1.1 1.30 , , -. 1.1 1.30 . , - , ? . - , - , ? , - , .
1.1
, . 1.1, h, , 䳺 P = mg FA = k mg. . t VB. - U a . 䳺 , . y(x), , = d VC j .
, , 1.1 .
1.1
1.1
1.2
̒ V a -, . 1.2, t l - h1 , - U. ³ , d h2 , y(x). VC, j.
̒ . - .
, , , , 1.2 .
1.2
1.2
1.3
, . 1.3, U, a . . ³ , f, =l t VB. , h 䳺 , , y(x) VC . ³ d. VC j.
1.3 .
1.3
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1.3
1.4
VA a , . 1.4. 䳺 P = mg 䳺 FA = kmg. y(x), VC,, j. xAy l, h1 d, h2, . 1.4.
.
- 1.4.
1.4
1.4
1.5
䳺 , . 1.5. VA, , = l, t VB. , U. y(x), VC, j . ³ S. . h.
, .
- 1.5 .
1.5
1.5
1.6
VA f, . 1.6. = l t, k , . ϳ a . y(x) 䳺 . d h, .1.6. VC j .
1.6.
1.6
1.6
1.7
, . 1.7, - . ³ AB = h t U , . - y(x) VC, j. d , . 1.7. .
- 1.7 .
1.7
1.7
1.8
m , . 1.8. , Q, t = l - VB. VB - U, - y(x ) . ³ =d, h, j , VC, .
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, , .
- 1.8 .
1.8
1.8
1.9
䳺 - , , , = l, VB. , . 1.9, a. t. ³ y(x) , VC, j . .
, h d . 1.9.
.
- 1.9 .
1.9
1.9
1.10
, . 1.10, . a , = l. m. 䳺 F f. t.
VB y(x) , VC, j . . г d h . 1.10. .
- 1.10 .
1.10
1.10
1.11
a -, = l t. - VA, - VB. f. y(x ), . 1.11. , , VC, j. . 1.11 d h. , .
- 1.11 .
1.11
1.11
1.12
VA, . 1.12. a VB. = l, t, 䳺 f. , VC, j . , y(x ), . h d, . 1.12.
- 1.12 .
1.12
1.12
1.13
m - = l t 䳺 F VB, . 1.13. VB U y(x) , VC, j . d , h, . 1.13. . , .
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- 1.13 .
1.13
1.13
1.14
m , . 1.14, a 䳺 P = =mg f. , t = l VB , , F = kmg, y(x) VC, j . ³ - . . 1.14 h d. .
- 1.14 .
1.14
1.14
1.15
m VA, - VB, . 1.15. = = l t 䳺 f Q. y(x ) , VC, j. ³ 䳺 . , . . 1.15 d h.
- 1.15 .
1.15
1.15
1.16
m , . 1.16, t = l, F, VB. U a y(x) , d h. VC, j . . .
- 1.16 .
1.16
1.16
1.17
m, , VB U, . 1.17, . = l 䳺 F f. t. ij y(x) , D, VC, j. , , D l, d, h, s H . 1.17.
, .
- 1.17 .
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1.17
1.17
1.18
, 䳺 - , U, a . = l VA VB . t. y(x ) . ³ d, h, . 1.18. ij . VC j .
, . , b, . 1.18, .
- 1.18 .
1.18
1.18
1.19
m VA, a , 䳺 P = mg, , y(x ) . VC j . 䳺 F = kmg . - t, - . , h, H, d s, . 1.19.
, , .
- 1.19.
1.19
1.19
1.20
- 䳺 Q VB, = l t. VB, a , 䳺 y(x) , VC j . l, h, d, . 1.20.
, , m, P = =mg. Q (P << Q). .
- 1.20 .
1.20
1.20
1.21
, U, . 1.21, = l, a -, . ³ , y(x ) . f. , - VB, t. 䳺 , . h d . 1.21. VC j , .
- 1.21 .
1.21
1.21
1.22
, 䳺 , VA, VB, U, a , . 1.22. = l t. , , , y(x) VC, j . ³ d h . 1.22.
, , , , U .
- 1.22 .
1.22
1.22
1.23
, 䳺 , U a . ³ y(x) , VC, j , . 1.23. = l t, VA, VB. , , , V , VB, VC U . , l, d h, . 1.23.
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, . b .
1.23 .
1.23
1.23
1.24
䳺 , VA, VB, = h t, . 1.24. , U a , y(x) , VC j . , l, . 1.24.
. .
- 1.24 .
1.24
1.24
1.25
˳ 䳺 , a , . 1.25. VA, V B, = l t. U . 䳺 y(x) , VC, j . h , d, . 1.25. .
