Question

show that Strain energy per unit volume of strained wire 1/2 ( stress) ( strain)​

Answer 1

Answer:

hi Buddy !! here is your answer !!

Young's modulus is the ratio of stress to strain. e.g., Y = stress/strain.

if we assume a wire of length L, area of cross section A is fixed at one end and stretched by suspended a load M from the other end due to this extension of wire is x.

so, Young's modulus of wire , Y = FL/Ax

or, F = YAx/L

we know, workdone , W = F.dx

so, W = (YAx/L)dx

or, W = 1/2 × YAx²/L

W = 1/2 × {YAx/L} × x

W = 1/2 × F × x

hence, Work done = 1/2 × load × extension

now, potential energy = workdone by external applied force

= 1/2 × load × extension.

so, strain energy = 1/2 × load × extension

now, strain energy per unit volume = 1/2 × load × extension/volume

= 1/2 × load × extension/(cross section area × length)

= 1/2 × (load/cross section area) × (extension/length)

= 1/2 × stress × strain

hence, energy per unit volume = 1/2 × stress × strain

I hope it will help you !!

Answer 2

Answer:

We know, Young's modulus is the ratio of stress to strain. e.g., Y = stress/strain. if we assume a wire of length L, area of cross section A is fixed at one end and stretched by suspended a load M from the other end due to this extension of wire is x. = 1/2 × load × extension.

Explanation: