Answer :
A 94 kg mountain climber hangs from a rope and stretches it by 33 cm, the Young's modulus for the rope is approximately 1.35 × [tex]10^9[/tex] N/m².
To determine the Young's modulus of the rope:
σ = E * ε
Here it is given that:
Mass of the climber, m = 94 kg
Change in length of the rope, ΔL = 33 cm = 0.33 m
Original length of the rope, L = 38.1 m
Diameter of the rope, d = 1.0 cm = 0.01 m
A = π * (d/2)²
A = π * (0.01 m/2)²
A ≈ 0.00007854 m²
Now,
ε = ΔL / L
ε = 0.33 m / 38.1 m
ε ≈ 0.008662
σ = Weight / A
σ = 921.2 N / 0.00007854 m²
σ ≈ 1.172 × [tex]10^7[/tex] N/m²
Finally,
E = σ / ε
E = (1.172 × [tex]10^7[/tex] N/m²) / 0.008662
E ≈ 1.35 × [tex]10^9[/tex] N/m²
Thus, the Young's modulus for the rope is approximately 1.35 × [tex]10^9[/tex] N/m².
For more details regarding Young's modulus, visit:
https://brainly.com/question/13257353
#SPJ4
