What is an elastic collision? Two bodies of masses m₁ and m₂ with velocities u₁ and u₂ collide head-on elastically. Write the conservation equations and the final velocities. Show that equal masses exchange velocities.

1. 1 · Define. In an elastic collision, both the total momentum and the total kinetic energy are conserved.
2. 2 · Draw before and after. [Two balls on a line. Before: m₁ with arrow u₁ and m₂ with arrow u₂. After: m₁ with arrow v₁ and m₂ with arrow v₂]
3. 3 · Conservation of momentum. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
4. 4 · Conservation of kinetic energy. ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂².
5. 5 · Final velocities. v₁ = [(m₁ − m₂)u₁ + 2m₂u₂]/(m₁ + m₂) and v₂ = [(m₂ − m₁)u₂ + 2m₁u₁]/(m₁ + m₂).
6. 6 · Equal masses. Put m₁ = m₂: the first terms vanish, so v₁ = u₂ and v₂ = u₁. The bodies exchange velocities.
7. 7 · Real-life link. A billiard ball stops dead when it hits an identical ball squarely, and light nuclei slow down neutrons in a reactor.
8. 8 · Close in one line. So in an elastic head-on collision of equal masses, the velocities are swapped.

Scoring tip: Write both conservation equations even if you only quote the final result. Each equation carries a mark.