τεχνικες διαφοροποιημενης διδασκαλιας στο μαθημα της φυσικης
Περι Φυσικης
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Πρόχειρες Σημειώσεις Φυσικής Γ Λυκείου Θετικής & Τεχνολογικής Κατεύθυνσης Ηράκλειο Κρήτης 2η ΄Εκδοση - Ιούλης 2013
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Περι Φυσικης
Transcript of Περι Φυσικης
-
&
2 - 2013
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1 91.1 pi . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.1 . . . . . . . . . . . . . . . . . . . . . . . . 91.1.2 pi . . . . . . . . . . 101.1.3 pi . . . . . . . . . . . . . . . . . . . . . . . 111.1.4 pi . . . . . . . . . . . . 131.1.5 pi . . . . . . . . . . . . 14
1.2 - . . . . . . . . . . . . . . . . . . . . . 161.2.1 pi . . . . . . . . . . . . 171.2.2 pi . . . . . . . . 221.2.3 pi . . . . . . . . 231.2.4 pi pi . . . . . . . 241.2.5 pi . . . . . . . . . . . . . . 251.2.6 pi pi ... . . . . . . . 27
1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 271.3.1 L - C . . . . . . . . . . . . . . . . . . . . . . . . . . 271.3.2 . . . . . . . . . . . . . 291.3.3 pi . . . . . . . . . . . . . . . . . . . . . . . 301.3.4 . . . . . . . . . . . . . . . 31
1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 371.4.1 . . . . . . . . . . . . . . . . . . . . . . . 371.4.2 . . . . . . . . . . . . . . . . . . . . . . 40
1.5 . . . . . . . . . . . . . . . . . . . . . . . 421.5.1 . . . . . . . . . . . . . . . . . . . . . . . 421.5.2 . . . . . . . . . . . . . . . . . . . . . . 45
1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2 512.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.3 . . . . . . . . . . . . . . 53
2.3.1 . . . . . . . . . . . . . . . . . 552.3.2 pi . . . . . . . . . . . 572.3.3 . . . . . . . . . . . . . . . . . . . 592.3.4 . . . . . . . . . . . . . . . . . . 62
2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.4.1 pi . . . . . . . . . . . . . 64
2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.5.1 . . . . . . . . . . . . . . . . . 68
2.6 . . . . . . . . . . . . . . . . . . . . . . . . 72
-
.
2.6.1 . . . . . . . . . . 732.7 - - . . . . . . . . . . . . . . . . . 75
2.7.1 . . . . . . . . . . . . . . . . . . . . . . . . 752.7.2 . . . . . . . . . . . . . . . . . . . . . . . . . 762.7.3 . . . . . . . . . . . . . . . . . . . . 79
3 813.1 . . . . . . . . . . . . . . . . . . . . 813.2 . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.2.1 . . . . . . . . . . . . . . . . . 843.3 pi - pi . . . . . . . . . . . . . . . 883.4 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.5 . . . . . . . . . . . . . . . . 94
3.5.1 953.6 - . . . . . . . . . . . . . . . . . . . . 101
3.6.1 . . . . . . . . . . . . . . . . . . . . . 1043.7 . . . . . . . . . . . 106
3.7.1 . . . . . . . . . . 1063.7.2 pi . . . . . . . . . . . . . . . 1063.7.3 pi . . . . . 1063.7.4 . . . . . . . . . . . . . . . . . . 1073.7.5 . . . . . . . . . . . . . . . . 1073.7.6 - . . . . . . . . . 1083.7.7 . . . . . . . . . . . . . . 109
4 1114.1 ,
pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.2
. . . . . . . . . . . . . . . . . . . . . . . . 1124.2.1 . . . . . . . . . . . . . . . . . . . . 1134.2.2 . . . . . . . . . . . . . . . . . . 1164.2.3 . . . . . . . . . . . . . . . . . . . . . 116
4.3 pi . . . . . . . . . 117
5 pi(Doppler) 1195.1 pi - pi . . . . . . . . . . . . . . . . . . 1195.2 pi - pi . . . . . . . . . . . . . . . . . 1205.3 pi - pi . . . . . . . . . . . . . . . . . 1215.4 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4
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I 2012 - 2013 125
II 329
5
-
- . pi pi .
pi pi - pi pi. pi, & pi , -pi & pi pi -.
pi , pi . pi- pi pi pi pipi .
pi pi 2012 - 2013 pi (http://www.study4exams.gr). http://www.perifysikhs.com.
. , Msc
-
1
1.1 pi
1.1.1
pi pi pi - . , .. pi pi (T ), (f) ()
() pi pi pi pi pi . t pi , pi pi:
T =t
N(1.1)
pi 1 s.
(f ) pi pi pi t, pi t. :
f =N
t(1.2)
1 Hz 1 s1
pi , pi :
f =1
T(1.3)
() pi pi- pi :
=2pi
T= 2pif (1.4)
pi 2pisec. 1rad/sec.
-
1.1.2 pi
pi pi . pi pi . pipi pi (...).
pi pi pi pi , pi . pi pi t, pi :
x = A(t+ 0) (1.5)
pi . pi, pi pi pi . = t + 0 pi pi t . pi .
t = T - = 2pirad
pi 0 t = 0 . pi pi ( , , pi). :
0 0 < 2pi
pi :
=dx
dt= max(t+ 0) (1.6)
pi max = A . , pi pi (x = 0).
pi pi :
=d
dt= max(t+ 0) (1.7)
pi max = 2A pi . pi, (x = A).
(1.5),(1.6),(1.7) pi, pi pi pi. pipi pi pi
10
-
pi-pi (1.7) (1.5) :
= max(t) = 2A(t) = 2x (1.8)
pi pipi pi pi x pi , , pi pi pi pi .
-pi pi :
= A2 x2 (1.9)
pi pipi pi pi pi pi-
x = A(t) xA
= (t) x2
A2= 2(t)
= A(t)
A= (t)
2
2A2= 2(t)
pi pipi pipi :
x2
A2+
2
2A2= 2(t) + 2(t) = 1 =
A2 x2
1.1.3 pi
pipi pi pi-, pi pi pi 0 = 0.
pi pi pi pi pipi pi-
) t = 0 0.
) , pi pi pi.
) pi pi pi , pi .
11
-
1.1: pi -
1.2: -
12
-
1.3: pi -
) pi, pi :
pi pi pi .
pi .
) pi pi pi, - ( pi ) , pi pi pi, ( pi- )
1.1.4 pi
pi..1 pi pi t = 0 (x = +A). pi .
... x = A(t + 0) t = 0 +A = A(0) (0) = +1 0 = 2kpi + pi/2 0 = pi/2rad
pi..2 pi pi t = 0 pi pi pi . pi .
13
-
... x = A(t + 0) t = 0 x = 0 0 = A(0) (0) = 0 0 = 2kpi 0 = 2kpi+pi.
t = 0, = max (0) = 1 0 = pirad
pi..3 pi pi - t = 0 x = +A/2 pi pi. pi .
... x = A(t + 0) t = 0 x = +A/2 A/2 = A(0) (0) = 1/2 0 = 2kpi+pi/6 0 = 2kpi + pi pi/6.
t = 0, < 0 (0) < 0 0 = pi pi/6 = 5pi/6rad(2) * t = 0 pi > 0 0 = pi/6rad
1.1.5 pi
m pi , pi , pi . pi pi pi pi :
F = m (1.10)
(1.8) pipi
F = m2x (1.11) D = m2, pipi :
F = Dx (1.12) D pi
pi . pi (1.12) pi , pi :
pi pi ,
pi pi pi ,
pi pi pi pi pi
pi F = 0
14
-
(1.12) pi, -pi pi pi pi pi 1.4 : (1.12) pi -
1.4: pi
, pi . pi pi pi , pi pi pi x pi pi pi pi- pi . , pi , pi pi x pi pi pi (1.12).
- pi
pi D = m2 pipi : =
Dm
pi = 2piT
pipi :
T = 2pi
m
D(1.13)
pi pipi pi pi pi .
pi
pi (1.12),(1.5) pipi :
F = Fmax(t+ 0) (1.14)
, Fmax = DA
15
-
1.5: -
1.2 -
pi pi pi pi - pi pi .
pi pi -pi Hooke F = kl pi k ( pi ) l pi pi pi . F pi (l0)
(F) pipi pi pi-pi , pi pi pipi, pipi - pi , pipi .
pi pi pi , pi pi ;
16
-
- pi pi m
1 : , pi pi pi x pi pi
2 : pi pi.pi pi (F = 0)
3 : pi pi F . pi , pi - pi pi x pi .
4 : F = Dx, D pi pi D.
5 : pi pi pi pi. pi pi pi (1.13) pi pi (1.5) 0
1.2.1 pi
pi pi pi pi . pi pi pi:
E =1
2DA2 (1.15)
pi pipi pipi pi pi , pi pi pi . pi.: pi pi .
& - -. pi pi :
K =1
2m2 (1.16)
U =1
2Dx2 (1.17)
17
-
(3
+6 C.>8145. F8; =82 @I=2 ' 81 =K5< I>.; CD6.; CD6
-
pi pi :
K =1
2m(max(t))
2 K = 12m2A22(t)
K = 12DA22(t) = E2(t) (1.19)
U =1
2D(A(t))2 U = 1
2DA2(t) = E2(t) (1.20)
pi 1.20 1.19 pipi pi pi pi . pi , pi :
1.6: E,K,U
: pi pi . :
K + U = E 12m2 +
1
2Dx2 = E
,pi = pi 1.15pi pipi pi :
19
-
() pi (x = 0) , - . E = Kmax =12m2max
() (x = A) , - E = Umax =12DA2
() pipi ( pi ..)
1
2m2 +
1
2Dx2 = E =
1
2DA2 =
1
2m2max (1.21)
pi pi pi , pi . pi pi- , pi pi pipi pi pi pi pi .
pi pi :
pi max = A :
E = Kmax 12DA2 =
1
2m2max A2 =
m
D2max A =
m
Dmax
pi D = m2 max = A
pi = A2 x2 :
1
2m2 +
1
2Dx2 = E =
1
2DA2 m2 = D(A2 x2)
D
m(A2 x2)
pi D = m2 = A2 x2
U = f(x), K = f(x) pi - pi :
U =1
2Dx2 A x +A
pi :
E = K + U K = E 12Dx2 A x +A (1.22)
pi pi pi .. pi 1.7:
20
-
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? &%- ( . $ ) *&
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) )
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) 0 0& , & , 1) )
, &* ( 0&
'
.
-
.1-1'
.&
*2 &, &$, ,&$, &
1.7: E,K,U pi
U = f(), K = f() pi - pi :
K =1
2m2 max +max
pi :
E = K + U U = E 12m2 max +max (1.23)
pi pi pi 1.8:
: pipi pi pipi pi pi -, pi pi. pipi :
U =1
2k(l)2 (1.24)
, pi k l pi pi pi .
