# How to integrate Fds

1. Jun 8, 2014

### Lourens

Hello,

For a practical I have to know the work done by drag force, but drag force which is bv2 is not constant over the path, how can this be done, or should I just add every tiny bit of work, supposing Fd is constant over that tiny path. Thanks for the help!

2. Jun 8, 2014

### Simon Bridge

Welcome to PF;
What, exactly, does the practical involve?

In general - you would use calculus to work out the work done where the force is not a constant.
You would need v(x) to do that.

In a practical you may be able to calculate the total work for the path from a few parameters depending on the setup.

3. Jun 8, 2014

### Lourens

Well, we dropped a table tennis ball from a certain height and determined the height before bouncing on the ground and the maximum height of the first bounce. We know the constant b, and calculated v by analyzing every frame of the film. Now we can determine the drag force of course also for every frame, and thereby also the work done, but is there another way to determine the work done by the drag force, without analyzing per frame, that is actually the question.

4. Jun 8, 2014

### Matterwave

You can use conservation of energy. If the final KE (before bounce) is not equal to the initial PE, then the energy lost is due to air resistance. After the bounce, the energy lost would be due to both air resistance and energy losses during the bounce (e.g. to sound and heat by striking the floor).

5. Jun 8, 2014

### Simon Bridge

What he says - work-energy theorem. You don't need the force because you know the change in energy.
Decide if energy taken by stuff other than drag is negligible (i.e. does the frame-by-frame indicate that the speed right after a bounce is very close to the speed just before the bounce?).