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Problem 4: A cable has an un-stretched length of 12 m and it stretches by 1.2 × 10-4 m when a stress of 6.4 × 108 Nm-2 is applied. What is the strain energy per unit volume in the cable when this stress is applied?

Solution

Given    Length o the cable, L = 12 m                       

Stretching, ΔL = 1.2 × 10-4 m

Stress = 6.4 × 108 N m-2

Asked   Strain energy, u

Formula               u = ½ (stress × strain)

Now stress is given, however, we should find the strain. We know that strain = ΔL/L. Put the given values,

Now put values in the formula to get the strain energy.

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