272 Linear Momentum and CollisionsAdditional ProblemsP9.54(a)When the spring is fully compressed, each cart moves with same velocity v. Applyconservation of momentum for the system of two glidersppif=:mmmm112212vvv+=+bgv=++12(b)Only conservative forces act, therefore ∆E=0.1212121222mvmm vkxm++Substitute for vfrom (a) and solve for xm.xmmmv mmmv mvmvmmvvkmmxmm vvmmmm211222222121212 122222=+++−−−+=+=−+bgbgej(c)mmffvvvv+Conservation of momentum:11 12v v−=−did i(1)Conservation of energy:121212122222+which simplifies to:mv vv212222−Factoring gives fff f1 1222vv vvv v v v−⋅−⋅+and with the use of the momentum equation (equation (1)),this reduces to22+=+orv1221=+−(2)Substituting equation (2) into equation (1) and simplifying yields:v2112122fm=+FHGI
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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 .