---
title: "A crane boom of length \\(L = 8.0\\text{ m}\\) and uniform mass \\(M = 240\\text{ kg}\\) is attached to a vertical wall by a frictionless pin joint at its base. The boom is held at an angle of \\(30^\\circ\\) above the horizontal by a horizontal steel cable connected to the boom at a distance \\(d = 6.0\\text{ m}\\) from the pin joint. The cable has a maximum allowable tension of \\(1.20 \\times 10^4\\text{ N}\\) before reaching its yield limit. Taking \\(g = 9.8\\text{ m/s}^2\\), what is the maximum downward vertical force \\(F\\) that can be applied to the tip of the boom without exceeding the cable’s tension limit?"
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url: "https://nerd-notes.com/ubq/120861/"
date_modified: "2026-08-23T04:43:42+00:00"
---

# A crane boom of length \(L = 8.0\text{ m}\) and uniform mass \(M = 240\text{ kg}\) is attached to a vertical wall by a frictionless pin joint at its base. The boom is held at an angle of \(30^\circ\) above the horizontal by a horizontal steel cable connected to the boom at a distance \(d = 6.0\text{ m}\) from the pin joint. The cable has a maximum allowable tension of \(1.20 \times 10^4\text{ N}\) before reaching its yield limit. Taking \(g = 9.8\text{ m/s}^2\), what is the maximum downward vertical force \(F\) that can be applied to the tip of the boom without exceeding the cable’s tension limit?

A crane boom of length \(L = 8.0\text{ m}\) and uniform mass \(M = 240\text{ kg}\) is attached to a vertical wall by a frictionless pin joint at its base. The boom is held at an angle of \(30^\circ\) above the horizontal by a horizontal steel cable connected to the boom at a distance \(d = 6.0\text{ m}\) from the pin joint. The cable has a maximum allowable tension of \(1.20 \times 10^4\text{ N}\) before reaching its yield limit. Taking \(g = 9.8\text{ m/s}^2\), what is the maximum downward vertical force \(F\) that can be applied to the tip of the boom without exceeding the cable's tension limit?

![A vertical gray wall on the left extends from top to bottom. A straight solid beam representing the boom of length \(L\) is attached at its lower-left end to the wall by a circular pin joint. The boom rises toward the upper right at an angle labeled \(30^\circ\) relative to a horizontal dashed line extending to the right from the pin. A horizontal line representing a cable connects the vertical wall to a point on the top edge of the boom at distance \(d\) from the pin. A downward vertical arrow labeled \(F\) points from the top-right tip of the boom. A downward vertical arrow labeled \(Mg\) points from the midpoint of the boom. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460222-POWV9V.jpg)

- **A.** \(2.84 \times 10^3\text{ N}\)
- **B.** \(4.02 \times 10^3\text{ N}\)
- **C.** \(5.20 \times 10^3\text{ N}\)
- **D.** \(6.93 \times 10^3\text{ N}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120861/*