Question

Dirivation for potential energy for spring

Answer 1

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.