A cable has an un-stretched length of 12 m and it stretches by 1.2 ｘ 10⁻⁴ m when a stress of 6.4 ｘ 10⁸ Nm⁻² is applied. What is the strain energy per unit volume in the cable when this stress is applied? Answer (3.2 ｘ 10³  Jm⁻³) 



Given Data:

Length of un-stretched cable = L =  12 m 

Change in Length = ΔL = 1.2ｘ10⁻⁴ m

Stress =  6.4ｘ10⁸ N m⁻²


To Find:

Strain Energy per unit Volume = ?



Solution:


Strain Energy per unit Volume can be calculated as

Strain Energy per unit Volume = `\frac{1}{2}`ｘ Stress ｘ strain

Strain Energy per unit Volume = `\frac{1}{2}` ｘ Stressｘ `\frac{ΔL}{L}`

by putting values

Strain Energy per unit Volume = `\frac{1}{2}` ｘ 6.4ｘ10⁸ N m⁻² ｘ `\frac{1.2ｘ10⁻⁴ m}{12 m}`

Strain Energy per unit Volume = `\frac{7.68 ｘ10⁴ N m⁻² }{24}`


Strain Energy per unit Volume = 0.32 ｘ10⁴ N m⁻² 


Strain Energy per unit Volume = 3.2 ｘ10³ J m⁻³ -------Ans.

 


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