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+=+bgvvv=++mmmm112212(b)Only conservative forces act, therefore ∆E=0.121212121122221222m vm vmmvkxm+=++bgSubstitute for vfrom (a) and solve for xm.xmmm vmmm vm vm vm m v vk mmxm mvvv vk mmvvm mk mmmm21211212222112222121212121222121212121222=+++−−−+=+−+=−+bgbgbgbgbgejbgbgbg(c)mmmmff11221122vvvv+=+Conservation of momentum:mmff111222vvvv−=−didi(1)Conservation of energy:12121212112222112222m vm vm vm vff+=+which simplifies to:mvvmvvff1121222222−=−ejejFactoring gives mmffff1111122222vvvvvvvv−⋅+=−⋅+di didi diand with the use of the momentum equation (equation (1)),this reduces tovvvv1122+=+ffdi dior
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