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Question

A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of (a) the stresses developed in the two wires and (b) the strains developed. Y of steel = 2×1011Nm2. Y of copper = 1.3×1011Nm2.


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Solution

Given that, Lsteel=LCu

and Asteel=ACu

(a)stress of CuStress of Steel=FCu ASteelACuFSteel

=FCuFSteel=1 [because FCu=FPSteel]

(b) Strain=Δ LSteelΔL Cu

=FSteelLSteel AcuYcuASteelYSteelFcuIcu

[Lcu=LSteel:Acu=ASteel]

YcuYSteel=1.3×10112×1011

ΔLSteelΔIcu=1320

ΔLcuΔLSteel=2013


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