21
-
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????????????????!#!??????? %&
? ???????????????????????????!"!?????????!#???$!%!??????????????????????????!"!?????????!#&'?$
???????????????????????????????????????????????????????!
? '%( ) * ?'
"""""""#? ? ?*+, *+,$? ? ??
???????!"# ? ? ?()* + , -& * + . ? -&(
? '%- ) . $ * ?'
""""""#? ? ?*+, *+,$? ? ??
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?? ????????? ???? ?? ????????? ????????? ???? ??????????? ?????? ????" #??????????????????????????????????????????????????????????????????????!
???????!"# ? ? ? ? ? ? ?&+,
( (./0
) )* + , -& ! !* + ? ? ? * + (?! ! . ? + ( . ?( (
? ?(
( ./0 ./0? ?? ? ? + 1( (
*+,? '? ) 0'
*+,$? *+, '?? ' *+,? ?
.'
.
.1(1-
2
-
(
*+,'? '
1.8: E,K,U
pipi pipi -.
pi pi pi pi:
WF = U() U () (1.25)
pi pi pi pi, , .
pi . & . -pi : 1.1 - 1.108, 2.1 - 2.60, 1.131 - 1.146, 1.149- 1.156, 1.160, 1.161, 1.172, 1.174, 1.176, 1.178, 1.179, 1.180, 1.183, 1.184,1.186, 1.187, 1.188, 1.190
1.2.2 pi
pi pi pi pi pi. pi. pi pi .
22
-
pi dxdt
dx
dt= = A(t) (1.26)
ddt
d
dt= = 2A(t) (1.27)
dPdt
dP
dt= F = DA(t) (1.28)
- dKdt, dUdt
K + U = E d(K + U) = 0, =, dK = dU
dK
dt= dU
dt(1.29)
pi
dK
dt=dWFdt
=F dxdt
= F dKdt
= D x (1.30)
, (1.5),(1.6) pi-pi :
dK
dt= DA(t)A(t) dK
dt= DA
2
2(2t) (1.31)
dU
dt= +
DA2
2(2t) (1.32)
1.2.3 pi
. , . , pipi .
pipi pi pi :
x = A(t) = max(t) = max(t+ pi2 )
23
-
= pi2
pi .
pi - , pi pi pi t pi = pi
2, pi pi
pi : = 2pi
Tt t = T
4
pi pi = +max, pi- pi +A T
4.
pipi pi pi pi :
x = A(t) = max(t) = max(t+ pi) = pi pi
pi. pi -
pi , pi pi pi t pi = pi, pi pi pi :
= 2piT
t t = T2
pi pi = +max/2, pi- pi +A/2 T
2.
pi .
1.2.4 pi pi
pi pi pi -. pi : pi pi pi .
pi (1.9) :
()= () () x = (t)
= t pi .
pi pi pi pi- pi pi . pi pi pi (). pi pi 0.
24
-
& -
14
: 22 xA -= :.... :
2 2 2 2 2 2D A D x m A m xw w
2D=m
2 21 1 1E = K +U = m + = m +2 2 2
2 2 2 2A xw w - 2 =22 xA -=
3.
: yy ...
: = x = A x = At =t .
: ... , .
: x = At .
+
-
tx
1.9: pi pi
pi . & . -pi : 1.162 - 1.165,1.169, 1.191, 1.192, 1.194,1.196, 1.197, 1.198, 1.200, 1.203, 1.33 - 1.70, 1.83 - 1.98, 1.101 - 1.108
1.2.5 pi
pi pi pi pi pi . pi . pi , .
m1,m2 pi - ~1, ~2 . pi pi. .
pipi pi pi, pi pi pi . ~1, ~2, . :
~Po() = ~Po() m1~1 +m2~2 = m1~1 +m2~2 (1.33)
Eo() = Eo() K1 +K2 = K 1 +K 2 + Epi (1.34)
25
-
pi Epi pi pi . pipi (Ko() > Ko())
pipi pi pipi pi pi-pi .
pipi pi . ~1, ~2, (1.33) :
Ko() = Ko() K1 +K2 = K 1 +K 2 (1.35) pipi
. pi pi pi :
1: pi ... pi ( pi )
2: pi - pi pi pi pipi ( pi.. pi x pi pi pi ...)
3: pi pipi pi (1.33),(1.35) . pi (1.33 .
4: pi E = K + U .
5: pi pi pi
pi pipi pi pi -pi pi pi pi . pipi pi - . pipi pi , pi pi 4 5 .
pi pi (- ) , pi .
26
-
pi . & . -pi : 2.136, 2.138, 2.139, 2.140, 2.141,2.143,2.145, 2.146, 2.148, 2.149, 2,150, 2.151, 2.153, 2.154, 2.155, 2.156, 2.158, 2.159,2.160
1.2.6 pi pi ...
m1,m2 pi pi - , 1 = 2 = . pi pi :
D = (m1 +m2)2 2 = D
m1+m2 =
D
m1+m2
& -
31
U = :
U= 2 2 2
max max max1 1 1U + K = + = m + m = m 2 2 2
2 2 2max + = . ....
K=3U
2 2max max max
1 1U + K = U U + 3U = U 4U = U 4 D x = D 2 2
= 2
2 2 2 4 x = x = x4 2
... 1m 2m , ( 1 2 = = ), 1 2m = m + m .
21 1D = m 2
22D = m
( ) =21 2 1 2D = m + m D + D ... , D (D=K).
1 : 1: ... m. 2: (
AA
1m
2m
21 1D = m
22
2D = m
( ) K=21 2D = m + m
pi D1, D2 pi pipi :
D1 = m12, D2 = m2
2
pi pi , pi D = k
pi pi ( ), pi pi N . pipi pi N = 0 pi pi.
1.3
1.3.1 L - C
pi pi pi C, - pi pi L pi .
27
-
- L-C.
pi pi V pi pi . pi Q UE pi . pi pi pi pi pi :
C =Q
V Q = CV (1.36)
UE =1
2CV 2 =
1
2
Q2
C(1.37)
t = 0, pi , pi pi pi . , pi pi , pi Lentz. pi pi pi pi pi Epi = Ldidt . VL = Epi = VC = qc , pi VC pi.
(4
(-4 -&!QMO)Q!* M+&+RM#*!)*
*81D7 1/?;=5147 /DB6H8A >H028;BF828.(.(2) =D6CI1D5. /26G1
5. =D68.?.=8A
-
(i = 0), pi pi pi Q T/2.
, pi pi, pi pi t = 0. pipi pi pi- pi pi . pi .
1.3.2
pi pi (q) (i) pi pi. pipi pi , pi pi pi :
T = 2piLC (1.38)
pi pi pi :
q = Q(t+ 0) i = I(t+ 0)
pi pipi pi x . pi Q pi ( pi ) I (pi ). pi = t + 0 pi 0 0 2pi.
pi pi pi pi pi , pi .
pipi pi t = 0 pi q = +Q pi i = 0 pi 0 = pi/2. pipi :
q = Q(t+pi
2) q = Q(t) (1.39)
i = I(t+
pi
2) q = I(t) (1.40)
pi I = Q, . ( ). (q) pi.
29
-
pipi pi t = 0 pi- (q = 0) pi pi I, pi 0 = 0. pipi :
q = Q(t) (1.41)
i = I(t) (1.42)
pipi pipi , pi pi pi pi. pi pi . pi pipi.
1.3.3 pi
pi pi - , pipi - pi (0 = pi/2. pi pipi pi.
1.11: -
pi
pi, pi pi pi t pi i q pi. i i , pi pi pi pi
30
-
1.12: -
. .
i =dq
dt(1.43)
pi q, i
, - pi pi pi ( t = 0, q = +Q). pi (1.43), q , i > 0. pipi (1.39) , (1.61 , pi pi (1.11),(1.12)
pi ( dq
dt> 0)
(dqdt> 0) pi. pi pi pi
pi pi (i > 0) pi pi pi (i < 0).
pi . & . -pi : 5.1 - 5.11, 5.69, 5.70, 5.71, 5.72,5.73
1.3.4
pi pi t = 0. pipi pi, pipi pi pi, pi :
31
-
UE =1
2
Q2
C(1.44)
pi, pi pi pi pi . , pi pi pi pi pi. pi pi, pi pi , pi pi pi pi pi :
UB =1
2LI2 (1.45)
. pi pi , pi pi, pi , pi pi . pi.
pipi pi pi pi , - :
E =1
2
Q2
C=
1
2LI2 (1.46)
pi pi (UE) pi pi (UB)pi pi :
UE =1
2
q2
C UB =
1
2Li2 (1.47)
UE,UB pi t = 0 pi 1.39 1.40 pipi pipi :
UE =1
2
(Q(t))2
C=
1
2
Q2
C2(t) UE = E2(t) (1.48)
UB =1
2L(I(t))2 = 1
2LI22(t) UB = E2(t) (1.49)
pi pipi pi pi pi pi pi pi pi , pi . .
32
-
1.13: E,UE, UB
pi pi pi pi pi. :
E = UE + UB 12
Q2
C=
1
2LI2 =
1
2
q2
C+
1
2Li2 (1.50)
pipi L C pi . pi pi L C :
pi Joule pi
pi pipi .
pi pi pi pipi :
pi I = Q
UB(max) = UE(max) 12LI2 =
1
2
Q2
C I2 = 1
LCQ2 I = Q (1.51)
pipi pi T = 2piLC = 1
LC
33
-
pi i = Q2 q2 (1.50) pi-pi :
1
2
Q2
C=
1
2
q2
C+
1
2Li2 Li2 = Q
2
C q
2
C i2 = 1
LC(Q2 q2)
i = Q2 q2 (1.52)
pi - UE UB q i. .
pi . & . -pi : 5.75 5.81, 5.83, 5.85, 5.86
pi pi-pi pi , pi - L C . pi :
pi pi dqdt
pipi :dq
dt= i (1.53)
pidVCdt
pi :
C =q
VC VC = 1
Cq dVC
dt=
1
C
dq
dt dVC
dt=
i
C(1.54)
pi i pi pi , - pi .
didt
pi pi (Lentz) pipi E = Ldidt , :
di
dt= E
L
E = VL = VC = qC
di
dt= q
LC di
dt= 2q (1.55)
34
-
pi pi dUEdt, dUBdt
pi pipi pi pi-pi :
E = UE + UB dE = 0 = dUE + dUB dUEdt
= dUBdt
(1.56)
pi PC pi PL pi. pipi :
dUEdt
= PC dUBdt
= PL (1.57)
dUEdt
= VCi =q
Ci (1.58)
pi . & . -pi : 5.87,5.88, 5.89, 5.91, 5.102, 5.103, 5.106,5.107, 5.109, 5.110, 5.112, 5.113, 5.114, 5.115, 5.116, 5.118, 5.119, 5.121
pipi pi... pi pi pi-pi t = 0 q, i pi pi pipi , pi pi pi pi- . pipi pi pi pi pipi pi pi pi. pi pi pipi :
pi pi pi () pi pi . pi pi Ohm :
I =E
R + r(1.59)
35
-
pi pi r . t = 0 pi pi pi-
UB = 12LI2 pi
pi . pipi pi t = 0, q = 0 i = +I
pi :
q = Q(t) (1.60)
i = I(t) (1.61)
pi pi pi pi pi q, i pi 0 = 0.
