Bounco

Meet Bounco, a rubber ball who comes back a little lower every time she bounces.

The coefficient of restitution, e, compares how fast two objects move apart after a collision with how fast they approached. A value of 1 means a perfectly elastic collision, where no kinetic energy is lost. A value of 0 means they stick together. Real balls fall in between.

For a ball bouncing on a hard floor, e can be found from heights alone, because speed depends on the square root of the drop height. Dropped from 1.00 m and bouncing back to 0.64 m, a ball has e = √(0.64 / 1.00) = 0.8.

Each bounce keeps e² of the kinetic energy, so this ball keeps 64% and loses 36% each time. The lost energy becomes sound, heat and vibrations in the ball and floor, which is why the bounces get lower and closer together until the ball rests.

Sports rules use this. Tennis and squash balls must bounce to set heights when dropped in tests, and golf club faces have a limit on how springy they may be.