How will the upward force exerted on the feet by the scale compare to a man's weight when the elevator is accelerating downward?

When an elevator accelerates downward, the situation affects how forces are perceived, particularly in relation to weight. Weight is the force exerted by gravity on an object, and in this context, it is the weight of the man.

In a regular scenario, when the elevator is at rest or moving at constant velocity, the upward force exerted by the scale on the feet of the man equals his weight. However, when the elevator begins to accelerate downward, the net force acting on the man changes.

The man still experiences the gravitational force pulling him downward, but the downward acceleration of the elevator effectively reduces the upward force that the scale needs to exert to balance out these forces. This results in the scale reading a value that is less than the man’s actual weight, as the acceleration of the elevator decreases the net force felt by the man.

This phenomenon is consistent with Newton's second law of motion, where the net force is equal to mass times acceleration. If the elevator accelerates downward, the acceleration due to gravity remains constant, but the effective weight (or scale reading) decreases because of the additional downward acceleration. Consequently, the scale will show a force that is less than the man's weight during this downward acceleration.