Question

Find the minimum diameter of an l = 19.1 m long copper wire that will stretch no more than 8.68 mm when a mass of 340 kg is hung on the lower end. (Hint: The Young's modulus of copper is 110.0 GPa.)

Answer 1

If we assume that the resulting change in length results in a negligible change in diameter of the wire, and an extension of 8.68mm is in the elastic region, the relationship is straight forward. \[\sigma = E \epsilon\]where \(\sigma\) is the normal stress, E is Young's modulus, and \(\epsilon\) is the strain.

We know that for a circular cross-section\[\sigma = {F \over A} = {4 mg \over \pi d^2}\]and\[\epsilon = {l - L \over L}\]where l is the final length and L is the original length.

These can be substituted back in and solved for d.