Chapter 16, Problem 1CQ

Describe a system in which elastic potential energy is stored.

To determine

To describe: The system in which elastic potential energy is stored.

Explanation of Solution

Introduction:

When particle is displaced from its equilibrium position, then the work done against the restoring force is stored as the elastic potential energy of the particle.

When the displacement of a particle from its equilibrium position is x, then the restoring force acting on that particle is given by

$F=-kx$

If we displace particle further through small distance dx, then work done against the restoring force is given by,

$dW=-Fdx$$dW=+kxdx$

The total work done in moving the particle from mean position (x=0) to displacement x is given by,

  $W={\displaystyle \int dW}$$W={\displaystyle \underset{0}{\overset{x}{\int }}kxdx}$$W=k{\frac{x}{2}}^2$

This work done is stored in the form of elastic potential energy.

$U=\frac{1}{2}k{x}^2$

Conclusion:

So, whenever particle is displaced from its equilibrium position then work done for such a system against restoring force is always stored as an elastic potential energy.