Question

obtain an expression for strain energy In a strained wire....


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Answer 1

Answer:

0+F/2 = F/2

U=1/2 ×F/A×L/l×Al

U=1/2×stress×strain ×volume

U=1/2×stress×strain ×strain

U=1/2×stress×(strain)2

U=1/2×young modules of elasticity ×(strain)2

Answer 2

Answer:

Hi mate.

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.

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.

Hope it helps you mate.

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