---
title: "A uniform rigid beam of mass \\(M\\) and length \\(L\\) is attached to a vertical wall by a hinge at its left end. The beam is held in a horizontal position by a taut, lightweight cable. One end of the cable is attached to the beam at a distance \\(3L/4\\) from the hinge, and the other end is attached to the wall above the hinge. The cable makes an angle \\(\\theta\\) with the horizontal beam. A small block of mass \\(m\\) hangs from a lightweight string attached to the rightmost end of the beam. The entire system is in static equilibrium."
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url: "https://nerd-notes.com/ubq/110291/"
date_modified: "2026-04-01T04:47:21+00:00"
---

# A uniform rigid beam of mass \(M\) and length \(L\) is attached to a vertical wall by a hinge at its left end. The beam is held in a horizontal position by a taut, lightweight cable. One end of the cable is attached to the beam at a distance \(3L/4\) from the hinge, and the other end is attached to the wall above the hinge. The cable makes an angle \(\theta\) with the horizontal beam. A small block of mass \(m\) hangs from a lightweight string attached to the rightmost end of the beam. The entire system is in static equilibrium.

A uniform rigid beam of mass \(M\) and length \(L\) is attached to a vertical wall by a hinge at its left end. The beam is held in a horizontal position by a taut, lightweight cable. One end of the cable is attached to the beam at a distance \(3L/4\) from the hinge, and the other end is attached to the wall above the hinge. The cable makes an angle \(\theta\) with the horizontal beam. A small block of mass \(m\) hangs from a lightweight string attached to the rightmost end of the beam. The entire system is in static equilibrium.

![A physical setup showing a vertical wall on the left side. A horizontal rectangular beam of length L is attached to the wall by a circular hinge at its left end. A straight cable connects from a point on the beam (marked with a dimension line as distance 3L/4 from the hinge) up to the vertical wall. The angle between the cable and the horizontal beam is marked with an arc and labeled theta. A small square block labeled 'm' hangs vertically from a string attached to the rightmost end of the beam. The beam itself is labeled 'M'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775018841-CcOjcw.jpg)

**Part a)** On the diagram of the beam below, **draw** and **label** the forces (not components) that act on the beam. Each force must be represented by a distinct arrow starting on, and pointing away from, the point of application. *(3 points)*

**Part b)** **Derive** an expression for the tension \(T\) in the cable. Express your answer in terms of \(M\), \(m\), \(L\), \(\theta\), and fundamental constants. *(3 points)*

**Part c)** **Derive** an expression for the magnitude of the horizontal component of the force exerted by the hinge on the beam. Express your answer in terms of \(M\), \(m\), \(L\), \(\theta\), and fundamental constants. *(2 points)*

**Part d)** The mass \(m\) of the hanging block can be changed. **Determine** the ratio \(m/M\) such that the vertical component of the force exerted by the hinge on the beam is exactly zero. *(2 points)*

**Part e)** Suppose the block is moved to a new position on the beam that is closer to the hinge. **Predict** whether the tension in the cable will increase, decrease, or stay the same. - [ ] Increase - [ ] Decrease - [ ] Stay the same **Justify** your prediction using physical principles. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110291/*