Question

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

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

Answer 1

Energy is conserved, but it changes form. When you drop a ball from height h it starts with gravitational potential energy mgh. Just before it hits the ground that energy is kinetic. If the ball does not rebound to the original height, some of that mechanical energy has been converted into other forms during the impact:

- elastic potential energy while the ball compresses (transient),
- then into internal energy (heat) because of internal friction and viscoelastic losses,
- sound energy radiated as the “thud”,
- energy transferred into the ground as vibrations,
- and possibly permanent (plastic) deformation of the ball or ground.

If the ball rebounds to a lower height h' < h, the gravitational potential energy at the top of the rebound is mgh'. The energy “lost” from the mechanical (potential + kinetic) budget is m g (h − h'), and that equals the sum of the amounts converted into heat, sound, vibrations, and deformation.

If you use the coefficient of restitution e (ratio of rebound speed to impact speed), the rebound height is h' = e^2 h, so the fraction of energy retained in the bounce is e^2 and the fraction lost is 1 − e^2.

In short: the missing mechanical energy isn’t destroyed — it’s redistributed into heat, sound, and other non-mechanical forms (and possibly transferred to the ground).