Answer to Question #145405 in Mechanics | Relativity for lexy

Question

You cling to a rope tied to the ceiling of an elevator. (That means you hold on to a rope above you and yourfeet do not touch the oor.)When the elevator accelerates upward at 0.5 meters per second squared, the tension in the rope is 682 N. Whatis your mass? You may assume the rope is massless. Put the answer in kg.

Answer 1

From the diagram,

$T=\textsf{tension in the rope}\\ m=\textsf{mass}\\ g=\textsf{acceleration due to gravity}\\ \textsf{and } a \textsf{ represents the upward acceleration of the elevator} \\\hspace{1cm}\\682N-mg=ma\\ 682N-m×9.81ms^{-2}=m×0.5ms^{-2}\\ 682N=m×0.5ms^{-2}+m×9.81ms^{-2}\\ 682N=m(0.5ms^{-2}+9.81ms^{-2})\\ 682N=m(10.31ms^{-2})\\ m=\frac{682N}{10.31ms^{-2}}\\ m=66.15kg$