Physics Demonstrations

Collision

Mass 1 (kg)
Mass 2 (kg)
Velocity 1 (m/s)
Velocity 2 (m/s)
Coefficient of Restitution (0-1)

In this demonstration, two balls collide in one dimension. Ball 1 (blue) begins on the left moving rightward with velocity $v_{1}$ , and Ball 2 (red) begins on the right moving leftward with velocity $v_{2}$ . The nature of the collision is controlled by the coefficient of restitution $e$ , defined as the ratio of the relative speed of separation to the relative speed of approach: $e = \frac{v_{2}' - v_{1}'}{v_{1} - v_{2}}$ Combined with conservation of momentum, the post-collision velocities are: $v_{1}' = \frac{m_{1} u_{1} + m_{2} u_{2} + m_{2} e (u_{2} - u_{1})}{m_{1} + m_{2}}$ $v_{2}' = \frac{m_{1} u_{1} + m_{2} u_{2} + m_{1} e (u_{1} - u_{2})}{m_{1} + m_{2}}$ Momentum is conserved in all collisions. Kinetic energy is conserved only when $e = 1$ (perfectly elastic). When $e = 0$ the collision is perfectly inelastic and the balls stick together. The animation displays both momentum and kinetic energy before and after the collision. Some questions to consider while viewing the demonstration: Set $e = 1$ and equal masses. What happens to each ball's velocity after the collision? Set $e = 0$ . Is kinetic energy conserved? Where does the lost energy go? Try a very heavy Ball 2 at rest. How does the mass ratio affect the outcome? Identify a real-world collision that is approximately elastic and one that is approximately inelastic.