Obtain an expression for potential energy of a spring

Asked by admin @ 20/08/2021 in Physics viewed by 300 People

Derive the expression for the potential energy stored in a spring?

CLASS - XI PHYSICS (Work, Energy and Power)

Answered by admin @ 20/08/2021

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:

$W = \int\limits^L_0 {F .} \, ds = \int\limits^L_0 {( k x)} \, dx,\ \ \ \ as\ displacement\ s= x\\ \\ W = k\int\limits^L_0 {x} \, dx = \frac{1}{2}k [x^2 ]_0^L = \frac{1}{2}k\ L^2 =\frac{1}{2}k x^2\\$ 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.

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