Would the tension increase, decrease or stay the same? Shc
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Transcribed Image Text:For the hinged beam and cable in example 9-6, what would happen to the tension in the cable as the angle was increased? Would the tension increase, decrease or stay the same? Show your reasoning.
Transcribed Image Text:**Title: Understanding Force Diagrams in Static Equilibrium**
**Figure 9-10: Example 9-6**
The diagram illustrates a horizontal beam attached to a vertical wall, supported by a hinge on the left and a tension cable on the right. This setup can be seen in real-world situations, such as signboards or shelves. Here's a detailed exploration of the forces acting on the system:
**Components of the Diagram:**
1. **Hinge:**
- Located on the left side, the hinge exerts both horizontal (\(F_{Hx}\)) and vertical (\(F_{Hy}\)) components of force on the beam. These forces ensure the beam remains stationary.
2. **Tension Force (\(\vec{F}_{T}\)):**
- The cable exerts a force at angle \(\theta\), providing vertical (\(F_{Ty}\)) and horizontal (\(F_{Tx}\)) components. This force counteracts the downward force due to gravity on the sign.
3. **Gravitational Force (\(mg\)):**
- Acts downward at the beam's center of gravity.
4. **Sign Weight (\(M\vec{g}\)):**
- The sign, represented as "Arlene's Book Store," adds additional weight, exerting a downward force at its attachment point on the beam.
5. **Coordinate Axes:**
- The \(x\)- and \(y\)-axes are shown to demonstrate the directions of the forces and components.
**Static Equilibrium Considerations:**
- For the system to be in equilibrium, the sum of all forces and moments (torques) must be zero.
- The horizontal and vertical forces should balance each other, ensuring that the sign and beam remain motionless.
In the context of physics and engineering, understanding such diagrams is crucial for analyzing and designing structures capable of withstanding various forces while remaining stable.
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