Double Ball Bounce

Introduction: Why does smaller ball bounce much higher than the height from which it was dropped when it is simultaneously dropped on top of a larger, more massive, ball?

Materials: Basketball, Tennis ball, Astro Blaster Toy, Lab Glasses, Numerous small bouncy balls

Procedures:

1. Hold the basketball about a meter above the floor

2. Drop the basketball and notice how high it bounces, it will certainly bounce up to a height lower than the height form which I dropped it.

3. Drop the tennis ball, it bounces up to a height lower that that form which it was dropped.

4. Now hold the tennis ball directly above the basketball so the balls are touching. Then drop both balls at the same time

5. Notice that the tennis ball goes shooting off above your head at a high speed; at a height twice as much as when it was dropped.

Scientific Principles: The two balls are dropped, one above the other. They hit the floor and the bottom ball reverses direction colliding with the upper ball.

Pictures of Materials:

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If the center of the ball drops by one meter it hits the floor with a speed about V1 = 4 m/s.

When the ball hits the floor the ball deforms, it becomes a squashed spring which pushes down on the floor. In return the floor pushes up on the ball slowing its downward speed at first and then accelerating it back up. If no energy is lost as heat when the ball deforms, then the ball leaves the floor heading up at the same speed with which it hit the floor, 4 m/s. It then rises to the same height from which it was dropped. If any energy is lost then the ball leaves the floor at a slower velocity and rises to a lower height.

The lower basketball behaves as described above. Bouncing upward off the floor at V1 = 4 m/s. The tennis ball is still falling at V1 = 4 m/s.

The tennis ball bounces off the basketball. It comes in at 8 m/s and it bounces up at 2V1 = 8 m/s.

The tennis ball is going upward 8 m/s faster than the basketball, but in the earth frame the basketball is going upward at 4 m/s so the tennis ball is going upward at 3V1 = 12 m/s = 8 m/s + 4 m/s.This is a general result, when a light ball is dropped onto the floor on top of a heavy ball and no energy is lost to heat then the light ball will bounce upward at three times the velocity with which it would have hit the floor if dropped alone.

This becomes even more impressive when you realize how high the light ball will bounce. The maximum height of a ball thrown straight upward occurs when the ball stops at the top of its trajectory.

All of its energy is potential energy, E = mgh where g is the acceleration of gravity, m is the mass of the ball and h is the height.

The energy as the ball leaves the floor is kinetic energy, E = 1/2 mv² . When this kinetic energy is converted to potential energy then 1/2mv² = mgh, and h = 1/2 v²/g. So the height is proportional to the velocity squared. Thus the tennis ball could go up to nine times higher than the height from which it is dropped.

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The tennis ball bounces off the basketball. It comes in at 8 m/s and it bounces up at 2V1 = 8 m/s.

The tennis ball is going upward 8 m/s faster than the basketball, but in the earth frame the basketball is going upward at 4 m/s so the tennis ball is going upward at 3V1 = 12 m/s = 8 m/s + 4 m/s.This is a general result, when a light ball is dropped onto the floor on top of a heavy ball and no energy is lost to heat then the light ball will bounce upward at three times the velocity with which it would have hit the floor if dropped alone.

This becomes even more impressive when you realize how high the light ball will bounce. The maximum height of a ball thrown straight upward occurs when the ball stops at the top of its trajectory.

All of its energy is potential energy, E = mgh where g is the acceleration of gravity, m is the mass of the ball and h is the height.

The energy as the ball leaves the floor is kinetic energy, E = 1/2 mv² . When this kinetic energy is converted to potential energy then 1/2mv² = mgh, and h = 1/2 v²/g. So the height is proportional to the velocity squared. Thus the tennis ball could go up to nine times higher than the height from which it is dropped.

Safety Regulations:When the ball is being dropped, stay at least two feet (extended arm) away to prevent the ball from hitting you. Also warn your audience to stay at least two feet away to observe the demonstration. To further one's safety; one could wear goggles while showcasing this demo.