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A coplanar force system is shown (1)Find the sum of the three forces (2) Reduce the force system to a force-and-couple resultant at O (3) Reduce the force system to a force-and-couple resultant at an arbitrary point A = (x, y) (4) Locate a point on the r-axis at which the force system can be reduced to a single force

A coplanar force system is shown (1)Find the sum of the three forces (2) Reduce the force system to a force-and-couple resultant at O (3) Reduce the force system to a force-and-couple resultant at an arbitrary point A = (x, y) (4) Locate a point on the r-axis at which the force system can be reduced to a single force

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 coplanar force system is shown
(1)Find the sum of the three forces
(2) Reduce the force system to a force-and-couple resultant at O
(3) Reduce the force system to a force-and-couple resultant at an arbitrary point A = (x, y)
(4) Locate a point on the r-axis at which the force system can be reduced to a single force

### Diagram Explanation for Educational Website #### Work Done by a Force This diagram illustrates the work done by different forces on an object as it moves along the \( x \)-axis. #### Description of the Diagram: 1. **Axes:** - The horizontal axis is labeled as \( x \). - The vertical axis represents distance in the vertical direction. 2. **Path and Forces:** - The object initially starts at the origin (0,0). - The object moves 1 meter to the right horizontally (along the \( x \)-axis) and 6 meters vertically upwards. - Then the object moves horizontally to 6 meters to the left. - The object proceeds to move 6 meters vertically downwards to match the movement of 6 meters upwards. - It then proceeds to move 6 meters horizontally in its initial path towards the right. 3. **Forces:** - **\( F_1 \)**: A horizontal force of 20 Newtons acting towards the right parallel to the \( x \)-axis (horizontal movement). - **\( F_2 \)**: A force of 20 Newtons with a magnitude of 20 Newtons. - **\( F_3 \)**: A force of 20 Newtons with a magnitude of 20 Newtons on the object at point 4 meters to the left. This diagram helps in understanding the forces that are acting on an object and illustrates how work is done by different forces as an object moves through various positions in the \( xy \)-plane. #### Key Concepts: - **Work Done by a Force**: The work \( W \) done by a force \( F \) on an object moving through a displacement \( d \) is calculated as \( W = F \cdot d \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and the direction of displacement. - **Direction of Forces**: The diagram shows the direction of forces acting in different segments of the path, critical for calculating work done in each segment. This visual can be used in physics education to demonstrate the principles of work, energy, and force vector components.
Transcribed Image Text:### Diagram Explanation for Educational Website #### Work Done by a Force This diagram illustrates the work done by different forces on an object as it moves along the \( x \)-axis. #### Description of the Diagram: 1. **Axes:** - The horizontal axis is labeled as \( x \). - The vertical axis represents distance in the vertical direction. 2. **Path and Forces:** - The object initially starts at the origin (0,0). - The object moves 1 meter to the right horizontally (along the \( x \)-axis) and 6 meters vertically upwards. - Then the object moves horizontally to 6 meters to the left. - The object proceeds to move 6 meters vertically downwards to match the movement of 6 meters upwards. - It then proceeds to move 6 meters horizontally in its initial path towards the right. 3. **Forces:** - **\( F_1 \)**: A horizontal force of 20 Newtons acting towards the right parallel to the \( x \)-axis (horizontal movement). - **\( F_2 \)**: A force of 20 Newtons with a magnitude of 20 Newtons. - **\( F_3 \)**: A force of 20 Newtons with a magnitude of 20 Newtons on the object at point 4 meters to the left. This diagram helps in understanding the forces that are acting on an object and illustrates how work is done by different forces as an object moves through various positions in the \( xy \)-plane. #### Key Concepts: - **Work Done by a Force**: The work \( W \) done by a force \( F \) on an object moving through a displacement \( d \) is calculated as \( W = F \cdot d \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and the direction of displacement. - **Direction of Forces**: The diagram shows the direction of forces acting in different segments of the path, critical for calculating work done in each segment. This visual can be used in physics education to demonstrate the principles of work, energy, and force vector components.
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