how does pressure relate to elastic potential energy?

Answer 1

The easiest example of elastic potential energy is a spring. Stored energy is force times distance.

Imagine replacing a compression spring with a balloon. The applied force increases the pressure inside the balloon. Do the same thing, but with a piston of known diameter. We can now write the relationship between the applied force and the pressure on the face of the piston: P = F/A (pressure = force / area