Can a Floor Do Work? The Deceptive Physics of a Bouncing Ball

The best physics questions have layers (like onions and ogres). Here’s the original question (then we will spice it up).

A ball has a mass of 0.1 kilograms and is dropped 1 meter above a floor. The ball bounces and returns to the original height. What was the work done by the gravitational force?

OK, let’s do a quick work-energy review.

Work-Energy Principle

One way we can model the motion of an object is to use work and energy. In short, we pick a system and look at the energy input (or output) of this system along with the changes in energy of the system. Let’s start with the definition of work. It’s basically a force (F) applied over some distance (Δr).

This uses the vector dot product. It operates two vectors and returns a scalar. It’s basically the projection of one vector onto the other. We have the option of using the magnitude of the force and displacement vectors along with the cosine of the angle (θ) between the two vectors.

For the change in energy (ΔE), the types of energy depends on the choice of system. If the system is just a point particle (like a ball with no dimensions) then there is really on one type of energy — kinetic energy (K).