# How can kinetic energy be conserved in an elastic collision

How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by the force exerted by the other? If they collide, path of the object will change so velocity should change as velocity is a vector quantity. So kinetic energy should also change.

• Look at the formula for kinetic energy and ask yourself: Does the direction of the velocity matter? – Javier Dec 10 '14 at 2:02
• @JavierBadia but velocity depend on direction – pcforgeek Dec 10 '14 at 3:35

## 1 Answer

When one says that "kinetic energy is conserved in an elastic collision" that means that the total kinetic energy of the system of particles involved in the collision doesn't change. It does not mean that the kinetic energy of each particle is unchanged. For a two particle system, the kinetic energy of each will change, but the sum won't.

Also, your statement about the change in direction of a particle doesn't matter.

$$K = \frac{1}{2}m (\vec{v}\cdot \vec{v})$$ for a single particle