(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two Railway cars, m_{1}and m_{2}, are moving along a track with velocities v_{1}and v_{2}, respectively. The cars collide, and after the collision the velocities are v'_{1}and v'_{2}. Show that the change in kinetic energy, K' - K, will be maximum if the cars couple together.

Hint: Set d(K' - K)/dv'_{1}= 0 and show that v'_{1}= v'_{2}.

2. Relevant equations

Conservation of linear momentum: m_{1}v_{1}+ m_{2}v_{2}= m_{1}v'_{1}+ m_{2}v'_{2}.

Kinetic energy K = 0.5mv^2

Difference in kinetic energy: K' - K = 0.5m_{1}v_{1}^2 + 0.5m_{2}v_{2}^2 - 0.5m_{1}v'_{1}^2 - 0.5m_{2}v'_{2}^2.

3. The attempt at a solution

I solved the conservation of momentum equation for v1 and substituted that into the K' - K equation. This yields v'_{2}= v_{2}.

I then solved the conservation of momentum equation for v2 and substituted that into the K' - K equation. I got v'_{1}= (m_{1}v_{1}- m_{2}v'_{2}) / (m_{1 - m2).}

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# Homework Help: Kinetic Energy / Momentum Problem

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