### Physics Problem: Suspended Beam Analysis(b) In the figure below, a uniform beam of weight 500 N and length 3.0 m is suspended horizontally. On the left, it is hinged to a wall; on the right, it is supported by a cable bolted to the wall at a distance \( D \) above the beam. The least tension that will snap the cable is 1200 N.1. **Question:** (a) What value of \( D \) corresponds to that tension? (b) To prevent the cable from snapping, should \( D \) be increased or decreased from that value?#### Diagram Explanation:The provided diagram depicts the following setup:- **Beam**: A horizontal beam of length 3.0 meters is shown.- **Hinge**: The left end of the beam is attached to the wall with a hinge.- **Cable**: A cable is depicted, bolted to the wall at a vertical distance \( D \) above the point where the cable attaches to the beam's right end.- **Distance \( D \)**: The vertical distance from the beam to the point where the cable connects to the wall is denoted \( D \).![Diagram](https://example.com/path/to/your/image)**Note**: You can visualize the forces acting on the beam, the weight acting downwards, the tension in the cable, and the reactions at the hinge.### Solution Steps:1. **Equilibrium Conditions**: - The sum of forces in both horizontal and vertical directions must be zero. - The sum of moments about any point must be zero. Normally, it's convenient to take moments about the hinge.2. **Calculation of Distance \( D \)**: - Using the moment equilibrium equation around the hinge: \[ \text{Moment from Weight (500 N) = Moment from Tension (1200 N)} \] Consider the perpendicular distances from the hinge to the lines of forces of weight and tension.3. **Preventing Cable Snap**: - Evaluate how the tension changes with \( D \). If increasing \( D \) reduces the required tension for equilibrium, then potentially, increasing \( D \) prevents the cable snap; otherwise, reducing \( D \) is necessary.### Analysis and Conclusion:- By calculating \( D \), you can find the exact point where tension reaches its maximum allowable value.

Draw the free-body diagram of the system.

(b) In the figure below, a uniform beam of weight 500 N and length 3.0 m is suspended horizontally. On the left it is hinged to a wall; on the right it is sup- ported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N. (a) What value of D corresponds to that tension? (b) To prevent the cable from snapping, should D be increased or decreased from that value? D Cable Beam

(b) In the figure below, a uniform beam of weight 500 N and length 3.0 m is suspended horizontally. On the left it is hinged to a wall; on the right it is sup- ported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N. (a) What value of D corresponds to that tension? (b) To prevent the cable from snapping, should D be increased or decreased from that value? D Cable Beam

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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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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

### Physics Problem: Suspended Beam Analysis

(b) In the figure below, a uniform beam of weight 500 N and length 3.0 m is suspended horizontally. On the left, it is hinged to a wall; on the right, it is supported by a cable bolted to the wall at a distance \( D \) above the beam. The least tension that will snap the cable is 1200 N.

1. **Question:**
(a) What value of \( D \) corresponds to that tension?
(b) To prevent the cable from snapping, should \( D \) be increased or decreased from that value?

#### Diagram Explanation:

The provided diagram depicts the following setup:

- **Beam**: A horizontal beam of length 3.0 meters is shown.
- **Hinge**: The left end of the beam is attached to the wall with a hinge.
- **Cable**: A cable is depicted, bolted to the wall at a vertical distance \( D \) above the point where the cable attaches to the beam's right end.
- **Distance \( D \)**: The vertical distance from the beam to the point where the cable connects to the wall is denoted \( D \).

![Diagram](https://example.com/path/to/your/image)

**Note**: You can visualize the forces acting on the beam, the weight acting downwards, the tension in the cable, and the reactions at the hinge.

### Solution Steps:

1. **Equilibrium Conditions**:
- The sum of forces in both horizontal and vertical directions must be zero.
- The sum of moments about any point must be zero. Normally, it's convenient to take moments about the hinge.

2. **Calculation of Distance \( D \)**:
- Using the moment equilibrium equation around the hinge:
\[
\text{Moment from Weight (500 N) = Moment from Tension (1200 N)}
\]
Consider the perpendicular distances from the hinge to the lines of forces of weight and tension.

3. **Preventing Cable Snap**:
- Evaluate how the tension changes with \( D \). If increasing \( D \) reduces the required tension for equilibrium, then potentially, increasing \( D \) prevents the cable snap; otherwise, reducing \( D \) is necessary.

### Analysis and Conclusion:

- By calculating \( D \), you can find the exact point where tension reaches its maximum allowable value.

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