Ответы:

1. a = g(T₂ -T₄)/(T₁ -T₃)

2. V₁ = 2^1/2V

3. F_тр = F/(1+t/)

4. x =mg/k +V(m/k)^1/2

5. V₁ = - 0.5((V² + F²/mk)^1/2 - (V² - F²/mk)^1/2), V₂ = 0.5((V² + F²/mk)^1/2 + (V² - F²/mk)^1/2), при V² > F²/mk

6. F = 2(2)^1/2mV²/L

7.  = V²L /(gl (2S-l))

8. U= V (1+m / M)^1/2

9. x = R /(1+4²)^1/2  0.15R

10.  = 4L / V, при V < U,  = L(V+U)²/(UV²)

11.  = 1/((gL/V²)² -1)^1/2

12. а =(а₁ - а₂)m/M

13. M = 3m/ cos(sin - cos) при  >tg

14. V = mgL(k/m)^1/2/(kL-mg) при kL > mg

15. V = (gL(2m+M)/(M+m))^1/2

16. U = V(₁-cos)/(-₁)

17. U = V₁(m₂-m₁)/(2m₂)

18. cos = 4cos - 3

19. R = H/((g₀/g)^1/2-1)

20.  = arccos(V/U)

21. H/H’ = 4/3

22. t = 2R/ V

23.  ₁ = arccos (2/3+1/(23)) для налетающего мячика;  ₂ = arccos (2/3 - 1/(23))

24. V = g/2

25. m = Mcos(2)

26. Q = mMV²/(2(m+M))

27. V_min = (L-l)(k(2-2+²))^1/2, где  = T/(k(L-l))

28. a = gm/(M+2m)

29. a = g(m-(M+m))/(M+2m-m) при m >(M+m), a = 0 при m  (M+m)

30. L_min = ((2v²/a)²+L²)^1/2 - 2v²/a

31. a_x = a - 2N/m при a > 2N/m, a_x = 0 при a 2N/m.

32. v = (gL)^1/2(2+(5^1/2-1)M/m)^1/2

33. F  Mg/(₂ - ₁)

34. При   120⁰ нить порвется выше крюка, при   120⁰ разрыв выше крюка.

35. Условие неподвижности бруска и доски: 1-2ctg  M/m  2ctg+1

36. tg  

37.  = 90⁰

38. u = (2gh)^1/2(()^1/2-1)/(()^1/2+1)

39. L = V₀²m₁m₃²/(2g(m₂+m₃)²(m₁+m₂+m₃))

40. T = mg(₂-₁)/(4+(₁+₂)²)^1/2 при ₂ > ₁

41. h = 3(H₁-H₂)/4

42. при  < m₂R₂/(m₁R₁) m₁g/(m₂R₂+m₁R₁) < ² < m₁g/(m₂R₂-R₁m₁); при  > m₂R₂/(m₁R₁) m₁g/(m₂R₂+m₁R₁) < ² < ; при  = m₂R₂/(m₁R₁) - застой

43. а₁ = а + (а+g)m/M

44. F = 0.5(mg + kL)

45. M/m_p = 3, V = V₀/2; с протоном столкнулось либо ядро трития Н³, либо ядро гелия три Не³.

46. T_BC = 2M²g/(2M+m)

47. m = M/2

48. F = m(a²+(a-v²/R)²)^1/2 Угол наклона вектора силы к горизонтали  = arctg(a/(a-v²/R).

49. F₀ = mg(1-r/R)/2

50. t = (2h/(g(1+m/M)))^1/2

51.  = arctg(0.29)  0.29 рад  17⁰

52. N = mg/((n(2+n))^1/2, T = mg(n+1)/((n(2+n))^1/2

53. Т₂-Т₁ = 4mg/3

54. x = V₀(2H₀/g)^1/2(1-(1-h/H₀)^1/2)

55. F = 2Mg(1+)

56. T = 2mMhg/(m+M)/L

57. T = (M-m)²V₀²/((M+m)2L)

58. V = (T₁-T₂)c/((T₁+T₂)

59. M = M_p, (т.е. ядро водорода)

60. L = 2(M+m)L₀/(2@M+m)

61.  = 3/(GT²)  5.610³ кг/м³

62. L(sin+cos)/(1+sin+cos) > x > L(sin-cos)/ (1+sin-cos)

63. L = (L₁²V₂² - L₂²V₁²)/( L₁V₂² - L₂V₁²)

64. _min = g/a

65. R = 5/16V²/g

66. L = 2mMUV/(g(m+M)²)

67. h = H((M-m)/(M+m))²

68. a = ((m₁-m₂)gL)/((m₁+m₂)2r)

69. A = mgH/4

70. a = gcos(+)/sin

71.  = tg 2m/(M+m)

72. t = (1+(2)^1/2)

73. X = 5L/3

74.   (g ctg-²r)/(g+²rctg)

75. V = 2(gHctg)

76. _min = tg

77. L = (m₁L₂+m₂L₁)/(m₁+m₂)

78. V = (2Fa(M+m)/(mM))^1/2

79. A = g – 2kL(ctg(/2)-cos(/2))/m

80. F = T/50

81. A = T(3)^1/2/m – g

82. /_o = 2

83. t = (2h/g)^1/2 - h/V

84. t = L/(u(1+²)^1/2)

85. T=4(R/g)^1/2

86. t= (2L₁/(gsin))^1/2 +(2L₂/(gsin))^1/2

87. >0 – 1 график, <0 – 2 графика

88.  = mgsincos/(M+mcos²)

89. ~6200

90. a) A=FScos(FS); б) A =mgl=10⁵ Дж