# Conservation of energy when dropping a ball [duplicate]

If we drop a bowling ball from one meter above the earth's surface, we are converting its gravitational potential energy to kinetic energy.

When it hits the floor, it transfers its kinetic energy to the earth, so now the earth is moving directly downward at a larger (but imperceptible) speed.

But let's say we dropped a hollow bouncy ball (eg a ping-pong ball) with the same mass. Now the ball can bounce back, elastically. Is this energy supposed to come from the compression and decompression of the inner gas molecules?

• I think you mean the earth moves at a smaller speed, not larger. Also, what object in this scenario contains gas molecules? Aug 13 '18 at 3:05
• @AaronStevens If Earth is impacted by a meteor, will it not cause it to go faster in that direction? It's the same for a small ball. Secondly, the object that contains gas molecules is the bouncy ball. Aug 13 '18 at 3:07
• By conservation of momentum, if a ball much less massive than the earth hits the earth with some velocity, the earth, which is much more massive than the ball, will move with a much smaller velocity than the ball was moving at. Also, typical bouncy balls are solid. If you are asking about a ball of gas colliding with the earth then you should edit the question to avoid confusion. Aug 13 '18 at 3:13
• @AaronStevens If the earth is moving at zero speed and we drop a ball, it will move slightly faster downward. Also, bouncy balls are typically hollow. Aug 13 '18 at 3:26
• Aug 13 '18 at 7:37

The Earth is not moving with a zero speed, but is moving toward the ball attracted by the ball with exactly the same force as the ball is attracted by the Earth (Newton's third law). When they collide, both stop moving. With a bouncing ball, the Earth does bounce back, but gradually slows down attracted by the ball and stops when the ball also stops as it reaches its initial height. If the Earth is hit by a meteor, the resulting speed will depend on the mass and speed of the meteor when it was far away from the Earth. If the meteor was not moving, but gained its speed only due to the Earth gravity, then the resulting speed would be zero according to the law of conservation of momentum. The energy in the bouncing ball is indeed stored and released due to the elastic compression and decompression of the ball material (as well as of the surface that the ball hits), whether this material is the air or rubber or both, etc. inside the ball.

If we drop a bowling ball from one meter above the earth's surface, we are converting its gravitational potential energy to kinetic energy.

It is the ball and the Earth which have the gravitational potential energy not the ball alone.

When it hits the floor, it transfers its kinetic energy to the earth, so now the earth is moving directly downward at a larger (but imperceptible) speed.

Not so.
Consider the ball and the Earth as an isolated system with both initially at rest and then let the ball fall down towards the Earth.
If there are no external forces acting on the system the total momentum of the ball and Earth system must be zero for all time.
As the ball moves towards the Earth it gains momentum but at the same time the Earth is moving towards the ball and gaining an equal amount of momentum but in the opposite direction. Each also gain kinetic energy but the ball will gain much more kinetic energy than the Earth because the mass of the ball is so much smaller than the mass of the Earth.
If the ball and Earth stick together after they collide then the system has no kinetic energy.
The mechanical energy the system had becomes heat, sound and is used to permanent deform the ball and the Earth - it is an inelastic collision.

But let's say we dropped a hollow bouncy ball (eg a ping-pong ball) with the same mass. Now the ball can bounce back, elastically. Is this energy supposed to come from the compression and decompression of the inner gas molecules?

If the collision between the ball and the Earth is perfectly elastic then the mechanical energy of the system will be stored as elastic (spring) potential energy when the ball and the Earth deform during their collision.
Then that elastic potential energy will be converted to kinetic energy of the ball and Earth but now they are moving away from one another.
They would keep moving until their separation was the the same as their initial separation at which time they would be at rest relative to one another.
The sequence would then be repeated.