Question

Steel wire rope is used to lift a heavy object. We use a 3.1m steel wire that is 6.0mm in diameter and lift a 1.7x103 kg object. Then, the wire elongates 0.17m. Calculate the Young’s modulus for the rope material.

Answer 1

Explanations & Calculations

• For the elongation, it bears as it supports the weight, the standards equation could be applied.

• The area of the wire,

$\qquad\qquad \begin{aligned} \small A&=\small \pi\,(3.0\times 10^{-3}m)^2=2.82\times10^{-5}m^2 \end{aligned}$

• Stress,

$\qquad\qquad \begin{aligned} \small \sigma&=\small \frac{F}{A}\\ &=\small \frac{1.7\times10^3kg\times9.8ms^{-2}}{2.82\times10^{-5}m^2}\\ &=\small 5.9\times10^8Pa \end{aligned}$

• Strain,

$\qquad\qquad \begin{aligned} \small \epsilon&=\small \frac{0.17m}{3.10m}=0.05 \end{aligned}$

• Then the Young''s modulus is,

$\qquad\qquad \begin{aligned} \small \sigma&=\small Y.\epsilon \\ \small Y&=\small \frac{5.9\times10^8Pa}{0.05}\\ &=\small \bold{1.18\times10^{10}\,Pa} \end{aligned}$