a#$*2#$ 1 #1)56)1*2#$ 2 25*0;
92)#?> 50 ) 129*>2
1. !'$0'/# #!#' 2. !'$0'/# #4!$D#1)/' 3. !'$0 1 <1)/!(!6!!!'$0 2 4. %$<! 1
)/$)*/$#$ 4# !'$0)(#" M($#9!##9 )"N#$#8 !!'$0N$
) &5(!'$0!$#'#! #(!' !'$0'#!)!(!#
#$'!''<!9!# g $D#1)/!(!' !(!6!'
12 2.
4 !"#$%$
Tips
! "!
$$C%* $ /% $$!?$C$% C! g +
2$+2"!% C! $7#% !+ $7$ $ 4
# % !
a = g a = g
12
!$#(!'<)(#" M($#9!##9
1. !'$0!#D/)!#!'$0#!(!6! #
2. 9(!'$0D/5!'$0)!(!&!# )D#0 # 0!)#!(!#
3. !# &)5(!'$0#! #(!' !'$0D#1)/!'
4. 0
($< 2.)
59. a*>*1;A59$):$ %%4:>*>*9
$?%/; )* )56>5 ))/$?a21#;##$)/#2
1. 5.3 2. 10 3. 16 4. 20
)/$)*/$#$ 4# 55C! '1'P:&!#! #!"##<1)/ '<! 1<!<D/5
# 0(# 50 $1)/ ! 2.5 !" $'<#
&' %(
(# ($)
! (!")
60 50 40 30 20 10 0 0 1 2 3 4 5
&!6!$ u s = t
50 = (2.5)
u = 40 m/s
&!# g v = u + gt
0 = 40 + (-g)(2.5)
g = 16 m/s2 12 3.
v = 0 0 # 0 , t = 2.5 s
s = 50 m
u
a = g = ?
Tips
! "!
>E 2 4 2 % ! #>!3&#$$ a g = 9.8 m/s2 (>E
10 m/s2) C+ 2$+2"!C! $$C%* $
! #$> 2 *..>+4 u ?! +%
!? u #$?# >2
+ u + s - s - g
- v
v = 0 0 # 0
+ u
+ v
+ g
+ s 1. v = u + gt
2. s = t 3. s = ut + gt
2
4. v2 = u2 + 2gs
12 !#&"#!"#'<! # 50 $1)/ <!&:!#&D# !(!6!$ 15 $/!" &"$D#1)/M(! 2 !" !#)##9!##!!#/$/!"2 1. 5.0 2. 10 3. 15 4. 20
($< 2.)
60. :)*>$)*/$#$a%)?A* (projectile motion) )/$)*/$#$?0>0:))56
* 3 2#$) 2##$:)#*2)*/$#$9$2)=) 129A5#;
05A2>2)#$*2#$ ##$:))
1. !6!5C 3 #!6!#<" 2 0 # 0<" 2. 1'##:5C 3 #1'##:#<" 2 0 # 0<" 3. 9$'5C 3 #9$'#<" 2 0 # 0<" 4. %$<! 1 )/$a) *:* 4# !5$9(: <")<<91: 0 # 0!6!!"#5C8(: '#'/!6!#<"0 # 0D#R1!6!!'< SD##$'!$) $"&5C vx & !#<"<"5C m !#<"$&'#<"5C m/3 (1<"5C 3 ')
)$& g ) #+ %!,-$
<"
m/3
m v2 = v1
v1
vx
vy = 0
0 # 0 v3
&'#<"
m/3 m/3
1
2 3
!6!&'#<"#!'/# 5C v1 , v2 v3 $%'< 'V25C )4<<()&(0#!'$0 N!#9$'<"'<N!#9$'&'#<"$W0'V:9$' N!#1'#:<"'<N!#1'#:&'#<" 5 <"<"N!#9$'!"#'< 0 1 vy = 0 &'#<"<"$#N!#9$'!"#'< 0 !('#'/! 1 2 SD#!'$6!'$#)5"8$#'!"# D#%&N!#9$'!"##!'/# 5C 0 ! 3 $#)5!'<"8#(!'<<"<" D#%&N!#9$'<"'<N!#9$'&'#<" 1. $# 1"2!'< N!#9$'<" = N!#9$'&'#<" mvx =
v3
v3 = 3vx 2. $#
1'##:#<"<" EK = mvx
2
1'##:#! 3 &'#<" EK3 = v32
EK3 = (3vx)2
EK3 = 3 mvx
2 EK3 = 3EK 3. N" 9$'#<"<" p = mvx
9$'#! 3 &'#<" p3 = v3
p3 = (3vx)
p3 = mvx
p3 = p 12 4.
