Question

A rock climber hangs freely from a nylon rope that is 14 mlong and has a diameter of 8.4 mm. If the rope stretches 4.7 cm , what is the mass of the climber? Young's modulus for nylon is Y=0.37×10^10 N/m2.

Answer 1

Given that the length of the rope, L = 14 m

Radius of the rope, r = d/2 = 8.4/2 mm = 4.2 mm = 4.2 x 10^-3 m

Stretch in the rope, x = 4.7 cm = 4.7 x 10^-2 m

The expression for the Young's modulus is given as -

Y = Stress / Strain

=> Y = (mg/A)/(x/L)

=> Y = mgL/Ax

=> m = YAx/gL

=> m = Y pi r^2 x/gL

Put the values-

m = [0.37 * 10^10 * pi * (4.2*10^-3)^2 * 4.7 * 10^-2]/(9.8*14) = 70.23 kg

Therefore, the mass of the climber = 70.23 kg (Answer)