Explain why doubling extension more than doubles elastic potential energy.

Doubling the extension of a spring results in more than double the elastic potential energy stored due to the quadratic relationship in the elastic potential energy equation, Ee = 0.5 x k x e². Here, 'k' is the spring constant and 'e' is the extension. When the extension is doubled, the new energy becomes Ee = 0.5 x k x (2e)² = 0.5 x k x 4e², which is four times the original energy. This demonstrates that energy stored in a spring increases with the square of the extension, highlighting the non-linear nature of elastic potential energy in elastic materials.