Physics - Elasticity Question with Solution | TestHub

The elastic potential energy stored per unit volume (energy density) in a stretched wire is given by the formula:$$U=\frac{1}{2}\times \text{Stress}\times \text{Strain}$$ Since Stress $=Y\times \text{Strain}$ (Hooke's Law), substituting Stress $=Yϵ$ into the energy density formula gives:$$U=\frac{1}{2}(Yϵ)ϵ=\frac{1}{2}Y{ϵ}^2$$