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Q.4) Determine the tensions in the three cables supporting a weight of 180 N as shown in figure below. Draw the necessary free-body diagram. 6 m 4 m 5 m 5 m 8 m 8 m

Q.4) Determine the tensions in the three cables supporting a weight of 180 N as shown in figure below. Draw the necessary free-body diagram. 6 m 4 m 5 m 5 m 8 m 8 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
Problem 1.1MA
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### Question 4: Determining Tensions in Supporting Cables **Problem Statement:** Determine the tensions in the three cables supporting a weight of 180 N as shown in the figure below. Draw the necessary free-body diagram. **Figure Description:** The provided figure illustrates a three-dimensional setup where a traffic light weighing 180 N is suspended by three cables connected to three different points labeled A, B, and C. The positions of these points and their respective distances from each other are key to solving the problem. **Details of the Diagram:** 1. **Point A:** - `x-coordinate (horizontal distance)`: 4 m from the origin. - `z-coordinate (vertical distance)`: 5 m from the origin. 2. **Point B:** - `x-coordinate`: 6 m from the origin. - No `y-coordinate` value provided (it can be inferred from the problem context or assumed as 0 in a typical layout). 3. **Point C:** - `y-coordinate`: 8 m from the origin. - `z-coordinate`: 5 m from the origin. 4. **Distances between points:** - The distance between points A and the origin is 8 m. - The distance between points B and the origin is 6 m. - The distance between points C and the origin is 8 m. **Free-Body Diagram:** In order to solve for the tensions in the three cables, a free-body diagram would need to be constructed. This diagram should show: - The traffic light at the origin (as the point of intersection of the cables) - The vectors representing the tensions in cables tied to points A, B, and C - The 180 N downward force representing the weight of the traffic light **Steps for Solution:** 1. **Construct the Free-Body Diagram:** - Identify all the forces acting on the traffic light. These forces include the weight acting downward (180 N) and the tensions in the three cables. - Establish the coordinate system (usually the Cartesian coordinate system with x, y, and z axes) where the traffic light is located at the origin. 2. **Formulate the Equations:** - Use the equilibrium conditions: The sum of forces in the x, y, and z directions must each be zero since the traffic light is stationary. - Represent the tensions in the cables
Transcribed Image Text:### Question 4: Determining Tensions in Supporting Cables **Problem Statement:** Determine the tensions in the three cables supporting a weight of 180 N as shown in the figure below. Draw the necessary free-body diagram. **Figure Description:** The provided figure illustrates a three-dimensional setup where a traffic light weighing 180 N is suspended by three cables connected to three different points labeled A, B, and C. The positions of these points and their respective distances from each other are key to solving the problem. **Details of the Diagram:** 1. **Point A:** - `x-coordinate (horizontal distance)`: 4 m from the origin. - `z-coordinate (vertical distance)`: 5 m from the origin. 2. **Point B:** - `x-coordinate`: 6 m from the origin. - No `y-coordinate` value provided (it can be inferred from the problem context or assumed as 0 in a typical layout). 3. **Point C:** - `y-coordinate`: 8 m from the origin. - `z-coordinate`: 5 m from the origin. 4. **Distances between points:** - The distance between points A and the origin is 8 m. - The distance between points B and the origin is 6 m. - The distance between points C and the origin is 8 m. **Free-Body Diagram:** In order to solve for the tensions in the three cables, a free-body diagram would need to be constructed. This diagram should show: - The traffic light at the origin (as the point of intersection of the cables) - The vectors representing the tensions in cables tied to points A, B, and C - The 180 N downward force representing the weight of the traffic light **Steps for Solution:** 1. **Construct the Free-Body Diagram:** - Identify all the forces acting on the traffic light. These forces include the weight acting downward (180 N) and the tensions in the three cables. - Establish the coordinate system (usually the Cartesian coordinate system with x, y, and z axes) where the traffic light is located at the origin. 2. **Formulate the Equations:** - Use the equilibrium conditions: The sum of forces in the x, y, and z directions must each be zero since the traffic light is stationary. - Represent the tensions in the cables
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