Drop height vs bounce height

1. Pick a drop height in the Drop height panel. The ball always starts from rest at that height. That means it is not moving when you let go.
2. Press Drop the ball. Watch it fall, hit the floor, and bounce back up.
3. Watch for the top of the first bounce. It goes by fast. That is why Slow motion is on to start.
4. Heights are measured to the bottom of the ball, like lining it up with a real meter stick. A piece of tape marks the top of each first bounce.
5. The chart beside the ball shows its height over time. You can see the drop, the hit, and the bounce all at once.
6. Each drop adds a row to the Trials table and a dot to the Bounce height vs drop height graph.
7. Turn on Show the best-fit line to draw a line through your dots. Turn on Add measurement error to make it more like a real lab.
8. Press Reset to drop again. Press Clear trials to start over, or Copy data to paste your results into a spreadsheet.

When you hold the ball up high, it has stored energy. This is called gravitational potential energy. The higher the ball, the more of it there is.

As the ball falls, that stored energy turns into kinetic energy, the energy of motion. The ball moves fastest just before it hits the floor.

When it hits, the ball squishes a little and then springs back. That push from the floor sends it back up. As it rises, it slows down and the energy turns back into stored energy.

Some energy is lost every time the ball hits the floor. It turns into heat and sound. You can hear the "click" when it lands. So the ball has less energy on the way up.

Less energy means it can't climb as high. A golf ball on tile bounces back to about 69% of the height it was dropped from. Drop it from 100 cm and it comes back to about 69 cm.

The dashed line on the graph shows a perfect bounce, where the ball comes back to the same height. Your dots will always land below it.

Each dot is one drop. Higher drops give higher bounces. The dots fall close to a straight line through zero.

A straight line through zero means the bounce is always the same fraction of the drop. Double the drop height, and the bounce height doubles too.

The slope of the best-fit line is that fraction. Slope means how steep the line is. You can also find it in the Bounce/Drop column of the table.

Turn on the realism switch, and the ball loses a little more bounce when it hits the floor faster. Then the dots bend a little below a straight line at the bigger heights.

Speed when it hits the floor: v = √(2 × g × h_drop)

Speed when it leaves the floor: e × v. Here e is the coefficient of restitution. It is a number that tells how bouncy the ball is. For a golf ball on tile, e = 0.83.

Bounce height: h_bounce = e² × h_drop. Since 0.83 × 0.83 is about 0.69, the ball comes back to about 69% of its drop height.

Gravity is g = 980 cm/s². The ball is 4.3 cm across, drawn a little larger so it is easy to see. The sim works out the falling motion exactly, so the recorded number always matches what you see.