KK_Chapter2_Sols

# An Introduction To Mechanics

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1. 2.3 1 N 2. 2.5 a = g m - M m + M ; T = 2 g mM m + M 3. 2.6 ω q g/R 4. 2.7 (a) F max = μM 1 g ± 1 + M 1 M 2 ² ; (b) F max = μg ( M 1 + M 2 ) 5. 2.9 r = v 2 0 tan θ g 6. 2.10 r orb = 6 . 63 R E 7. 2.11 T up = m/ 2( ω 2 l + 2 g ) 8. 2.12 t 0.18 sec 9. 2.13 ¨ z 1 = ± 2 m 2 - m 1 m 1 +4 m 2 ² g 10. 2.14 a A = 2 g ± m B m C 4 m A m B + m A m C + m B m C ² ; a B = 2 g ± m A m C 4 m A m B + m A m C + m B m C ² ; a C = 2 g ± m A m C + m B m C 4 m A m B + m A m C + m B m C ² 11. 2.16 ¨ x = A + g 2 ; ¨ y = A - g 2 12. 2.17 (a) tan θ = μ ; (b) a = g sin θ - μ cos θ cos θ + μ sin θ (c) a = g sin θ + μ cos θ cos θ - μ sin θ 13. 2.18 a = 4 F M + m - g 14. 2.19 F = M 3 g ± M 1 + M 2 + M 3 M 2 ² 15. 2.21 T ( x ) = F ± 1 - xm l ( m + M ) ² 16. 2.28 v max = r gr ± sin θ + μ cos θ cos θ - μ sin θ ² ; v max = r gr ± sin θ - μ cos θ cos θ + μ sin θ ² 17. 2.29 (a) a ( t ) = ( - ωv 0 t r + (2 ωv 0 ) ˆ θ ; (b)
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Unformatted text preview: t slip = r μ 2 g 2-4 ω 2 v 2 ω 4 v 2 ; (c) θ slip = cos-1-r 1-4 ω 2 v 2 μ 2 g 2 ! 18. 2.30 ¨ r A ( t ) = ω 2 ± m A r A-m B ( l-r A ) m A + m B ² 19. 2.31 (a) ω = q k 1 k 2 m ( k 1 + k 2 ) ; (b) ω = q k 1 + k 2 m 20. 2.33 A = r-v /γ 2 ; B = r + v /γ 2 ; choose v =-r γ 21. 2.37 y = 2 π 2 x 2 gT 2...
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