A person of mass 80 kg is inside a lift of mass 920 kg and presses the button on the control panel.

Question

A person of mass 80 kg is inside a lift of mass 920 kg and presses the button on the control panel. The lift starts moving upwards with an acceleration $2.0 \mathrm{~m} / \mathrm{s}^{2}$. If $g=10 \mathrm{~m} \mathrm{s}^{-2}$, the tension in the supporting cable is

Professor PC Thomas Classes · Answer

Mass of person $m=80 \mathrm{~kg}$, mass of lift $M=920 \mathrm{~kg}$. Total mass $M_{total} = 80 + 920 = 1000 \mathrm{~kg}$. Acceleration $a = 2.0 \mathrm{~m/s}^2$ upwards. Tension $T - M_{total}g = M_{total}a \implies T = M_{total}(g + a) = 1000(10 + 2) = 1000 	imes 12 = 12000 \mathrm{~N}$.