A container of weight W is suspended from ring A to which cables AC and AE are attached. A force P is applied to the end F of a third cable that passes over a pulley at B and through ring A and that attached to a support at D. Knowing that P=1000N , determine the tension in AC.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Title: Analysis of Cable Tension in a Multi-Cable System**

**Introduction:**

In this problem, we explore the tension in cable AC of a suspended weight system. A container of weight \( W \) is suspended from ring \( A \) to which cables \( AC \) and \( AE \) are attached. A force \( P \) is applied to the end \( F \) of a third cable that passes over a pulley at \( B \) and through ring \( A \), and is attached to a support at \( D \). Given that \( P = 1000 \, \text{N} \), our task is to determine the tension in cable \( AC \).

**Diagram Explanation:**

The diagram depicts a 3D spatial arrangement of the cables connected to the ring \( A \). 

1. **Axes:**
   - The coordinate axes \( x \), \( y \), and \( z \) are indicated for spatial reference. 
   - The point \( A \) is the junction where all the cables meet and where the weight \( W \) is attached directly below.

2. **Cable Intersections:**
   - \( AC \) and \( AE \) are horizontal cables anchored at distances from \( A \) given in the \( xy \)-plane.
   - Cable \( BE \) passes over a pulley at \( B \) and redirects the force applied at point \( F \).

3. **Key Measurements:**
   - The distance from \( B \) to the vertical plane containing \( A \) is \( 0.86 \, \text{m} \).
   - The height difference between \( A \) and \( B \) along the z-axis is \( 1.20 \, \text{m} \).
   - The distance from \( C \) to \( A \) along the x-axis is \( 0.78 \, \text{m} \).
   - Points \( E \) and \( D \) are horizontally aligned along the y-axis, each \( 0.40 \, \text{m} \) from their connection points on the plane.

**Objective:**

To calculate the tension in cable \( AC \), analyzing forces exerted at ring \( A \) due to the applied force \( P \), and the layout and constraints described. This will involve using principles from statics, specifically equilibrium conditions for forces
Transcribed Image Text:**Title: Analysis of Cable Tension in a Multi-Cable System** **Introduction:** In this problem, we explore the tension in cable AC of a suspended weight system. A container of weight \( W \) is suspended from ring \( A \) to which cables \( AC \) and \( AE \) are attached. A force \( P \) is applied to the end \( F \) of a third cable that passes over a pulley at \( B \) and through ring \( A \), and is attached to a support at \( D \). Given that \( P = 1000 \, \text{N} \), our task is to determine the tension in cable \( AC \). **Diagram Explanation:** The diagram depicts a 3D spatial arrangement of the cables connected to the ring \( A \). 1. **Axes:** - The coordinate axes \( x \), \( y \), and \( z \) are indicated for spatial reference. - The point \( A \) is the junction where all the cables meet and where the weight \( W \) is attached directly below. 2. **Cable Intersections:** - \( AC \) and \( AE \) are horizontal cables anchored at distances from \( A \) given in the \( xy \)-plane. - Cable \( BE \) passes over a pulley at \( B \) and redirects the force applied at point \( F \). 3. **Key Measurements:** - The distance from \( B \) to the vertical plane containing \( A \) is \( 0.86 \, \text{m} \). - The height difference between \( A \) and \( B \) along the z-axis is \( 1.20 \, \text{m} \). - The distance from \( C \) to \( A \) along the x-axis is \( 0.78 \, \text{m} \). - Points \( E \) and \( D \) are horizontally aligned along the y-axis, each \( 0.40 \, \text{m} \) from their connection points on the plane. **Objective:** To calculate the tension in cable \( AC \), analyzing forces exerted at ring \( A \) due to the applied force \( P \), and the layout and constraints described. This will involve using principles from statics, specifically equilibrium conditions for forces
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