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Q-1. The pot in the figure has a mass of 50 kg and it is supported by three cables AB, AC and AD. Determine the tension force acting in each cable: B 2.5 m 6 m -2 m- D 6 m 3 m

Q-1. The pot in the figure has a mass of 50 kg and it is supported by three cables AB, AC and AD. Determine the tension force acting in each cable: B 2.5 m 6 m -2 m- D 6 m 3 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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**Question 1:** The pot in the figure has a mass of 50 kg and is supported by three cables AB, AC, and AD. Determine the tension force acting in each cable. **Description of the Diagram:** The figure shows a pot hanging and being supported by three cables labeled AB, AC, and AD. The coordinates and measurements for each point are as follows: - Point A is the point where all three cables converge and support the pot. - Cable AB extends from point A to point B. Point B is located at a distance of 2.5 meters along the x-axis and 6 meters along the z-axis from point A. - Cable AC extends from point A to point C. Point C is located at a distance of 2 meters along the x-axis from point A. - Cable AD extends from point A to point D. Point D is located at a distance of 2 meters along the x-axis and at 3 meters along the y-axis from point A. ### Explanation and Calculation: To determine the tension forces in cables AB, AC, and AD, we will need to consider the forces acting on point A due to each of the cables and ensure that the vector sum of these forces equals the gravitational force acting on the box. The gravitational force is \( 50 \, \text{kg} \times 9.81 \, \text{m/s}^2 \). This involves setting up a system of equations based on the equilibrium condition, ensuring the sum of forces in each direction (x, y, and z) equals zero. The detailed steps to determine the tension forces include: 1. Resolve each tension force into its component forces. 2. Apply the equilibrium conditions for forces in the x, y, and z directions. 3. Solve the system of equations for the tensions in each cable. The geometry of the setup and the given measurements will help in establishing the direction cosines for each of the cables, which are essential in breaking the forces into their respective components. The educational website could provide a detailed step-by-step solution, discussing vector components, equilibrium equations and the method to solve such systems involving multiple forces.
Transcribed Image Text:**Question 1:** The pot in the figure has a mass of 50 kg and is supported by three cables AB, AC, and AD. Determine the tension force acting in each cable. **Description of the Diagram:** The figure shows a pot hanging and being supported by three cables labeled AB, AC, and AD. The coordinates and measurements for each point are as follows: - Point A is the point where all three cables converge and support the pot. - Cable AB extends from point A to point B. Point B is located at a distance of 2.5 meters along the x-axis and 6 meters along the z-axis from point A. - Cable AC extends from point A to point C. Point C is located at a distance of 2 meters along the x-axis from point A. - Cable AD extends from point A to point D. Point D is located at a distance of 2 meters along the x-axis and at 3 meters along the y-axis from point A. ### Explanation and Calculation: To determine the tension forces in cables AB, AC, and AD, we will need to consider the forces acting on point A due to each of the cables and ensure that the vector sum of these forces equals the gravitational force acting on the box. The gravitational force is \( 50 \, \text{kg} \times 9.81 \, \text{m/s}^2 \). This involves setting up a system of equations based on the equilibrium condition, ensuring the sum of forces in each direction (x, y, and z) equals zero. The detailed steps to determine the tension forces include: 1. Resolve each tension force into its component forces. 2. Apply the equilibrium conditions for forces in the x, y, and z directions. 3. Solve the system of equations for the tensions in each cable. The geometry of the setup and the given measurements will help in establishing the direction cosines for each of the cables, which are essential in breaking the forces into their respective components. The educational website could provide a detailed step-by-step solution, discussing vector components, equilibrium equations and the method to solve such systems involving multiple forces.
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