: pi . & . -pi : 5.93, 5.94, 5.95, 5.96, 5.97, 5.99, 5.100,5.123, 5.124, 5.126, 5.127, 5.128, 5.131, 5.132
L C mk pi pi LC pi . , pi pi .
- L Cpi x q i Q max = A I = Q U = 1
2Dx2
UE =12q2
C
K = 12m2 pi
UB =12Li2
k 1C
m pi pi L T = 2pi
mk
T = 2piLC
pi - pi pi L C pi pi .
36
-
1.4
1.4.1
pi pi - pi. , pi pi . pi ( ) pi pi . pi , pi pi pi pi. pi pi ,pi pi .
pi pi pi pi-. pipi pipi pi .
F = b (1.62) pi
pi . pipi 2 pi :
F = m Dx b = m (1.63)
1.14: pi pi pi
b pi pi pi pi pi pi . S.I. 1kg/s. pi pi pi b. , - pi pi.
pi pi -pi, pi pi pi-, pi pi pi x , , pi.
pi pi pipi :
pi . pi pi pi pi b.
37
-
pi , pi pi -. pipi pi b pi pi , pi, pi pi .
pi b, - pi pi. b , pi pi pi, pi .
pi pi :
A = A0et (1.64)
pi A0 pi t = 0 = b2m . S.I. s1.
pipi pi pi (1.64)pipi pi 50% pi pi t1/2 pi pipi pi.
A = A02
t1/2:
A02
= A0et1/2 1
2= et1/2 2 = et1/2 ln2 = t1/2 t1/2 = ln2
(1.65)
pipi pi -, pi pi .
pi pipi . :
A = A0et, t = T, = 0, 1, 2, ...
pi pipi pipi pi-, pi , . , :
A0A1
=A1A2
=A2A3
= ... =AA+1
= . (1.66)
pi: pi t1 = T t2 = (T+1)T - :
AA+1
=A0e
(T )
A0e(T+1)= eT = .
38
-
1.15:
pi pi pi:
E =1
2DA2 =
1
2D(A0e
t) E = 12DA20e
2t E = E0e2t (1.67) pi, pi pi
:
39
-
1.16: pi pi
E0E1
=E1E2
=E2E3
= ... =EE+1
= . (1.68)
pi pi pi pi :
dE
dt= F = b2 (1.69)
1.4.2
L C , pipi pi pi , pi pi . . pi pi pi .
pipi , pi - R, pi pi pi pi - pi b. pi, pi - pi . - pi - Joule, pi pi pi - . R, pi
40
-
pi q pi t , , pi .
1.17:
pi pi pipi pi :
41
-
pi R , , pi .
pi, pi , pi pi. pi . pi - .
pi pi pi.
pi pi pi :
Q = Q0et (1.70)
pi Q0 pi t = 0 = R
2L R L
pi pi. pipi pi pi .
pi pipi pi , pi :
Q0Q1
=Q1Q2
= ... =QQ+1
= . (1.71)
pi pipi . pi pi (QR) pi :
QR = E0 E1 = 12
Q20C 1
2
Q2
C(1.72)
: pi . & . -pi : 6.1 - 6.38, 6.50, 6.51, 6.52, 6.53, 6.55, 6.56,6.58, 6.60, 6.61, 6.62, 6.63, 6.65, 6.66, 6.67, 6.68, 6.70
1.5
1.5.1
pi - . pi pi pi pi , . pi , , :
42
-
f0 =1
2pi
k
m(1.73)
pi . pi f0 ( pi pi pipi f0. .
f0 pi pipi , - .
pi ( ) - f pi f0 pi- pi :
=
20
(b
2m
)2, 0 =
D
m
pi F = b. pipi < 0 f < f0. pipi pi b pi ( ) pi f = f0.
pi , pipi - pi (pi.. F = F0(t+)). . 2 pipi pi :
F = m b Dx+ F = m (1.74) pi ,pi , pi pi- pi. pi - - pi pipi pi . .:
, - pi , pi- pi pi -.
pi pi . (f)
43
-
(f0). pi .
pi pi pi f
. , f pi . pi , pi f0, pi pi pi , f . .
pi , pi .
pipi pi pi (b = 0), f = f0, pi pi. pi pi pi ( ) pi .
pi (b), pi pi pipi- pi pi pi. f pi f0. pi pipi pi pipi.
pi ,
pi , pi , -, pi .
1.18: pi pi
, pi pi- F, -. pi- pi ( F) - -pi pi - ( F ) pi pi . pi pi - pi - pi pi. , - - pi, pi
44
-
. pi, - (F) . E = Kmax = Umax, .
1.5.2
L C (pi.. pi pi pi ) :
f0 =1
2piLC
(1.75)
pi ( - LC), . , - (R 6= 0), pi - f0 ( pi pipi - ).pi , pi . pi pi pi , pi .
, pi f , . , pi pi , f f0 LC. pipi L C . pi pi pi I - f , R.
1.19: pi pi
pi - -. pi pipi pi- - R , pi - I , pi pi pi pi pi - , pi pi f0 -.
45
-
- pi pi pi . pi L C - . pi , f0 f .
: pi . & . -pi 7.1 - 7.29, 7.33-7.37, 7.39, 7.40-7.43
1.6
pi , pi pi- pipi . pi , , pipi, pi , , pi pi pi . pi . pi pipi .
pi pi , pi . pi pi:
pi pi pi,
pi A1 A2 .
pi :
x1 = A1(t) x2 = A2(t+ )
pi , pi pi pipi . :
x(t) = x1(t) + x2(t) = A1(t) + A2(t+ )
pipi pi pi :
x = A(t+ ) (1.76)
pi
46
-
A =A21 + A
22 + 2A1A2 (1.77)
=A2
A1 + A2(1.78)
pi pipi pipi pipi pi , pi x1 =A1(t).
1.20: pi pi-
pipi pi pi pi pi - .
pipi
() = 0 ,(1.77),(1.78) :
A =A1 + A2 + 2A1A2 =
(A1 + A2)2
A = A1 + A2 (1.79)
= 0 = 0rad pipi pi pi A1, A2 pi .
() = pirad, (1.77)- :
A =A1 + A2 2A1A2 =
(A1 A2)2 A = |A1 A2|
(1.78) = 0 = pirad.
pipi pi pi pi pi pi pi ( = 0, A1 > A2, = pi, A1 < A2).
47
-
pi 1.77 pipi pi :
E = E1 + E2 + 2E1E2 (1.80)
pi E1, E2 pi .
pi pi -, pi , pi -. pi pi: pi pi pi,
pi ,
1 2 . pi pi :
x1 = A(1t) x2 = A(2t)
pi , pi pi pi pi- . :
x(t) = x1(t) + x2(t) = A(1t) + A(2t) = A((1t) + (2t))
pipi :
x = 2A
(1 2
2t
)
(1 + 2
2t
)(1.81)
pi 1, 2 pi , pi pi pi :
48
-
pi
A = 2A(1 2
2t
)(1.82)
pi pi(1+2
2t). pi pi pi
pi , pi pi |A| = 0 |A| = 2A. pi
(1+2
2t)
=1 + 2
2' 1 ' 2 (1.83)
pi (1.81) :
x = A(t) (1.84)
pipi pi pi pipi pi pi |A| pi , , pi 2A. pi. :
pi pipi pi pi pi , pi - pi .
T ( -pi) pi, .
pi pi pi (1.82)pipi pi A :
2A
(1 2
2t
)= 0
|1 2|2
t = (2+ 1)pi
2
pi = 0, 1, 2, ... = 0 = 1 , pi -
t1 t2 pi pi . pi pi :
T = t2 t1 = 3pi|1 2| pi
|1 2| T =2pi
|1 2| =2pi
2pi|f1 f2|
49
-
1.21:
pi pi :
T =1
|f1 f2| (1.85)
pi pi pi :
f =1
T= |f1 f2| (1.86)
: . & . -pi 8.1 - 8.44, 8.50 - 8.53, 8.55-8.59, 8.62 - 8.65, 8.67, 8.68, 8.70, 8.71,8.73-8.76, 8.78, 8.83-8.88, 8.90, 8.92, 8.94-8.98
50
-
2
2.1
pi .
pi, pi, : pi pi , pi pi .
. pi pi pi pi ,
pi pi -pi . , , -, pi pi pi pi . pi pi pi pi pi . pi ( . pi ), pi .
pi ,
( pi ) pi pi , pi pi pi . pipi , pi pi ( ), pi ... , pi pi pi pi , , pi pi .
pi pi , pi- .
2.2
, pi , :
-
, pi . ( , , pi) pi pi pi.
, pi . ( , , , ) c = 3 108m/s.
, :
, pi . .
pi , pi pi . pi pi .
, pi pi . pi .
2.1:
, :
, pi pi - . pi . - , pi - pi .
, pi pi pi . - , . pi . pi , .
, :
, pi pi pipi .
, pi .
52
-
2.2:
2.3
:
. pi, pi
pi , pi pi , f pi , pi - pi pi pi pi, pi pi. , , pi . :
() -pi pi . - pi t1 = T t2 = 2T , pi pi. -pi pi pi :
pi pi.
(f ) pi - .
, pi , pi pi pi .
() pi pi .
.
53
-
() pi . - pi, pi :
=x
t(2.1)
pi x pi pi t pi . pi pipi . pi pi .
.
2.3:
() pi - pi pi pi (2.1)t = T x = , :
=
T = f (2.2)
54
-
pi f . pi-pi . f pi pi pi . pi, pi , pi .
2.3.1
pi pi pi pi pi.
pi pi pi , pi pi f pi pi x (pi pi ) .
pi (x = 0) (=0) pi , pi pi pi y = 0 ( > 0). pi !
y = A(t) = A
(2pi
Tt
)(2.3)
pi pi pi .
pi pi pi ()=x pi pi :
t1 =x
(2.4)
pi t :
t t1 = t x
(2.5)
, pipi pi pi , pi pi :
y = A2pi
T
(t x
)= A2pi
(t
T xT
) y = A2pi
(t
T x
)(2.6)
(2.6) pi
55
-
x, pi pi , pi . pi = 2pi x
.
t pi pi (2.3), pi pi :
y = A
(2pi
Tt+
)= A
(2pi
Tt+ 2pi
x
) y = A2pi
(t
T+x
)(2.7)
pi x pi - pi .
