Tensile stress and strain: What is the maximum length of a metal cable that can hang vertically supported from one end of the cable? The Young's modulus of this metal is 2.10 × 10¹¹ N/m², its tensile strength (the maximum tensile stress it can support without breaking) is 7.40 × 10⁸ N/m², and its density is 7.60 × 10³ kg/m³. A) 9.94 km B) 4.22 km C) 456 km D) 1.75 km E) 24.8 km

Question

Quizplus · Accepted Answer

The maximum length of the cable is determined by the tensile strength and density. Using the formula for tensile stress (σ = ρgh), where ρ is density, g is acceleration due to gravity, and h is height, we solve for h: h = σ / (ρg). Substituting the given values, h = (7.40 × 10^8 N/m^2) / (7.60 × 10^3 kg/m^3 × 9.81 m/s^2) ≈ 9.94 km.

Tensile Stress and Strain: What Is the Maximum Length of a Metal