Question

A composite wire of uniform diameter 30mm
consisting of a copper wire of length 2.2m and
a steel wire of length 1.6m stretches under
a load by 0.7 mm calculate the load
Given that young modules of copper is
1:1X10" Pascal for the steel 2.0 x 10 Pascal​

Answer 1

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

OR

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

Also learn more

A uniform wire of steel of length 2.5m and density 8.0g/cm³ weighs 50g. When stretched by a force of 10kgf the length increases by 2mm. Calculate Young's modulus of steel. ?

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