Elastic and Inelastic Collisions

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.

Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions.

Elastic collisions, target at rest


Elastic Collisions

An elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed. This implies that there is no dissipative force acting during the collision and that all of the kinetic energy of the objects before the collision is still in the form of kinetic energy afterward.

For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic. Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic.

"Collisions" in which the objects do not touch each other, such as Rutherford scattering or the slingshot orbit of a satellite off a planet, are elastic collisions. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles out of contact with each other.

Collisions in ideal gases are very nearly elastic, and this fact is used in the development of the expressions for gas pressure in a container.

Elastic collisions, target at rest Standard examples, elastic collisions

Swinging Balls

A popular demonstration of conservation of momentum and conservation of energy features several polished steel balls hung in a straight line in contact with each other. If one is pulled back and allowed to strike the line, one ball flies out the other end. If two balls are sent in, two come out, and so forth.

Swinging balls movie

Inelastic Collisions

Perfectly elastic collisions are those in which no kinetic energy is lost in the collision. Macroscopic collisions are generally inelastic and do not conserve kinetic energy, though of course the total energy is conserved. The extreme inelastic collision is one in which the colliding objects stick together after the collision, and this case may be analyzed in general terms:


Derivation of kinetic energy loss expressions


Inelastic Collision Examples

Most ordinary collisions are classified as inelastic collisions because some of their kinetic energy is converted to other forms such as internal energy. Links to some examples are provided.

Forces in Car Crashes




Airliner and duck

Ballistic pendulum

One dimensional

Two dimensional

Franck-Hertz experiment

Two-truck collision

K.E. Lost in Inelastic Collision


Copyright 2005 -  S. B. EglI