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Two couples act on a rectangle with a base of 7 m and a height of 4 m. Determine the magnitude and direction of the resultant moment, knowing that F = 80N and G = 25N. 70° F

Two couples act on a rectangle with a base of 7 m and a height of 4 m. Determine the magnitude and direction of the resultant moment, knowing that F = 80N and G = 25N. 70° F

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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Answe should be 735.7 nm cw
### Problem Statement Two couples act on a rectangle with a base of 7 meters and a height of 4 meters. Determine the magnitude and direction of the resultant moment, knowing that \( F = 80 \, \text{N} \) and \( G = 25 \, \text{N} \). ### Diagram Explanation The diagram depicts a rectangle positioned horizontally. - The rectangle has a base of 7 m (along the horizontal axis) and a height of 4 m (along the vertical axis). - Four forces act on the rectangle at its corners: - In the upper left corner, a force \( F \) of 80 N is acting at an angle of 70° above the horizontal axis. - In the lower right corner, a force \(-F \) of 80 N is acting at an angle of 70° below the horizontal axis. - In the lower left corner, a force \(-G \) of 25 N is acting leftward along the horizontal axis. - In the upper right corner, a force \( G \) of 25 N is acting rightward along the horizontal axis. ### Analysis - The forces form a couple system, which implies that each pair of forces will create a moment about the center of the rectangle. - The moment caused by a couple is calculated by multiplying the force by the perpendicular distance between the lines of action of the force pair. ### Magnitude and Direction Calculation 1. **Forces \( F \) and \(-F \) (at 70°)** - Perpendicular distance between \( F \) and \(-F \) in the horizontal direction is 7 m. - Component of force \( F \) along the vertical axis: \( F \sin(70°) \) - Component of force \(-F \) along the vertical axis: \(-F \sin(70°) \) - Effective vertical force: \( (F - F) \sin(70°) = 0 \). - Therefore, no moment contribution in the horizontal pairs. 2. **Forces \( G \) and \(-G \)** - Perpendicular distance between \( G \) and \(-G \) in the vertical direction is 4 m. - Component of force \( G \) along the vertical axis: \( G \cos(0°) = G
Transcribed Image Text:### Problem Statement Two couples act on a rectangle with a base of 7 meters and a height of 4 meters. Determine the magnitude and direction of the resultant moment, knowing that \( F = 80 \, \text{N} \) and \( G = 25 \, \text{N} \). ### Diagram Explanation The diagram depicts a rectangle positioned horizontally. - The rectangle has a base of 7 m (along the horizontal axis) and a height of 4 m (along the vertical axis). - Four forces act on the rectangle at its corners: - In the upper left corner, a force \( F \) of 80 N is acting at an angle of 70° above the horizontal axis. - In the lower right corner, a force \(-F \) of 80 N is acting at an angle of 70° below the horizontal axis. - In the lower left corner, a force \(-G \) of 25 N is acting leftward along the horizontal axis. - In the upper right corner, a force \( G \) of 25 N is acting rightward along the horizontal axis. ### Analysis - The forces form a couple system, which implies that each pair of forces will create a moment about the center of the rectangle. - The moment caused by a couple is calculated by multiplying the force by the perpendicular distance between the lines of action of the force pair. ### Magnitude and Direction Calculation 1. **Forces \( F \) and \(-F \) (at 70°)** - Perpendicular distance between \( F \) and \(-F \) in the horizontal direction is 7 m. - Component of force \( F \) along the vertical axis: \( F \sin(70°) \) - Component of force \(-F \) along the vertical axis: \(-F \sin(70°) \) - Effective vertical force: \( (F - F) \sin(70°) = 0 \). - Therefore, no moment contribution in the horizontal pairs. 2. **Forces \( G \) and \(-G \)** - Perpendicular distance between \( G \) and \(-G \) in the vertical direction is 4 m. - Component of force \( G \) along the vertical axis: \( G \cos(0°) = G
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