Question

What happens to the energy of a ball when it hits the ground and doesn’t bounce back to its original height?

Answer 1

The total energy is conserved, but the ball’s mechanical energy (gravitational potential + kinetic) is partly converted into other forms when it doesn’t bounce back to the original height. Specifically:

- Before impact you have mgh (gravitational potential). Just before impact that is kinetic energy.
- On impact some energy is stored briefly as elastic potential (if the ball and ground deform), then most of that goes into non-mechanical forms:
- Heat (internal energy) in the ball and ground from internal friction and damping,
- Sound (an acoustic pulse),
- Permanent (plastic) deformation or vibrations in the ball and/or ground,
- Small amounts in surface waves, etc.

If the ball rebounds to height h′ (< h) the mechanical energy after the collision is mgh′, so the energy dissipated is
m g (h − h′),
which equals the sum of the heat, sound, and deformation energies. The temperature rise is usually tiny, and the lost mechanical energy shows up as increased internal energy and greater entropy of the surroundings.