Momentum Problem

Question

Three identical metal spheres are on a frictionless surface. The first sphere (which is positioned towards the left in relation to the other two spheres) travels at velocity v and collides elastically into the others. If the other two spheres are touching initially at rest, which of the choices below best predicts the motion of the spheres after the collision?

a) number of moving spheres: 2; speed of moving spheres: both at 1/2v

b) number of moving spheres: 1; speed of moving spheres: both at 2v

c) number of moving spheres: 2; speed of moving spheres: both at v

d) number of moving spheres: 1; speed of moving spheres: v

e) number of moving spheres: 3; speed of moving spheres: v/3

Answer 1

You are describing what is commonly called "Newton's Cradle".

This is solved using conservation of momentum and energy. The momentum of the incoming sphere might be matched by 2 sphere travelling at v/2, or 1 sphere at v.

Applying conservation of energy**:

The incoming energy is 1/2 * m * v² and is the same for one sphere leaving at v.

For 2 spheres leaving at v/2, the energy would be 1/2 * 2m * (v/2)² = 1/4 * m * v². so energy is not conserved

**in an elastic collision, both momentum and energy are conserved.