Question

A lift contains a person of mass 70kg. The lift itself has mass 500kg. The tension in the cable holding the lift is 6000N.
a) what is the acceleration?
b) is the lift moving up or down?
c) What is the reaction force of the lift on the person?

Answer 1

You have 6,000 N of force pulling upward from the cable. You have 9.81 m/s^2 (70 kg + 500 kg) = 5591.7 N of weight pulling down.The net force is 6000 - 5591.7 = 408.3 N. There is more force pulling up, so we know the lift is moving up (because 6000 > 5591.7).

We know F = ma. The net upward force we found to be 408.3 N. Total mass is 500 + 70 = 570 kg. So acceleration is F/m = 408.3/570 = 0.7163 m/s^2 upward.

Reaction force of lift on person: We know everything is accelerating up at 0.7163 m/s^2. We also know gravity has acceleration of 9.81 m/s^2. Total acceleration is 0.7163 + 9.81 = 10.5263 m/s^2. Remember F = ma, so F = 70 kg * 10.5263 m/s^2 = 736.8 N of force.

Hopefully I didn't make any math mistakes.