Classical Mechanics (Kibble & Berkshire) · Problem 10.13
The angular momentum principle — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · collisions
Problem
Show that, in an elastic head-on collision between two spheres, the relative velocity of the spheres after impact is the negative of the relative velocity before impact.
A tube is fixed in the vertical position with its lower end on a horizontal floor. A ball of mass M is released from rest at the top of the tube followed closely by a second ball of mass m. The first ball bounces off the floor and immediately collides with the second ball coming down. Assuming that both collisions are elastic, show that, when m/M is small, the second ball will be projected upwards to a height nearly nine times the length of the tube.