---
title: "A block of mass \\(m\\) is held stationary against a rough vertical wall by an external force of magnitude \\(F\\). The force is applied at an angle \\(\\theta\\) above the horizontal, as shown in the diagram. The coefficient of static friction between the block and the wall is \\(\\mu_s\\). Which of the following expressions represents the minimum force \\(F\\) required to prevent the block from sliding down the wall?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/114583/"
date_modified: "2026-07-03T04:46:04+00:00"
---

# A block of mass \(m\) is held stationary against a rough vertical wall by an external force of magnitude \(F\). The force is applied at an angle \(\theta\) above the horizontal, as shown in the diagram. The coefficient of static friction between the block and the wall is \(\mu_s\). Which of the following expressions represents the minimum force \(F\) required to prevent the block from sliding down the wall?

A block of mass \(m\) is held stationary against a rough vertical wall by an external force of magnitude \(F\). The force is applied at an angle \(\theta\) above the horizontal, as shown in the diagram. The coefficient of static friction between the block and the wall is \(\mu_s\). Which of the following expressions represents the minimum force \(F\) required to prevent the block from sliding down the wall?

![A rectangular block of mass m is shown pressed against a vertical line representing a wall on the right. A force vector arrow F points toward the wall and upward, making an angle theta with a dashed horizontal line. The tip of the arrow contacts the center of the block.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783053964-77ODH3.jpg)

- **A.** \(F = \dfrac{mg}{\sin\theta + \mu_s \cos\theta}\)
- **B.** \(F = \dfrac{mg}{\cos\theta + \mu_s \sin\theta}\)
- **C.** \(F = \dfrac{mg}{\sin\theta - \mu_s \cos\theta}\)
- **D.** \(F = \dfrac{mg}{\mu_s \cos\theta}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114583/*