Difference Between Elastic and Inelastic Collision

Main Difference – Elastic vs. Inelastic Collision

Collision can be classified as either elastic or inelastic. The main difference between elastic and inelastic collisions is that, in elastic collisions, the total kinetic energy of the colliding objects before the collision is equal to the their total kinetic energy after the collision. In inelastic collisions, the total kinetic energy of the objects after the collision is less than the total kinetic energy of the objects before the collision.

What is Elastic Collision

An elastic collision is a collision where the total kinetic energy of the bodies before the collision is equal to their total kinetic energy after the collision. This type of collision is impossible to observe in the macroscopic world, as at least a small amount of kinetic energy is lost during collisions. Note that, if the collision occurs in a closed system, then the total momentum is conserved. The total energy is also conserved—however, some of the kinetic energy has been transformed into other forms.

A collision between two billiard balls are, to a good approximation, elastic. Elastic collisions are more plausible for collisions between fundamental particles. However, even in these interactions, some of the kinetic energy may be lost in the form of radiation.

Difference Between Elastic and Inelastic Collision - Billiards

Difference Between Elastic and Inelastic Collision – Collisions between billiard balls can be elastic to a good approximation

What is Inelastic Collision

An inelastic collision is a collision in which the total kinetic energy of the colliding particles before the collision is greater than the total kinetic energy of the particles after the collision. During the impact, the kinetic energy is converted to other forms, such as heat or the energy used to cause deformations in the colliding bodies. A collision is said to be perfectly inelastic if the colliding bodies stick and move together after the collision.

Coefficient of Restitution

A coefficient of restitution describes to which degree the collision between two particles is elastic. It is a measurement of the ratio of relative velocities of the bodies before collision to the velocities of bodies after the collision. If two particles have velocities $u_1$ and $u_2$ before collision and velocities $v_1$ and $v_2$ after collision, then the coefficient of restitution $e$ is defined as:

$e=\frac{v_2-v_1}{u_1-u_2}$

A collision is elastic if $e=1$ . For inelastic collisions, $0\leqslant e<1$ . If the collision is perfectly inelastic, then $e=0$ .

Difference Between Elastic and Inelastic Collision

Kinetic Energy Conservation

Elastic collisions conserve kinetic energy.

In Inelastic collisions, the total kinetic energy of the colliding bodies before the collision is greater than the total kinetic energy of the bodies after the collision.