Question

Three equal masses m are placed in contact with each other forming a straight line segment. Another mass M (not equals to m) strikes a mass m at the end of the line segment with a speed v. This collision is one-dimensional and elastic.

(a) (8 points) Considering the conservations of momentum and energy of the system, show that at least two masses are in motion after the collision. (Hint: show that no solution exists to satisfy the momentum and energy conservations if we assume only one mass is in motion after the collision.)

(b) (6 points) Consider the case M < m. If only two masses are in motion after the collisions, which ones are they and what are their speeds?

(c) (6 points) Solve the same problem as (b), but for the case m < M < 2m.

Answer 1