You are standing on a bathroom scale in an elevator that is not moving, and the scale reads 500 N. If the elevator were instead moving downward at a constant velocity of 4.50 m/s, what would the scale read?
A) 100 N
B) 450 N
C) 500 N
D) 750 N
E) 250 N

Question

Quizplus · Accepted Answer

When the elevator is not moving, the scale reads the normal force exerted by the floor to support your weight, which is equal in magnitude and opposite in direction to your weight. Therefore, your weight is 500 N.

When the elevator is moving downward at a constant velocity, there is no net force acting on you, since the gravitational force and the normal force still cancel each other out. However, since you are now in a non-inertial reference frame (the accelerating elevator), you experience a fictitious force known as the "inertial force" or "pseudo force", which pushes you upward with a magnitude equal to your mass times the acceleration of the elevator (-4.50 m/s^2). This inertial force is what the scale reads as an additional force, so the scale reading will be the sum of the normal force and the inertial force.

Using Newton's second law (F = ma) and assuming your mass is 50 kg, we can calculate the magnitude of the inertial force:

F_inertial = m * a = 50 * (-4.50) = -225 N

Note that the negative sign indicates that the inertial force is directed upward (opposite to the direction of the elevator's motion).

Therefore, the scale reading when the elevator is moving downward at a constant velocity of 4.50 m/s is:

F_scale = F_weight + F_inertial = 500 + (-225) = 275 N

This is less than the scale reading when the elevator is not moving, but it is still larger than some of the answer choices, so the correct answer is C) 500 N.

You Are Standing on a Bathroom Scale in an Elevator