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Elastic and Inelastic Collisions

Momentum is always conserved in collisions. Energy however is not always conserved. In fact collisions can be classified into three types, according to whether kinetic energy is conserved or not:

Elastic Collision – Kinetic Energy is conserved. In general energy is conserved by being converted into a form of potential energy – elastic or electric potential energy for example – then back into kinetic energy. The term collision here is used in a general way – that is bodies need not actually physically touch each other. When electrically charges particles of like charge near each other, they repel. The kinetic energy with which they approach each other is changed into electrostatic potential energy then back into kinetic energy.

Example: A truck of mass m moving with speedcollides with a stationary truck also of mass The first truck is brought to rest and the second truck moves off with speedThe kinetic

energy before the collision () equals the kinetic energy after the collision.

Inelastic Collision – Kinetic Energy is not conserved. In energy is changed into a form which cannot be recovered – heat, light and sound energy, or the energy of deformation of the colliding bodies. When cars collide, a lot of energy is absorbed by the structure of the cars. In fact the structure of a car is designed to absorb a lot of energy, so safeguarding the occupants. Obviously this energy cannot be converted back into kinetic energy, so car crashes are inelastic collision with loss of kinetic energy.

Example:

The kinetic energy before the collision is

The kinetic energy after the collision is

The loss in kinetic energy is

Perfectly Inelastic Collision – Maximum loss of Kinetic Energy, subject to the conservation of linear momentum. Bodies collide and stick together.

The kinetic energy before the collision is

The kinetic energy after the collision is

The loss in kinetic energy is