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The bouncing ball

Energy and power · level 3, lesson 5 of 6

A question to start

Drop a ball from 1 m. It bounces back up, but not quite to 1 m. Then lower, and lower, until it rolls to a stop. If energy is never destroyed, why doesn't the ball bounce back to where it started?

The idea

Follow the energy of one bounce:

  1. Held up: height energy.
  2. Falling: height energy turns into moving energy.
  3. Hitting the floor: the ball squashes, storing elastic energy, and stops for an instant.
  4. Springing back: the elastic energy turns back into moving energy, and the ball flies up.
  5. Rising: moving energy turns back into height energy.

At each step a little energy escapes: as sound (the bounce you hear), as heat in the ball and the floor (the ball warms slightly as it squashes), and as heat in the air it pushes through. So less energy is left for each bounce, and each one is lower.

dropped from 1 m75 cm56 cm42 cm

A bouncy ball wastes little energy and bounces back high. A soft ball, like a beanbag, turns almost all its energy into heat when it lands, and does not bounce at all.

On Mars, with very thin air, a dropped ball would bounce back to almost the same fraction of its height as on Earth: that depends on the ball and the floor, not on gravity. But each bounce would last longer, because the ball falls and rises more slowly.

Worked examples

1. A tennis ball. Dropped from 1 m on a hard floor, it bounces to about 55 cm: a bit over half its energy is kept each time.

2. Counting bounces. A ball that keeps three-quarters of its height each bounce: 1 m, then 75 cm, 56 cm, 42 cm, 32 cm, and so on. It never quite reaches zero by the sums, but soon the bounces are too small to see.

Try it

  1. Name the forms of energy in a bounce.
  2. Where does the energy go that is lost on each bounce?
  3. A ball bounces back to 60 cm after being dropped from 1 m. What fraction of its energy did it keep?
  4. Would a ball dropped on Mars bounce to the same fraction of its height? Faster or slower?
Answers
  1. Height, moving and elastic energy, plus sound and heat.
  2. Into sound and heat (in the ball, the floor and the air).
  3. About 60%, since height energy goes with the height.
  4. About the same fraction, but each bounce would be slower and last longer.

Common mistake

"The ball loses energy because gravity pulls it down." Gravity gives back on the way down all the energy it takes on the way up. The losses are from sound, heat and the air.

Where it leads