12 <"&D#!#(<1)/< )04! " 6<"5C 4"/
3. 5 4. 6
)/$a)*:*
4#
!5$9(:
'V25C )4<<()&(0#!'$0 N!#9$'D#'<N!#
9$'&'#D#$W0'V:9$' 5 D#N!#9$''/# #'< 0
1('#) u = 0
&'#D#$#N!#9$''< 0 !('#'/19$'$'$"8##
9$'$#'D#!'<<!$:!5C8(:
1"2R19$'&'#D# m1v1 = m2v2
&'#D#4('/# 2 )!(!6!#$'! 11)/)# (
) m1 , m2 v = ( s = vt ) v #$'!)
100 = 50 2x = 9-x
x = 3 m 12 1.
D#
m1 = 100 kg m2 = 50 kg
9 m
u1 = 0 u2 = 0
&'#D#
v1#$'! v2 #$'!
9 - x x 1)/)
12 64(N ! 30 "9' 64(! ! 60 "9' ()"#4"'< 6$<:' '6'/# ##N'' $# 1. 64(N)64(!)
Tips
!
C p & %% %$!? 24
! " +!?+% 4 $ kg m/s
&
1. &)*
- 7% C!$ E = 7% CE ( ∑4 = ∑&'#4 ) - 7% &"!$ E = 7% &"E ( ∑ !4 = ∑ !&'#4 )
- E!># u1 + v1 = u2 + v2
2. &$)*
- 7% C!$ E = 7% CE ( ∑4 = ∑&'#4 ) - 7% &"!$ E " 7% &"E ( ∑ !4 " ∑ !&'#4 )
- !E#??$$ E$!E! #E! 2$ !?
),- C! "+!!?+% 4 ?!?!#??! " C
% +
!'$0! m )!(!6! v
9$' p = mv
p = mv m
v
4
u1 u2
m1 m2
&'#4
v1 v2
m1 m2
2. 64('/# #)!('$6!' 3. 64('/# #9$'' 4. 64(N1'##:5C 2 #64(! ($< 4.)
,' #+
62. 1)* A #)56 1.2 )1 B )/$30$*91)* B 5g#
5#$?*)56 0.6 )15; 230#;*91)* A 5#$
?*91)* A )56)915;
1. 0.4 2. 0.5
3. 0.6 4. 0.8
)/$1A*
4#
!5$9(: # 5"2(!##55
#&! A !&! B !'$0#&! A (! B 5 #&! A B #($'!') FB_A = FB_B = W #A V_Ag = #B V_Bg 1.2#B V_A = #B 0.6V V_A = 0.5V 12 2
Tips
# FB #&M"% #% !3!? $ 2$>% %$!?
*3!% % $!? $
- FB +%* ↑
- # $ FB = mg
- # $ mg > FB
mg FB
V
mg FB
V FB = (mg)#&! = ρ#&!Vg
#A = 1.2#B FB_B
W
#&! B
FB_A
W
#&! A
FB_A = W FB_B = W
#B
V_A = ? V_B = 0.6V
12 )%!'$0&D#&(##&! A B N5W'#5 $# 1. #($'!##&!'/# #' 2. #&! B !'$0!&' 3. #&! A !'$0!&' 4. #&! A !&! B ($< 2.)
