A composite wire of uniform diameter 3mm

Asked by admin @ 10/08/2021 in Physics viewed by 1391 People

A composite wire of uniform diameter 30mm

consisting of a copper wire of length 2.2m anda steel wire of length 1.6m stretches undera load by 0.7 mm calculate the loadGiven that young modules of copper is1:1X10" Pascal for the steel 2.0 x 10 Pascal

Answered by admin @ 10/08/2021

The load on the copper and steel wire is 176.8 N

Explanation:

Given data:

Radius "r" = 3 /2 = 1.5 mm = 1.5×10^−3 m

Length of copper wire = 2.2 m

Length of steel wire = 1.6 m

Young modules of copper = 1.1 x 10^11 Pa

Young modules of steel = 2.0×10^11 Pa

Since area of cross-section A of each wire is same, hence stress is same of both wires.

Stress F / A = y × strain = YΔl / l

As stress on copper wire = stress on steel wire

Ycu . Δlcu / lcu= Ysteel . Δlsteel / lsteel

Δlcu / Δlsteel = Ysteel × Icu / Ycu × lsteel

= (2.0×1011)×2.2 / (1.1×1011×1.6) = 2.5

As Δl cu - Δsteel = 0.7×10^−3

2.5 Δl steel + Δl steel = 0.7×10^−3

Δl steel = 0.7×10^−3 / 3.5 = 2.0×10^−4 m

and Δl cu = 2.5×2.0×10^−4 = 5.0×10^−4 m

Load F= A . Ycu × Δlcu / lcu = πr^2×Δlcu / Icu

= 22 / 7 × (1.5×10^−3)^2×(1.1×10^11)×5.0×10^−4 / 2.2

= 176.8 N

Thus the load on the copper and steel wire is 176.8 N

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