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If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD?

If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD?

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 2 (Problem 3-53, 14th Ed.) **Problem Statement:** If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD? **Illustration Description:** The accompanying diagram shows a three-dimensional setup where a crate is suspended. The diagram includes: - A crate hanging from point A. - Point A is connected by strut AD to point D at the bottom of a wall. - Point A is also connected to point B, which is 4 ft higher vertically and 6 ft away horizontally. - Point D is 6 ft away from A horizontally on the x-axis. - Cable BC is extending from point B to point C. - Point C is located 5.5 ft vertically above point D and directly above it (along the z-axis). - Lastly, point C is 2 ft horizontally and 2 ft vertically away from point B (forming a right triangle with B and D). **Steps to Solve the Problem:** 1. **Determine the Geometry and Coordinates:** - Identify the coordinates of each point (A, B, C, D) in 3D space. - Calculate the lengths of the cables AB, BC, and AD using the Pythagorean theorem in 3-dimensional space. 2. **Analyze the Forces:** - Apply static equilibrium equations to the forces acting on points A and B. - Decompose forces into their components in the x, y, and z directions. - Consider the maximum allowable tension in each cable (300 lb). 3. **Calculate the Maximum Weight:** - Using the equilibrium equations, solve for the maximum weight of the crate that results in tensions not exceeding the given limit. - Ensure that the resultant force on strut AD is also within permissible limits. **Conclusion:** By evaluating the static equilibrium conditions and the geometry of the system, you can determine both the maximum weight of the crate and the force in strut AD. These ensure the safety and effectiveness of the system design while maintaining the structural integrity under the given load constraints.
Transcribed Image Text:### Question 2 (Problem 3-53, 14th Ed.) **Problem Statement:** If the tension developed in each cable cannot exceed 300 lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD? **Illustration Description:** The accompanying diagram shows a three-dimensional setup where a crate is suspended. The diagram includes: - A crate hanging from point A. - Point A is connected by strut AD to point D at the bottom of a wall. - Point A is also connected to point B, which is 4 ft higher vertically and 6 ft away horizontally. - Point D is 6 ft away from A horizontally on the x-axis. - Cable BC is extending from point B to point C. - Point C is located 5.5 ft vertically above point D and directly above it (along the z-axis). - Lastly, point C is 2 ft horizontally and 2 ft vertically away from point B (forming a right triangle with B and D). **Steps to Solve the Problem:** 1. **Determine the Geometry and Coordinates:** - Identify the coordinates of each point (A, B, C, D) in 3D space. - Calculate the lengths of the cables AB, BC, and AD using the Pythagorean theorem in 3-dimensional space. 2. **Analyze the Forces:** - Apply static equilibrium equations to the forces acting on points A and B. - Decompose forces into their components in the x, y, and z directions. - Consider the maximum allowable tension in each cable (300 lb). 3. **Calculate the Maximum Weight:** - Using the equilibrium equations, solve for the maximum weight of the crate that results in tensions not exceeding the given limit. - Ensure that the resultant force on strut AD is also within permissible limits. **Conclusion:** By evaluating the static equilibrium conditions and the geometry of the system, you can determine both the maximum weight of the crate and the force in strut AD. These ensure the safety and effectiveness of the system design while maintaining the structural integrity under the given load constraints.
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