Question

b) For safety in climbing, a mountaineer uses a nylon rope that is 50 m long and 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6m. Find its Young's modulus.​

Answer 1

72 it’s young’s module

Answer 2

The Young's modulus of the nylon rope is approximately 3.92 x 10^4 N/m^2.

Step-by-step explanation:

We can use the formula:

Young's modulus = Stress / Strain

where:

Stress = Force / Area

Strain = Elongation / Original length

Calculate the stress:

Force = Weight of climber = 90 kg * 9.81 m/s^2 = 882.9 N

Area = π * (diameter/2)^2 = π * (0.01 m/2)^2 = 7.85 x 10^-5 m^2

Stress = 882.9 N / 7.85 x 10^-5 m^2 = 1.12 x 10^7 N/m^2

Calculate the strain:

Strain = Elongation / Original length = 1.6 m / 50 m = 0.032

Calculate Young's modulus:

Young's modulus = 1.12 x 10^7 N/m^2 / 0.032 = 3.92 x 10^4 N/m^2

Therefore, the Young's modulus of the nylon rope is approximately 3.92 x 10^4 N/m^2. This value indicates that the rope is relatively elastic and able to withstand significant deformation without breaking, ensuring safety for the climber.