---
title: "A person of mass \\(m\\) stands on a scale in an elevator. The elevator is moving upward with a speed \\(v\\) but is slowing down with a constant acceleration of magnitude \\(a\\). Which of the following correctly compares the magnitude of the scale reading \\(F_N\\) to the person’s weight \\(mg\\) and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/109263/"
date_modified: "2026-03-21T18:52:20+00:00"
---

# A person of mass \(m\) stands on a scale in an elevator. The elevator is moving upward with a speed \(v\) but is slowing down with a constant acceleration of magnitude \(a\). Which of the following correctly compares the magnitude of the scale reading \(F_N\) to the person’s weight \(mg\) and provides a correct justification?

A person of mass \(m\) stands on a scale in an elevator. The elevator is moving upward with a speed \(v\) but is slowing down with a constant acceleration of magnitude \(a\). Which of the following correctly compares the magnitude of the scale reading \(F_N\) to the person's weight \(mg\) and provides a correct justification?

![A rectangular elevator car containing a stick-figure person standing on a small platform scale. An arrow labeled 'v' points upward next to the elevator. An arrow labeled 'a' points downward next to the elevator. A coordinate axis is shown to the side with 'y' pointing upward as the positive direction.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774119140-W00wGP.jpg)

- **A.** The scale reading \(F_N\) is less than \(mg\) because the acceleration is directed downward, which requires the magnitude of the downward gravitational force to be greater than the magnitude of the upward normal force.
- **B.** The scale reading \(F_N\) is greater than \(mg\) because the elevator is moving in the upward direction, which requires the magnitude of the upward normal force to be greater than the magnitude of the downward gravitational force.
- **C.** The scale reading \(F_N\) is less than \(mg\) because the upward motion of the elevator partially cancels the effect of the gravitational field on the person's mass.
- **D.** The scale reading \(F_N\) is greater than \(mg\) because the elevator is slowing down, which requires an additional upward force to counteract the person's upward inertia.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109263/*