A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m². What is the elongation of the rod due to this object? A) 1.2 cm B) 0.46 cm C) 0.12 cm D) 1.8 cm E) 0.047 cm

Question

Quizplus · Accepted Answer

The force acting on the rod can be found using F = mg = 1000 * 9.8 = 9800 N. The cross-sectional area of the rod can be found using A = πr^2 = π(0.004)^2 = 5.03 * 10^-5 m^2. The stress on the rod can be found using σ = F/A = 9800/5.03 * 10^-5 = 1.95 * 10^8 N/m^2. The strain on the rod can be found using ε = σ/E = 1.95 * 10^8/210,000,000,000 = 9.29 * 10^-4. The elongation of the rod can be found using ΔL = ε*L = 9.29 * 10^-4 * 5 = 0.00464 m = 0.46 cm. Therefore, the correct answer is B.

A 1000-Kg Object Hangs from the Lower End of a Steel