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A 3m x 4m rigid board of weight W is free to rotate about the hinge. Equilibrium is maintained by a rope connecting a point B (with a = 2m) at the edge of the board to a point A (0,1,2) on the wall. Tension in the rope is found to be 500 N. Note the chosen x-y-z coordinate frame. (a) Draw a free body diagram of the board (without hinge) only. (b) Find the moment induced by the rope tension about the hinge. (c) Find weight of the board W.

A 3m x 4m rigid board of weight W is free to rotate about the hinge. Equilibrium is maintained by a rope connecting a point B (with a = 2m) at the edge of the board to a point A (0,1,2) on the wall. Tension in the rope is found to be 500 N. Note the chosen x-y-z coordinate frame. (a) Draw a free body diagram of the board (without hinge) only. (b) Find the moment induced by the rope tension about the hinge. (c) Find weight of the board W.

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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A 3m x 4m rigid board of weight W is free to rotate about the hinge. Equilibrium is maintained by a rope connecting a point B (with a = 2m) at the edge of the board to a point A (0,1,2) on the wall. Tension in the rope is found to be 500 N. Note the chosen x-y-z coordinate frame. (a) Draw a free body diagram of the board (without hinge) only. (b) Find the moment induced by the rope tension about the hinge. (c) Find weight of the board W.

The image depicts a rectangular plate placed in a three-dimensional coordinate system with axes labeled x, y, and z. ### Diagram Explanation: 1. **Coordinate System:** - The x-axis runs horizontally in the plane of the plate. - The y-axis runs horizontally out of the plane to the right. - The z-axis runs vertically upwards. 2. **Plate Dimensions:** - The plate is rectangular with dimensions 4 meters along the x-axis and 3 meters along the y-axis. 3. **Forces on the Plate:** - A point labeled A is located at the top left corner of the plate. - A force T is represented by a blue arrow pointing diagonally from point A toward point B, which is on the opposite corner of the plate. - A force W is shown as a vertical blue arrow pointing downward from point B on the z-axis. 4. **Angle and Distance:** - The angle α is marked between the edge of the plate on the y-axis and the line from point B extending along the y-edge of the plate. 5. **Supports:** - The plate is depicted as being supported on the left edge along the x-axis with brackets, suggesting it is fixed or hinged at this edge. ### Educational Context: This diagram can be utilized to explain concepts in physics and engineering, such as analyzing torque and equilibrium in static systems, calculating resultant forces, and understanding force components in three-dimensional spaces. It provides a clear visual representation for solving practical problems related to forces acting on rigid bodies in equilibrium.
Transcribed Image Text:The image depicts a rectangular plate placed in a three-dimensional coordinate system with axes labeled x, y, and z. ### Diagram Explanation: 1. **Coordinate System:** - The x-axis runs horizontally in the plane of the plate. - The y-axis runs horizontally out of the plane to the right. - The z-axis runs vertically upwards. 2. **Plate Dimensions:** - The plate is rectangular with dimensions 4 meters along the x-axis and 3 meters along the y-axis. 3. **Forces on the Plate:** - A point labeled A is located at the top left corner of the plate. - A force T is represented by a blue arrow pointing diagonally from point A toward point B, which is on the opposite corner of the plate. - A force W is shown as a vertical blue arrow pointing downward from point B on the z-axis. 4. **Angle and Distance:** - The angle α is marked between the edge of the plate on the y-axis and the line from point B extending along the y-edge of the plate. 5. **Supports:** - The plate is depicted as being supported on the left edge along the x-axis with brackets, suggesting it is fixed or hinged at this edge. ### Educational Context: This diagram can be utilized to explain concepts in physics and engineering, such as analyzing torque and equilibrium in static systems, calculating resultant forces, and understanding force components in three-dimensional spaces. It provides a clear visual representation for solving practical problems related to forces acting on rigid bodies in equilibrium.
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