Types of Collisions
The phenomenon in which momentum and/or kinetic energy is transferred from one object to another is called collision. The simplest system deals with two objects colliding. There are two main types of collision: elastic and inelastic.
In the case of elastic collision, both the kinetic energy K and momentum p are conserved. This means that the sum of the momenta before the collision will be equal to the sum of momenta after the collision. The same applies for the kinetic energy. At this point it is helpful to remember the related formulas:
p = m x v
K = (1/2) x m x v^2
It is obvious that both of these quantities are related to the motion of the object and both depend on its mass m and velocity v. However, their relationship is different. Although both quantities have a linear dependence on the mass, they differ in the velocity dependence. The kinetic energy is exponentially related to the velocity. This means that if the velocity of an object is doubled, its momentum will be doubled as well, whereas its kinetic energy will increase by a factor of four. The action of billiard balls is a good example of elastic collision.
In the case of inelastic collision, only the momentum is conserved. What is happening to the kinetic energy is that an amount of this energy is lost in a variety of ways, such as heat (through friction) and deformation. If we could add up the remaining kinetic energy and the energy lost or transferred to the environment, it would equal the original amount of kinetic energy.
Most examples in everyday life are inelastic collisions, including car accidents, a bullet hitting a target, etc.
For more information on how to solve elastic and inelastic collision problems, check out the articles, How to Solve Elastic Collision Problems and How to Solve Inelastic and Plastic Collision Problems.