Final answer:
In an accelerating elevator, the normal force is greater than the force of gravity, followed by the force due to acceleration. The frictional force is negligible and thus considered the smallest or non-existent in this scenario.
Step-by-step explanation:
When considering the forces acting on a person standing on a bathroom scale in an accelerating elevator, Newton's laws help us understand the magnitude of these forces. As the elevator accelerates upward, the normal force exerted by the scale must be greater than the person's weight (the force of gravity), because it has to support the weight and provide the upward acceleration. Consequently, the normal force is the greatest. The force of gravity remains constant, as it is the weight of the person. The force due to acceleration is the net force required to accelerate the person upward and will depend on the rate of acceleration. In many elevators, frictional force can be considered negligible in this situation, especially if the scale is assumed to be frictionless. Therefore, when ranking these forces while the elevator is accelerating upwards, the normal force would be the largest, followed by the force of gravity, then the force due to acceleration, and finally the frictional force, which could be considered the smallest or non-existent.