Accelerated Motion Problem (Elevator)

Question

A person is in an elevator, standing on a scale. The person weighs 600 N (mass of 60 kg).

1. What does the scale read while the elevator is moving at a constant 3.0 m/s downward?

2. What does the scale read when the elevator is accelerating downward at 1.5 m/s^2?

3. What does the scale read when the elevator is accelerating upward at 2.5 m/s2?

4. What would the free body diagrams of the three situations look like?

Answer 1

When the elevator is moving at constant velocity either upward or downward, there is no acceleration acting on the person; so, the scale reads 600N.

When the elevator is moving downward with an acceleration of 1.5 m/s² there is a net force on the person equal to 60kg x 1.5 m/s², so there must be a force opposing the force of gravity (600N) equal to the difference between the force of gravity and the force due to the downward acceleration F = 600N - 60kg x 1.5 m/s³

= 510 N weight.

When the elevator is accelerating upward at 2.5 m/s², there is a net upward force on the person = 60kg x 2.5 m/s² = 90 N. As the force of gravity is downward at 588 N, there must be a force pushing up on the person greater than the gravitational force so that the net upward force is 90 N. This is 588 N + 90 N = 678 N weight.

You should be able to draw the free body diagrams with this information.