Solve this:

​Q11.) What is meant by P$\in$ in a stretched wire  find a relation for it and also determine the elastic P. $\in$ per unit vol of the wire .

 

 

 

Dear Student,

Solution:

When a wire is stretched, some work is done against the internal restoring forces acting between particles of the wire. This work done appears as elastic potential energy in the wire.

Consider a wire of length l and area of cross section a. Let F be the stretching forces applied on the wire and Δl be the increase in length of the wire.

Initially, the internal restoring force was zero but when length is increased by Δl ,

the internal force for an increase in length Δl of the wire

= (0 + F)/2 = F/2

Hence, work done on the wire, w = average force × increase in length = [F/2 ] × Δl

This is stored as elastic potential energy U in the wire.

∴ U = (1/2) × F × Δl = (1/2) × F/a × Δl/l × al

= (1/2)(stress) × (strain) × volume of the wire

∴ elastic potential energy per unit volume of the wire

u = (1/2)(stress) × (strain) = (1/2) (Young’s modulus × strain) × strain

( Young’s modulus = stress / strain)

∴ u = (1/2) (young’s modulus ) × (strain)^2


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