63. ;3A*C: 2 # r *: R 2A*) 2)=1;3#$A*9
# r ) v )=1;3#$A*9 # R )56)9
1. %& 2. &%
3. &'%' 4. %
'&'
)/$1A*
4#
!5$9(: 5"2(!##55
'$& Av #'/# #'
A1v1 = A2v2
πr2 v = πR2v2
#&! A #&! B
v1 = v 1. A1
'8 r
v2 = ? 1. A2
'8 R
v2 = %'&' 12 4
12
$#
1. )<<5( ((#/%10##D/1'$& #D/
2. '$&#/%D/('<'$6!#/%
3. '$&#/%&g55$<'
4. 1. 3
($< 1.)
Tips
#.%$)
- $) (#0) 12 $) , Av) % % 3#$>O > !
$
- %1 !$$7% &"$ $ #&+!"
C$$ $ !O@>$ % 7$ $
- 7%8 !$$ 4% % &$ !!2% $!? 4% !
#?? !? 2 h $! #$%*!?E% %
P1 + ½ #v12 + #gh1 = P2 + ½ #v22 + #gh2 A1
v1
v2 A2
P1
P2
h1
h2
A1v1 = A2v2 !$)#
<:
h v v = )2gh
64. **>?0iAja)??3 n a* #$ P *:5 V %*?*)l*#$1a)*0*
1i)56)9
1. PV 2. PV 3.
-./ 4.
-./01
)/$2
4#
1'##:R(#90#k 5C1'### 1 90
& <EK> = KBT --- (1)
)# PV = N KBT
'#'/ KBT = -.0 =
-./01
(1)
<EK> = -./01
12 4
%# = Av
k n 9
!' P
5"$ V
<EK> = ?
12
1'##:#k ! m '#5p02&M" T 5C (k 1 9! M)
1. mRT 2. MRT 3.
2 RT 2.
2 RT
($< 3.)
Tips
#%9!* ( < EK > )
&"1% C!% #!Q < EK > $&" 1% C! &> 1
C! $2 (J)
*&"*% #!Q N C!$!? N< EK >
N< EK > = NKB T
= PV ( PV = NKB T )
= nRT ( PV = nRT )
- T # P @2 # ?2"
- 3C n = %!90 49!9 45 =
!k 6! 9 7
< EK > = KB T
+6 )' 7 <EK>
,- 1 )'
65. 3)/)2#$#1 a)2)*=#;3))29B 92)*/$*9
)/)2)*= >5
)/$*/$)*/$#$A51)/392):2 *:C1*/$ *f:1*/$
:2*:*/$C9)2)/)56A
1.
2.
3.
4.
)/$*/$*
4#
#) 4)!$#' 2 %$'
)"#4)!(5 4)! ) 4) !(
! $#'<)" !))5 4)!!!6!)
# #"
)"#4)!5 4)!( ) 4)!
! $#''<)" !)) 5 4)!(!!6!)
1"D/ #"
12 3
12
)$< 4) 5(#&D#N$D#('<%1# ))$<%1# )
'V2$
1. 2.
3. 4.
( 3.)
Tips
&
72!E !#$!? # ? !>! %
!!? # Z %!
E ! ! !!? # Z !
0(D
5(4)$D#
)$<
)
0(D
5(4)"
)$<
)
66. *3))#A29*25*5E 1 2 1 ) >5 )/$5#$1*3)
)#)%/$92A2)##$0 2)=)#9 ) 340 )/# )#?:#$0#$#$#$
)jm 1. 80 2. 255 3. 420 4. 695
)/$)#
4#
5(5p" '1#(" (#'#5(5p)!(!# (L = 1 m) (<'<
!(!)5C 89 , 89 ,
:89 ,
;89 , ...
