---
title: "A small block of mass \\(M\\) is suspended in static equilibrium by three light strings that meet at a single knot, as shown. String 1 extends upward and to the left, making an angle \\(\\theta_1\\) with the horizontal. String 2 extends upward and to the right, making an angle \\(\\theta_2\\) with the horizontal. String 3 hangs vertically downward, directly supporting the block. Which of the following expressions represents the tension \\(T_1\\) in String 1 in terms of \\(M\\), \\(g\\), \\(\\theta_1\\), and \\(\\theta_2\\)?"
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url: "https://nerd-notes.com/ubq/120572/"
date_modified: "2026-08-23T04:41:40+00:00"
---

# A small block of mass \(M\) is suspended in static equilibrium by three light strings that meet at a single knot, as shown. String 1 extends upward and to the left, making an angle \(\theta_1\) with the horizontal. String 2 extends upward and to the right, making an angle \(\theta_2\) with the horizontal. String 3 hangs vertically downward, directly supporting the block. Which of the following expressions represents the tension \(T_1\) in String 1 in terms of \(M\), \(g\), \(\theta_1\), and \(\theta_2\)?

A small block of mass \(M\) is suspended in static equilibrium by three light strings that meet at a single knot, as shown. String 1 extends upward and to the left, making an angle \(\theta_1\) with the horizontal. String 2 extends upward and to the right, making an angle \(\theta_2\) with the horizontal. String 3 hangs vertically downward, directly supporting the block. Which of the following expressions represents the tension \(T_1\) in String 1 in terms of \(M\), \(g\), \(\theta_1\), and \(\theta_2\)?

![A schematic diagram showing a block of mass \(M\) suspended in static equilibrium. Three light strings meet at a central junction knot. String 1 extends upward and to the left at an angle \(\theta_1\) above a horizontal dashed reference line passing through the knot. String 2 extends upward and to the right at an angle \(\theta_2\) above the same horizontal dashed line. String 3 hangs vertically downward from the knot, connected to a rectangular block labeled \(M\). The upper ends of String 1 and String 2 terminate at a horizontal ceiling with hatch marks. No other forces, vectors, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-cable-diagram-1787460099-0Z4w74.jpg)

- **A.** \(T_1 = \dfrac{Mg \sin\theta_2}{\sin(\theta_1 + \theta_2)}\)
- **B.** \(T_1 = \dfrac{Mg \cos\theta_1}{\sin(\theta_1 + \theta_2)}\)
- **C.** \(T_1 = \dfrac{Mg \cos\theta_2}{\sin(\theta_1 + \theta_2)}\)
- **D.** \(T_1 = \dfrac{Mg \cos\theta_2}{\cos(\theta_1 + \theta_2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120572/*