Question

A copper wire is 1.6 m long and its diameter is 1.1 mm. If the wire hangs vertically, how much weight (in N) must be added to its free end in order to stretch it 2.8 mm?

Answer 1

Answer:

Weight required = 194.51 N

Explanation:

The elongation is given by

            $\Delta L=\frac{PL}{AE}$

Length , L= 1.6 m

Diameter, d = 1.1 mm

Area

   $A=\frac{\pi d^2}{4}=\frac{\pi \times (1.1\times 10^{-3})^2}{4}=9.50\times 10^{-7}m^2$

Change in length, ΔL = 2.8 mm = 0.0028 m

Young's modulus of copper, E = 117 GPa = 117 x 10⁹ Pa

Substituting,

      $\Delta L=\frac{PL}{AE}\\\\0.0028=\frac{P\times 1.6}{9.50\times 10^{-7}\times 117\times 10^9}\\\\P=194.51N$

Weight required = 194.51 N