# Elastic and Inelastic collisions

As long as there are no net external forces acting on objects as they collide, the total momentum will be the same before and after the collision. The same is not true for kinetic energy, however. Physicists sometimes describe collisions based on the kinetic energy of the items before and after the collision.

Elastic
These collisions DO CONSERVE the total kinetic energy of the items. Sub-atomic particles smashing into each other inside particle detectors often undergo elastic collisions. A familiar example in everyday life is the collision of billiard balls.

Two billiard balls of mass 1 kg each are moving to the right. Initially, the blue ball moves at 5 m/s and the red ball at 2 m/s. After they collide, the blue ball moves at 2 m/s.

1. Use conservation of momentum to find the final speed of the red ball.
2. What is the initial KE of the system?
3. What is the final KE of the system?
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Inelastic
Much more common in everyday life are interactions which DO NOT CONSERVE kinetic energy. Cars colliding on the road, a bat striking a baseball, a bullet embedding itself in a torso -- these are all inelastic collisions. If the objects stick together afterwards, the collision must be inelastic.

Joe throws a baseball (M = 0.14 kg) towards home plate at v1 = 45 m/s. Alice fires a bullet (m = 0.05 kg) towards the pitcher's mound at v2 = 400 m/s. The bullet embeds itself into the ball.

1. Use conservation of momentum to find the final speed of the combined object.
2. What is the initial KE of the system?
3. What is the final KE of the system?