Annexe C • Réponses
17.5 (a) Δx = 2,18 cm
(b) V = −49,4 cm s −1
17.6 T = π
2L/g
17.8 T = π
MR 2 /K
17.9 T ≈ 1,4 s
17.10 (a) T A = 2π
d
g
, T B = 2π
I c + Md 2
Mgd
(b) ¨
θ A = −
g
d
sin θ 0 , ¨
θ B = −
Mgd
I c + Md 2 sin θ 0
(c) ˙
θ A =
2g
d
(1 − cos θ 0 ), ˙
θ B =
2Mgd
I c + Md 2 (1 − cos θ 0 )
17.11 ω 0 = 28 s −1
17.12 (a) θ 0 = arctan(1/3)
(b) θ(t) = θ 0 −
J
M
gl
4
288
125
sin
⎛
⎜ ⎜ ⎜ ⎜ ⎜ ⎝
g
l
4
9
10
t
⎞
⎟ ⎟ ⎟ ⎟ ⎟ ⎠
17.13 T ≈ 42 min
17.14 (b) T A = 2π
√
m/(k 1 + k 2 ), T B = 2π
√
m(k 1 + k 2 )/k 1 k 2
17.15 A = (v/4)
√
M/2k, T = 2π
√
M/2k
17.16 (a) x = d
(b) V CM = (d/3)
√
k/m, A = d
√
2/3
17.17 v 1 = v 0 − X
K
M 1 (1 + M 1 /M 2 )
v 2 = v 0 + X
K
M 2 (1 + M 2 /M 1 )
17.18 x max = (m + M)μg/k
17.19 (a) E = 10 6 ergs
(b) k = 7,8 × 10 3 g s −2
(c) x = 16 cm
17.20 (a) ν = (1/2π)
√
k(1/I 1 + 1/I 2 )
(b) A 1 /A 2 = −I 2 /I 1
17.22 (a) T = 2π
l/g
(b) T = (2πL/
√
3d)
l/g
17.23 T = π
29a/g
17.24 m = KR/2g
290