1"2"s:" 1 89 = 1 < = 4 m
v = f < '#'/ f = 8 f = 99
f = 85 Hz
1"2"s:" 2 89 = 1 < = 9 m
'#'/ f = 8
$$$$
, = $
, =#
1 m
%91#
<4 1 m
f = 99/ f = 255 Hz 12 2
12
(#!(!) λ $#%5%&" '1##<5(5p'/# # !(!#$#'<
1. @9 2. @ 3. λ 4.
@
($< 1.)
1 m 3<4
Tips
# )!88%
! & % > C[#["\ !!!#! % !#$!3#
!2! 2? $! & % > C[#["\ !!!#!
% @> 3>! CC!% !+ 2$!?2! 2?$
$C!% !+?! ! 3#$]?&!! 2
!
- $ \3#$?& #\3#$]?&
λ/4 λ/2 λ/4 λ/4 λ/2
&5(5p &5(5p
,,> !# 1
,,> !# ,.1
67. **/$2*>#$#:::* 2 × 10-4 ) )l#$
>?* 80 )m) a31*3#$ 2 >?$*l 4.0
**) */$#$*##$a)
1. 400 2. 500
3. 600 4. 700
)/$
4#
!5$9(:
# "$ < !#) d B = n λ 2x10-4 9C
DE.G = 2 λ
λ = 5x10-7 m = 500 nm 12 2
n = 2
d = 2x10-4 m
"$
#
λ = ?
R'< #
!# A0
!# A2
L = 0.80 m
x = 4x10-3 m
12
8DV!(/(!< 9(4&#%" # #N$$"# 12,000 /S6$"$
1<!< !#%0 20° '<!# &&!(!)# #&!(9$ (sin20 = 0.342)
Tips
)" ">1) 0>
1. 1) 2.
" ( A0 , A1 , A2 , _ , An) " (N1 , N2 , N3 , _ , Nn)
" (N1 , N2 , N3 , _ , Nn) " ( A0 , A1 , A2 , _ , An)
d sinθ = nλ d B = nλ
d sinθ = (n - )< d B = (n -
)< n = 1, 2, 3, x
n = 0, 1, 2, 3,
a = !!## "$(!
d = 4#&## "$ &)$$"#
L = (&!# "$ &)$$"#D#R'< #
x = $%(:##<) &)< !#1"2 0D##< !##
) L >> d &) θ ( [ sin θ I tan θ
a sinθ = nλ a B = nλ
a sinθ = (n + )< a B = (n +
)<
n = 1, 2, 3, x
n = 0, 1, 2, 3,
a &) d
"$(!
"$ &)$$"#
#
!(!) λ
R'< #
!# A0
!# A1
) N1
θ
L
x
1. 285 2. 342 3. 364 4. 410
($< 1.)
68. 129*>2
. 1#$92)*/$5:?0ADDn9ADDnA1;)2 )*/$#$15:?0ADDn
2#$92)*/$5:?0)560
1. ADDnC13# ;lC)
. ADDnX93*#)56 >
1. 2.
3. 4. 0
)/$ADDn
4#
. $# ###4)50y yD/'<$%&# D/'< #
)#50y
. $# #y# y"8#10# &)$!'8##
. $# M(# #y '#'/ yM(#$'!%5C8(:
12 4
&1&1 1
# 11
12
Tips
.%$??@
$+!"ZZ 7$% +!"ZZ$3#$ B # A ( VB b VA ) > ZZ E [
$$!?>! 1$ !3#$ A B VB b VA = J5KLM = NOM =
MPOM = Ed
A 2$ "(∞) VA = 0 VB = JRKLM
[ !$$+!"ZZ3#$> >!3 1 $ ! "3#$*
$??@
- ZZ+!+!"ZZ 2(+)+!"ZZ3(-)
VA VB
+
+
+
F +q
d
A B
E -
-
-
VB - VA = Ed
y<050 + y<050 -
- +
E
y)#N$'!%
y#$'!%!#S' y#$'!%#
!$#
. y"88'(:y #5('#8'(:y$%
. "8## yN$!'# y
. 8'(:y5C<! , < &)5C8(:
1. 2.
