ELEVATOR APPARENT WEIGHT

The key insight is that the scale does not directly measure weight — it measures the normal force it must exert to keep the person in contact with its surface. When the elevator accelerates upward, the scale has to do two jobs at once: support the person against gravity, and provide the extra push upward to accelerate them. Step 1: The person's true weight is W = mg = 70 × 9.807 ≈ 686.5 N. This is the downward gravitational pull that never changes regardless of what the elevator does. Step 2: For the person to accelerate upward at 2.5 m/s², Newton's second law requires a net upward force of F_net = ma = 70 × 2.5 = 175 N. Step 3: Drawing a free-body diagram for the person, two forces act: gravity W downward, and normal force N upward. The net force is N − W = F_net (upward positive). Solving: N = W + F_net = 686.5 + 175 = 861.5 N. The result makes intuitive sense: you feel heavier in a rising elevator, and you feel lighter when it brakes. If the elevator were in free fall (a = −g downward), the normal force would be zero and you would be weightless. The apparent weight is N = m(g + a), where a is positive upward.