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. . (, , , ) , . . . . . .
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- , x,y,z - .
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- D t.
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OX
;
V0X 0 - t=0.
(aX=const)
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- , ; - , .
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j.
Dj - Dt.
:
w0 j0 - .
.
, :
; .
1. (). t1=2 t2=4 , t1 t2.
OX.
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(/).
V1 V2:
, /;
, /.
/.
: V1=7 /, V2=11,4 /, /.
2. = 25 V0 = 15 / a = 300 . t S ?
.
OY , OX . OX , OY :
, y0=H, ,
t=tn, x=S, y=0.
(1) (2) |
(2), tn=3,1c.
tn (1), S=41.
: tn=3,1, S=41.
3. R V=kt k=const. .
.
, ;
.
.
.
:
4. , R , t1 . a b - . N2 t2 . j0=0.
:
.
:
.
j (j=2pN2) w ,
: ; .
1.1. 196 4 . .
1.2. ? 3 /, 9 /. .
1.3. , t = 0,1 ?
1.4. . 2 , - 1 . , ?
1.5. V0 = 5 /. τ = 2 c . .
1.6. , , τ = 2 V01 = V02 =29,4 /. ?
1.7. . , , .
1.8. , , h = 8,75 ∆t = 3 . , .
1.9. V0 = 4 /. , V0 . h ? .
1.10. =5 /2. , , n- , , . V0 = 0.
1.11. 2 2 20 . 60 /. , . .
1.12. τ. r?
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1.13. . τ =1 . ? , V0 = 0.
1.14.
V0 = 20 /.
h = 15 ? V ? .
1.15. . τ = 2 c S = 40 . V0 V .
1.16. , S = 5 . 1 , . α ? .
1.17. . 3 . , . .
1.18. , V0 = 9,8 /, , . ?
1.19. , α = 300 , h: t1 = 10 t2 = 50 . .
1.20. V0 = 200 / α = 600 . h R .
1.21. α . , S 4 h.
1.22. . t = 3 α = 600. V0 ?
1.23. α = 600 c V0 =19,6 /. τ = 0,5 .
1.24. , V0 = 9,8 /, , . α ?
1.25. V0 = 10 / α = 450 . , S = 3 ?
1.26. h = 20 V0 = 10 /. S ?
1.27. τ = 10 n = 300 /. , .
1.28. R = 10 τ, , V = 79,2 /. τ.
1.29. . 50 n1 = 4 / n2 = 6 /. e.
1.30. R = 200 S = 2t3 (). an aτ? .
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1.31. XY X = 2t0,5t3 (), Y = 2t t2 (). V .
1.32. R = 10 . an= 4,0 /2, α = 600. .
1.33. R = 4 S = 10 + t2 - 2t. a τ, an t = 2 .
1.34. = 4t - - 0,05t2. , . . , , .
1.35. , , S = 2t t2 + t3 (). 1 5 .
1.36. , , S = 2 + 12t - -6t2 + 4t3 (). 1 4 .
1.37. , R = 7 , S = 4 + 2t + 0,5t2 (). a .
1.38. n0 = 10 / n = 6 /. N = 50 . e t.
1.39. . φ = 6t -2t3. e .
1.40. 20 5/2. 2 ?
1.41. R = 0,2 , . φ = 3 + 0,1t3 - t. t = 5 τ, an .
1.42. ε ~ t. t = 0 ω = 0. an ~ tk. k.
1.43. φ = A + Bt + Ct2, A = 10 , B = 20 /c, = -2 /c2. t = 4 c , R = 1 .
1.44. R = 4 , , . . t = 3 h =1,5 . .
1.45. R = 20 aτ = 5 c/2. an = 2aτ?
1.46. V0 = 19,6 / α = 300 . R .
1.47. V0 = 19,6 / α = 300 . τ = 1,5 .
1.48. V0 = 9,8 /. ?
1.49. . R ~ Vk. k. .
1.50. . ~ Vk. k. .
1.51. S = 8 . h = 6 . . V0 , ? a ?
1.52. , S = 20 c V0 = 20 /. ? ?
1.53. h = 10 V0 = 10 / . ? a ?
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1.54. , α = 300 . h = 80,0 . , .
1.55. d = 5 (""). , t φ = φ0 e-at sin ωt (φ0 = π/3, a = 1 c-1, ω = 1 -1). "" , . "" t=0.
2.
( ) :
.
- , , - , - , - - .
1. . a = 300 . . , a = 2 /2 .
: , , . .
II
. (1)
OY , OX . (1)
O: , (2)
OY: . (3)
. (4)
(2) (4), (3):
.
.
: .
2. , 0,2 / 2, /. , 0,1. , . g = 9,8 /c 2,
: . II :
, .
OX OY.
(1)
(2)
an = w2 R, FTP = μN.
(2) N = m (a1 + g),
FTP = mm (a1 + g).
(1):
mw2R =mm (a1 + g).
,
.
R = 0,1 .
: R = 0,1 .
3. , , m. , (F = kV), , a1 = g/2. k = const.
, a = dV / dt, F = kV, :
:
:
.
t = t1 a1 = g/2:
:
.
.
: .
2.1. , α = 300, l = 167 . , μ = 0,2?
2.2. m = 2,5 (α = 300) t = 5 S = 9 . V0 = 1 /, μ = 0,1. F?
2.3. , α = 300. , μ = 0,4?
2.4. , h = 2 , α = 450? , , α = 300.
2.5. α = 300. l = 2 . , , t = 2 . μ.
2.6. , α = 300. l = 2 , μ = 0,2. , V0 = 0?
2.7. , α = 300. S t S = ct2, = 1,5 /2. μ.
2.8. l = 13 h = 5 m = 26 . μ = 0,5. F : ) ; ) ?