, pi , pi pi . pi pi pi pi , pi pi pi xM pi :
pi pi pi
yM = A2pi
(t
T xM
)(2.8)
VM = A2pi
(t
T xM
)(2.9)
pi
M = 2 yM M = 2A2pi(t
T xM
)(2.10)
pipi pi - m pi . pipi , :
0 tT xM
0 t xM
(2.11)
, m pi pi pi D = m2 :
1
2Dy2 +
1
2mv2 =
1
2DA2 (2.12)
56
-
pi y pi pi pi v .
2.3.2 pi
pi pipi piy pi pi . pi t pi x . pi pi pi pipi pi . 2 pipi pi.
) pi - Ox, x = x1 pi :
y = A2pi
(t
T x1
)= f(t), t x1
pi y . pi
2.4: pi pi pi x1 .
pi . - pi , pi, pi.
) pi . t = t1, :
y = A2pi
(t1T x
)= f(x)
57
-
2.5: pi . pi , pi pi .
pi y Ox - pi x.
pi
1 : pi t = t1 y = f(x) pi pi .
2 : pi pi (x = t) pi ( /4).
3 : pi y (x = 0) t1,
58
-
pi 1 x = 0.
4 : pi pi pi pi pi , pi t1. t1 pi .
pi . & .pi : 9.1 -9.27, 9.70, 9.73, 9.74, 9.76, 9.78, 9.79, 9.81, 9.82,9.85, 9.87, 9.89, 9.90, 9.91 - 9.94, 9.96 - 9.98, 9.100 - 9.105, 9.107, 9.109
2.3.3
pi:
= 2pi
(t
T x
)(2.13)
(rad) . pi (2.13)pipi pi pi x pi pi t. Ox (x = x1) t t = t1 pi x pi pi .
pi 0. t pi pipi. , pi pi .
2.6: -
pi . pi - x = x1 :
M = 2pi
(t
T x1
), t x1
pipi pi - pi .
pi - t . d
pi .
59
-
. t1 t2 pi :
= 2pi
(t2T x1
) 2pi
(t1T x1
) = 2pi
Tt
2.7: -
t t1 :
M = 2pi
(t1T x
)
pi t1.pi .
. -
Ox pi pi pi xA xBpi . t :
A = 2pi
(t
T xA
)
B = 2pi
(t
T xB
) pi xB > xA A > B.
:
= 2pi
(t
T xA
) 2pi
(t
T xB
) = 2pix
pi pipi pi :
) x = , :
= 2pi
pi :
60
-
yA = A(A) yA = A(B + 2pi) = A(B) yA = yB: pi pi pi pipi , - pi pi pi . :
x = , = 1, 2, ...
pi pipi pipi : pi , pi
) x = (2+ 1)2, :
= (2+ 1)pi
pi,
yA = A(A) yA = A(B + (2+ 1)pi) = A(B) yA = yB
: pi pi pi pi pipi , pi - . :
x = (2+ 1)2, = 0, 1, 2, ...
2.8: pi pi , 2, 3, ..., pi pi
2, 3
2, 5
2, ....
61
-
pi . & .pi : 9.28 - 9.58, 9.122, 9.123, 9.126, 9.127, 9.128, 9.130 -9.136, 9.139, 9.140, 9.143 - 9.150, 9.153
2.3.4
(x = 0), pi pi, 0,
y = A(2pi
Tt+ 0)
:
y = A
(2pi
Tt 2pi
x+ 0
) y = A2pi
(t
T x
+02pi
)(2.14)
pipi pipi pi (2.6).
0 pi :
pi pi t = 0, pi pi t = 0 pi pi pi pi . pi t = 0 = 2pi
(tT x
+ 0
2pi
)= 0,
t = 0 ,
t = 0 pi v = vmax. pipi pi pi t = 0, pi pi ( pi ).
pipi pipi t = 0 (x = 0) v = +vmax.
pi pi 0 0 2pirad , pi pi pipi .
pi . & .pi : 9.156, 9.158, 9.160, 9.162, 9.163
62
-
2.4
pi . pi pi, pi pi :
pi pi pi pi , pi pi pi .
y = y1 + y2 + ...
pi :
pi pipi, , pi ,
-
: pi pi , pi .
pi pi pi- , pipi . pi , pi - pi pi pi .
pi pi pi .
63
-
2.4.1 pi
pi pi, . :
= .
, pipi . pi :
y1 = A(1t), y2 = A(2t+ )
pi :
= (2t+ ) 1t = (2 1)t+ pi , pipi
, : 2 1 = 0 2 =1 f2 = f1
pi ( = 0), pi pi. pi .
pi pi pi pi pi .
pi pi
pi pi 1 2 pipi pi , pi . pi pipi r1 r2 pi pi 1 2 .
pi pi pi , pi pi pi :
y1 = A2pi
(t
T r1
) y2 = A2pi
(t
T r2
)64
-
pi :
=2pi
(r1 r2) (2.15)
pi pi pi pipi, pi pi pi pi piy = y1 + y2. :
y = A2pi
(t
T r1
)+ A2pi
(t
T r2
) pipi :
y = 2A
(2pi r1 r2
2
)2pi
(t
T r1 + r2
2
)(2.16)
pi (2.16) pipi pi pi :
|A| = 2A|(
2pi r1 r22
)| (2.17)
= 2pi
(t
T r1 + r2
2
)(2.18)
pi (2.17) pipi pi pi pi pi .
pi pi pi pi pi pi pi 0 2. pi
. pi , =2, :
|(
2pi r1 r22
)| = 1
(2pi r1 r2
2
)= 1 2pi |r1 r2|
2= Npi
pipi pi pi pi pi pi pipi , pi 2.
|r1 r2| = N, N = 0, 1, 2, ... (2.19) pipi pi pi pi - pi ( = 2Npi)
65
-
. pi , =0 :
(2pi r1 r2
2
)= 0 2pi |r1 r2|
2= (2N + 1)
pi
2
pipi pi pi pi pi pi pi pipi
2pi . pi
|r1 r2| = (2N + 1)2
N, = 0, 1, 2, ... (2.20)
pipi pi pi pi - pi ( = (2N + 1)pi
2)
pi pi r1 r2 = . pi. pi pi pi pi pi pi. pi .
pi ( ) -pi (2.19). pi pi pi pi (-=2).
66
-
pi pi ( )pi pi . pi pi pi pi (=0).
pi pi pi pipi, pi pi pi 0 < A < 2A
1 : pi 1 2, pi - A1 A2, pi pi pi pi (1.64), pi :
A =A21 + A
22 + 2A1A2 (2.21)
pi = 2pi |r1r2|
pi pi pi .
2 :pi pipi - pi pi . pipi pi , pi pi pi .
3 : pipi pi pi- pi pipi pi (0) pi. pi :
y = y1 + y2 = A2pi
(t
T r1
)+ A2pi
(t
T r2
+02pi
)(2.22)
pi pi pi.
pi . & .pi : 10.1 - 10.35, 10.46, 10.48, 10.49, 10.51, 10.55, 10.57,10.58, 10.60, 10.61, 10.62, 10.65, 10.68 - 10.75, 10.77, 10.78, 10.80, 10.82,10.83, 10.84
2.5
pi, pi - pi ,pi pi .
pi pipi pi .
pi pi, pi pi .
67
-
2.9: .
pi pi pi pipi pi pi pi. pi pi , pi . pi pi pi pi , pi pi . pi , , pi pi pi. 3 , . pi pi pi, pi pi pi . pi .
pipi :
pi pi pi .
pi pi pi. pi .
pi pi.
2.5.1
pi , pi . xx , pi pi pi pi.
pi pi (x = 0) , pi pi pi pi pi pi, y1 = y2 = A2piT t, pi pi
68
-
pi :
y = y1 + y2 y = 2A2piTt
pi pi t = 0 pi pi pi ( = 0.
pi pi :
y1 = A2pi
(t
T+x
) y2 = A2pi
(t
T x
) pi pi pi pi pi x pi t :
y = y1 + y2 = A2pi
(t
T+x
)+ A2pi
(t
T x
)
y = 2A(
2pix
)
(2pi
Tt
)(2.23)
(2.23) . :
A = 2A(
2pix
)(2.24)
pi x .pi (2.23), (2.24) pi :
y = A(
2pi
Tt
)(2.25)
pi pi pipi :
pi pi
pi |A| , pi .
pi , pi , pi :
v = A(
2pi
Tt
) = 2A
(2pi
Tt
)
69
-
pi:
. , A = 2A, :
2A2pix
= A 2pix
= 1 2pix
= k pi
x = k 2, k = 0, 1, 2, ... (2.26)
pi pi pi - , pi pi, pi 0,
2, 2
2, ..., k
2
pi =2. . pi - x
2.
. pi |A| , =0, :
2A2pix
= 0 2pix
= 0 2pix
= (2k + 1) pi
2
x = (2k + 1) 4, k = 0, 1, 2, ... (2.27)
pi pi pi - ,pi pi, pi
4, 3
4.5
4, (2k + 1)
4,
pi . . pi
2.
pi pi pi - pi pi
d = |x x| = |k 2 (2k + 1)
4| =
4
0 pi ,
pi pi pi . = t y = A(t).
.
70
-
2.10: pi .
pi pi -
2, , ,
pi pi pi , - . = pirad. pi pi = t+ pi y = A(t+ pi).
.
pi , pi
, pi pi . pi , pipi L :
L =
2, = 1, 2, ..
pipi pi pi pipi, pi
, pipi :
L =
4+
2, = 1, 2, ..
pi pi pi ,
pi pi . . pi, pi , ( ) pi. pi pi
71
-
pipi pi pi pi t = T
2.
- pi
pi pi 2 pi
-
pi pi pi-
-
- . - pi - pi
2pi
pi pi pi pi -
pi - pi pi .
pi . & .pi : 11.1 - 11.36, 11.46 - 11.50, 11.52 - 11.59, 11.61, 11.63,11.64, 1.66 - 11.69, 11.71, 11.72, 11.75 - 11.79, 11.81
2.6
- pi. . .
pi . c = 3 108m/s
pi
pi - pi. pi pi pi . , pi ( ) pi - . , , pipi, pi pi pi pi . pi :
pi .
72
-
pi pi pi. - pi pi pi pi , pi pi ,pi . pipi - pi . pi . pi pi- pi pi .
pi Maxwell pi pipi :
, - pi .
pi ( c)
E
B= (2.28)
, pi , pi pi.
pi pi pi - pi x :
E = Emax2pi
(t
T x
)(2.29)
B = Bmax2pi
(t
T x
)(2.30)
pi Emax, Bmax pi .
pi :
2.6.1
pi pi pi-. pi , pipi , pi pi pi.
73
-
2.11: pi pipi , x. ~B pi pi y ~E pi pi z
pi pi - pi . pi , pi pi.
c :
c = fpi
. pi pi -
, . pi pi pipi.
