# Why do things bounce?

## Main Question or Discussion Point

This has always bugged me, and I don't think that I've ever gotten a satisfactory explanation (even though it's a really simple issue):

Why do things bounce?

The way I see it, you have a ball falling towards the ground. The ground has no momentum, the ball has momentum pointing towards the ground. When the ball hits, the momentum is transferred from the ball to the ground. The ground hardly moves, because the earth is massive, so the change in velocity is negligible. Yet, the net velocity in the system is now zero: how does the ball end up with a momentum opposite (minus a bit) of its original momentum?

On a similar note, same scenario: a ball is bouncing, the ball has a mass m and a directed velocity vector v leading to a momentum of p. The ball hits the ground. How are the forces resolved? In other words, obviously some forces cause the ball to reverse direction, and I know that they are equal and opposite, but how does the ball get a double dosage of this force (enough to cause it to stop and then reverse direction) and how are the forces calculated (I know that force is momentum over time, but how do we find the time?)

Thanks.

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double dosage?
no, that's not it, the force*time that the ball receives and the ones that the ground receives are the same,
the magnitude? this is determined by the characteristics of the things that's colliding, that's all

if u try to picture the system by looking at the ball only, u will see that it is just about a thing that is colliding with another thing with the former will be given a force by the latter which magnitude depends on the characteristics of both of them

hope i was of any help

dst
You can think of a sort of "pressure wave" moving through the ball if it's solid and elastic. This "wave" reflects off the opposing side (or if it's hollow, by the immediate region) and hence gets directed back in towards the ground, lifting it back off the ground.

Also, remember that a ball full of flour or a fluid won't bounce at all! It depends on the density, structure, and a few other things.

russ_watters
Mentor
Nate, it is easiest to think of the ball simply as a spring. When it hits the ground it is compressed, storing some of the energy it had when it was moving. Also, momentum is a vector quantity - if the ball is moving back in the opposite direction, in a perfectly eleastic collision, it has transferred nearly 2x its own momentum to the earth:

m1v1=m1(-)v1+m2v2
m2v2=2m1v1

Ah, ok, so the force that causes the ball to bounce is contained in the ball, and is not related to the surface it is bouncing against. When it hits, its deformation and reformation causes the 'bounce' and also applies that additional momentum into the wall.

Now, how are the forces resolved? In other words, a ball of mass m with velocity v hits a wall. How do we find the force on the wall? In other words, how do we find the time component?

that..would be hard, as it is almost instantaneous...

dst
High speed camera?

Unless you want to solve for contact time given an object moving at some velocity with some coefficient of restitution and elasticity and whatnot.

russ_watters
Mentor
Yes, in real-world situations it is a little difficult because of the time of the impact and the variability of the deformation, but again, if you use a spring, it is easy. But either way, the force is the deformation times the spring constant (or modulus of elasticity).

You probably consider golf balls to be relatively hard/rigid. Check out this video: http://www.youtube.com/watch?v=2Y57pw_iWlk&feature=related

It's actually probably good enough to estimate the forces and spring constant if you were so inclined. It says in the description that the video was shot at 10,000 fps and it looks to me like the ball was only in contact for aboutt 5 frames. If the ball leaves the club at 150mph, that's an average acceleration of 300,000 mph/sec or 14,000 g's.

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So the force on the ground when hit by a ball is equal to the deformation * the balls elasticity? I'm assuming that the amount of deformation is based off of the balls momentum: how is this calculated?

russ_watters
Mentor
Acceleration is change in speed divided by time. Force is acceleration divided by mass - or change in momentum divided by time.

I know, but we don't know the time here. That was (part of) my original question: how do we calculate the time over which the momentum is transferred (and thus the force transferred)?

there are a lot of factors that determine how much time that it takes on a momentum transfer, for example when we ourself try to give a certain magnitude of momentum to a certain thing, we ourself can determine how long it will takes by adjusting the force that we give, and that's why, even in the case of a ball bouncing off a wall, the case would be: measure the time, then measure the 'average' force

Ah, ok, so the force that causes the ball to bounce is contained in the ball, and is not related to the surface it is bouncing against.
This is wrong. If a ball bounces off a hard wall it won't lose much speed right? Well what if it bounces off say a haystack instead? If the final speed is less than the initial speed what does that say about the change in momentum compared to an elastic bounce? And what does that say about impulse? And force?

Why do things TOUCH?

Thank you for bringing up this question, Nate!
An even simpler variant of this question has long bugged me.

How do 2 things TOUCH without creating an infinite force between them?

How do I bring my 2 fingers together, from what looks to me, the observer,
a small but constant speed, to a complete stop, without creating a deadly
infinite force that shatters my fingers apart?

Again, the issue is a practically nearly 0 time of change in momentum.
If one can prove mathematically that, in reality, the speed of my fingers is not
a step function of time but actually a smooth function of time - actually,
C-infinite, since before t=t(contact) I have a positive speed, while for all
t>t(contact) my speed is constant at 0, I would like to see that.

By "prove mathematically", I mean prove from some fundamental laws of physics,
such as the inverse square Coulombic forces repelling particles between my two
fingers as they come near each other (never really in contact).

I've tried to do this derivation, but failed. The problem is: how do I get a C-infinity function for my speed (or displacement) of my finger, given physical laws which are analytic (i.e. smooth) functions of time for all the time both before and after "contact"?
By "contact", I mean, it looks like contact on the macroscopic scale.