, - .
- 1.15 .
1.25
1.25
1.26
m = l a 䳺 Q, . 1.26. f1, t. VB 䳺 . f2. t D = d D . , , D l, s, h d . 1.26.
1.26 .
1.26
1.26
1.27
m - V a y(x) , s - h, VB, j , . 1.27. 䳺 P = mg, t. , VB , R = kmg, d . k . = d .
, -. -
;
- 1.27 .
1.27
1.27
1.28
m = l a , y(x) , . 1.28. 䳺 f, VA , VB, t. ³ , VC, j. d h, . 1.28.
,
.
- 1.28 .
1.28
1.28
1.29
m a f, . 1.29. = l 䳺 t VB. , , 䳺 , U b . y(x ) . d h , . , VC j. , .
- 1.29 .
1.29
1.29
1.30
a m 䳺 P = mg Q = kmg, . , VB. = l t. y(x ) , VC, j . г d h, . 1.30. , .
- 1.30 .
1.30
1.30
2.1 1
. ³ 䳺 f = 0,2 AD a = 15, . 1.31. , = l = 2 h = 1 AD, U=8/ . VB, . ³ y(x) , VC, j. DC DC = d = 5 .
H DC, j VC, y(x), VA, AD.
AD -
, .
. , . - Q = (M + m)g (M , m ), N FT. y(x) 䳺 P = mg. : .
, - . 1.32. M + m
Ax
, (1.1)
,
.
ϳ (1.1)
= g (sina - f cosa) = 9,8 (0,259 0,2 0,966) = 0,64. (1.2) (1.2)
V x = = 0,64 t + C1, Vx =
x = + = 0 ,32 t2 + C1t + C2
1.31
:
x = 0 Vx = VA t = 0,
: C1 = VA, C2 = 0.
(1.2) :
Vx = 0,64 t + VA, x = 0,32 t2 + VA t. (1.3)
(1.3) , x = l = 2, Vx = VB, t . ϳ (1.3)
VB = 0,64 t + VA, 2 = 0,32 t2 + VA t (1.4)
1.32
(1.4) , : VA, VB, t.
. 1.33.
1.33
xOy.
:
m = S Xk, m = S Yk. (1.5)
䳺 , :
S Xk = 0, S Yk = - mg.
, (1.5) :
= 0, = - g. (1.6)
(1.6)
Vx = C3, x = C3 t + C4,
(1.7)
Vy = - g t + C5, y = - 0,5 g t2 + C5 t + C6.
(1.6) :
Vx = VB cosa + U sina,
Vy = U cosa - VB sina,
t = 0, x = 0 y = h.
3 6 :
C3 = VB cosa + U sina, C4 = U cosa - VB sina, C5 = 0, C6 = h.
ϳ (1.7)
Vx = VB cosa + U sina,
Vy = U cosa - VB sina - g t,
(1.8)
x = (VB cosa + U sina) t,
y = (U cosa - VB sina) t - 0,5 g t2 + h.
(1.8) . , t = T, x = OD +d, y = 0, . . 1.33. OD = h ctga. (1.8),
d + h ctga = (VB cosa + U sina) T,
(U cosa - VB sina) t - 0,5 g t2 + h= 0.
ϳ
(VB cos15o + 8 sin15o) T = 5 + 0,5 ctg15o,
(1.9)
(8 cos15o - VB sin15o) T - 0,5 gT2 + 1 = 0.
(1.9) VB
VB2 51,6 VB + 183,73 = 0. (1.10)
: VB1 = 47,75, VB2 =3,85.
ϳ VB1 VB2 (1.9) , - . ϳ : 1 = 0,18, T2 = 1,51.
³ VB (1.4), VA. ϳ VB1 VB2 (1.4) - VA1 = 47,72 VA2 = 3,5.
. - (1.8) VB -
VB1 VB2. VB = VB1 = 47,75 :
.
t.
. (1.11)
VB = VB2 = 3,85
.
ϳ t :
. (1.12)
1.34
(1.11) (1.12) xOy - . 1.34, 1 (1.11), 2 - (1.12). . 1 , 2 x = 3,97. (1.10) , (1.12). : VB =3,85/, T = 1,51, VA = 3,5 /.
j, VC . VCx VCy. (1.8), - , VB, T, :
,
.
j tgj = | VCx / VCy |, ,
xOy . 1.34.
tgj = 5,79 / 8,07 = 0,7174, j = 35o40`.
- . Vy = 0.
t = tm. (1.8) Vy :
.
y(t) (1.8) y = H t = tm = =0,687 c, :
.
³: H = 3,32 , j = 35o40`,
VA = 3,5 /.