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 pp if = : mm m m 11 22 1 2 vv v += + bg v = + + 12 (b) Only conservative forces act, therefore E = 0. 1 2 1 2 1 2 1 2 2 2 mv m m v kx m + + Substitute for v from (a) and solve for x m . x mmm v mmm v m v m v m m v v km m x mm v v m m m m 2 1 1 2 2 2 2 2 2 1212 12 1 2 2 2 2 2 = ++ +− + = + =− + b g b g ej (c) m m ff vvv v + Conservation of momentum: 11 1 2 v v −= di d i (1) Conservation of energy: 1 2 1 2 1 2 1 2 2 2 2 2 + which simplifies to: mv v v 2 1 2 2 2 2 Factoring gives fff f 1 1 2 2 2 vv vv v v v v −⋅ ⋅+ and with the use of the momentum equation (equation (1)), this reduces to 2 2 +=+ or v 122 1 =+ (2) Substituting equation (2) into equation (1) and simplifying yields: v 2 1 1 21 2 2 f m = + F H G I
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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