The elastic energy stored in a wire of Young' | vedclass

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(C) When a wire is stretched,work is done against the interatomic forces. This work is stored in the wire in the form of elastic potential energy.The

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$\frac{	ext{Stress}^2 	imes 	ext{Volume}}{2Y}$

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(C) When a wire is stretched,work is done against the interatomic forces. This work is stored in the wire in the form of elastic potential energy.The elastic potential energy $(U)$ per unit volume is given by:$U = \frac{1}{2} 	imes 	ext{stress} 	imes 	ext{strain}$Therefore,the total elastic energy $(W)$ stored in a wire of a given volume is:$W = \frac{1}{2} 	imes 	ext{stress} 	imes 	ext{strain} 	imes 	ext{volume}$From the definition of Young's modulus $(Y)$:$Y = \frac{	ext{stress}}{	ext{strain}} \implies 	ext{strain} = \frac{	ext{stress}}{Y}$Substituting the expression for strain into the energy equation:$W = \frac{1}{2} 	imes 	ext{stress} 	imes \left( \frac{	ext{stress}}{Y} ight) 	imes 	ext{volume}$$W = \frac{	ext{stress}^2 	imes 	ext{volume}}{2Y}$

The elastic energy stored in a wire of Young's modulus $Y$ is

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