In which of the following cases will the normal force on a box be the greatest? a. when the box is placed in a stationary elevator b. when the box is placed in an elevator moving upwards at constant velocity c. when the box is placed in an elevator accelerating downward d. when the box is placed in an elevator accelerating upward

 D. When the box is placed in an elevator accelerating upward

Explanation:

Looking at the answer choices, we know that we want to find out how the normal force varies with the motion of the box. In all cases listed in the answer choices, there are two forces acting on the box: the normal force and the force of gravity. These two act in opposite directions: the normal force, N, in the upward direction and gravity, mg, in the downward direction. Taking the upward direction to be positive, we can express the net force on the box as N - mg.

From Newton's Second Law, this is also equal to ma, where a is the acceleration of the box (again with the upward direction being positive). For answer choices (A) and (B), the net acceleration of the box is zero, so N = mg. We can see how the acceleration of the elevator (and, hence, of the box) affects the normal force. The larger the acceleration (in the positive, i.e., upward, direction), the larger the normal force is to preserve the equality: N - mg = ma, N = ma+ mg. Answer choice (D), in which the elevator is accelerating upward, results in the greatest normal force, since in that case the magnitude of the normal force is greater than gravity by the amount ma.