question_answer

If S is the stress and \[\Upsilon \] is Young's modulus of the material of a wire, what is the energy stored in the wire per unit volume in terms of S and \[\Upsilon \]?                                     

Answer:

                Elastic potential energy stored per unit volume                 \[u=\frac{1}{2}\text{Stress }\!\!\times\!\!\text{ Strain}=\frac{1}{2}\times \text{Stress}\times \frac{\text{Stress}}{\Upsilon }=\frac{{{S}^{2}}}{2\Upsilon }\]