Q.2) Two cylinders A and B are resting on a set of perpendicular surfaces and are held in equilibrium by a steel rod that makes angle e with the horizontal. Determine the tension in steel rod, the angle 0, and the reactions of the supporting surfaces on the cylinders. Draw the necessary free-body diagrams. WB = 200 N В WA = 800 N %3D To A Cable 60° 30°
Q.2) Two cylinders A and B are resting on a set of perpendicular surfaces and are held in equilibrium by a steel rod that makes angle e with the horizontal. Determine the tension in steel rod, the angle 0, and the reactions of the supporting surfaces on the cylinders. Draw the necessary free-body diagrams. WB = 200 N В WA = 800 N %3D To A Cable 60° 30°
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Equilibrium and Tension Analysis in a System of Two Cylinders
**Problem Statement:**
Two cylinders, A and B, are resting on a set of perpendicular surfaces and are held in equilibrium by a steel rod that makes an angle \(\theta\) with the horizontal. Given the weights of the cylinders \(W_A = 800 \, \text{N}\) for cylinder A and \(W_B = 200 \, \text{N}\) for cylinder B.
**Objective:**
1. Determine the tension in the steel rod.
2. Determine the angle \(\theta\).
3. Determine the reactions of the supporting surfaces on the cylinders.
4. Draw the necessary free-body diagrams (FBD).
**Diagram Explanation:**
- **Cylinder A** (\(W_A\)):
- Weight: 800 N.
- Rests on a surface inclined at an angle of \(30^\circ\) to the horizontal.
- Connected to a cable.
- **Cylinder B** (\(W_B\)):
- Weight: 200 N.
- Rests on a surface inclined at an angle of \(60^\circ\) to the horizontal.
- Connected to the same cable.
- **Cable:**
- Connects cylinders A and B.
- Forms an angle \(\theta\) with the horizontal between the two cylinders.
**Solution Approach:**
1. **Free-Body Diagrams (FBD):**
Draw the FBD of each cylinder, showing the forces acting on each, including weight (\(W_A\) and \(W_B\)), normal reaction forces from the surfaces (\(N_A\) and \(N_B\)), frictional forces if any (which may be neglected if surfaces are smooth), and the tension \(T\) in the cable.
2. **Equilibrium Equations:**
Set up the equilibrium equations for each cylinder. For horizontal and vertical forces in both cylinders, the sum of forces must be zero.
- For Cylinder A:
\[
\sum F_x = 0 \quad \text{(Horizontal forces)}
\]
\[
\sum F_y = 0 \quad \text{(Vertical forces)}
\]
- For Cylinder B:
\[
\sum F_x = 0 \quad \text{(Horizontal forces)}
\]
\[
\sum F_y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1a8ba3-371b-48d7-95b6-c118f740fa83%2F73c41027-c899-45cf-aa36-5e4ace022194%2F5d4etba_processed.png&w=3840&q=75)
Transcribed Image Text:### Equilibrium and Tension Analysis in a System of Two Cylinders
**Problem Statement:**
Two cylinders, A and B, are resting on a set of perpendicular surfaces and are held in equilibrium by a steel rod that makes an angle \(\theta\) with the horizontal. Given the weights of the cylinders \(W_A = 800 \, \text{N}\) for cylinder A and \(W_B = 200 \, \text{N}\) for cylinder B.
**Objective:**
1. Determine the tension in the steel rod.
2. Determine the angle \(\theta\).
3. Determine the reactions of the supporting surfaces on the cylinders.
4. Draw the necessary free-body diagrams (FBD).
**Diagram Explanation:**
- **Cylinder A** (\(W_A\)):
- Weight: 800 N.
- Rests on a surface inclined at an angle of \(30^\circ\) to the horizontal.
- Connected to a cable.
- **Cylinder B** (\(W_B\)):
- Weight: 200 N.
- Rests on a surface inclined at an angle of \(60^\circ\) to the horizontal.
- Connected to the same cable.
- **Cable:**
- Connects cylinders A and B.
- Forms an angle \(\theta\) with the horizontal between the two cylinders.
**Solution Approach:**
1. **Free-Body Diagrams (FBD):**
Draw the FBD of each cylinder, showing the forces acting on each, including weight (\(W_A\) and \(W_B\)), normal reaction forces from the surfaces (\(N_A\) and \(N_B\)), frictional forces if any (which may be neglected if surfaces are smooth), and the tension \(T\) in the cable.
2. **Equilibrium Equations:**
Set up the equilibrium equations for each cylinder. For horizontal and vertical forces in both cylinders, the sum of forces must be zero.
- For Cylinder A:
\[
\sum F_x = 0 \quad \text{(Horizontal forces)}
\]
\[
\sum F_y = 0 \quad \text{(Vertical forces)}
\]
- For Cylinder B:
\[
\sum F_x = 0 \quad \text{(Horizontal forces)}
\]
\[
\sum F_y
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