Bouncing Ball

Why does a ball never bounce back as high as you dropped it from? Pick a ball and a floor, drop it and watch the energy bars on every bounce.

Ball
Ground
Height
2.00 m
Speed
0.00 m/s
Bounces
0
Bounciness e
0.75

The maths, live

Start energy PE = m × g × h₀PE = 0.058 × 9.81 × 2.0 = 1.14 J
Next bounce h = e² × last heighth = 0.75² × 2.00 = 1.13 m
Energy kept each bounce = e²56% kept, 44% lost
PE + KE + lost = start energy1.14 + 0.00 + 0.00 = 1.14 J

Which ball keeps the most energy on each bounce? Try the same ball on concrete, carpet and grass.

How it works

As the ball falls, its gravitational potential energy (PE = m × g × h) turns into kinetic energy. When it hits the ground it squashes, and some of that energy turns into heat and sound. Only what is left can lift the ball up again.

How bouncy a ball is can be measured by its coefficient of restitution, e: how fast it leaves the ground compared with how fast it hit it. The ball keeps e² of its energy each bounce, so the next bounce height is e² × the last one. A superball has e ≈ 0.9 and keeps about 81% of its energy. Clay has e ≈ 0 and does not bounce at all.

Try this

  1. Drop a tennis ball from 2.5 m. Real tennis balls must bounce back between 1.35 m and 1.47 m. Does this one pass?
  2. Which ball bounces the most times before it stops?
  3. Drop the same ball on concrete, carpet and grass. Where does the missing energy go?