3. 4. 0
($< 3.)
69. 0X5:?0 6.4 × 10-19 >* * 1.0 × 10-20 a* 2)= 2.0 × 106 )/#
)12>)*=$3)1 1.0 )* >5 1f:#$0X3*)*/$#$;l
)*/$#$)$2 1a)#$)5*#$A5)#$ a*-)/#
1. 0 2. 2.0x10-14
3. 2.8x10-14 4. 4.0x10-14
)/$ADDn *:)*= 1
4#
1"25$9(: ) &60M)5C!# !(#&6 F = qvB %
&5C# 8(:# 9('$6!#$'!'<'$6!2("#
+%==?,-,@+
%==?,-,@+
5 9$'5(5 ∆p = √2 mu (1# mu = mv) ∆p = √2 x1.0x10-20x 2.0x106 ∆p = 2.8x10-14 kg-m/s 12 3
12
9(: 69 0M)5C!#'8!9#
1. 2.5x104 m 2. 3.1x104 m
v = 2.0x106
u = 2.0x106
m = 1.0x10-20
F
∆p = mv - mu
-mu
mv
Tips
,*B*$??@)C
@ZZ q %>? #$4! B >#*1!!? #$4!
# ! #$4! ##$4! F = qvB !3$ @ 3>+! %
@!
- +% ##$4! F C>E!e % >E %** >+% 4 v **
#$4! B *#$ E*+% # F !3$ @?! (+q) >!
@? (-q) E$ +% # F %!?+E*% *#$
B
v
F
F v +q
&6"8$'/#R&V
θ X 90° B
v
F
F v +q
&6"8$'/#RV
θ X 90°
3. 4.3x104 m 2. 5.1x104 m
($< 2.)
70. ?>5 )?:A2#$5
1. 0 2. 0.2 3. 1.4 4. 2.9 )/$ADDn *:)*= 1 4# 1"25$9(: 5C!#<<! 9$<":
$! < &Y&E = &'&Z
=
::
5 = 5 5C!#<": 0 &N$'!$ 20 Ω 12 1
'A,'%==? 6
$%,"#B ,-
+ - 12 V
2 Ω 5 Ω 20 Ω
25 Ω 10 Ω A
12 9(: 70 #& y!#!# 1. 2.05 A 2. 3.10 A 3. 4.50 A 2. 5.00 A ($< 1.) 71. ?>5 2)=5:?0#?0 5 AaD 2#1 2 a*a *:)*/$ADDn
1*3))56 V = 20sin100t )/$3a*) )=5:?0 ?:A2#$a*
Tips
!%
$!# 7$ R5 !$%* # $ Vc = Vd
* Vac = Vad
I1R1 = I2R3 --- (1)
# Vcb = Vdb
I1R2 = I2R4 --- (2)
(1)\ (2)
d
c
b a
I
I1 I2
I1
I2
R5
R4 R3
R2
+ -
R1
I
]^] =
]]_ /
]^] =
]]_
1+' %%==?($
V
R
C
1. 10 2. 10√2 3. 20 4. 20√2
)/$ADDn *:)*= 2
4# 1"25$9(: 5"2'/#&(!##55
#)y#&#%" v = 20sin100t
)(<'< v = Vm sin`t Vm = 20 ` = 100 &!$$'!6<50 XC =
ab =
C:CDc = 2x10
3 Ω &#%"y $'!6<50 C $'!$ R $'<<0
&!$! Z = dR f Xb Z = )2h10 f 2h10 Z = 2√2 x103 Ω yN C R ''<
Irms = .klmn
Irms = ol√'n
Irms = 'p√'
√CE Irms = 5x10
-3 A
!$#8'(:('#N#$'!6<50 Vrms C &
Vrms C = Irms XC
Vrms C = 5x10-3x2 x103
Vrms C = ?
