Calculate the strain energy per unit volume in a brass wire of length 3 m and area of cross-section 0.6 mm^2 when it is stretched by 3 mm
Calculate the strain energy per unit volume in a brass wire of length 3 m and area of cross-section 0.6 mm2 when it is stretched by 3 mm and a force of 6 kg-wt is applied to its free end.
1 Answers
Given: L = 3 m, F = 6 kg wt = 6 × 9.8N = 58.8N, A = 0.6 mm2 = 0.6 × 10-6 m2, = 3 mm = 3 × 10-3 m
To find: Strain energy per unit volume (u)
Formulae:
i. Stress = \(\frac{F}{A}\)
ii. Strain = \(\frac{l}{L}\)
iii. u = \(\frac{1}{2}\) × Stress × Strain
Calculation:
From formula (i),
Stress = \(\frac{F}{A}=\frac{58.8}{0.6\times10^{-6}}\) = 98 × 106 N/m2
From formula (ii),
Strain = \(\frac{l}{L}=\frac{3\times10^{-3}}{3}\) = 10-3
From formula (iii),
u = \(\frac{1}{2}\) × Stress × Strain
= \(\frac{1}{2}\) × 98 × 106 × 10-3
u = 49 × 103 J/m3
Strain energy per unit volume in the brass wire is 49 × 103 J/m3