Elastic Potential Energy per Unit Volume – Rankers Physics
Topic: Solid and Fluids
Subtopic: Solids

Elastic Potential Energy per Unit Volume

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length \(100\text{ cm}\) to stretch it by \(1\text{ mm}\) is (if Young's modulus of the wire \(= 2.0 \times 10^{11}\text{ N m}^{-2}\) )
\(10^7\)
\(10^5\)
\(10^{11}\)
\(10^{17}\)

Solution:

Energy per unit volume is \(u = \frac{1}{2} \times Y \times (\text{strain})^2\). Strain \(= \frac{Delta l}{l} = \frac{10^{-3}\text{ m}}{1\text{ m}} = 10^{-3}\). Thus, \(u = \frac{1}{2} \times (2.0 \times 10^{11}) \times (10^{-3})^2 = 10^5\text{ J/m}^3\).

Leave a Reply

Your email address will not be published. Required fields are marked *