. pi105m . pi , pi LC pi . . pi 30cm 1mm pipi.
pi . pi , .
pi . pi pi pi 1 mm 7 105m pipi. pipi pi pi pi pi . pi pi pi pi , pi pi pi pi-, .
74
-
. pi pi . - pi 400nm - 700nm ( 1nm = 109m). pi pi . pipi pi pi pi . :700 630 nm 630 590 nm 590 560 nm 560 480 nm 480 440 nm 440 400 nm
pi . pi pi3, 8 107m 6 108m pipi. pi pi. pi pi , pi . pi pi. pi pi .
pi 108m 1013m pipi. pi pi pi- pi - . pi , .
. pi pipi pi - pi pi - pi . pi 1010m 1014m. pi - pi pi pi.
pi . & .pi : 12.1 - 12.16, 12.19 - 12.26
2.7 - -
2.7.1
pi pi , pi -
. . ) ) pi .
75
-
pipi pi pi pi, pi pi . , pi pi-, . pi . pi pi pi pipipi pi (), pi- . pi. -pi .
pipipi pi pi pi , pi . pipipi pi .
pipipi pi pipi pipi (pi) pi - (). pipi :
pipipi , pi pipi pipi ( pipi pipi)
pipi pi
pi = (2.31)
2.7.2
pi - pi , pi , - pipi pi , -. . pi : pi-, - pi , pi pi pi .
.
pi pi - . pi - - pi pipi - ().
76
-
pi , pi . c pi n .:
n =c
(n = 1) = c. (n > 1) c > pi. pipi :
pipipi , pi- , pipi , pipi.
, pipipi .:
pi
=n2n1 n1pi = n2 (2.32)
pipi Snell ()pi pi Snell
) pi 1 (n1) pi 2 (n2 > n1), pi , pi pipi ( < pi).pi:
pi
=n2n1
> 1 pi > pi >
() pi pi 2 (n2) 1 (n1 < n2), pi pipi ( > pi).pi:
pi
=n2n1
< 1 pi < pi <
() pipipi pi- , . pi:pi
=n2n1 n1pi = n2 n1 0 = n2 = 0 = 0
77
-
, pi pi
pi n1 pi n2 :
f , pi pi pipi pi pi . pi pi pi .
pi = c
n.
, .
f , pi = f pipi pi . pi ( ) pi , .
c = 0f , 0 . = f , . pipi pipi.
c
=0 n = 0
= 0
n(2.33)
pi n > 1 0 > .
78
-
2.7.3
pi pi pipipi pi, pi a na. pipipi pi pi b nb < na.
pi Snell pipi :
ab
=nbna
pi nb < na pipi b > a. pipi b pi pi
pipi a a pi pi pi -
pi ( ) crit.
pi pi Snell b = 90
o
crit90o
=nbna crit = nb
na
pipi pi , pi- pipipi pi
79
-
pi pi a. .
pi, , pi pi -, pi pi pi - , pi pi.
! pi pi pipi .
pi a na = n ( ) nb = 1 a :
crit =1
n(2.34)
pipi pi . pi.. crit = 41, 1o , crit = 24o. pi pi ( )pipi ! pi .
pi . & .pi : 13.1 - 13.50, 13.55 - 13.58, 13.60, 13.61, 13.62, 13.64,13.65, 13.67, 13.68, 13.70 - 13.77, 13.79, 13.80, 13.81, 13.83, 13.84, 13.87,13.88, 13.89
80
-
3
3.1
, pi R, pi . pi dt ds pi pi d.
~ t, -, pi pi ds pi dt.
dsd
-
pi
, pi, pi pi :
=2
R= 2 R (3.3)
pi pi . pi .
pi , .
pi pi ,pi pipi :
=
t= 0t 0 = t
.
, pi R. pi dt d~ d~ .
( pi) pi
, - pi.
pi ~ t , pi .
=d
dt(3.4)
pi pi , pi , . pi 1m/s2.
82
-
pi ~ - pi ~ pi ~ = ~ + ~ . pi =
2 +
2
pi
pi ~ t -, pi .
=d
dt(3.5)
pi d~. - pi 1rad/s2. pi 1rad/s2 1rad/s 1s.
= R pi :
d = R d ddt
= Rd
dt = R
pi pi pi , - .
pi pi pi, pi :
=
t= 0t 0
pi pipi pipi :
= 0 + t (3.6)
pi () - (t) pi pi- :
pi pi = t
83
-
pi pi t = 0 t pi pi pi pi . pi :
= 0t+1
2t
2 (3.7)
pipi pi ( < 0) pi-pi : = 0 | |t = 0t 12 | |t2.
pi .
s pi = ddt pi =
ddt
s = t = t
pi = 0 + t = 0 + ts = 0t+
12t
2 = 0t+12t
2
pi = 0 ||t = 0 | |ts = 0t 12 ||t2 = 0t 12 | |t2
3.2
3.2.1
pi , pi . , , pi . pi .
pi , pi pi- pi pi . , , pi , pi pi () ( pi).
pi , .
84
-
, .
3.1:
, pi pi pi:
pi
pi -pi pi pi .
, pi. pi ( pi) pi -
pi , pipi , pipi pi . pi pi pi . . - , pi pipipi. pi -pi pi pi pi .
pipi .
(cm) pi pi , pi .
, .
85
-
pi pi . 2 - :
~F = m~cm (3.8)
, pi , pipi . pi . pi pi . pi .
, pi .
pi , . pi .
pi pi pi pi () .
pi
pi pi pipi, -. pi , pi pi pi.
pi pi pi ():
. , pi , ~cm
86
-
. pi , pi pi pi pi pi pi pi
R , -, pi - pi . dx dt, pi pi d , pi ds, . pi pi, (dx = ds) pi :
d =ds
R ds = R d dx = R d
pi pipi pipi 1 , pi , .
x = R (3.9) (cm = dxdt )
( = ddt) pipi :
dx
dt= R
d
dt cm = R (3.10)
pipi pi pi - 2 . pi = R pi pipi cm = . pi- :
, , pi .
2 pi pi pi- pi . pi pipi pi pi pi - (~ = ~cm+~). pi pipi pipi :
:
o = cm
:
= cm = 0
87
-
:
z = cm + = 2cm
:
M =2cm +
2 =
2cm
pi pipi , pi , . dt dcm d. pi (cm = dcmdt ) pi ( =
ddt
) :
cm = R dcm = R d dcmdt
= R ddt cm = R (3.11)
pipi pi pi , 3 . pi = R pi pi pi , pipi cm =
, , pi- pi pi pi .
pi pi pi (~cm) , pi (~) pi (~).
pi . & .pi : 1.1 - 1.50, 1.55, 1.57, 1.58, 1.60, 1.61, 1.62, 1.65, 1.66,1.69, 1.72, 1.75, 1.77, 1.86 - 1.92, 1.94, 1.97, 1.98, 1.100, 1.101, 1.102, 1.105
3.3 pi - pi
pi
pi (~ ) pi pi .
)pi pi
, pi pi zz. ~F , pi
88
-
pipi pi pi pi pi l ().
pi pi pizz, ~ , pi :
pi
pi pi
F pi pi l pi pi, :
= F l (3.12)
pi 1N m.
pipi pi, , , (Fx) pi pipi (Fy) pi pi . pi :
= Fx l = Fl (3.13)
pi pi :
pi pi .
pi pi pi pi pi pi pi .
pi ( )pi , pi pi -pipi , pi pi pi .
)pi pi
pi pi , . , , pi , : pi pi
89
-
pi pi pipi pi . pipi pi pi pi pi pi pi.
pi pi , ~ , :pi
pipi pi pi
pi pi
F pi pi l pi . :
= F l
pi pi :
pi .
) pi
~F1 ~F2, pi - , pi . pi , pi , pi pi - pi pi (F1 = F2):
= F1x1 + F2x2 = F1(x1 + x2) = F1d pi -
~ , pi :
pipi ,
pi pi
~F1 pi pi d . :
= F1 d (3.14)
90
-
pi pipi pi pi pipi pipi pi pipi pi pipi .
pi . & .pi : 2.1 - 2.21,2.58, 2.59, 2.60, 2.62, 2.63, 2.65, 2.67
pi
, pi pi pipi. pi pipi :
)
~F = 0 (3.15)
pi pipi , pi - . pi ( = 0), pi pi ( ).
) pi pi pipi
= 0 (3.16)
pi pipi , pi - . pi ( = 0), pi pi .
pi -:
1: pi pi .
pi ( pi.. , , ). pi pi:
pi pi pi pipi, pipi pi .
2: pi x y pi .
91
-
3: pi pipi :
Fx = 0, Fy = 0, = 0
, pi pi . pipi pi pi , pi pi pipi.
4: pi pipi. - pi pi .
pi . & .pi : 2.22 - 2.55,2.81, 2.82, 2.85, 2.87, 2.90 - 2.99, 2.102,2.104, 2.105, 2.107, 2.108, 2.111, 2.113, 2.116, 2.118, 2.123.
3.4 pi
, pi pi - zz, pi pi . m1,m2, ...,m, pi pi . m1,m2, ...,m pi , r1, r2, ...r, .
pi I pi zz pi pi pi pi pi- pi pi. :
I = m1r21 +m2r
22 + ...mr
2 (3.17)
pi S.I. 1kg m2.
pi pi pipi pi - m, pi r, pi zz pi pi pipi pi :
I = mr2 (3.18)
:pi , pi pi - pi .
92
-
m1, m2, ..., m . m1 + m2 + ...m = M . pi pi R, pi R pi pi. pi :
I = m1r21 +m2r
22 + ...mr
2 = m1R
2 +m2R2 + ...mR
2
I = (m1 +m2 + ...m)R2 I = MR2
(Steiner)
pi Icm pi pi pi pi Ip pi pipi p, pi pi pi d pi pi pi, Steiner:
Icm pi pi pi pi , pi pi pi pi pi pi d pi pi pi pi pi pi pi pi d. :
Ip = Icm +Md2 (3.19)
:pi , pi pi pi pi- .
Steiner :
Ip = Icm +Md2 Ip = Icm +MR2 = MR2 +MR2 Ip = 2MR2
pi pipi pipi pi pi pi :
pi .
pi pi pi , pi .
pi pi.
93
-
3.2: pi pi , pi pi .
3.5
pi pi , pipi , , pipi . () pi (pi) :
~F = m~ (3.20)
pipi . .
, pi pi , pipi pi. (pi) pi ( pi) :
= I (3.21)
pipi -, pi pi :
pi pi pi , pipi pi , pi pi pi pi -.
pi 3.21 pi pi pi.
94
-
pi
pi pi 3.21 pipi pi pi , pi pi .
pi pi , , . :
m pi pi . - .
pi I pi pipi . .
