AP® Physics 1: Algebra-Based · Unit 2 · Topic 2.5
Elevators and Apparent Weight
Apparent weight is just the normal force a scale reads, and that force changes whenever you accelerate. In an elevator, speeding up or slowing down makes you feel heavier or lighter than your actual weight, which only depends on gravity.
A bathroom scale cannot measure gravity directly. It measures the normal force pushing up on you, and that is what you feel as your weight. When you stand still, the normal force exactly balances gravity, so the scale reads your actual weight. But the moment you accelerate, Newton's second law says the net force on you must match ma, so the normal force has to shift away from mg to make that happen.
Write the equation for a rider on a scale, taking up as positive: N - mg = ma, so N = mg + ma. If the elevator accelerates upward, a is positive, and N is bigger than mg, you feel heavy. If the elevator accelerates downward, a is negative, and N is smaller than mg, you feel light. Notice that velocity never appears in this equation. Only acceleration changes the reading, which is why the long stretch of steady-speed travel feels completely normal: a = 0 means N = mg, no matter how fast you are actually moving.
This topic is the clearest real-world use of Newton's second law applied vertically, and it sets up free fall as a limiting case. If the cable snaps, the elevator and rider both fall with a = -g, so N = mg + m(-g) = 0. The scale reads zero. This is apparent weightlessness: gravity is still fully acting, but nothing is pressing the rider against the floor anymore, since floor and rider accelerate together.
Key terms
- Apparent weight
- The normal force a scale reads, which can differ from actual weight when accelerating.
- Actual weight
- The gravitational force on an object, equal to mg, unaffected by acceleration.
- Normal force
- The contact force a surface exerts perpendicular to itself, here provided by the scale or floor.
- Free fall
- Motion under gravity alone, with acceleration equal to g, producing zero apparent weight.
Watch it explained
- How it worksHow does the scale reading track the normal force rather than your actual weight?
- Worked exampleFind the scale reading for a 60 kg rider in an elevator accelerating up at 2 m/s squared.
- Common mistakeWhy doesn't a rider feel heavy during the long stretch of an elevator ride at steady speed?
- Going furtherWhat would the scale read if the elevator cable snapped and everything fell freely?
Check yourself
End of topic.