R = 2x103 Ω
C = 5 qF
v = 20sin100t
i
Vrms C = 10 V
12 1
12
!#y5<!($'!$!$ 100 9&: $'!&(!%!&(!% 0.05
s $'!6<50!0 10 9' #)y#&#%"5C v = 100sin1000t $
' y&!#5C
Tips
R L C
1. *
$ R 3 L #!4? C #?? ! !# ZZ7$ R , L # C
$! #$!?!# ZZ% * I = V/Z ( $$+!" V " VR + VL + VC )
2.
$ R 3 L #!4? C #??% $+!"$ R , L # C
$! #$!?$+!"% V = IZ ( $!# I " IR + IL + IC )
!$! Z = )R f XBrXb
IL
C
L
V
R IR
VR = VL = VC
I I IC
!$! s = d
&' f tu r
tv
I
V
L
I
C R
1. 1.0 A 2. 2.0 A
3. 2.5 A 2. 3.0 A
($< 1.)
72. #$#%4:5f)*>5
2a%*$292#;?3 10 ?:29225g )*#):
#;5f#$??:%#92 21?25gA5a%*#;292)* 1
1. 40 2. 80
3. 120 4. 160
)/$DE)*#
4#
5 ($'!# ''$'# 5D#&D# N/N0 = 0.5 4! 6 4'!9#
'#'/ T1/2 = 6 4'!9#
A = wpx 9( n =
yY/'
t = 1 !' &) 24 4'!9# n = 9z = 4 ) A = 10 ' & A0
RLC ' Z = )R f XBrXb s = d
&' f tu rtv
3 6 12 9
1.25
1 0.75 0.5
0
0.25
! (4'!9#)
N/N0
0
A = wpx 10 = wpZ A0 = 160 '
12 4
12 9-126 D#4!"$ 12.5 !' 2&D#9/ 10 ' $#4!D#&)9-126 ( 2.5 ' 1. 7 !' 2. 25 !' 3. 30 !' 4. 40 !' ($< 2.)
Tips
G*
#!noC"!!?! % M! $$2#??>O !4 >>E !*
! 3 ?$ O
A = ! t > O ?!
A0 = ! % (t = 0)
t = >E>!
T1/2 = E
- M! M>$ M! $!4 M>$ ?#!$
! ! !$ α , | , - ! %* 2$!?3M! 2$%*
A = ~p 9( n =
Y/'
0 "0$"%, #
#$ 2 : DE
12 98 F 103 (?3 6 12) 12*: 4.0 : 24 : :3#$3fA2*9:3 92*:)# 2
)0: 2 3#$/) 5 925p1; 2 3#$
2 5 925p;
: 1.414 × 2 = 2.828 92)56 2.83
1.414 × 3 = 4.242 92)56 4.24
9.8 × 5 = 49.0 92)56 49.00
98. 1f:#$*D3*)*/$#$1;2) 2 )/#2 )#$ $;3)A2 700
)##;#*#$a*
)/$*:q)*$#$
4#
!5$9(:
1"2)#!'$0('()!"#
W) 2 #"!$'
∑Fy = ma N mg = ma
700 m(9.8) = m(2)
m = ;.G m = 59.32 kg Ans
N = 700 N
a = 2 m/s2
mg m = ?
99. 5) 30 )m) ##$15 ) 200 /) 235*2$
)% 5*#2$C>0* 1.0 a* *25*920)*/$#$1;-*9$
5?:/?)A2#$0 #$)m) (A2C*121 )
Tips
7 2
!]% 2 #&M"[$$+2"!3!? 3>!$>+!?#
&M" C%% $#7!?%% #&M" ##7!7!?%
)0,)"*&B
2 1 # 2 $*3!% $!E %$!?#E ! T
2 3 $*3!% $$!?$#]! N E !3!?