, pi , pi - pi pi. , pi pi .
pi . & .pi : 3.1 - 3.25, 3.27, 3.28, 3.29, 3.32, 3.33, 3.36, 3.38
= I
. = 0 pi = 0. pi , pi pi pi . - , ( = 0), , ~, ~.( ).
. =. , pi =. , pi pi - pi, pi, .
3.5.1
pi pi pi , pi , pi- pi:
95
-
~F = 0, = 0 pi~F 6= 0, = 0 pi .
pi ~cm~F = 0, 6= 0 pi pi
pi pi , pi
~F 6= 0, 6= 0 ( pi - pi ~cm pi pi pi pi pi )
pi . & .pi :4.1 - 4.14,4.52, 4.53, 4.55, 4.56, 4.57, 4.60, 4.63, 4.64,4.66, 4.68, 4.69, 4.70
, pi ( , pi) pi pi :
() pi pi .
() -.
() , -.
, pi - :
pi pi pi .
pi pi .
pi :
~F = m
, pi :
= 0 + t, x = 0t+1
2t2
96
-
pi pi :
= I
pi - :
= 0 + t, = 0t+1
2t
2
pi pi pi pi - pi , . - pi pi x s = R = x. pi pi pipi - pipi pi pi pi pi pi pi :
cm = R
pi pipi .
pi . & .pi : 4.74, 4.76 - 4.82, 4.84, 4.86 - 4.89, 4.91, 4.92, 4.93
pi pi- - .
:
pi .
pi, :
~F = m~cm
, :
= I
pi pi pi - pi .
97
-
, pi pi pi -, pi- cm :
cm = R
:pipipi
. -: pi pi , m R pi pi - . pi, pi pi . - pi . pi (~w) (~T ) , pi pi pi . pipi :
:
F = mcm mg T = mcm
:
= Icm TR = Icm
cm = R
pi . & .pi : 4.109, 4.111, 4.113, 4.120, 4.124, 4.134, 4.138, 4.144,4.146
. pipi: pipi pi (w) pi (T ), pi pi pi pi pi pi - . :
98
-
:
Fx = mcm mg T = mcm
:
= Icm TR = Icm
cm = R
pi pi :
pi pi (cm) pi pi , :
cm =mg T
m
pi pi, pi TR, pi , pi pi , pi pi cm R, pi cm = R .
, pi , pi pi pi , pi .
, pi pi , pi pi, pi , .
pi pipi pi , cm . pi pipi , pi pi .
99
-
pi pipi pi pi , cm . pi pipi , pi pi pi .
(~w), (~T ) - pi pi ( ~N ). pi pipi pi pi pi pi- :
0 T sN pi
, pipi :T < sN
T = sN , . pipi cm 6=R
pi pi pipi .
, R pi pi Icm pipi, pi pipi, pi , pi : pi pi cm pi -
: Fx = mcm = Icm cm = R
pi pi pi : x = 1
2cmt
2 t =
2xcm
pi pi - : cm = cmt cm =
2cmx
pi . & .pi - : 4.13 - 4.16, 4.19 - 4.44, 4.114, 4.116, 4.117, 4.119, 4.4.121,4.122, 4.127, 4.129, 4.130, 4.131, 4.132, 4.136, 4.137, 4.141, 4.143
. pi pi
pipi , L pi pi Icm = 112ML
2 pi pi pipi pi pi , pipi pi.
100
-
pi pi pi pi - , pi !
- pi pipi pipi :
(o) = I(o)
Steiner pi pi pi pi:
I(o) = Icm +M
(L
2
)2=
1
3ML2
pi pi pi pi :
(o) = MgL
2
pi ( = 0) pi pi MgL
2
pipi pi pi pi :
=3
2L
! . pi pi pi pi.
pi . & .pi - :4.150, 4.152, 4.153, 4.155, 4.156, 4.157, 4.158, 4.159, 4.161,4.163
3.6 -
, (~P ). , pi ~L.
) .
m pi pi - r, ~P ,pi .
101
-
, pi zzpi pi pipi , ~L pi :
pi
pi pi
p pi r . :
L = pr L = mr (3.22) S.I. 1kgm2/s. ,
(3.22) :L = m(r)r L = mr2 (3.23)
pi pi pi( = Fr). pi pi pi. pipi pi r pi pi (~), pi pipi pi.
) .
-pi pi pi pi- zz, pi pi, pi .
pi pi pi zz ~ . m1,m2, ...,m, pi pi -. pi , pi zz ~ 1 = r1, 2 = r2, ..., = r.
:
L1 = m1r21, L2 = m2r
22, L... = mr
2
102
-
pi pi. :
L = L1 + L2 + ...+ L L = m1r
21 +m2r
22 + ...+mr
2
L = (m1r21 +m2r
22 + ...+mr
2)
L = I
pi I = m1r21 +m2r22 + ...+mr2 pi , pi pi zz. pi :
pi pi pi ~L, pi :
,
pi pi
pi I , pi pi, pi . :
L = I (3.24)
-pi. , pi pi .
pi: pi pi pi pi pi pi pi. pi pi pi pi pi pi . pi , pi pi pi pi ( ).
)
pi pi .
pi pi ~L1, ~L2, ..., ~L ~L :
~L = ~L1 + ~L2 + ...+ ~L
103
-
pi -
pi pi pi pi pi dt d, pi pi (3.24) pipi :
L = I dL = Id dLdt
= Id
dt= I = dL
dt
: pi pi , pi pi- pi , .
pipi pi = I, pi .
pi, pi pi .
pi . 3 , - , -pi pi pi :
=dL
dt(3.25)
pi pi -, pi pi pi L , pi .
pi . & .pi - : 5.26 - 5.36, 5.60 - 5.63, 5.65, 5.67, 5.69, 5.70 - 5.72, 5.74,5.76, 5.79, 5.83, 5.84, 5.86, 5.87
3.6.1
pi = 0 :
=dL
dt= 0 L = .
: pi pi ( pi pi ) , ( pi ) pi .
104
-
pi = 0 - pi .
pi
pi pi pi . , - pi , pi pi , , -. :
~L = ~L (3.26)
pi pi pi pi pi pipi pi pipi .
I1 pi 1 I2 pi 2 pi pipi :
I11 = I22
pi pipi pi pi , . pi pi pi .
pi pi: pi pi pi, pi pi pi pi . , pi pi pipi , pi .
pi : pi 1,4 2,5 , pi . , pi , , pi - km. pi pi , pi . pi pi . pi pi
13000
s, pi pi 25 . pi . & .pi -
: 5.1 - 5.25, 5.37 - 5.49, 5.93, 5.95 - 5.99, 5.101, 5.102, 5.105,5.107, 5.108, 5.109, 5.111, 5.112
105
-
3.7 -
3.7.1
M pi ~. pi , m1,m2, ...,m pi ~. pi pi pi. :
K =1
2m1
2 +1
2m2
2 + ...+1
2m
2 K = 12M2 (3.27)
pipi pi pi , pi .
3.7.2 pi
pi ~ pi zz, pi .
pi , - m1,m2, ...,m, pi pi pi r1, r2, ..., r, pi pi. ~ 1 = r1, 2 = r2, ..., = r.
pi pi pi. -:
K =1
2m1
2 +1
2m2
2 + ...+1
2m
2 (3.28)
K =1
2m1
2r21 +1
2m2
2r22 + ...+1
2m
2r2
K =1
2(m1r
21 +m2r
22 + ...+mr
2)
2 K = 12I2
3.7.3 pi
~cm ~. . :
K = K +Kpi =1
2M2cm +
1
2Icm
2 (3.29)
106
-
pi M Icm pi , pi pi pi .
3.7.4
~F pi x pi pi W = ~F ~x. pi pi pi pi .
pi R, pi pi- pi pi pi pi , pi ~F - . pi d, pi pi ds = Rd. pi pi ds pi pi pi :
W = Fds dW = FRdpi = FR pi pi
pi pipi :
dW = d (3.30)
pi , pi W , pi d dW . pi pi pi :
W = (3.31)
W pi pi . pi pi pi pi pi.
3.7.5
pi pi ~F , pi pi pi pi . pi dt pi pi d, pi dW :
dW = d dWdt
= d
dt
107
-
pi dWdt
- (P ) . pi t :
P = (3.32)
S.I. 1Watt. pi :
P = F.
P pi pi W , pi pi pi pi t,pi t.
P =W
t(3.33)
3.7.6 -
pi pipi , pi pi pi 6= 0, pi pi pi pi pi K = 1
3I2.
pi pi pi pi . pipi pi pi pi - (....) :
K2 K1 = W 12I22
1
2I21 = W (3.34)
pi pipi pi - pipi pi pi. - . pi , , . pi pi .
t pi x pi pipi pi , :
x = R
108
-
pi pi pi pi- - .:
Kpi = W = (TR)
- . :
K = W = Wxx Tx K = W = Wxx TR
pipi pi :
Kpi + K = TR +Wxx TR K = Wxx
pi pipi pipi pi:
, t. .
pi - (....), pi pi pi .
3.7.7
.... pi pi ( pi.. , ). pipi pi pipi :
E = K +Kpi + U = o (3.35)
pi pipi , pipi pi - pipi pipi (U = 0). pi pi pi .
pi . & .pi - : 6.1 - 6.62, 6.90, 6.92, 6.93, 6.114, 6.116, 6.117, 6.118, 6.120.6.121, 6.122, 6.123, 6.124, 6.125, 6.127, 6.130, 6.131, 6.132, 6.133, 6.136, 6.137,6.139, 6.141, 6.143, 6.144, 6.145, 6.148, 6.149, 6.152, 6.155, 6.161, 6.167, 6.171,6.172, 6.146, 6.147, 6.153, 6.156, 6.159, 6.160, 6.163, 6.164, 6.165, 6.166,6.170, 6.174
109
-
-
pi: x : : = dx
dt : = d
dt
pi: = ddt
pi: = ddt: ~F pi : ~: m pi : I : :~F = m~ = I ~P = m~ L = I~F = d
~Pdt
= dLdt
: : ~F = 0, : ~P =. = 0, : L =. : piW = Fx W = : pi:P = F P = : pi:K = 1
2m2cm K =
12I2
- :
:
W = 12m22 12m21 W = 12I22 12I21
pi pi pipi pi pi . pi . pi .
110
-
4
pi . :
pi .
pi pi pi , pi pi pi (pi.. ). - .
pi pi, pi pi pi pi-. pi pi , pi pi , -pi pi, - .
-, pi pi pi . pi-pi .
4.1 , pi .
() () ()
pi , pi - pi pi pi .
-
pi pi pi .
pi pi .
pi .:
~F =d~Podt
= 0 ~Po = ~Po(pi) = ~Po() , .
4.2 -.
pi pi pipi pi , . pi :
pi pi pi-, pi . pi pi pi pi -. pi , , , pi .
