4. Two masses of 3 kg and 5 kg collide head-on, the former moving to the right with the speed 5 m/s and the latter moving to the left with the speed 3 m/s.After collision they stick together. What amount of mechanical energy is lost?

Question

5. A cylinder with a uniform density is rolling over a plane. What fraction of its kinetic energy is rotational kinetic energy?

Answer 1

4. Their momenta cancel and the stuck-together mass won't move, because
5x3 - 3x5 = 0.
All mechanical energy is lost.

5. Compare (1/2) I w^2 (the rotational KE) with the sum of (1/2) Iw^2 and (1/2) M V^2.
Note that I = (1/2) M R^2 (for solid cylinders) and
V = R w (for rolling objects). You should end up with a fraction independent of M, R and w.