.
, , .. .
: M = m1 + m2 + + mn
, () , .. , () .
, , : , .
, .
() , R, ( ): R = F1 + F2 + F3 + + Fn
. , , , - .
, , .
I
, , - (), .. , ( ), , : F = å F = 0; V = const.
, - , . oe , - . .
II
, , , , . a = SF /m
.
.
.
1. , .. , F1, F2,..., Fn, , co6 , ( ).
2. a, , a1, a2,..., an . a , , , . . , .
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3.. R V ( ), .
, (R = const), ( = const).
, R = 0, a = 0 , , V = const, .. .
4. , .
, .
(R = const, R ^V), (V = const), , .. .
( ) , . , R , , , , : Rn = mV2/r r, r - .
III
, .. , ; . F12 = - F21
.
, , , .
.
, .
( ) , ( ) ( ):
F = G m1 m2/R2, G = 6,67 10 2 /2 .
.
, . , .
m M, :
F = G m M / R2, R .
m M h , :
F = G m M / (R+h)2, R .
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, , . , .
, mg, , g, , - .
(w = 0, 00727 -1) h << R g :
g = G M / R 2, M - , R - .
, , , h << R
, , . . F = m g
, .
.
, , .. (). , , , , () , .
P0, , P, .
, : P0 = m g, , (): P = m (g - a).(. 1a) P = m (g + a).(. 1b).
, P = nP0, n .
n = 0 , n > 1 - .
, .
: F = - k Dx, k (), Dx .
. , .
.
s : s = F/ S
: e = Dl / l0, Dl - , l - , l0 - .
s = e , ( : , , )
.
: F = - k Dl. S l0, F/S l0 = k Dl / S l0 F/S = (k l0/ S) e, s =(k l0/ S) e, (k l0/ S) = .
, . : , 1.
, , .
F = m N, m - , , N [ N = - P (III )].
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, , . , V n, n = 2 3.
, .
.
F, .2, ( , ), , , . .
F, , . : F = - F. F F (. . 3) a 450
F , , , F (F = m N). , : 0 < F < m N.
. , , m . .
, , () , . (SF = m a). , ( , ..) , . , , , , . ( ) ( ), .
.
( ) . : : a = V2 / R, V , R , .
.
1. m1 m2, , F, . T.
: m 1; m2; F; T -?
.
, .
: å F = m
: F + m1 g + T1 = m1 a1
: m2 g + T2 = m2 a2
:
: F - m1g - T1 = m1a1
m2g + T2 = m2a2
.. , : 1 = 2 = 1 = 2 = , : F - m1g - T = m1a
- m2g = m2a
, : = Fm2/(m1 + m2).
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:
: = F m2 / (m1 + m2).
2. , 2,5 1,5 . . .
: m 1 = 2,5 ; m2 = 1,5 . -? T -?
.
: å F = m
: m1 g + T1 = m1 a1
: m2 g + T2 = m2 a2
:
: - m1 g + T1 = m1a1
- m2g + T2 = m2a2
.. , : 1 = 2 = 1 = 2 = , : - m1g + T = m1a
- m2g + = m2a
: = g (m1 - m2)/ (m1 + m2)
, : = m2 (g + a)
: ;
, : = 2,5 /2, = 18,75 .
3. 90 , 1,2 /2 ? g = 9,8 /2.
: m = 90 ; a = 1,2 /2; -?
.
, : mg N, III- , .. .
, .
: SF = ma N + mg = ma
:
: N - mg = ma, N = m (g + a), P = m (g + a)
: [ P ] = /2 =
: = 90 (9,8 + 1,2) = 990 .
4. 4,5 , 2 /2? 0,5.
: m = 4,5 ; a = 2 /2; m = 0,5. F -?
.
, : mg, , F, F N.
, .
: SF = ma N + mg + F + F = ma
:
: N - F = 0, .. , .. a = 0.
: F - mg = - ma, a = a, .. F - mg = - ma.
: F = m N ( ).
: m F - mg = - ma,
F = m(g - a)/ m.
: [ F ] = /2 =
: F = 4,5 (10 - 2)/0,5 = 72 .
5. 13 5 26 . 0,5. , ?
: l = 13 ; h = 5 ; m = 26 ; m. = 0,5; a = 0. F -?
.
, : , F, N, F mg.
, .
: SF = ma F + N + F + mg = ma
:
: F + mg - F = 0, .. a = 0 ( ), mg - mg .
: N - mg = 0, .. a = 0 ( ), - mg .
: F = m N ( ).
mg = , mg = ( )
:
F + - = 0, F = mg
: [ F ] = =
: F = = 20 .
6. , 15 , . 1 /. .
: R = 15 = 0,15 ; n = 1 /.m -?
.
, : mg, F N.
, .
: SF = ma
mg + F + N = ma
:
: F = ma.
: N - mg = 0, .. .. , .. a = 0..
, , , . . , .
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:
F = m N ( ).
:
m mg = ma, a = m g, a = w2R ( ),
m g = w2R, w = 2pn ( ),
, , m g = 4 p2 n2 R, m = 4 p2 n2 R/ g
: [ m ] = = 1
: m = = 0,6.
7. R , , , , V = 90 /, .
: V =90 / = 25 /; P = 0,5 P0; R -?
.
, : mg, N. , a .
, .
: SF = ma N + mg = ma
:
: N - mg = - ma, a = V2/R ( ), N = mg - mV2/R.
3- N = - , N = 0,5 N0, N0 = mg ( ).
: 0,5 mg = mg - mV2/ R, R = V2 /0,5 g
: [ R ] = =
: R = = 125 .
8. 360 / 500 . , 80 .
: V =360 / = 100 /; R = 500 ; m = 80 ; D -?
.
, : mg, N. , a , - .
, .
: SF = ma
1 N1 + mg = ma 1
2: N2 + mg = ma 2
:
: 1
- N1 + mg = - ma 1, N1 = ma 1 + mg.
2:
N2 + mg = ma 2, N2 = ma 2 mg.
3- N = - P, P = N DP = DN.
, , .. , : 1 = ma 1 + mg.
2 = ma 2 - mg.
D = 1 - 2, D = ma + mg - ma + mg = 2 mg