, pi pi .
pi pi pi pi pi . pi - , pi pi. pi pi
pi pi :
Ko(pi) = Ko()
112
-
pipi, pi - ( pi.. pi pi). pipi () pi .
pi - pi pi pi pi , pi. pi pi , pi pi pi. pi - pi
pipi pi - . pi . pi pi :
Ko(pi) Epi = Ko() Ko(pi) > Ko()pi Epi pi
pi.
4.2.1
m1 m2, pi pipi ~1 ~2. pi- ~1 ~2, pi - pi. pi pi pi - pi pi pipi.
~Po(pi) = ~Po() m11 +m22 = m11 +m22 (4.1)pi pi .
Ko(pi) = Ko() 12m1
21 +
1
2m2
22 =
1
2m1
1
2+
1
2m2
2
2 (4.2)
113
-
(4.1) :
m1(1 1) = m2(2 2)
(4.2) :
m1(21 12) = m2(22 22)
pipi :
1 121 12
=2 22
2 22 pipi 1 + 1 = 2 + 2 2 = 1 + 1 2
(4.1) pi 1 .
1 =m1 m2m1 +m2
1 +2m1
m1 +m22 (4.3)
2 =2m1
m1 +m21 +
m2 m1m1 +m2
2 (4.4)
pi pi - pi , pi pipi pi pipi .pipi pi, pi pi !
pipi
. m1 = m2 = mpi pipi (4.3),(4.4) pipi :
1 = 2 2 = 1
, pi , .
pipi pi pi pi , pi pipi.
. pi (2 = 0) pi (4.3),(4.4) pipi :
1 =m1 m2m1 +m2
1 (4.5)
114
-
2 =2m1
m1 +m21 (4.6)
pipi pi , (1 = 0) pi 2 = 1
pi
pi (m1
-
pi pi pi :
pi =y
=y
pi y = y = pipi pipi pi .
pi = (4.7) pi pi pi pipipi
pi pi. pi , pi pi pipi .
4.2.2
m1 m2 pi pi pipi ~1 ~2. ~1 ~2.
~Po(pi) = ~Po() m11 +m22 = m11 +m22pi pi .
Ko(pi) Epi = Ko() 12m1
21 +
1
2m2
22 Epi =
1
2m1
1
2+
1
2m2
2
2
pi Epi pi . pi ~V , . pi pipi pi pi pi . pi .
4.2.3
pipi pi , pi pi pi pipi. pi m1 m2 -. ~1 ~2. pi .
116
-
xOx
Po(pi)(x) = Po()(x) m11 = m11x +m22x
yOy
Po(pi)(y) = Po()(y) m11 = m11y m22y
Ko(pi) = Ko() 12m1
21 +
1
2m2
22 =
1
2m1
1
2+
1
2m2
2
2
pipi pipi , 4 - . pi pi ( pi ).
pi pi pi pi . pipi .
4.3 pi-
, pi t, pi , ( ) pi .
pi ~V Umax pi . pi .
pi pipi :
~Po(pi) = ~Po(t) m11 +m22 = m1V +m2V V = m11 +m22m1 +m2
pi pipi :
Ko(pi) = Ko(t) + Umax 12m1
21 +
1
2m2
22 =
1
2m1V
2 +1
2m2V
2 + Umax
pi Umax pi pi pi - pi.
117
-
pi . & .pi : 8.1 - 8.76, 8.102, 8.103, 8.104, 8.106, 8.118, 8.119,8.121, 8.126,8.127, 8.130, 8.131, 8.133, 8.134, 8.136, 8.139, 8.143, 8.144, 8.146,8.149, 8.151, 8.154, 8.156, 8.164, 8.168, 8.170, 8.173, 8.174
118
-
5
pi(Doppler)
pi . , pi pipi. pi pi .
, pi - pi , pi pi , pipi. . . pi , pi .
pi pipi pi pi Doppler:
Doppler pi, pi pi , pi pi pi pi pipi.
pi , , .
S pi, fS pi, ~S pi. pi pi-, fA pi pi ~A pi. ~S , ~A pi pi pi pi.
, pi pi -, . ~S ~A pi . pi pi pi .
5.1 pi - pi
pi pi S pi pipi pi fS. , pi :
= fS fS =
-
pi pi . pi- . pi pi . pi , pi pi pi , pi fA, pi . , pi pi, pi, pi pipipi.
fA = fS =
pipi pi pi
pi - pi pi - pi pi !
5.2 pi - pi
pi pi
pi pi pi - pi S ~A, pi . pipi pi pi pi pi- , pi , pi pi - pi -.
pi- ~A,B = ~A ~B, pi ~A,~B pi pi pi.
pipi pi pi pi pipi :
~ = ~ ~A = (A) = + A pi pi pipi pi pi : =
fS.
pi , pi pipi
, pi pi. pi pi :
fA =
= + A
= + A/fS
fA = + A
fS
120
-
pi + A > pipi pi pi - pi ( ) pi pi pi pipi (fA > fS).
pi pi
pi pi pi pi pi S ~A. pi pi pi pi pi, pi , pi pi . pipi:
~ = ~ ~A = A = A pipi pi pi :
fA =
= A
= A/fS
fA = A
fS
pi A < pipi pi pi - pi () pi pi pi pipi (fA < fS).
5.3 pi - pi
pi pi
pi pi S ~S, pi pi . - , pi pi pi pi. pi = fS .pi pi pi pi- pi , pi pi pi pi pi pipi.
pi A pi pi . pi pipi . pi pipi pi pi. pi pi x = ST pi pi. pi pi ST . pi A pi pi .
121
-
pi pi :
fA =
A=
ST =
fS S
fS
fA = S fS
pi S < pipi pi pi - pi () pi pi pi pipi (fA > fS).
pi pi
pi pi S pi ~S pi pi- , pi pi pipi pi pi , pi pi pi ST . pi pi +ST . pi pi :
fA =
A=
+ ST=
fS
+ SfS
fA = + S
fS
pi + S > pipi pi pi - pi () pi pi pi pipi (fA < fS).
5.4 pi
pi pi , pi pi pi pi pipi pipi.
fA = A S fS (5.1)
pi pi pipi : pi pi pi,
pi , pi pi pi . pi!
pi (+) - pi pi pi pi (-) pi pipi pi pi.
pi pi (-) pi pi pi pi (+) pi pi pipi pi.
122
-
pipi
Doppler pi pi-, pi (tA). pi pi pipi tS. pi :
fA =NAtA
fS =NStS
pi pi pipi (NS) pi pi (NA). pipi :
fAtA = fStS tA = fSfA
tS
, pi pi , fA = fS, .
pi pi pi pi pi pi
pi ~S pi pi pi - pi, pipi pi pi pipi -. pi pi pi pi pi - pi pi - pi .
pi pi
pi pi , pi pi .
pipi pi S(t) . pi pi pi S = A(t+ 0).
pipi pi - A(t). pi pi pi S = St
pi . & .pi : 9.1 - 9.45, 9.50, 9.51, 9.53, 9.54, 9.56, 9.57, 9.58, 9.61,9.62, 9.63, 9.65, 9.67, 9.68, 9.71
123
-
124
-
I
2012 - 2013
-
pi 1 - 2012
. pipi pi
.1. pi . pi x pi pi :
.
.
.
. pi pi
.2. pi pi :
. x = 0
. pi x
. x = A. pi
.3. pi pi pi :
.
. pi x
.
. x = 0
.4. pi :
.
.
.
.
127
-
.5. pi pi :
. pi
. ,
. ,
. , .
.6. pi pi- :
. pi pi
. pi pi
. pi pi
. pi pi pi-
.7. pi pi pi pi pi pi pi- pi:
.8. pi pi :
.
. pi
128
-
. pi2
. pi4
.9. pi pi - pi ,
. t1 pi.
. t3 pi.
. t1, pi.
. t4, pi.
.10. pi pi pi pi ,
. t1 pi.
. t2 .
. t3 .
. pi t2 t4 T4 .
129
-
.11. pi pi - , pi pi . pi pipi pi
. t = T4 pi pi pi
.
. t = T4
pi .
. t = T2
pi .
. t = 3T4
pi .
.12. pi - t = 0 pi-. pi pi pi pi pi- pi pi pi - .
130
-
.13. pi pi pi pi . pi pi :
. pi
.
. pi
. pi
.14. pi pi pi :
. pi
. pi pi
. pi
. pi pi
.15. pi . pi- :
. pi
.
. pi
.
.16. pi pi pi x = A(t + pi2 ). - pi , - pi :
. T2 3T
4
. 0 T4
. T4 T
2
. 3T4 T
131
-
.17. pipi pi , :
. pi.
. A.. pi pi .
. A x 0.
.18. pipi pi , :
. x = 0 .
. pi pi .
. pi .
. pi pi.
.19. pipi pi , :
. .
. pi pi .
. pi pi .
. pi max.
.20. - pi - pi . pi pi pi - :
. .
.
. pi
. pi
132
-
.21. pi l , m pi pi f0. 3m, :
. f03
. f0
.
3f0
.
3f03
.22. - . :
. pi .
. pi pi .
. .
. pi pi .
.23. m pi . - :
. .
. .
. .
. pi .
.24. pi pi-:
. .
. .
133
-
. .
. pi max 0.
.25. pi - pipi pi . pi pi . :
. pi pi.
. pipi.
. .
. pipi.
.26. pi- pi m = 1kg pi pi .
. pi 5s
. pi 100N/m
. pi 10m/s2
. pi pi F = 10x
.27. pi x = f(t) pi pi pi .
. 2s 6s .
. 0s, 4s 8s -.
134
-
. t = 6s pi a = 116m/s2(pi2 = 10).
. 4s 6s pi .
.28. pi pi pi x = A(t + pi2 . pi pi = f(t)
.29. pi - pi pi. pi pi :
. pi .
. pi pi.
. pi pi.
. pi pi.
135
-
. pipi pi
.1. , m, pi . - , pi pipi 3. :
. .
. pi.
. pi.
pi pi pi .
.2. pi pi pi . t1 pi.
pi pi :
pi pi pi .
136
-
.3. , pi . pi pi -pi d, pi E1 pi pi, pi pi . , pi pi pi pi pi d pi. E2 pi pi :
. E1.
. pi E1.
. pi E1.
pi pi pi .
.4. (1) (2), - m1 m2 (m1 = 4m2) , pi k1 k2 . pi . , F -pi x :
pi pi pi .
137
-
.5. 1 m - pi pi . - pi, pi - Fmax pi max. 1 2, pi m2 pi 1 pi . 2 pi :
) pi :
. pi 1.. 1.. pi 1.
) pi :
. pi 1.. 1.
pi pi pi .
.6. m = 1kg pi - pi pi pi pi x = 0, 02(4pit)(S.I.). pi x pi pi :
. U = 72pi2x2(S.I.)
. U = 16x2(S.I.)
. U = 144 72pi2x2(S.I.)
pi pi pi , - .
.7. () () pi - xA = Apit xB =2Api2 t.
