# 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.