Why would a bathroom scale tell you that you've gained weight if you were standing on one in an upwardly accelerating elevator?

Question

BlackTom AI · Accepted Answer

Consider the scenario of standing on a bathroom scale inside an elevator that is accelerating upward. The key idea is apparent weight, which is the normal force the scale exerts on you.
Option 1: 'The scale exerts an upward force greater than usual to move you upward.' This captures the core physics: when the elevator accelerates upward, you need extra upward force to accelerate your mass upward, so the scale must push up harder on your feet. The increased normal force makes the scale read a higher value.
Option 2: 'Your weight increases to resist the upward pushing force of the scale.' In physics terms, your true weight due to gravity does not change with elevator motion; what changes is the apparent weight. The statement anthropomorphizes weight and misattributes the increase to a resistance by your body, which is not the correct mechanism.
Option 3: 'The further from Earth you get, the stronger its gravity gets.' This is incorrect for everyday elevator scenarios near Earth's surface. Gravity does not appreciably increase just by moving a few meters away from Earth’s surface; gravitational force remains essentially constant over such small vertical distances.
Option 4: 'Acceleration causes scales to malfunction.' This is not accurate as a general rule. The scale isn’t malfunctioning; it’s responding to the actual forces acting on you in the accelerating frame, yielding the higher reading as explained by the dynamics of non-inertial frames.

ASTR-1-45046-F25 Lecture: Orbits

Why would a bathroom scale tell you that you've gained weight if you were standing on one in an upwardly accelerating elevator?

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