Question

A rock climber hangs freely from a nylon rope that is 15 m long and has a diameter of 8.3 mm. If the rope stretches 5.1 cm, what is the mass of the climber? Young's modulus for nylon is Y=0.37Ã10^10N/m^2.

Answer 1

Mass of the climber = 69.38 kg

Step-by-step explanation:

Change in length

`\Delta L=(PL)/(AE)`

Load, P = m x 9.81 = 9.81m

Young's modulus, Y = 0.37 x 10¹⁰ N/m²

Area

`A=(\pi (8.3* 10^(-3))^2)/(4)=5.41* 10^(-5)m^2`

Length, L = 15 m

ΔL = 5.1 cm = 0.051 m

Substituting

`0.051=(9.81m* 15)/(5.41* 10^(-5)* 0.37* 10^(10))\\\\m=69.38kg`

Mass of the climber = 69.38 kg