Question

A person hangs from a nylon rope (Young's modulus of 5 x 109 N/m2) as seen in the picture below. The rope stretches by 2 % and has a diameter of 0.03 m. What mass does the person have to stretch the rope by this amount? (The answer may not be realistic!)

Answer 1

Answer:

959183.7 kg  

Explanation:

from the question we have :

young modulus = 5 x 10^{9} N/m^{2}

strain = 2% = 2÷100 = 0.02

diameter = 0.03 m

radius = 0.015 m

acceleration due to gravity (g) = 9.8 m/s^{2}

we can get the mass from the formula below

young modulus = stress ÷ strain

where

stress = \frac[force}{area} = \frac {mass x g}{area}

area = 2πr = 2π x 0.015 = 0.094

therefore    

young modulus = \frac{\frac {mass x g}{area}}{strain}

 5 x 10^{9}  =  \frac{\frac {mass x 9.8}{0.094}}{0.02}

mass =  \frac{5 x 10^{9} x 0.02 x 0.094}{9.8}

mass = 959183.7 kg