(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).}

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Kinetic Energy / Momentum Problem

**Physics Forums | Science Articles, Homework Help, Discussion**