Understanding Apparent Weight in Accelerating Elevators
Have you ever experienced a sudden heaviness in your stomach when an elevator quickly starts rising, or a brief floating sensation as it slows down near your floor? These familiar sensations stem from fundamental principles of classical mechanics governed by Sir Isaac Newton’s laws of motion. When you stand inside an elevator, a scale under your feet measures the contact force supporting you—known as the normal force—rather than directly measuring Earth’s gravitational force upon your body.
Real Weight vs. Apparent Weight
Your true gravitational weight remains constant near the Earth's surface and is calculated as $W = mg$, where $m$ represents mass and $g$ represents gravitational acceleration. However, the apparent weight is the normal force exerted by the elevator floor pushing upward against you. When the elevator remains stationary or moves at a constant velocity, the net acceleration is zero ($a = 0$), meaning normal force balances gravitational force ($N = mg$). Consequently, your apparent weight matches your true weight exactly.
Dynamics of Upward Acceleration
When an elevator ascends and accelerates upward, it must exert an additional force to change your velocity. According to Newton's second law ($\sum F = ma$), the upward normal force must exceed the downward gravitational pull. Rearranging the equation yields $N = m(g + a)$. Because the acceleration value adds directly to gravity, the normal force increases, causing a weighing scale to register a higher value. Conversely, when a rising elevator approaches its destination floor, it must decelerate. This downward acceleration vector reduces the required normal force to $N = m(g - a)$, resulting in a lower scale reading and a temporary feeling of lightness.