For climbing the Sawatch range of Rocky mountains you used a 50-m nylon rope of 10 mm diameter.You noticed the rope elongated by 1.50 m when it supported your 65-kg mass on one end.The Young's modulus of the rope material is A)54 * 10⁶ N/m². B)112 * 10⁶ N/m². C)271 * 10⁶ N/m². D)356 * 10⁶ N/m². E)980 * 10⁶ N/m².

Question

Quizplus · Accepted Answer

The elongation of the rope can be calculated using the formula:

ΔL = FL/EA

where ΔL is the elongation, F is the force applied (weight of the climber), L is the length of the rope, E is the Young's modulus, and A is the cross-sectional area of the rope.

In this case, ΔL = 1.50 m, F = 65 kg × 9.81 m/s² = 637.65 N, L = 50 m, and A = π(10 mm/2)² = 78.54 × 10⁻⁶ m². Substituting these values into the formula and solving for E, we get:

E = FL/(ΔL × A) = 637.65 N × 50 m/(1.50 m × 78.54 × 10⁻⁶ m²) ≈ 271 × 10⁹ N/m²

Therefore, the best choice is C.

For Climbing the Sawatch Range of Rocky Mountains You Used