### Determining the Minimum Distance for a Hanging Weight on a Supported Beam#### Problem Statement:As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle (\(\theta\)) of \(30^\circ\). The length of the beam (L) is \(3.2\) m, the coefficient of static friction between the wall and the beam is \( \mu_s = 0.40 \), and the weight of the beam is represented by \(w\). Determine the minimum distance \(x\) from point \(A\) at which an additional weight \(2w\) (twice the weight of the rod) can be hung without causing the rod to slip at point \(A\).#### Diagram Explanation:The diagram illustrates the scenario described in the problem statement. Below are the key features of the diagram:- **Beam AB**: A horizontal beam of length \(L = 3.2\) m.- **Angle \(\theta\)**: The angle between the supporting cable and the horizontal beam is \(30^\circ\).- **Point A**: The beam is in contact with the wall at point A. - **Point B**: The beam is attached to the supporting cable at point B.- **Force of Friction (f)**: At point A, the force of friction acts horizontally to prevent slipping.- **Cable Support**: The cable attached at point B is inclined at \(30^\circ\) and supports the beam against the wall.Variables to Determine:- **\(x\)**: The minimum distance from point A where the additional weight (\(2w\)) can be hung on the beam without causing it to slip at point A.

Given: Length of beam, L = 3.25 m coefficient of static friction, μs = 0.4 angle the cable makes…

As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of e- 30°, the length of the beam is - 3.25 m, the coefficient of static friction between the wall and the beam is ,- 0,400, and the weight of the beam is represented by w. Determine the minimum distance x from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.

As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of e- 30°, the length of the beam is - 3.25 m, the coefficient of static friction between the wall and the beam is ,- 0,400, and the weight of the beam is represented by w. Determine the minimum distance x from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Determining the Minimum Distance for a Hanging Weight on a Supported Beam

#### Problem Statement:
As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle (\(\theta\)) of \(30^\circ\). The length of the beam (L) is \(3.2\) m, the coefficient of static friction between the wall and the beam is \( \mu_s = 0.40 \), and the weight of the beam is represented by \(w\). Determine the minimum distance \(x\) from point \(A\) at which an additional weight \(2w\) (twice the weight of the rod) can be hung without causing the rod to slip at point \(A\).

#### Diagram Explanation:
The diagram illustrates the scenario described in the problem statement. Below are the key features of the diagram:

- **Beam AB**: A horizontal beam of length \(L = 3.2\) m.
- **Angle \(\theta\)**: The angle between the supporting cable and the horizontal beam is \(30^\circ\).
- **Point A**: The beam is in contact with the wall at point A.
- **Point B**: The beam is attached to the supporting cable at point B.
- **Force of Friction (f)**: At point A, the force of friction acts horizontally to prevent slipping.
- **Cable Support**: The cable attached at point B is inclined at \(30^\circ\) and supports the beam against the wall.

Variables to Determine:
- **\(x\)**: The minimum distance from point A where the additional weight (\(2w\)) can be hung on the beam without causing it to slip at point A.

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