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Q.Calculate the strain energy per unit volume in a brass wire of length 3 m and area of cross-section 0.6 mm2^2 when it is stretched by 3 mm and a force of 6 kgwt is applied to its free end.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2018Subjective· 3mImportance★★★★★
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Strain energy density is 12×stress×strain\tfrac12\times\text{stress}\times\text{strain}; compute stress and strain from the given force, area, length and extension, then combine.

Given: length L=3L = 3 m, area of cross-section A=0.6 mm2=0.6×10−6 m2A = 0.6\ \text{mm}^2 = 0.6\times10^{-6}\ \text{m}^2, extension x=3 mm=3×10−3x = 3\ \text{mm} = 3\times10^{-3} m, force F=6F = 6 kg wt =6×9.8=58.8= 6\times 9.8 = 58.8 N.

Stress:

Stress=FA=58.80.6×10−6=9.8×107 N/m2.\text{Stress} = \frac{F}{A} = \frac{58.8}{0.6\times10^{-6}} = 9.8\times10^{7}\ \text{N/m}^2.

Strain:

Strain=xL=3×10−33=1×10−3.\text{Strain} = \frac{x}{L} = \frac{3\times10^{-3}}{3} = 1\times10^{-3}.

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