Elastic Collisions

In an elastic collision no kinetic energy is lost. Momentum and the total kinetic energy are both conserved:

$$\tfrac{1}{2}m_1 v_1^2 + \tfrac{1}{2}m_2 v_2^2 = \tfrac{1}{2}m_1 v_1'^2 + \tfrac{1}{2}m_2 v_2'^2$$

In the picture: $18\ \mathrm{J}$ before, 2 + 16 = $18\ \mathrm{J}$ after.

An elastic bounce: the light cart comes back, the heavy one moves off.

Equal masses, one at rest: the moving one stops and the other takes its velocity.