# Homework Help: Does a ball always bounce the same fraction of the previous height?

1. Jun 11, 2014

### Tizyo

1. The problem statement, all variables and given/known data

I need to know whether a ping pong ball bounces the same fraction of the previous height or does the fraction change? For ex. if I drop the ball from 1m and it bounces back to 0.7m, it decreased by 30%, will it always decrease by 30%, or will the percentage change?

2. Relevant equations

3. The attempt at a solution

I have done an experiment and it looks like the percentage of the height that it decreases by will increase, in my case first it was decreasing by ~25%, then 20% and by the end it was about 15%, there was a big uncertainty in my results, but it looked like it had a tendency to decrease. Can I explain/prove that somehow? Or is it just the uncertainty playing tricks on me?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 11, 2014

### ChiralWaltz

How many bounces did you measure in the experiment?

3. Jun 11, 2014

The collision between the ball and the surface is inelastic and one can't really tell how inelastic. If the coefficient of restitution is variable, then we can have different decrease percentage of height.

4. Jun 11, 2014

### Staff: Mentor

To expand on what Adithyan said, the ball deforms when it bounces, and this deformation is accompanied by dissipation of mechanical energy by the ball material. Since the deformation is larger when the ball is dropped from a larger height, there will be a greater dissipation of mechanical energy compared to the deformation resulting from a drop from a smaller height. It's all related to the deformational mechanics of the ball material.

Chet

5. Jun 11, 2014

### ChiralWaltz

Which semester of physics is this for?

6. Jun 11, 2014

### BiGyElLoWhAt

Also I believe that air resistance will play a role in this. Drag is proportional to v^2 and if the ball doesn't reach the same height as it did the last iteration, it will not reach the same velocity, and thus the difference will be proportional to $v_{t}^2 - v_{0}^2$

You're probably neglecting drag, but all in all it does play a role in real life situations.

Edit:
Especially if you're using something to the effect of a ping pong ball, which seems to be rather popular these days.

Last edited: Jun 11, 2014
7. Jun 11, 2014

### Tizyo

I get that the coefficient of restitution of the ping pong ball is about 0.82 in the beginning and then it increases up to 0.9.
Also, is the way I calculate COR correct? For ex. this is a sample of my data:

Max height of 2 bounces: 1.04m --> 0.70m
COR=(0.70/1.04)^0.5=0.82

Is this a correct way to calculate COR?

Also, should I ignore the change in COR, because I am trying to model the trajectory of the ball and it gets complicated if the percentage, by which the height of the next bounce decreases, changes.

8. Jun 11, 2014

### haruspex

Sure, but why should the fraction of energy lost be higher for a longer drop? (I'm not saying it isn't, but I don't see a suggestion here of why it would be.)
For a ping-pong ball, some of the elasticity might come from the compression of the air inside, but that should be almost adiabatic, and I think it would be a minor contributor anyway.

BiGyElLoWhAt's drag explanation sounds the most likely to me.

9. Jun 11, 2014

### Tizyo

So should I ignore it? :D

10. Jun 11, 2014

### haruspex

That depends on what you are trying to do.
If you are trying to prove experimentally that it always bounces to the same fraction, you've proved it doesn't (barring experimental error).
If you're trying to show that the same fraction of energy is lost each bounce, in the bounce itself, you need some way to correct for loss from drag. That could be hard.
If you're trying to come up with a model for how much is lost each bounce, all causes included, you need to construct a mathematical model that allows for both elastic losses and drag, then plug in the data to determine the parameters.