. fA = 4fB
. fA = 2fB
138
-
. fA = fB
. fB = 4fA
. max,A = 2max,B
. max,A = 4max,B
. max,A = max,B
. max,A = max,B2
pi pi pi .
.8. m - k -pi. pi pi - . pi -. , 2k , . pi pi pi pi - . pi . pi max,1max,2 :
. 2
. 1
. 12
pi pi pi .
.
.1. m = 2kg pi - = 10rad/s. t = 0 pi pi- Fmax = +20N.
. pi pi pi .
. pi { pi . pi [0, 2pi).
139
-
. t1 = pi4 .
. t1.
.2. , m = 2kg, pi -. pi d = 0, 4m t0 = 0 pi q1 = 0, 1m, 1 = 2
3m/s pi
pi
. pi pi pi D .
. pi -pi x pi pi , S.I.
. pi 0 -. pi [0, 2pi]).
. pi pi, pi , pi .
.3. pi - m = 0, 5kg, pi pi .
. pi pi .
. .
. , pi . (pi2 w pi2
. pi pi 75% .
140
-
.4. m = 0, 1kg pi -, pi pi d = 40cm. pi t = 0, 1pis. t0 = 0 pi x0 = 0, 1
3m
.
. pi .
. pi
. pi , pi , 1 =
3m/s
. pi 0 .
. pi pi , t2 = 3T4
.5. , m = 0, 5kg, pi - f = 5piHz , pi d = 2m. - , , F1 F2, pi F2 F2 = 10N . t = 0 pi pi x1 =
3
4 m.
. pi pi pi D .
. pi 0 .
. pi pi % pi , t = 0.
. F1 .
141
-
.6. , k = 100N/m, pipi, =30. pi pi , , m = 1kg. pi pipi x0 = 0, 1m t = 0, - u0 = 3m/s pi pi pi pipi, pi .
. pi .
. pi pi .
. pi . pi .
. pi pi - .
g = 10m/s2
.7. pi pi t = 0 - (x > 0), pi pi K = 3U .pi pi pi10sec.
.
.
. pi pi x = 0, 1m pi ., =
3m/s. pi
142
-
. x = f(t), u = f(t) pi pi.
. pi t = 0 pi pi
.
.1. m = 100g k = 10N/cm, pi -. F = 2102N , pi pi - pi , pi pi-. pi pi pi d = 0, 1m pi t = 0 .
. pi pi x0 pi pi .
. pi
. pi pi pi pi .
. pi pi pi , F . pi .
143
-
.2. , m = 0, 5kg, k = 200N/m pi pipi. F = 50N pi , . , pi ,pi .
. pi pi pi- pi k .
. pi . pi , pi t = 0, , pi . pi pi .
. pi , pi- .
. pi EE , pi
F .
.3. 1 2, m1 =m2 = 10kg, pi - k100N/m . . 1 , 1 2. t = 0 pi , pi 1 pi .
144
-
. pi pi 1 2 - pi 1 .
. pi pi .
. pi pi, pi- x { t. pi - , 1 pi. : pi2 = 10
. 2 pi pi, pi , pi , U = 180J , pi pi pi : 2 1 . g = 10m/s2
.4. k = 100N/m pi. pi 1 m1 = 0, 8kg. pi 2 m2 = 0, 2kg. - pi. pi E = 2J .
. pi , - t pi pi 1 pi pi.
. pi , pi pi 1, pi x pi pi .
. pi pi y pi pi , pi pi .
. pi , pi pi pi pi pi pi pi .
g = 10m/s2.
145
-
.5. k = 400N/m pi- 1 m1 = 3kg, pi pi pi. 1 pi 2 m2 = 1kg. pi pi pi , V pi pipi, pi , pi . pi .
. pi - Do, D1 D2 1 2.
. pi , - pi , pi - : i) 12, ii) 1 iii) 2.
. pi pi 1 2 pi x pi pi , pi A = 3cm.
. pi Vmax, 1, 2 2 pi 1. pi g = 10m/s2 1 2 = 0, 5.
146
-
.6. k1 =300N/m k2 = 600N/m 1 2, , pi , m1 = 3kg m2 = 1kg. - pi. pipi pi 1 d = 0, 4m pi- k1 . pi 2 . pipi .
. pi pi 1 2.
. 12 pi pi .
. pi pi .
. pi , .
. pi pi pi m1 2 pi pi m1
.7. pi m = 10kg pi pi pi k = 10N/cm
. , pi - .
. pi pi ` . g = 10m/s2.
pi pi .. , E = 5J .
147
-
. pi pi .
. pi x pi pi pi pi x, .
. pi .
.8. m = 2kg pi pi - k = 200N/m, pi . pi- pi pi (.) pi pi pi pi =
3m/s
pi . pi , (t = 0) - , pi pi ( pi pi .) g = 10m/s2. pi - pi .
. pi pi -.
. .
. pi pi, , pi- : - , - , -.
. pi pi . x1 = 0, 1
3m
148
-
. pi 1 pi t = 0, .
. pipi , pi .
. t2 pi pi , t = 0, pi , :
1. 2. 3.
.9. - pipi. M = 3kg. pi m = 1kg pi pi pi y1 = 0, 4m. - pi pi y2 = 0, 8m pi pi t = 0.
. pi pi D .
. .
g = 10m/s2.
149
-
.10. pipi = 30o. k1 = 60N/m k2 = 140N/m . , 1, m1 = 2kg pi (pi ). t0 = 0 1 .
- 2012
. pi 1 pi .
. pi pi 1 pi pi . pi pi .
pi pi 1 ,pi pi ( ) 2 - m2 = 6kg. 2 pi 1 pi pi . pi .
. pi 2.
. pi pipi -pi 1 2, 2 1.
150
-
.11. pipi - k1 = 60N/m k2 = 140N/m -. , m = 2kg (pi ). pi A = 0, 2m pi to = 0 .
pi - 2012
. pi pi .
. pi pi pi pi . pi .
. pi pi x.
. pi x = A2
k2. pi pi .
.12. 1 m1 = 1kg pi pi - pipi pi = 30o. 1 k = 100N/m pi pipi, pi .
5
1 d1 = 0,1m .
1. 1 .
5 2.
1.
5 1 = 0,3m. 2 m2 = 1kg , 1, .
3. 2
.
6
5 7
pi 1 d1 = 0, 1m pi pi pipi .pipi - 2010
151
-
() pi 1 pi .
() pi 1.
1 pi pipi pi pi ` = 0, 3m.pi 2 m2 = 1kg pipi, pi 1, .
5
1 d1 = 0,1m .
1. 1 .
5 2.
1.
5 1 = 0,3m. 2 m2 = 1kg , 1, .
3. 2
.
6
5 7
() pi pi 2 .
() pi pi pi pi pi pi .
152
-
2 - pi 2012
. pipi pi
.1. pi - L C, pi pi pi
. pi
. pi
. pipi
. pipi
. 41, 4%
. 41, 4%
.2. pi LCpi :
. pi pi
. pi pi pi
. pi pi
. pi pi
.3. L C . pi pipi pi pi pi
.
.
.
.
153
-
.4. L C . pi pipi pi pi - pi pi
.
.
.
.
.5. - LC, pi pi pi
. pi
. pi
. pi pi
. pi pi
. pi pi
. pi pi
.
.6.pi pi pi - L C pi pi. pi pi pi, pi
. , pi.
. pi.
154
-
. , pi .
. pi pi
. pi pi -.
.7. L C pi pi- pi pi . pi :
.
.
.
.8. L C , t =0 pi. pi pi pi
. T = 2pi
LC
. = 1LC
. f = 2piLC
. T = 2piLC
155
-
.9. L C pi t = 0 pi. pi pi pi pi - ;
. pi pi q = Q(t+ pi2)
. pi i = I(t)
. pi I = 2pifQ,pi f
. q = Q2, i = Q
2
3LC
.10. pi t = 0 pi. pi pi pi pi ;
. t = 0 pi pi .
. pi pi - pi pi pi.
. pi pi - pi .
. .
156
-
.11. L C -. t = 0 pi . pi pi pi pi.
. pi pi Q pipi : I = Q
2piLC
. pi pi pi pi t = 0 .
. UE pi UB pi : UB + UE = L2 I
2
. pi pi 4 pi .
. pi pi.
.12. pi pi L C . pi pi . pi pi pi pi :
. T8
.T4
.3T8
.3T4
. pipi pi
.1. LC -. pi - - pi pi : i =
Q2 q2
.2. L C , pi T . t = 0 pi pi pi . pi pi, t1 = t0+ 3T4 , :
.
157
-
.
.
pi pi pi .
.3. pi - q t , 0 t0 , LC. pi pi L2 = 4L1. pi pi :
. C2 = C9. C2 = C4. C2 = C3 pi pi pi .
.4. , . pi - . pi - , . , :
. 4E9
. 2E3
. 9E4
pi pi pi .
158
-
.5. , pi , pi - pi . pi, pi-:
. pi .
. , pi pi pi .
. , pi pi pi .
pi pi pi .
.6. LC (1) pi - C pi pi L , - L C (2) pi, pi pi 4L. pi - (1) pi V pi (2) pi 2V - . E2E1 :
. 1
159
-
. 2
. 4
pi pi pi .
.7. pi pi pi , pi C = C1+C2 q = q1+q2 (pi pi). pi , piC2 = 3C1, pi pi pi i = I(t), pi . t1 = T3 ,pi pi pi .
(pi:ylikonet.gr)
. pi pi pi-:)T1 = T , ) T1 = T2 , )T1 =
T3.
pi pi pi .
. :) E1 = E, ) E1 = 916E, ) E1 =
716E, ) E1 = 416E
pi pi pi .
160
-
.
.1. pi pi C, pi pi L pi,pi . pi Q = 100C pi, pi - . pi t pi pi- q = 60C . i = 80mA . pi-:
. .
. pi pi pi pi t.
. t.
.2. C pi pi . pi pi pi, pi pi L = 0, 4H, pi. t = 0 pi,pi . pi pi q =0, 4(1000t)C .
. pi pi.
. pi .
. pi pi pi 0, 2103A.
161
-
.3. pi pi C = 40C, pi pi L = 4mH pi, pi . pi- V = 100volt pi, pi -.
. pi .
. pi pi pi.
. .
. pi () .
.4. pi - pi L = 4mH , pi C = 160F . pi pi , pi . pi pi t = 0 pi , pi - . E = 2 105J . pi:
. pi .
. .
. pi t1 , pi pi pi pi pi.
. pipi t1.
.5. : pi E = 5V , pi C = 8 106F , pi pi- L = 2 102H. pi 1 pi 2
( - 2010)
. pi Q pi.
162
-
pi 1 =0 pi2. LC .
. pi pi .
. - pi pi.
. pi pi pi pi pi pi pi pi pi.
.5. pi pi E = 100V olt. pi
