Chapter 14, Problem 41A

To determine

To Describe: The process through which potential energy can be determined.

Explanation of Solution

Introduction:

Potential energy in a spring is equal to one-half times the product of the spring constant and the square of the displacement.

The force versus displacement graph of a spring is linear. The base of the triangle formed by the graph is x , which represents the displacement, and the height of the triangle is the force, which according to the Hooke’s law is $kx$ . Work done is being represented by the area under the graph and is equal to $\frac{1}{2}k{x}^2$ . This area is found to be same as the elastic potential energy that is stored in the spring as a result of this work.

Therefore, the potential energy in a spring can be determined form the area under the curve of a force versus displacement graph.

Conclusion:

Hence, the potential energy in a spring can be determined form the area under the curve of a force versus displacement graph.