Question

How to find the sum of the forces in the y direction of an elevator?

Answer 1

The way to calculate the sum of the forces in the y direction of an elevator; has been outlined below

Equilibrium of Forces

If you are in an elevator by itself, then the combined system of you and the elevator could have 3 possible situations which are;

• The elevator has no acceleration because it is standing still or moving with constant velocity.

• The elevator has an upward acceleration because it is accelerating upward, or decelerating while it's way down.

• The elevator has a downward acceleration since it is accelerating down, or decelerating while on the way up.

Now, in the vertical y direction, there are three forces namely;

• The force of gravity.
• A downward normal force.
• An upward force from the tension in the cable holding the elevator.

Thus, the sum of forces in the y-direction with the normal force acting on you from the elevator are any of the following;

N = mg;  provided that the elevator is at rest or moving at constant velocity.

N = mg + ma; Provided that the elevator has an upward acceleration.

N = mg - ma; Provided that the elevator has a downward acceleration.

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