---
title: "A uniform horizontal beam of mass \\(M\\) and length \\(L\\) is attached to a vertical wall by a frictionless hinge. A small block of mass \\(m\\) is securely glued to the top of the beam at a distance \\(x\\) from the hinge. A cable attached to the right end of the beam and the wall supports the system, keeping the beam perfectly horizontal. The cable makes an angle \\(\\theta\\) with the beam, as shown in Figure 1."
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url: "https://nerd-notes.com/ubq/111544/"
date_modified: "2026-04-12T02:43:37+00:00"
---

# A uniform horizontal beam of mass \(M\) and length \(L\) is attached to a vertical wall by a frictionless hinge. A small block of mass \(m\) is securely glued to the top of the beam at a distance \(x\) from the hinge. A cable attached to the right end of the beam and the wall supports the system, keeping the beam perfectly horizontal. The cable makes an angle \(\theta\) with the beam, as shown in Figure 1.

A uniform horizontal beam of mass \(M\) and length \(L\) is attached to a vertical wall by a frictionless hinge. A small block of mass \(m\) is securely glued to the top of the beam at a distance \(x\) from the hinge. A cable attached to the right end of the beam and the wall supports the system, keeping the beam perfectly horizontal. The cable makes an angle \(\theta\) with the beam, as shown in Figure 1.

![A vertical wall is on the left. A horizontal beam extends to the right from the wall, connected by a hinge at the wall. A small rectangular block is resting on the beam. An angled line representing a cable connects the rightmost end of the beam to a point higher up on the vertical wall. The length of the entire beam is labeled 'L'. The distance from the hinge to the center of the block is labeled 'x'. An angle arc at the right end of the beam between the beam and the cable is labeled 'theta'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775961816-ROE6s0.jpg)

**Part a)** On the diagram below representing the beam, **draw** and **label** the forces (not components) that are exerted on the beam. Each force must be represented by a distinct arrow originating at the point where the force is exerted on the beam. *(3 points)*

**Part b)** **Derive** an expression for the tension \(T\) in the cable. Express your answer in terms of \(M\), \(m\), \(x\), \(L\), \(\theta\), and physical constants, as appropriate. *(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 \(M\), \(m\), \(x\), \(L\), \(\theta\), and physical constants, as appropriate. *(2 points)*

**Part d)** The cable suddenly breaks. The block remains glued to the beam and does not slip. **Derive** an expression for the initial angular acceleration \(\alpha\) of the beam-block system immediately after the cable breaks. Express your answer in terms of \(M\), \(m\), \(x\), \(L\), and physical constants, as appropriate. (The rotational inertia of a uniform rod of mass \(M\) and length \(L\) about its end is \(\dfrac{1}{3}ML^2\)). *(2 points)*

**Part e)** Consider a new scenario where the block is moved to the far right end of the beam (\(x = L\)) before the cable breaks. **Predict** whether the initial angular acceleration of the system immediately after the cable breaks would be greater than, less than, or equal to the initial angular acceleration of the beam if the block were removed entirely. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111544/*