Question

a lunch delivery person delivering to customers in a large skyscraper rides to and from the various floors on an elevator. during those elevator rides the magnitude of the force pushing up on her feet by the elevator floor is bigger than the force pushing down on the floor by her feet.
a when the elevator is moving upward and gaining speed.
b when the elevator is moving upward but losing speed.
c when the elevator is moving upward at constant speed.
d when the elevator is moving down with increasing speed.
e never. these two forces are always equal in magnitude.

Explanation:

To solve this, we use Newton's third law (action - reaction forces) and Newton's second law (net force and acceleration). The force of the elevator floor pushing up on the feet (normal force, \(F_N\)) and the force of the feet pushing down on the floor (action - reaction pair) are always equal in magnitude according to Newton's third law, regardless of the elevator's motion (whether it's accelerating, decelerating, or moving at a constant speed). This is because Newton's third law states that for every action, there is an equal and opposite reaction. The motion of the elevator (acceleration or constant speed) affects the net force on the person (related to \(F_N\) and weight \(mg\) by \(F_{net}=F_N - mg=ma\)), but the action - reaction pair (floor - foot forces) are always equal.

Answer:

E. Never. These two forces are always equal in magnitude.