Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Transcribed Image Text:### Determining Tension in Cables AB, AC, and AD
#### Problem Statement:
If the magnitude of the vertical force \( F \) is 1.06 kN, determine the tension in cables AB, AC, and AD.
#### Diagram Explanation:
The provided diagram is a 3-dimensional representation of a structural system involving a vertical force \( F \) and four cables, denoted as AB, AC, AD, and AO. The origin \( O \) is located at the ground level, directly below the point where the vertical force \( F \) of 1.06 kN is applied.
1. **Coordinate System**:
- The origin \( O \) is at the intersection of the x, y, and z axes.
- The positive z-axis points upward.
2. **Positions of Anchoring Points**:
- Point \( A \) is located vertically above the origin, at a height of 6 meters on the z-axis.
- Points \( B, C \), and \( D \) are the ground anchoring points of the respective cables.
- \( B \) is located 3 meters along the negative x-axis and 3 meters along the negative y-axis from \( O \).
- \( C \) is located 2 meters along the negative x-axis and 1.5 meters along the positive y-axis from \( O \).
- \( D \) is located 3 meters along the positive x-axis and 6 meters along the positive y-axis from \( O \).
3. **Cables**:
- **Cable AB**: Stretches from point \( A \) to ground point \( B \).
- **Cable AC**: Stretches from point \( A \) to ground point \( C \).
- **Cable AD**: Stretches from point \( A \) to ground point \( D \).
To solve for the tensions in cables AB, AC, and AD, it is essential to use static equilibrium principles, where the sum of forces in all three dimensions (x, y, z) must equal zero.
**Note**: Vector and trigonometric methods will typically be required to resolve the forces in each of the cables and find the tensions accurately.
This example is commonly used in engineering education to teach the principles of static equilibrium and vector resolution of forces.
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