# Deformation of a ball when it falls on a rigid surface

Suppose, we drop a rubber ball on the floor. The ball collides with the floor, comes to rest and often bounces back up to lower height. I'm trying to look at this from the force perspective, not energy or momentum.

The ball, on hitting the ground, gets deformed, and being elastic, exerts some force on the ground to get back to its original state. Hence, the ground provides a normal reaction greater than the weight, which gives the ball an upward acceleration causing it to bounce back up.

However, what compresses the ball in the first place ? There is some stress acting on the ball, but where does it originate ?

I like to think of it as, the lower surface of the ball comes to rest first, while the center of mass keeps moving due to inertia. This creates the stress, that deaccelerates the center of mass, till it comes to a halt. Is this the source of the compression stress ? I'm not sure.

There seems to be another explanation : when the ball drops on the ground, even when the reaction matches the weight, the ball has a downward velocity. Hence the ground must provide a force greater than the weight, to stop this velocity. This weight compresses the ball, which tries to retain its shape, and thus apply a greater force on the ground, which in turn leads to greater reaction and more compression until the ball stops. At this point, this total reaction accelerates it backwards i.e. upwards.

Are these two explanations equivalent ? If not, what is the correct explanation ? From a purely force perspective, where does the compressive stress originate. If I consider the ball to be something like a mass on a spring, that suggests the first explanation is correct.

I think the the second explanation is needlessly convoluted, and that the first explanation is the correct one. It is the inertia and the acceleration of the top of the ball relative to the lower half, that creates the compression, that ultimately increases the normal reaction, causing the ball to bounce back up.

Is this correct ?

• A series of photographs which may be of interest in the post What work is done by the wall when a ball hits it? Commented Aug 26, 2021 at 7:34
• @Farcher thanks a lot for this. So, it is a combination of the internal forces and the initial reaction force that compresses the ball. Then the ball tries to become normal again, by exerting a force on the wall. This increases the reaction force, making the ball accelerate backward. My question was regarding the cause and effect. Does the ball get compressed first and then increase the reaction force, or does the reaction force increase immediately causing ball to compress. I think its the former. Please verify ? Commented Aug 26, 2021 at 7:44