. - , . , .
11. 1. 15 . .
, . . .
- (4.6) (4.8)? (4.7) vX = vX (t). . . , ? , aX. ? t1 £ t £ t2
t ³ t4 aX = 0. 0 < t < t1 , t2 < t < t4 , , 0 < t < t1. aX(t), 16.
SX(t)? (4.6) (4.8)? , aX = const. SX(t) ? (4.8) t1 £ t £ t2 t ³ t4 , aX = 0, 0 < t < t1
t2 < t < t4 . , aX < 0, . , , , .
, , . t = t3, vX = 0. , 17.
. , t1 £ t £ t2 . , , t3 . t = t4, t = t5.
(4.6) (4.8) . , ; , .
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11. 2*. 18 , x, x. x = 3 . .
. , . .
? . (4.6) (4.8)? = onst, , . - ? . (3.2):
aX = DvX / Dt. (11.1)
DvX / Dt ? vX = vX(t), . , vX = vX(x)? (3.1):
vX = DSX / Dt = Dx / Dt. (11.2)
Dt (11.1) (11.2),
aX = vX DvX / Dx. (11.3)
, (11.3), ? vX , DvX / Dx = k . 0 £ x £ 1 x > 5 k = 0, x
k = = = 1 -1.
,
0, 0 £ x £ 1,
|
0, x ³ 4.
:
1) aX = k×vX(x=3) = 1 c-1×2 / = 2 /2;
2) aXM , aXM = k×vX(x=1) =
1 c-1×4 / = 4 /2.
, , , .
11. 3*. , . , 1 , 2 /. 1 ?
l 1 = 1 v = k / x v1 = 2 / l 2 = 2 t ? |
x, ( 19) k, . l 2 , t (. 19).
, (4.6) (4.8) , (3.1), :
v = DS / Dt = Dx / Dt. (11.4)
? v x (. 19); Dx , Dt. t? t , t = S Dt. ?
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Dt (11.4), v x:
Dt = = . (11.5)
t = . (11.6)
? ? ? (4.6) . , . . (11.6) Dx x / k = 1 / v. ? 1 / v x. , (11.6), 20.
, (11.6) , l 1 l 2 (.20):
t = (l 2 l 1). (11.7)
v1 v2 :
v1 / v2 = l 2 / l 1. (11.8)
(11.8) (11.7),
t = 75 c.
/ .
, - .
. 11 .
12.
12. 1. , v0, h . t v ?
: t = ; v = .
12. 2. v0 = 1000 /c a = 300 . t ? H ? S ?
: t = = 102 ;
H = = 12,7 ; S = = 88,4 .
12. 3. v a , S, h?
: v = .
12. 4. v = 14 / , a = 450 . l ? S ?
: l = v2 7,1 ; s = 57 .
12. 5. , , a = 450 v = 10 /. s = 5 2. m , . r = 100 /3.
: m = 2 r s v2 g1 sin a = 7,1 .
12. 6. h. H (H > h) . , .
: v = (H h) .
12. 7. R . . v , , , ?
: v = .
12. 8. ( ), , , .
12. 9. 21 . . ? .
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: 12 24 .
12. 10. H v1. a v2 . L , ?
: L = H .
12. 11*. v = 10 / , , d = 5,0 . H = 1,0 . n , ? .
: n = = 90.
12. 12*. v: , a . v21 , , , .
: v21 = v .
12. 13*. L . v. u ? .
: u = .
12. 14*. R = 100 . v = v0 / cos a, v0 = 100 /, a , . , a = 600.
: a = = 8,0 /2.
12. 15*. a . , , a .
: sin a < 0,94, a < 70,50.
12. 16*. . x(t) s(t). v1 t1 = 6
s1 = 100 , 200 ?
:
s1 = 200 , v1 = s / t + g t /2 ≈ 63 /; s1 = 100 ,
40 /,
20 /.
III
-
.
, , ?.
. ( ) . , . .
. (), , , . , , , .
.
m = , (13.1)
m , , , , , .
. 1 2, , , :
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1 = 2. (13.2)
( ). .
, . , , , (13.1), , . , .
, (13.1), . , , , . . , , .
, , .
, :
F = k S. (13.3)
F , S , k , .
( ) m1 m2, r,
F = G . (13.4)
, r , .
, :
= m . (13.5)
. .
, , . , :
= k , (13.6)
k .
( ), , , , . F N , ( ):
F = m N. (13.7)
m . . .
. . , :
0 £ F £ m N. (13.8)
( ) , , . .
, .
, , , . .
, . .
, , , .
, , , , ( , ). , , .