∑F = ma
!'$0! m !#(<1)/ #'1P: ∑F %&)!(!# a ∑F = ma
m ∑F = ma
a
5 1
mg
T m
5 2
m2g m1g
T
T T
T m1 m2
5 3
mg
m m
N
)/$ *:%*
4#
!5$9(:
!'$0)(#" M($#()&(0# 5"#1'##!'$0$%&# [ #
$%&#$% 0 ∑E2 = ∑E1
½ kx2 = mgh
½ kx2 = mgx
½ (200)x2 = (1)(9.8)x
x = .G x = 0.098 m = 9.80 cm. Ans
h = x = ? ∑E1 = mgh
m ∑E2 = ½ kx2
m
m = 1 kg
k = 200 N/m u = 0
v = 0
Tips
# 7*H%#
#% Ek &% !3 !"$ 2 ( J )
#.% Ep & 2$> 3#$! !"
$ 2 ( J ) #?$ !
1. #.%! "
2. #.%)*
7*H%# p &% 3#$$O $ q
∑E - W1-->2 = ∑E
p m 4 v >+>
!4 &" $!? 1/2 mv2 &
" $ kg m2/s2 = kg m/s2 m= N m = J
$!?q
m
v
Ek = mv
2
h
$%&##"#
m
Ep = mgh p m 2$ 2!3#$ h
&+!"C$?!?3#$ $!? mgh
&+!"C$ $ kg m/s2 m = N m = J
$!?q
x
F
! 0
k Ep = kx
2
p m 72! 2$!? 2!> !
2!!> x !3#$
&+!"$ $!? 1/2 kx2 &+!"$
$ N/m m2 = N m = J $!?q
∑E - W1-->2 = ∑E Ep1 + Ek1 - W1-->2 = Ep2 + Ek2
mgh + ½ mu2 F$h = 0 + ½ mv2
W1-->2 5C###$ &)# (
F$
u
v 2
1
h
m
m
100. :>?0i 2 a* )/$*0fX>* 20 )m*)m# i?: 2 150 ?>*
:>92#$?>*
)/$2
4#
!5$9(: 5"2'/#&(!##55
∆Q = ∆U + ∆W
∆Q = nR∆T + ∆W -150 = - (2)(8.31)(20) + ∆W ∆W = 348.60 J Ans
n = 2 9
∆T = 20° C ∆Q = -150 J ∆W = ?
Tips
I 1 %!$%
& >!??? ∆Q $$!? 7% &@>&%* ∆U !?3C??∆W
∆Q 1'##! << + 1'##!<< -
∆U 1'##M(<<1"D/ + 1'##M(<<# -
∆W #%9(<< + #&'<<< -
∆Q ∆U
∆W ∆Q = ∆U + ∆W
∆U = NKB∆T = nR∆T =
P∆V ( PV = NKBT)
∆W = F∆s = PA∆s = P∆V
")#&(1) $
101. $09;3$ )=X%10>?310 10 )m)
3X%#$)1)=>?C;3#$)m) 392 #)1;3) 4/3 *:#
)1 ) 1
)/$ *: 0f
4#
!5$9(: 5"2(!##55
)#!'$0$!"# 0 1 2 6 SD#%& tan sin '#'/
=
/ θY/ θ' =
/'/Y
=
/'/Y
= 9/
s = 30.00 cm. Ans
s = ? s
θ2 θ1
θ2
θ1
8 n2 =1
/% n1 = 4/3
10 cm M1
!'$0
102. )*=* me 5:?0 -e 9:)12$*:C5:?0ADDn>1
4 a* *:C 60 )m) *: 30 )m) >5 )*=2#%*?*#$
)*=a* (eV) ??:#$5*1C5:?0ADDn2%# (AC*1a21
a*)
E 30 S$"$
60 S$"$
"$
+ + + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - -
Tips
J JB7
) 4 &# ! % ! 4>*3 C72 2$>
!+ 4 2$*!$**& !+E! !$*3 *!% # >
!+$!!$!!?>*3 !% @& ss 4 !$ JB7 #
!% s >*3!$ J 3#$@&C$ # !>!
