# When a ball at rest is dropped, can it rebound to a greater height than its original height?

Apr 6, 2017

Usually, no.

#### Explanation:

A ball has a gravitational potential energy given by $m g h$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is the height.

When the ball falls, some of its gravitational potential energy is converted to other forms of energy, such as kinetic energy and rotational energy.

When it rebounds, these other forms of energy is converted back to gravitational potential energy.

During this process, some of its energy is lost from friction, heat, sound, etc. This means that it cannot be rebound back to its original height.

However, this only means that its final gravitational potential energy $m g h$ is lower than original. Usually, this corresponds to a loss in height $h$. But if the ball gained energy during falling and rebounding (such as if the ball ejects some of its matter towards the ground, a force is applied to the ball during falling or rebound, etc.), its rebound height might be greater than its original height.

But, usually, the ball will not be rebound to a height greater than its original height.