Answer to Question #267818 in Physics for Melly

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).