Elastic potential energy

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The elastic potential energy is defined as a work (force x distance) needed to compress or expand an elastic body. The potential energy of a string or spring of length l that has modulus of elasticity λ under an extension of x is then

E = \frac{\lambda x^2}{2l}

This formula is obtained from the integral of Hooke's law:

U_e = \int {k x}\, dx = \frac {1} {2} k x^2

The equation is often used in calculations of positions of mechanical equilibrium.

Elastic Potential Energy is the kind of energy that is stored in a bow, or in a catapult, or in a spring.

The energy stored = the work done to stretch the bow, so:

Elastic Energy (joules) = Average Force (newtons) x Distance (meters)

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