270_Physics ProblemsTechnical Physics

270_Physics ProblemsTechnical Physics - 272 Linear Momentum...

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272 Linear Momentum and Collisions Additional Problems P9.54 (a) When the spring is fully compressed, each cart moves with same velocity v . Apply conservation of momentum for the system of two gliders p p i f = : m m m m 1 1 2 2 1 2 v v v + = + b g v v v = + + m m m m 1 1 2 2 1 2 (b) Only conservative forces act, therefore E = 0. 1 2 1 2 1 2 1 2 1 1 2 2 2 2 1 2 2 2 m v m v m m v kx m + = + + b g Substitute for v from (a) and solve for x m . x m m m v m m m v m v m v m m v v k m m x m m v v v v k m m v v m m k m m m m 2 1 2 1 1 2 1 2 2 2 2 1 1 2 2 2 2 1 2 1 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 1 2 1 2 2 2 = + + + + = + + = + b g b g b g b g b g e j b g b g b g (c) m m m m f f 1 1 2 2 1 1 2 2 v v v v + = + Conservation of momentum: m m f f 1 1 1 2 2 2 v v v v = d i d i (1) Conservation of energy: 1 2 1 2 1 2 1 2 1 1 2 2 2 2 1 1 2 2 2 2 m v m v m v m v f f + = + which simplifies to: m v v m v v f f 1 1 2 1 2 2 2 2 2 2 = e j e j Factoring gives m m f f f f 1 1 1 1 1 2 2 2 2 2 v v v v v v v v + = + d i d i d i d i and with the use of the momentum equation (equation (1)), this reduces to v v v v 1 1 2 2 + = + f f d i d i or
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