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The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces?
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The following coplanar forces are acting at a point, the given angles ...
Understanding the Forces
To determine the resultant of the given coplanar forces graphically, we will break down each force into its horizontal and vertical components based on the angles provided.
Force Breakdown
- 100N at 30°
- Horizontal: 100 * cos(30°)
- Vertical: 100 * sin(30°)
- 200N at 80°
- Horizontal: 200 * cos(80°)
- Vertical: 200 * sin(80°)
- 40N at -150°
- Horizontal: 40 * cos(-150°)
- Vertical: 40 * sin(-150°)
- 120N at -100°
- Horizontal: 120 * cos(-100°)
- Vertical: 120 * sin(-100°)
- 70N at -60°
- Horizontal: 70 * cos(-60°)
- Vertical: 70 * sin(-60°)
Graphical Representation
1. Draw each force on a graph using a protractor to measure angles accurately.
2. Use a scale (e.g., 1 cm = 20 N) to represent the forces.
3. Draw the forces head-to-tail to find the resultant vector.
Resultant Calculation
- Sum all horizontal components to get the total horizontal force.
- Sum all vertical components to get the total vertical force.
Magnitude and Direction
- Magnitude: Use the Pythagorean theorem to calculate the resultant force.
- Direction: Calculate the angle of the resultant using the tangent function (inverse tangent of vertical sum/horizontal sum).
Conclusion
The graphical method provides a clear visual representation of the forces acting at a point, allowing for an accurate determination of the resultant force's magnitude and direction. This method emphasizes the importance of vector addition in solving problems related to forces in physics.
To determine the resultant of the given coplanar forces graphically, we will break down each force into its horizontal and vertical components based on the angles provided.
Force Breakdown
- 100N at 30°
- Horizontal: 100 * cos(30°)
- Vertical: 100 * sin(30°)
- 200N at 80°
- Horizontal: 200 * cos(80°)
- Vertical: 200 * sin(80°)
- 40N at -150°
- Horizontal: 40 * cos(-150°)
- Vertical: 40 * sin(-150°)
- 120N at -100°
- Horizontal: 120 * cos(-100°)
- Vertical: 120 * sin(-100°)
- 70N at -60°
- Horizontal: 70 * cos(-60°)
- Vertical: 70 * sin(-60°)
Graphical Representation
1. Draw each force on a graph using a protractor to measure angles accurately.
2. Use a scale (e.g., 1 cm = 20 N) to represent the forces.
3. Draw the forces head-to-tail to find the resultant vector.
Resultant Calculation
- Sum all horizontal components to get the total horizontal force.
- Sum all vertical components to get the total vertical force.
Magnitude and Direction
- Magnitude: Use the Pythagorean theorem to calculate the resultant force.
- Direction: Calculate the angle of the resultant using the tangent function (inverse tangent of vertical sum/horizontal sum).
Conclusion
The graphical method provides a clear visual representation of the forces acting at a point, allowing for an accurate determination of the resultant force's magnitude and direction. This method emphasizes the importance of vector addition in solving problems related to forces in physics.
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The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces?
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The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces?.
The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following coplanar forces are acting at a point, the given angles being measured from horizontal. 100N at 30° ,200N at at 80°,40N at -150° ,120N at -100 and 70N at -60°. Determine graphically the magnitude and direction of the five forces?.
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