When is energy conserved in collisions

A high speed car collision is an inelastic collision. In the above example, if you calculated the momentum of the cars before the collision and added it together, it would be equal to the momentum after the collision when the two cars are stuck together.

However, if you calculated the kinetic energy before and after the collision, you would find some of it had been converted to other forms of energy. An elastic collision occurs when the two objects "bounce" apart when they collide. Two rubber balls are a good example. In an elastic collision, both momentum and kinetic energy are conserved. Almost no energy is lost to sound, heat, or deformation. The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

A collision in which total system kinetic energy is conserved is known as an elastic collision. For more information on physical descriptions of motion, visit The Physics Classroom Tutorial. Detailed information is available there on the following topics:. Physics Tutorial. My Cart Subscription Selection.

Return to List of Animations. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available. When starting to investigate collision problems, we usually consider situations that either start or end with a single body. The reason for this self-imposed limitation is that such problems can be solved by applying momentum conservation alone, namely the result that the total linear momentum of an isolated system is constant.

The analysis of more general collisions requires the use of other principles in addition to momentum conservation. To illustrate this, we now consider a one-dimensional problem in which two colliding bodies with known masses m sub 1 and m sub 2 , and with known initial velocities u subscript 1 x end and u subscript 2 x end collide and then separate with final velocities v subscript 1 x end and v subscript 2 x end.

The problem is that of finding the two unknowns v subscript 1 x end and v subscript 2 x end. Conservation of momentum in the x -direction provides only one equation linking these two unknowns:. In the absence of any detailed knowledge about the forces involved in the collision, the usual source of an additional relationship between v subscript 1 x end and v subscript 2 x end comes from some consideration of the translational kinetic energy involved. The precise form of this additional relationship depends on the nature of the collision.

Collisions may be classified by comparing the total translational kinetic energy of the colliding bodies before and after the collision. If there is no change in the total kinetic energy, then the collision is an elastic collision.

If the kinetic energy after the collision is less than that before the collision then the collision is an inelastic collision. In some situations e. In the simplest case, when the collision is elastic, the consequent conservation of kinetic energy means that. This equation, together with Equation 1 will allow v subscript 1 x end and v subscript 2 x end to be determined provided the masses and initial velocities have been specified. We consider this situation in more detail in the next section.

Real collisions between macroscopic objects are usually inelastic but some collisions, such as those between steel ball bearings or between billiard balls, are very nearly elastic. The kinetic energy which is lost in an inelastic collision appears as energy of a different form e.