# Derive the expression for the potential energy stored in a spring? CLASS - XI PHYSICS (Work, Energy and Power)

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2014-10-10T21:01:56+05:30
The extension produced x is directly proportional to the force applied to extend or compress the spring. F=kx were k is spring constant. The work done to stretch or compress the spring is stored as its PE W= integral 0 to x (Fdx) =0 to x (kxdx) =1/2 kx^2
2014-10-11T01:54:05+05:30

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The characteristic of a spring is that the force needed to stretch or compress a spring by an amount x is equal to k x and is in the direction opposite to the extension or compression. Here k is called the spring constant.

Restoration Force of the spring (compression or tensile) Fs = - k x  = - external force F

Work done by the external force in compressing the spring from x = 0 to x = L can be obtained by:

is the energy given by the external force to the spring with an extension x.

This energy is stored as potential energy in the spring.