, ,
.
( ) x
f(t) - .
x
Ds - , Dt. Ds Dx = x2-x1 , .. Ds ³ 0.
x
x
x
, r=R-const
, :
- ; - ; w - ; e - ; R - .
m, ,
.
- , .
, :
)
- ( - );
x - ;
)
)
- ; m1 m2 - ; r - ( ). :
) ()
f - ; N - .
(i=2)
,
- , ; - , .
, ,
,
:
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- ; x - ;
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- ; m1 m2 - ; r - ( );
) , ,
g - ; h - , ( h<<R,
R ).
, , :
1. x = A + Bt + Ct3, = 2 , = 1 /, = - 0,5 /3. , t = 2.
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. x, A, B C t:
x = (2 + 1×2 - 0,5×23) = 0.
:
.
, :
t = 2
= (1 - 3×0,5×22) /c = - 5 /c;
= 6(- 0,5) × 2 /2 = - 6 /2.
2. j = A + Bt + Ct2, A= 10 , = 20 /, = - 2 /2. , =0,1 , t =4 .
. , , , , , (.1):
,
w - ; e - .
(1),
. (2)
w , :
t = 4
w = [20 + 2(-2)4] / = 4 /.
, :
= 2 C = - 4 /2.
w, e r (2),
/ = 1,65 /2.
3. m1, , m2. , , . e ?
. , ,
(1)
1 - ; u2 2 - .
(1), e u2. . , :
(2)
(3)
(2) (3):
u2 (1) u1 m1,
, .
4. , m= 80 (.2), , m1 = 100 m2 = 200. , , . .
: , . : ( ). ( ) .
; (1)
(2)
z , e. ,
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(3)
- ( ) z.
, . (3) , (1) (2):
(4)
(4) m1, m2 m , , - . (4)
5. . u1, , , (R=6,37×106 )? , ,.
. , . . ,
1 + 1 = 2 + 2, (1)
1, 1 2, 2 - ( ) ( , ) .
,
, - . 2 , - :
1, 1, 2 2 (1),
, GM/R2=g (g - ),
.
:
/ = 7,9 /.
1
101. V0=4 /. , V0 . h ? .
102. =5/2. , , - , , . V0= 0.
103. , a=60. V1=54 / V2=72/. V ?
104. V0=10 / =-5/2. , Δs, , Δr t=4c .
105. . V1=18 /. V2=22 /, V3=5/. V .
106. a = 30 vo = 30 /. an at t = 1 .
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107. w = p/6 /. Ds, t = 4 , Dr? , - r, , j = p/3 .
108. = 1 + 1 t + 1 t2 = 2 + 2 t + 2 t2, 1 = 7 /, 1 = - 2 /2, 2 = - 1 /, 2 = 0,2 /2. t = 5 .
109. w = 1 /
t = 9,9 . ? R = 2 .
110. R = 30 e. at , , t = 4
an = 2,7 /2.
111. V=250 / m=8 . m1=6 U1 =400/c . U2 .
112. , V1=3 /, , , , U1 =4 /. U2x . m1=210, m2=70 .
113. , , a=30 . U2 , U1 =480/c. m2=18, m1=60 .
114. m1=70 , V1=9 /, m2=190, V2=3,6 /, . ? , ?
115. , , m1=2,5 a=30 V=10 /. V0 , m2=60 ? .
116. , . . m1=60 , m2=20 . ( ) , ( ) V=1 /? .
117. , V = 400 /, . , 40% , U1= 150 /. U2 .
118. m = 200 ( , ) V=1 /. , m1=200 . U1 U2 .
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119. l =3,5 m1=200 , m2=80 ? .
120. 1= 3 = 120 . 1 =60 2 =90 . , ?
121. 1= 8 , l =1,8 , 2 = 4 . , a=3? . , .
122. , 1= 300 , 2 = 8 . h , . , .
123. m1 =1 V1= 4 / 2=2 , V2 = 3 /. 1 u2 ? , , .
124. 1 =3 V1 =2 / 2 = 5 . ? , , .
125. h 1 =0,5 , 2= 120 . , .
126. 1= 4 V1= 5 / m2 =6 , V2= 2 /. u1 u2 . , , .
127. m1 = 10 V = 300 /. m2 = 200 , k =25 /. ? , .
128. 1 = 5 V1 = 1 / 2 = 2 . u1 u2 . , , .
129. , , . , V1 = 600 /, , V2 = 580 /. ?
130. 1 = 2 40% . 2 . , , .
131. k1 = 400 / k2 = 250 /, D l = 2 .
132. h = 600 1 = 3,0 , m = 1,5 . A ? h ?
133. k = 500 / F = 100 H. A , D l = 2 .
134. k1 = 0,5 / k2 = 1 / . D l = 4 .
135. A, k = 800 /, = 6 , Dx= 8 ?
136. , D l = 3 . , h = 8 ?
137. k = 150 / m = 8 . V , Dx = 4 .
138. , m = 16 , V = 0,6/, , D l = 8 . k .
139. l == 2 , . '/ l, . V .
140. h = 40 , D = 3,0 d = 2,0 ? r 2,8×103 /3.
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141. G h = 1000 . g R.
142. m = 2 :
1) h = 1000 ; 2) ?
143. m = 30 . , . g R .
144. v =5 /. ?
145. = 90 . . g R .
146. , ? , 81 60 .
147. h =520 . . g R .
148. , h =1000 . g R .
149. , , 13 3,84×108 .
150. ? , R 390 R 6 .
2
.