Equations valid for elastic collisions

In this post, we will briefly mention the equations valid for elastic collisions. We can use these equations to solve numerical problems related to elastic collisions.

The Equation for the conservation of momentum (for elastic collision)

Now, to solve problems involving one-dimensional elastic collisions between two objects, we can use the equation for the conservation of momentum.

First, the equation for conservation of momentum for two objects in a one-dimensional collision is:

Substituting the definition of momentum p = mv for each initial and final momentum, we get

where the primes (‘) indicate values after the collision; The equation assumes that the mass of each object does not change during the collision.

Equation for the Kinetic energy conservation (for elastic collision)

Kinetic energy is only conserved for elastic interactions. Hence, the following equation is valid only for elastic collisions.

Σ KE _{before elastic collision} = Σ KE _{after an elastic collision}

Take Away

For elastic collisions, we can use the equations for (1) momentum conservation, and (2) kinetic energy conservation, as both momentum and kinetic energy are conserved in elastic collisions.