One end of a nylon rope of length 4.5 m and diameter 6 mm is fixed to a tree limb. A monkey weighing 100 N jumps to catch the free end and stays there. Find the elongation of the rope and the corresponding change in the diameter. Young modulus of nylon =`4.8xx10^11Nm^(-2)` and poisson ratio of nylon =`0.2`.

Explanation

As the monkey stays in equilibrium the tension in the rope equals the weight of the monkey. Hence,
`Y=stress/strain =(T/A)/(l/L)`
`=or l=(TL)/(AY)`
or elongation `=((100N)xx(4.5m))/((pixx9xx10^-6)xx(4.8xx10^11Nm^-2))`
`=3.32xx10^-5m`
`Again poisson ratio `=(/_\d/d)/(l/L)=((/_\d)L)/(ld)`
or `0.2 =(/_\dxx4.5m)/((3.32xx10^-5m)xx(6x10^-3m))`
or /_\d=(0.2x6xx3.32xx10^-8)/4.5`
`=8.8xx10^-9m`