Elastic collision in 1D

Problem

Elastic collision in 1D. Two $1\;\text{kg}$ balls, one at $+3\;\text{m/s}$ and the other at rest. Calculate the velocities after a head-on elastic collision.

Solution

For a head-on elastic collision between equal masses, the velocities are exchanged (a notable property: simultaneous conservation of momentum and kinetic energy with $m_1 = m_2$). So the moving ball stops and the stationary one moves off: $\ev{v_1' = 0, \quad v_2' = +3\;\text{m/s}}$ Check. Momentum: $1\cdot 3 = 1\cdot 3$ ✓. Kinetic energy: $\tfrac{1}{2}\cdot 3^2 = \tfrac{1}{2}\cdot 3^2$ ✓.

Links

Topics: Momentum and collisions Concepts: Elastic collision · Conservation of momentum