3#$@& 4
s
s
θ2 θ1
θ2
θ1 D
C
B A 8 n2
/% n1
!R
M1
!'$0
=
^
=
^ =
^
()#!"# 0 0 1 , 2
6 %& tan sin
)
)/$ADDn
4#
1"25$9(: 5"2(!##55
#)#"$5C!9#91:519<&#( )#)
y"$#y F = qE %!"#"8D/ 2(!'6)5!
'<!(!6!# %& #)'V291:'#!
1"2!"#
∑Fy = may F = may
(e)E = meay
ay =
sy = uyt + ½ ayt2
0.15 = 0 + ½ t2
t = d.
1"2!'<
sx = vxt
0.6 = vx d.
vx = 0.6 d eE0.3me
&1'##:#"$2("#
sy = 15 S$"$ m
V = 4 V
ay F = qE
vy vx = ux
ux # 30 S$"$
sx = 60 S$"$
+ + + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - -
uy = 0
Ek = ½ mevx2
Ek = ½ me(0.6 d eE0.3me
)2
Ek = ½ (0.36) eE0.3
Ek = ½ (0.36) .zCDY Zp.E
. (#$ E = V/d)
Ek = 8.0 x 1.6x10-19 J
Ek = 8.00 eV Ans
103. 2laD#$##$#$)%:)jm (1015 Hz) *a*:)# m$#Dp) 2.5
)*=a* ??:392)*=#$)? 5gf#;A5:02)*=9:Aja)?
#$>9:%/;92) )2)5; 3 )2 3921%*) 4 × 10-15
)*=a*-#
)/$DE:
4#
Tips
$??@,
ZZ %!2C" $ ZZ E 3 ( ) ! O
@> ZZ$ ZZ$! 3ZZ q>? ZZ E #
ZZ F=qE !3$ * b % + % ZZ #
+ % b % ZZ !] !7!! (72E!?72E)
#$!2! (72E!?72o)... Eo#$*!]..
E
F = qE -q +q F = qE +
+
+
-
-
-
!5$9(: 5"2'/#&(!##55
&1'##%&"$$s9( 1)/ n = 1 $05('<
1'## n = 3 !5('<('# "%&" 5$' 3
∆E = | E1 E3| 9( E1 = -13.6 eV
E3 = Y' =
.z' = -1.51 eV
∆E = | -13.6 (-1.51)|
∆E = 12.09 eV ) EKmax = ∆E = 12.09 eV W = 2.5 eV hf = EKmax + W
4x10-15 f = 12.09 + 2.5
f = 3.65x1015 Hz = 3.65 1$s"$S: Ans
)% #<N"!9&!%&"$#9&&0
$0'V:1'## 1'##5( # hf
'<1'##: # 0#"$ EKmax !'<
1'##4(D"$!&)#:4'# W
hf = EKmax + W
e-
hf EKmax + W
W = 2.5 eV
EKmax = ?
f = ?
n = 2
n = 1
n = 3
E1
E2
E3
Tips
B72%!?!C
!]!># 2!!?7C #3> ! !C ! !
*$CZC !
- !]! !t"& &$ !# hf (!$ % & CZ ) $
$!?&" 2 % ! EKmax !?&>E>! ! Zn!"E
W [$$!E% C
#$K!
! > n = 1 [ 2$> &* ?&!!!> 2$>?&
2%* n 2 ! 2$> !& !? 2$ &* $ & !>2 !#$4!ZZ
e-
hf EKmax + W
#! #
hf = EKmax + W
En = Y/'
n = 2
n = 1
n = 3
E1 = -13.6 eV
E2 = -3.40 eV
E3 = -1.51 eV
n = n
5$' 1 eV = 1.6x10-19 J
)l*12? PAT2 DE 5w 2552 >A2
?>/ a?12 PAT2
DE a .?B 0:: #92m#)= B2S *: >/$A5
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