Final answer:
The normal force exerted by the elevator on a person will be greater than their weight when the elevator is accelerating upward. This is because the normal force has to counteract the person's weight and provide the additional force for upward acceleration. Once the elevator achieves constant velocity, the normal force equals the person's weight, as there is no more acceleration.
Step-by-step explanation:
The question concerns a person standing in an elevator that is accelerating upward, and we are to discuss the normal force exerted by the elevator floor on the person. In the context of physics, particularly Newton's laws of motion, the normal force is defined as the force exerted by a surface that supports the weight of an object resting on it. When an elevator accelerates upward, the normal force (n) must not only balance the weight of the person (w), but also provide the additional force required for the upward acceleration.
If we apply Newton's second law, which states that the sum of the forces is equal to the mass times the acceleration (F = ma), we can determine the scale reading. In the accelerating elevator, the force from the scale (Fs) will be the weight of the person plus the additional force needed to accelerate that person upwards. Thus, the figure (a) and (b) along with the free-body diagram and Newton's laws analysis indicates that the scale reading would be greater than the person's regular weight on the surface of the earth when the elevator is accelerating upwards.
However, once the elevator achieves a constant velocity, whether moving upward, downward, or stationary, the acceleration is zero (a = 0), and the scale would read the actual weight of the person, as there is no longer a need for additional force to change the velocity.