---
title: "A uniform ladder of mass \\(M\\) and length \\(L\\) rests against a smooth vertical wall and on a rough horizontal floor. A worker of mass \\(M\\) stands on the ladder at a distance \\(d\\) measured along the ladder from its base on the floor. The system is evaluated in the three static configurations shown in the table.  | Configuration | Inclination angle \\(\\theta\\) | Worker position \\(d\\) | | :— | :— | :— | | 1 | \\(60^\\circ\\) | \\(L\\) | | 2 | \\(45^\\circ\\) | \\(\\dfrac{L}{2}\\) | | 3 | \\(30^\\circ\\) | \\(0\\) |  Which of the following correctly ranks the minimum coefficients of static friction between the ladder and the floor, \\(\\mu_1\\), \\(\\mu_2\\), and \\(\\mu_3\\), required to prevent slipping in configurations 1, 2, and 3, respectively?"
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url: "https://nerd-notes.com/ubq/124412/"
date_modified: "2026-09-28T14:05:14+00:00"
---

# A uniform ladder of mass \(M\) and length \(L\) rests against a smooth vertical wall and on a rough horizontal floor. A worker of mass \(M\) stands on the ladder at a distance \(d\) measured along the ladder from its base on the floor. The system is evaluated in the three static configurations shown in the table.

| Configuration | Inclination angle \(\theta\) | Worker position \(d\) |
| :— | :— | :— |
| 1 | \(60^\circ\) | \(L\) |
| 2 | \(45^\circ\) | \(\dfrac{L}{2}\) |
| 3 | \(30^\circ\) | \(0\) |

Which of the following correctly ranks the minimum coefficients of static friction between the ladder and the floor, \(\mu_1\), \(\mu_2\), and \(\mu_3\), required to prevent slipping in configurations 1, 2, and 3, respectively?

A uniform ladder of mass \(M\) and length \(L\) rests against a smooth vertical wall and on a rough horizontal floor. A worker of mass \(M\) stands on the ladder at a distance \(d\) measured along the ladder from its base on the floor. The system is evaluated in the three static configurations shown in the table.

| Configuration | Inclination angle \(\theta\) | Worker position \(d\) |
| :--- | :--- | :--- |
| 1 | \(60^\circ\) | \(L\) |
| 2 | \(45^\circ\) | \(\dfrac{L}{2}\) |
| 3 | \(30^\circ\) | \(0\) |

Which of the following correctly ranks the minimum coefficients of static friction between the ladder and the floor, \(\mu_1\), \(\mu_2\), and \(\mu_3\), required to prevent slipping in configurations 1, 2, and 3, respectively?

![A side-view schematic showing a straight rectangular bar representing a ladder leaning against a vertical line representing a wall on the right and resting on a horizontal line representing the floor at the bottom. The ladder makes an angle labeled \(\theta\) with the horizontal floor at its base. A dimension line parallel to the ladder spans its full extent and is labeled \(L\). A filled circle sits on the upper face of the ladder at a distance from the base, with a parallel dimension line from the base to the center of the circle labeled \(d\). The vertical wall has no hash marks, while the horizontal floor has diagonal hash marks beneath it. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604314-nwLqeI.jpg)

- **A.** \(\mu_1 > \mu_2 > \mu_3\)
- **B.** \(\mu_3 > \mu_2 > \mu_1\)
- **C.** \(\mu_2 > \mu_1 = \mu_3\)
- **D.** \(\mu_1 = \mu_3 > \mu_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124412/*