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.
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.
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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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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.
![**EXAMPLE 9-6: Hinged Beam and Cable**
A uniform beam, 2.20 m long with mass \(m = 25.0\) kg, is attached by a small hinge to a wall, as shown in Figure 9-10. The beam is held in a horizontal position by a cable that makes an angle \(\theta = 30.0^\circ\) with the beam. It supports a sign with mass \(M = 28.0\) kg at its end. Determine the components of the force \( \mathbf{F}_H \) that the wall (through hinge action) exerts on the beam, and the tension \( F_T \) in the supporting cable.
**APPROACH**
Figure 9-10 shows the free-body diagram of the beam, illustrating the forces acting on it. The diagram includes the known forces \( F_T \) and \( mg \), and a guess for \( F_H \). With three unknowns \( F_{H\text{X}}, F_{H\text{Y}} \), and \( F_H \) and the given \(\theta\), three equations are set up: \( \Sigma F_{\text{X}} = 0, \Sigma F_{\text{Y}} = 0, \Sigma \tau = 0 \).
**SOLUTION**
1. **Vertical Forces:**
\[
\Sigma F_{\text{Y}} = 0 \implies F_{H\text{Y}} + F_{T\text{Y}} - mg - Mg = 0. \tag{i}
\]
2. **Horizontal Forces:**
\[
\Sigma F_{\text{X}} = 0 \implies F_{T\text{X}} - F_{H\text{X}} = 0. \tag{ii}
\]
3. **Torque Equation:**
Choosing the axis at the point where \( F_T \) and \( Mg \) act, the equation becomes:
\[
(-F_{H\text{Y}})(2.20\, \text{m}) + mg(1.10\, \text{m}) = 0.
\]
Solving for \( F_{H\text{Y}} \), we have:
\[
F_{H\text{Y}} = \left(\frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe591ff8b-7fbf-41eb-ab1a-65fc8e854653%2Fd9c46f00-1535-4dbe-a7ae-ff66985e4123%2Fy3ij2tc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**EXAMPLE 9-6: Hinged Beam and Cable**
A uniform beam, 2.20 m long with mass \(m = 25.0\) kg, is attached by a small hinge to a wall, as shown in Figure 9-10. The beam is held in a horizontal position by a cable that makes an angle \(\theta = 30.0^\circ\) with the beam. It supports a sign with mass \(M = 28.0\) kg at its end. Determine the components of the force \( \mathbf{F}_H \) that the wall (through hinge action) exerts on the beam, and the tension \( F_T \) in the supporting cable.
**APPROACH**
Figure 9-10 shows the free-body diagram of the beam, illustrating the forces acting on it. The diagram includes the known forces \( F_T \) and \( mg \), and a guess for \( F_H \). With three unknowns \( F_{H\text{X}}, F_{H\text{Y}} \), and \( F_H \) and the given \(\theta\), three equations are set up: \( \Sigma F_{\text{X}} = 0, \Sigma F_{\text{Y}} = 0, \Sigma \tau = 0 \).
**SOLUTION**
1. **Vertical Forces:**
\[
\Sigma F_{\text{Y}} = 0 \implies F_{H\text{Y}} + F_{T\text{Y}} - mg - Mg = 0. \tag{i}
\]
2. **Horizontal Forces:**
\[
\Sigma F_{\text{X}} = 0 \implies F_{T\text{X}} - F_{H\text{X}} = 0. \tag{ii}
\]
3. **Torque Equation:**
Choosing the axis at the point where \( F_T \) and \( Mg \) act, the equation becomes:
\[
(-F_{H\text{Y}})(2.20\, \text{m}) + mg(1.10\, \text{m}) = 0.
\]
Solving for \( F_{H\text{Y}} \), we have:
\[
F_{H\text{Y}} = \left(\frac
Expert Solution
Step 1: Determine the requirement of the question:
We need to determine that whether tension in the cable increases/decreases/stays same if the angle increases.
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