Question

Illustrate on the equations of gravitational potential energy and elastic potential energy as the quantities vary, for instance double or triple the value of quantities.

Answer 1

For gravitational potential energy:

$$E=mgh.$$

We see that the potential energy is directly proportional to the height, so, increasing the height h twice (thrice) would increase the energy twice (thrice).

For elastic potential energy:

$$E=\frac12kx^2.$$

The energy is proportional to the second power of extension. So, increasing the extension or compression twice (thrice) would increase the energy 4 times (16 times).