Question

Explain the concept of elastic potential energy in a stretched wire and hence obtain the expression for it.

Answer 1

The work done by external applied force during stretching is stored aspotential energy (U) in the wire and is called as strain energy in the wire. This is an expression for strain energy orpotential energy per unit volume ofstretched wire. This is also called as the energy density of the strained wire. Its S.I.

Answer 2

The concept of elastic potential energy in a stretched wire

Explanation:

When a wire is positioned below a tensile stress, work is done towards the inter-atomic forces. The work is stored withinside the wire in the shape of elastic potential energy".

Expression : Consider a wire of cross section A and of duration L is subjected to a deforming force F alongside the length of the wire. let the length of the wire is elongated via way of means of l.

Young's modulus (y)=FL/Al.

F=yAl/L . . . (1)

Work done due to further elongation of small length dl

Work done (dw)= F× dl =(yAl/L)dl . . . (2)

Total work done is increasing the length of the wire from L to (L + l)

w=$\int\limits^l_0 {yAl/l} \, dl$= yA/2×l²/L

w=1/2×y×(lL)²×Al

=1/2×y×strain²×volume of the wire

w=1/2×stress×strain×volume of the wire

This work is stored int he wire int he form of elastic potential energy (u).

∴ Elastic potential energy per unit volume (u)=12×σε.