# Collisions

Collision is an interaction between two or more bodies in which sudden changes of momentum take place. For example, striking a ball with a bat.

The Newton's third law of motion leads to the law of conservation of momentum (momentum can neither be created nor destroyed). The momentum of a system remains constant so long as no external forces act on it.

m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

When a bullet of mass m is fired from a gun of mass M with a velocity v, then the gun recoils with a velocity mv/M. When a shot is fired from a gun, the momentum of the shot and the momentum of the gun are equal in magnitude but opposite in direction.

When a shot of mass m with a velocity v gets embedded in a block of mass M free to move on a smooth horizontal surface, then their common velocity = mv/(m+M).

When a moving shell explodes, its total (vector sum) momentum remains constant but its total kinetic energy increases.

### Elastic Collision

- Both kinetic energy and linear momentum are conserved.
- Total energy is constant.
- Bodies will not be deformed.
- The temperature of the system does not change.

Two bodies of equal masses moving in opposite directions with the same speed collide, if the collision is elastic, each body rebounds with the same speed.

A body collides with another body of equal mass at rest. The collision is oblique and perfectly elastic. The two bodies move at right angles after collision.

### Inelastic Collision

- Linear momentum is conserved.
- Kinetic energy is not conserved.
- Total energy is conserved.
- Temperature changes.
- The bodies may be deformed.
- The bodies may stick together and move with a common velocity after collision.
- If the bodies collide and move together after collision; the collision is perfectly inelastic.