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# Contact Time of a Bouncing Ball

ninjakannon
I'm trying to work out an equation for the contact time of a bouncing ball and am completely stuck, but I'll explain my thoughts and we'll see where we get. An equation isn't really necessary, but a rough idea of how certain factors affect the contact time would be very useful.

Obviously, the contact time depends on a whole load of factors. I'm ignoring deformations of the surface the ball lands on, assuming that it is rigid, immovable and completely horizontal. When the ball lands it will compress slightly, a wave would travel through the ball, reach its top, and reflect back downwards. This would cause the ball to exert a force on the ground and it would bounce back upward.

But how long does this take? If the ball collides with a greater velocity, I assume the amplitude of the wave through the ball would be greater. Would this wave always have a constant speed (that I assume would then be dependant on the density of the ball) despite varying contact velocities?

Thanks for any help on this one.
ocalhoun
 ninjakannon wrote: But how long does this take? If the ball collides with a greater velocity, I assume the amplitude of the wave through the ball would be greater. Would this wave always have a constant speed (that I assume would then be dependant on the density of the ball) despite varying contact velocities?

I do think the wave's speed should be constant for any particular ball.

Do you mean that you're trying to make an equation that will determine how long a bouncing ball will be in contact with what it bounces off of?
ninjakannon
Yes, that's what I mean - it's for a simulation I'm trying to create.

If the wave's speed is constant for any particular ball then that would imply that the contact time was always the same, would it not? But that can't be right, from what I've worked out so far I get the feeling that the contact time increases the lower the ball's contact velocity is. However, I'm really not sure.
ocalhoun
^I would think that the contact time would actually be longer because the faster ball would compress more (creating a higher amplitude wave), deforming it more, so that it would stay in contact longer.
Then again, perhaps the two effects cancel each other out, so it is constant for any particular ball.

I think this equation is the type of thing you need to verify with experiment as you go along. If you could get your hands on a very fast frame-rate video camera (the kind they film explosions with) and a few varying balls, you could do a few experiments to find out just what affects the contact time and how.
ninjakannon
That sounds to me like the 'only' (or rather the easiest) way to do it. However, I neither possess a high capture rate camera nor know of where I could get my hands on one.

I had a go with a normal video camera, then slowed the video down on computer to see whether there was any observable change. As you can imagine, the 25-30 frames per second didn't reveal anything at all. Although, I believe it got a frame or 2 of the ball when slightly compressed, it was hard to tell.

I think I can get away with fudging the contact time in my simulation, I am more curious as to what the actual result is.
Gagnar The Unruly
This seems like something physicists would've already figured out. Have you tried using Google or going to a University library? I bet there's an mechanical physics textbook with the right equations in it.
ocalhoun
^You might be able to rig something up with electronics...

Use large balls, put a metal mesh around them. Connect the mesh to one side of a circuit, the metal plate it bounces on to the other side of the circuit. Put a very accurate timer in the circuit that will count time only while the mesh is in contact with the metal plate. Allow the ball to bounce only once (catch it after one bounce), then look at the timer. Reset timer. Change the ball or the speed it hits at, repeat.

You could probably manage that for under \$100.