---
title: "A sled of mass \\(m\\) rests on a flat horizontal surface where the coefficient of static friction is \\(\\mu_s\\). In Scenario 1, a force of magnitude \\(F\\) is applied to the sled at an angle \\(\\theta\\) above the horizontal, where \\(0 < \\theta < 90^\\circ\\) and \\(F\\sin\\theta < mg\\). In Scenario 2, a force of the same magnitude \\(F\\) is applied to the sled at the same angle \\(\\theta\\) below the horizontal. Which of the following correctly pairs the difference in the normal force exerted on the sled, \\(F_{N,\\text{below}} – F_{N,\\text{above}}\\), with the scenario and condition under which the sled cannot be made to slide from rest regardless of the magnitude of \\(F\\)?"
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url: "https://nerd-notes.com/ubq/120599/"
date_modified: "2026-08-23T04:41:52+00:00"
---

# A sled of mass \(m\) rests on a flat horizontal surface where the coefficient of static friction is \(\mu_s\). In Scenario 1, a force of magnitude \(F\) is applied to the sled at an angle \(\theta\) above the horizontal, where \(0 < \theta < 90^\circ\) and \(F\sin\theta < mg\). In Scenario 2, a force of the same magnitude \(F\) is applied to the sled at the same angle \(\theta\) below the horizontal. Which of the following correctly pairs the difference in the normal force exerted on the sled, \(F_{N,\text{below}} – F_{N,\text{above}}\), with the scenario and condition under which the sled cannot be made to slide from rest regardless of the magnitude of \(F\)?

A sled of mass \(m\) rests on a flat horizontal surface where the coefficient of static friction is \(\mu_s\). In Scenario 1, a force of magnitude \(F\) is applied to the sled at an angle \(\theta\) above the horizontal, where \(0 < \theta < 90^\circ\) and \(F\sin\theta < mg\). In Scenario 2, a force of the same magnitude \(F\) is applied to the sled at the same angle \(\theta\) below the horizontal. Which of the following correctly pairs the difference in the normal force exerted on the sled, \(F_{N,\text{below}} - F_{N,\text{above}}\), with the scenario and condition under which the sled cannot be made to slide from rest regardless of the magnitude of \(F\)?

![A side-by-side schematic showing two identical rectangular blocks of mass \(m\) resting on a horizontal surface. On the left, labeled Scenario 1, a rectangular block sits on the ground; a solid arrow labeled \(F\) originates from the right side of the block pointing upward and to the right at an angle \(\theta\) above a horizontal dashed reference line. On the right, labeled Scenario 2, an identical rectangular block sits on the ground; a solid arrow labeled \(F\) points downward and to the right toward the upper-left corner of the block at an angle \(\theta\) below a horizontal dashed reference line. In each scenario, an arc indicates the angle \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460112-ozp68b.jpg)

- **A.** Difference in normal force: \(2F\sin\theta\) Condition: Scenario 2 only, when \(\tan\theta \ge \dfrac{1}{\mu_s}\)
- **B.** Difference in normal force: \(2F\sin\theta\) Condition: Scenario 2 only, when \(\tan\theta \ge \mu_s\)
- **C.** Difference in normal force: \(F\sin\theta\) Condition: Scenario 2 only, when \(\tan\theta \ge \dfrac{1}{\mu_s}\)
- **D.** Difference in normal force: \(F\sin\theta\) Condition: Scenario 1 only, when \(\tan\theta \ge \mu_s\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120599/*