Vikas TU
Last Activity: 5 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