1. The problem statement, all variables and given/known data Two Railway cars, m1 and m2, are moving along a track with velocities v1 and v2, 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: m1v1 + m2v2 = m1v'1 + m2v'2. Kinetic energy K = 0.5mv^2 Difference in kinetic energy: K' - K = 0.5m1v1^2 + 0.5m2v2^2 - 0.5m1v'1^2 - 0.5m2v'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 = v2. I then solved the conservation of momentum equation for v2 and substituted that into the K' - K equation. I got v'1 = (m1v1 - m2v'2) / (m1 - m2).