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PHYS310_homework_09_solutions

PHYS310_homework_09_solutions - Homework set 9 due...

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Homework set 9, due Wednesday, November 2, 11:30 am Following problems from Analytical Mechanics by Fowles & Cassiday 1. 7.3 b g v v v = - o r r r Since momentum is conserved and the bullet and gun were initially at rest: 0 b g mv Mv = + r r g b v v γ = - r r , m M γ = ( 29 1 b v v γ = + o r r 1 b v v γ = + o r r 1 g v v γ γ = - + o r r 2. 7.6 When a ball reaches the floor, 2 1 2 mv mgh = . As a result of the bounce, v v ε = . The height of the first bounce: 2 1 2 mgh mv = 2 2 2 2 2 2 v v h h g g ε ε ′ = = = Similarly, the height of the second bounce, 2 4 h h h ε ε ′′ = = Total distance 2 4 2 0 2 2 1 2 n n h h h h ε ε ε = = + + + = - + K Now 0 1 n n a ar r = = - , 1 r < . 2 2 2 2 0 2 1 1 2 1 1 1 n n ε ε ε ε = + - + = - + = - - total distance 2 2 1 1 h ε ε + = - For the first fall, 2 1 2 gt h = o , so 2 h t g = o For the fall from height h : 1 2 2 h h t g g ε = = Accounting for equal rise and fall times:

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Total time ( 29 2 0 2 2 1 2 2 1 2 n n h h g g ε ε ε = = + + + = - +
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