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The energy stored in a strained wire is: A. 1/2 x stress x strain B. 1/2 x load x extension C. 1/2 x extension x stress D. None

The energy stored in a strained wire is:
A. 1/2 x stress x strain
B. 1/2 x load x extension
C. 1/2 x extension x stress
D. None

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
 Young's modulus , Y = stress/strain.
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

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