---
title: "A ring of negligible mass remains in static equilibrium under the influence of three coplanar forces, as shown in the accompanying diagram. Two forces, each with a magnitude of \\(10 \\, \\text{N}\\), act on the ring at an angle \\(\\theta\\) above the horizontal—one directed to the right and the other to the left. A third force, \\(F\\), acts vertically downward. Determine the magnitude of force \\(F\\)."
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url: "https://nerd-notes.com/ubq/30546/"
date_modified: "2026-05-01T21:06:45+00:00"
---

# A ring of negligible mass remains in static equilibrium under the influence of three coplanar forces, as shown in the accompanying diagram. Two forces, each with a magnitude of \(10 \, \text{N}\), act on the ring at an angle \(\theta\) above the horizontal—one directed to the right and the other to the left. A third force, \(F\), acts vertically downward. Determine the magnitude of force \(F\).

A ring of negligible mass remains in static equilibrium under the influence of three coplanar forces, as shown in the accompanying diagram. Two forces, each with a magnitude of \(10 \, \text{N}\), act on the ring at an angle \(\theta\) above the horizontal—one directed to the right and the other to the left. A third force, \(F\), acts vertically downward. Determine the magnitude of force \(F\).

![A circular ring is centered in the diagram. Two force vectors, each labeled '10 N', pull upward and outward from the top left and top right sides of the ring, forming an angle 'θ' with the horizontal dashed line extending from each side of the ring. A third, thicker downward-pointing force vector is labeled 'F' originating from the bottom center of the ring.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-30546-1777669233-49j8kC.jpg)

- **A.** \(20 \, \text{N}\)
- **B.** \(10 \cos \theta \, \text{N}\)
- **C.** \(10 \sin \theta \, \text{N}\)
- **D.** \(20 \cos \theta \, \text{N}\)
- **E.** \(20 \sin \theta \, \text{N}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/30546/*