Momentum
Beginner
Collision
Source: High school physics (Chinese)
Problem Sets:
momentum - 1110
Problem
Two small balls of equal mass move towards each other at the same speed. After a head-on collision, they both move in the opposite direction at their original speeds.
Is this collision elastic? Why?
Yes.
An elastic collision conserves total kinetic energy. Let the mass of each ball be $m$ and their initial speed be $v$. The initial total kinetic energy is $K_i = \frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. After the collision, their speeds are still $v$, so the final total kinetic energy is $K_f = \frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. Since $K_i = K_f$, the collision is elastic.