The Physics of Jumping: From Humans to The Hulk
This is a great physics problem. Let’s use the work-energy principle to look at the forces on a jumping human. As the title says, after that I’m going to do the same thing except with The Hulk. Hulk smash.
The best thing about using a jumping human example is that we can see two different ways to use the work-energy principle (adapted from the best intro physics textbook — Matter and Interactions, Chabay and Sherwood)
Work-Energy Principle
The work-energy principle basically says that the work done on an on object is equal to its change in energy. Yes, that’s basically just repeating the title “work-energy”. We need to break this down (and then consider what we mean by “object”).
We can define work as a force (F) applied over a displacement (Δr).
Yes, that’s a dot product since work (W) is a scalar and F and Δr are vectors. Don’t worry — we are just going to deal with simple cases of work. This work changes the energy of system. Yes, the “system” is very important. We have a couple of options for the system. First, there is the point-particle system. This assumes the object is just a point mass. In that case, it can only have kinetic energy (K) which we define as:
