A steel wire and a copper wire, both possessing equal length and equal cross-sectional area, are joined end to end and the combination is subjected to a tension. Determine the ratio of the stress developed in the steel wire to the stress developed in the copper wire. Let Y of steel = 2 10¹¹ N/m ^2 and Y of copper = 1.3 10¹¹ N/m ^2 .

Step-by-step solution

Stress is defined as the internal restoring force per unit area. When the wires are joined end to end and subjected to a tension, they are in a series combination. Therefore, the same force F acts on both the steel and copper wires. It is given that both wires have the same cross-sectional area A . The stress in the steel wire is _ s = F A . The stress in the copper wire is _ c = F A . The ratio of the stress developed in the steel wire to that in the copper wire is _ s _ c = F/A F/A = 1 .