Final answer:
The scale reading in an elevator is F = m(g + a) when accelerating upward, F = m(g - a) when accelerating downward, and Fs = mg when at constant velocity or stationary.
Step-by-step explanation:
The expression for the scale reading in an elevator cab during vertical motion is F = m(g + a) when the elevator is accelerating upward, and F = m(g - a) when it is accelerating downward. At a constant velocity, whether upward, downward, or stationary, the acceleration is zero (a = 0), and thus the scale reading Fs equals the gravitational force (mg), which is the weight of the person or object on the scale.
For instance, if the elevator is accelerating upward, you feel heavier, and the scale shows a reading greater than your actual weight. Conversely, if the elevator accelerates downward, you feel lighter, and the scale reading decreases. When the elevator is in free fall, which means accelerating downward at g, the scale reading will be zero, and you will experience weightlessness.