What Determines the Decreasing Height of a Bouncing Ball?

[Liam Lau]

Homework Statement

Why does a ball bounce less and less high, even though the force exerted by the ground on the ball is the same, due to Newton's third law. I do understand the ball loses energy as heat energy.

Homework Equations

F=ma ; F₁=-F₂

The Attempt at a Solution

I'm just curious why this happens. Thanks. I know the ball loses kinetic energy, and I know that the force initially applied on the ball determines the height of the bounce.

 

[jbriggs444]

Homework Statement

Why does a ball bounce less and less high, even though the force exerted by the ground on the ball is the same, due to Newton's third law.

The force on the ball is the same as what?

 

[AbhinavJ]

Try searching for coefficient of restitution, youll get your answer.

 

[andrevdh]

As it rises its kinetic energy is converted into gravitational potential energy.
At the top all of the kinetic energy is converted into potential energy and its
speed is momentarily zero since kinetic energy is zero. So the maximum
height it reaches is determined by its kinetic energy at the bottom.

 

[AbhinavJ]

As it rises its kinetic energy is converted into gravitational potential energy.
At the top all of the kinetic energy is converted into potential energy and its
speed is momentarily zero since kinetic energy is zero. So the maximum
height it reaches is determined by its kinetic energy at the bottom.

According to this, as energy is conserved, the ball should reach the same height again, and keep on bouncing till the same height. This is true for the ideal world. The question asks why the height gets reduced after each successive bounce or collision to be precise. This is due to the properties of the material the ball is made of, and the the coefficient of restitution of that material. It includes the energy dissipated to the sorroundings.
https://www.physicsforums.com/index.php?threads/763082/

 

[Liam Lau]

Thanks for all the comments, but there is one thing I am confused with. Does the height of the ball bounced not depend on the force exerted of the ball when it is thrown at the ground? The point I'm trying to make is that doesn't Newton's third law state the Force of the ball hitting the ground is equal to the ground pushing back at the ball, I was just wondering why this doesn't affect the height the ball bounces back.

 

[jbriggs444]

Thanks for all the comments, but there is one thing I am confused with. Does the height of the ball bounced not depend on the force exerted of the ball when it is thrown at the ground? The point I'm trying to make is that doesn't Newton's third law state the Force of the ball hitting the ground is equal to the ground pushing back at the ball, I was just wondering why this doesn't affect the height the ball bounces back.

The force the ground exerts on the ball is equal at all times to the force that the ball exerts on the ground. But that is irrelevant. The force that the ball exerts on the ground affects the ground. It does not affect the ball. The only force that is relevant is the force that the ground exerts on the ball.

As the ball hits the ground and compresses, the force exerted on the ball by the ground is slowing the ball down. Eventually the ball reaches its low point and starts rebounding upward. From that point on, the force exerted on the ball by the ground is speeding the ball up.

The relevant question is whether the [time integral of] the force of the ground on the ball during the compression is equal to the [time integral of] the force of the ground on the ball during the rebound. In general, the two will not be equal. Instead, the force during the rebound will be somewhat less. Often the ratio between the two will be more or less constant. That constant is called the "coefficient of restitution".

 

[andrewkirk]

This is probably a much smaller effect than that described by jbriggs, but the ball also loses energy through air resistance as it rises and falls, so irrespective of the amount of energy lost during contact with the ground, the speed and kinetic energy of the ball immediately before hitting the ground will be less than what it had just after the last time it left the ground.

 

[andrevdh]

Well, Liam said that he knows kinetic energy is lost in the collision with the ground.
So if he is happy with that then the potential energy at the top should be less after
each bounce.

Work is being done by pushing the ball back upwards by the ground and as we know
this energy needs to come from somewhere. What would be the source of this energy?

 

[Liam Lau]

The force the ground exerts on the ball is equal at all times to the force that the ball exerts on the ground. But that is irrelevant. The force that the ball exerts on the ground affects the ground. It does not affect the ball. The only force that is relevant is the force that the ground exerts on the ball.

As the ball hits the ground and compresses, the force exerted on the ball by the ground is slowing the ball down. Eventually the ball reaches its low point and starts rebounding upward. From that point on, the force exerted on the ball by the ground is speeding the ball up.

The relevant question is whether the [time integral of] the force of the ground on the ball during the compression is equal to the [time integral of] the force of the ground on the ball during the rebound. In general, the two will not be equal. Instead, the force during the rebound will be somewhat less. Often the ratio between the two will be more or less constant. That constant is called the "coefficient of restitution".

Thanks, this clarified the confusion I had.