2.9. . a , F = 200 , α = 450? m = 50 . μ = 0,1.
2.10. m1 = 3 m2 = 5 , = 24 . F m1? μ = 0,2.
2.11. : ) ; ) . , , .
2.12. m , . a , ?
2.13. , m1 = 1 , m2 = 2 . h = 1 . t ?
2.14. , m = 95 . m1 = 7,5 , m2 = 2,5 . S t = 2 ? .
2.15. . m1 = 0,5 m2 = 2 , , . μ = 0,05. F .
2.16. m1 = 5 m2 = 2 , . m2, a = 5,4 /2.
2.17. . m1 = 1 , m2 = 2 , . m , F = 1 . .
2.18. , α = 300. m1 = 20 , m2 = 12 , . c a = 4 /2. m2 . .
2.19. m = 300 α = 300, , β = 600 . , μ = 0,1.
2.20. , . 30 . , , 3 . ?
2.21. m F, α . , , μ?
2.22. , α = 300 , m = 500 . , V0 = 2 /. μ = 0,01.
2.23. M = 100 m = 100 a = 0,1 /2. F T, m = 0,006.
2.24. m = 10 , F α = 300 . τ = 1 V1 = 2 / V2 = 4 /. μ = 0,15. F.
2.25. , , F. : ) ; ) ?
2.26. b, , , . w.
2.27. l m. , ? , n .
2.28. , l = 1,5 , n = 28 /. a ?
2.29. , V = 36 /, . R.
2.30. , 0. . 0. 0 n = 45 /? α = 450 . μ = 0,2.
2.31. . F, m?
2.32. R = 200 . , , ? V = 100 /.
2.33. , l = 1 , . T α = 600 .
2.34. ; , .
2.35. m = 100 . ?
2.36. m = 25 l = 2,5 F = 500 . a , ?
2.37. R = 40 . a = 300. u ?
2.38. , V = 900 /, " ". R, ?
2.39. , l = 25 , . n = 2 /, m = 60 . F.
2.40. R ω. , . ? ( α, ).
41. , R = 90 ? a ? μ = 0,4.
2.42. R. h ? .
2.43. m = 3 V = 36 / R = 20 . c F , , , α = 300 c ?
2.44. ω , ? l.
2.45. R = 40 . ? V = 50,4 /, μ = 0,6.
2.46. V , , ?
2.47. V " " R = 6 , ?
2.48. , , . a , ?
2.49. r = 0,1 . , n = 10 /. m = 100 .
2.50. n = 2 /c . . , r = 5 ?
2.51. , d = 2,0 . μ = 0,25. , , ?
2.52. m = 50 . μ = 0,4. α F = 300 , ? ?
2.53. m0 = 0,5 , . t = 0 μ = 50,0 /. , , 5 c (, ).
2.54. m1 = 10,0 m2 = 20,0 , c F = 100 . a F, ? , μ = 0,3.
2.55. R = 1,0 . , l1 = π/6 l2 = π/4 . , t = 0 V0 = 0. , , .
:
,
n , .
F =const
A=FDrcosa,
a - . Dt
.
,
- dt.
.
,
h .
,
k , x .
, ,
E+E=const.
.
1. m1, V2, m2 U1 . U2 ? .
,
.
, :
,
:
2. M l. . V0 , ? . . m.
: V - , U - .
OX
mV0 = (m + M) V. (1)
, OX.
; - (m+M)gh , h = 2R =2l.
. (2)
. (2¢)
, . II :
(3)
(1) V0:
. (4)
(3)
(5)
(5) (2¢),
V0, (4)
:
3. , ? V, m, k.
, , , , .. V=const.
N , :
, R - .
:
3.1. m = 2,0 h = 20 V = 15 /. , .
3.2. s h = 1,5 α = 450? μ = 0,2.
3.3. . F α = 300. , . m = 100 , μ = 0,33, s = 50 .
3.4. τ = 5 V = 64,8 /. m = 600 , μ = 0,04. , , .
3.5. ? V0= 36 /, V= 21,6 /, μ = 0,1, h = 12 , l = 80 , m = 4×13 .
3.6. A, k = 800 /, Dx1 = 6 , ∆2 = 8 ?
3.7. h = 8 l = 100 . m = 60 . , V = 11 /?
3.8. m = 100 a = 0,2 /2. μ = 0,1, l = 50 , α = 300. A ?
3.9. V = 80 /. S = 150 . , m = 1000 , μ = 0,02?
3.10. S = 2 V1 = 36 V2 = 72 /. , m = 103 , m = 0,001.
3.11. m = 106 V = 36 / 10 1 . m = 0,002. , .
3.12. l , V0, α, μ? , μ , V0, l0.
3.13. m = 4 h = 10 S = 80 V0 = 36 /. , V = 21,6 /? m = 0,1.
3.14. V = 14,4 /. , m = 6 , α = 100, μ = 0,09?
3.15. S = 5 V = 2 /. , m = 400 μ = 0,01.
3.16. m = 2 = + Bt + Ct2 + t3, = 10 , = -2 /, = 1 /2, = - 0,2 /3. , , t1 = 2 t2 = 5 .
3.17. m = 10 , , F = 100 , α = 300 . , , S = 10 . , μ = 0,1.
3.18. m = 103 h = 9 t = 3 . : 1) ; 2) . V0 = 0.
3.19. m = 2000 a=100 , S = 100 V = 36 /. μ = 0,05; V0 = 0. .
3.20. m = 2 h = 1 = 78,5 . a ?
3.21. m = 20 , , F = 6000 . V = 54 /. , .
3.22. m = 10 d = 4 V1 = 600 / , , V2 = 400 /. .
3.23. m1 = 990 ,