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Analytical Mech Homework Solutions 88

Analytical Mech Homework Solutions 88 - 7.8 1 1 1 2 From...

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7.8 From eqn. 7.2.15, 2 2 2 1 1 2 2 1 1 1 2 2 2 i i i v m v m = = + T m v Meanwhile: ( ) 2 2 2 2 1 1 2 2 1 2 1 2 1 2 1 1 1 1 2 2 2 2 cm m v m v m m mv v m v v m m m µ + + = + + G G G G ( ) 2 2 2 2 2 2 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2 m v m v m m v v m m v v v v m = + + + + G G G G 2 2 1 1 2 2 1 1 2 2 m v m v = + Therefore, 2 2 1 1 2 2 cm v T m v µ = + 7.9 From Prob. 7.8, 2 2 1 1 2 2 cm v T m v µ = + and since v v Q T T = cm cm = : 2 2 1 1 2 2 Q v v µ µ = From eqn. 7.5.4, v v ε = ( ) 2 2 1 1 2 Q v µ ε = 7.10 Conservation of momentum: 1 1 1 1 2 2 m v m v m v = + 2 1 1 1 m v v v m = 2 2 2 2 2 2 1 1 1 2 2 1 1 2 m m v v v m m = + 2 2 v v Conservation of energy: 2 2 1 1 1 1 2 2 1 1 1 2 2 2 m v m v m v = + 2 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 1 1 1
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