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A 150 lb cylinder is supported by two cables AC and BC that are attached to the top of vertical posts. A horizontal force P, which is perpendicular to the plane containing the posts, holds the cylinder in the position shown. What is the magnitude of force P required to hold it in place?

A 150 lb cylinder is supported by two cables AC and BC that are attached to the top of vertical posts. A horizontal force P, which is perpendicular to the plane containing the posts, holds the cylinder in the position shown. What is the magnitude of force P required to hold it in place?

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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-Free Body Diagram
-Unit vectors calculated correctly and multiplied by unknown magnitudes
-Components separated and set equal to zero to get three equations.  Solve for AC, BC and P. attach the imagae
**Problem Statement:** A 150 lb cylinder is supported by two cables AC and BC that are attached to the top of vertical posts. A horizontal force P, which is perpendicular to the plane containing the posts, holds the cylinder in the position shown. What is the magnitude of force P required to hold it in place? **Diagram Explanation:** In the diagram, there's a 3D coordinate system with the axes labeled x, y, and z. - Point A is at the top of the first post, which is 10.8 feet in the x-direction and 15 feet in the z-direction. - Point B is at the top of the second post, also 10.8 feet from the origin in the x-direction, but on the opposite side. - Point C is where the cables meet on the x-y plane, 3.6 feet from the origin along the positive x-axis. - The distance between Points A and C, and between B and C, is depicted as tension cables connecting the cylinder to the tops of the posts. - A horizontal force P is applied in the negative x-direction from point C. - The cylinder is hanging from point C vertically downward to point O, which is at the origin of the coordinate system. **Measurements:** - The two supports A and B are each 15 feet tall. - The point C is 3.6 feet along the x-direction from the vertical through the cylinder's center O. - The horizontal distance between the bases of the posts supporting A and B is 2 x 10.8 feet or 21.6 feet along the x-direction. - The force P acts perpendicular to the axis formed by the posts at a horizontal distance of 7.2 feet from the base of post A. The problem involves calculating the tension and force vectors required to maintain equilibrium of the 150 lb cylinder.
Transcribed Image Text:**Problem Statement:** A 150 lb cylinder is supported by two cables AC and BC that are attached to the top of vertical posts. A horizontal force P, which is perpendicular to the plane containing the posts, holds the cylinder in the position shown. What is the magnitude of force P required to hold it in place? **Diagram Explanation:** In the diagram, there's a 3D coordinate system with the axes labeled x, y, and z. - Point A is at the top of the first post, which is 10.8 feet in the x-direction and 15 feet in the z-direction. - Point B is at the top of the second post, also 10.8 feet from the origin in the x-direction, but on the opposite side. - Point C is where the cables meet on the x-y plane, 3.6 feet from the origin along the positive x-axis. - The distance between Points A and C, and between B and C, is depicted as tension cables connecting the cylinder to the tops of the posts. - A horizontal force P is applied in the negative x-direction from point C. - The cylinder is hanging from point C vertically downward to point O, which is at the origin of the coordinate system. **Measurements:** - The two supports A and B are each 15 feet tall. - The point C is 3.6 feet along the x-direction from the vertical through the cylinder's center O. - The horizontal distance between the bases of the posts supporting A and B is 2 x 10.8 feet or 21.6 feet along the x-direction. - The force P acts perpendicular to the axis formed by the posts at a horizontal distance of 7.2 feet from the base of post A. The problem involves calculating the tension and force vectors required to maintain equilibrium of the 150 lb cylinder.
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