# If an object is mass m with a velocity u collides with a stationary object of mass m, how much kinetic energy is lost?

Sep 23, 2017

There will be no loss of kinetic if the collision is elastic and in all cases momentum will be conserved. If the collision is inelastic some energy is converted to heat.

#### Explanation:

Energy is always conserved, so the kinetic energy of objects which collide is conserved unless some of the energy was converted into another form during the collision. If the collision is inelastic some energy is converted to heat but momentum is conserved.

So, before the collision a mass $m$ has velocity $u$. It hits another object of mass $m$ which is at rest. After the collision the combined bodies have mass $2 m$ and velocity $v$. Now momentum is conserved so:

$m u = 2 m v$

This means that $v = \frac{u}{2}$ and momentum is conserved.

The change in kinetic energy is:

$\frac{1}{2} m {u}^{2} - \frac{1}{2} 2 m {v}^{2} = \frac{1}{2} m {u}^{2} - m {u}^{2} / 4 = \frac{1}{4} m {u}^{2}$

So, the loss of kinetic energy is $\frac{1}{4} m {u}^{2}$.