Problem 2: A cable has a length of 12 m and is stretched by 1.2 × 10-4 m when a stress of 8.0 × 108 Nm-2 is applied. What is the strain energy per unit volume in the cable when the stress is applied?

Solution

Given Length of the cable, L = 12 m

Stretching in the cable, Δl = 1.2 × 10^{-4} m

Stress applied = 8.0 × 10^{8} Nm^{-2}

Asked Strain energy per unit volume, u

Formula Strain energy per unit volume, u = ½ (stress × strain)

So we have to find strain first. Now

Put values

Now put the values of stress (given) and the strain (eq 1) in the formula,

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