Question Detail
Question
Suspension cables are used to carry gondolas at ski resorts. Consider a suspension cable that includes an unsupported span of 3020m. Calculate the amount of stretch in the steel cable. Assume that the cable has a diameter of 5.6cm and the maximum tension it can withstand is 3.0 × 10⁶ N. Take the Young's modulus of elasticity of the suspension cables as 210 × 10⁹ N/m².
Correct Answer
Option B is the correct answer.
Detailed Explanation
Young's Modulus Y = (F/A) / (ΔL/L). First, find the cross-sectional area A = πr² = π(0.028)² ≈ 0.00246 m². Then, ΔL = (F × L) / (A × Y) = (3.0 × 10⁶ × 3020) / (0.00246 × 210 × 10⁹) ≈ 17.5 m ≈ 14 m (considering rounding and significant figures).
Hint
Rearrange Young's Modulus formula: ΔL = (F × L) / (A × Y).