Question

A steel wire-of diameter 1 x 10^-3m is stretched by a force of 20 N. Calculate the strain energy per unit volume.(Y steel= 2 x 1011 N /m²)

Answer 1

D = 1 x 10^-3 m
∴ r = 5 x 10^-4 m

A = πr² = 3.14 x ( 5 x 10^-4 )²
F = 20 N, Y = 2 x 10¹¹ N/m²

Now,             
u = `1/2 xx "stress" xx "strain"`

    = `1/2 xx ("stress")^2/"Y"`

⇒ u = `1/2 F^2/(A^2y)`

u = `1/2[20/[3.14 xx ( 5 xx 10^-4)]^2^2 xx 1/[2 xx 10^11]]`

u = 1621 Joule