Question

An 800N elevator hangs by a steel cable for which the allowable stress is 1.2×10⁸ n/m².What is the minimum diameter required if the elevator accelerates upwards at 1.5m/s²?

Answer 1

$$T=ma+W=\frac{a}{g}W+W\\T=PA=0.25\pi d^2P\\\frac{a}{g}W+W=0.25\pi d^2P\\ \frac{1.5}{9.8}800+800=0.25\pi (1.2\cdot10^{8})d^2\\d=3.1\cdot10^{-3}\ m$$