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hree forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Carefully draw a neat, labeled, free body diagram of particle C. Based on your FBD develop two equilibrium equations in terms of the symbols defined on your free body diagram. Find angles α and β. FB= 117.92 kn Fc= 93.507 K

hree forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Carefully draw a neat, labeled, free body diagram of particle C. Based on your FBD develop two equilibrium equations in terms of the symbols defined on your free body diagram. Find angles α and β. FB= 117.92 kn Fc= 93.507 K

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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Three forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Carefully draw a neat, labeled, free body diagram of particle C. Based on your FBD develop two equilibrium equations in terms of the symbols defined on your free body diagram. Find angles α and β. FB= 117.92 kn Fc= 93.507 Kn
### Equilibrium of a Particle **Principles:** For a particle to be in equilibrium, the sum of the forces acting on it must be zero. This requires that the sum of the forces in the x-direction (ΣFx) and the sum of the forces in the y-direction (ΣFy) are both equal to zero. 1. **ΣFx = 0** 2. **ΣFy = 0** **Given Data:** - Height \( h \) = 2.5 ft - Distance \( d_1 \) = 4.75 ft - Distance \( d_2 \) = 3 ft - Load \( W \) = 50 lb **Problem Statement:** Determine the numeric force values with three significant figures for the system shown in the diagram. The load \( W \) is 50 lb. **Diagram Analysis:** The diagram depicts a particle C, which is in equilibrium under the action of: - A horizontal member connected at points A and B. - Two slanted members forming angles \( \alpha \) and \( \beta \) with the horizontal member. - A vertical load \( W \) hanging from point C. - \( A \) and \( B \) are points where the horizontal member is supported. - \( h \) is the vertical distance from the horizontal member to the point C. - \( d_1 \) is the horizontal distance from point A to C. - \( d_2 \) is the horizontal distance from point C to B. ### Detailed Description of Diagram: 1. **Horizontal Member (AB):** - Positioned horizontally with a total length \( d_1 + d_2 \). - Ends labeled A and B. 2. **Vertical Distance (h):** - Shown as a vertical line from the horizontal member down to C. 3. **Angles (\( \alpha \) and \( \beta \)):** - \( \alpha \) is the angle between the horizontal member and the left slanted member. - \( \beta \) is the angle between the horizontal member and the right slanted member. 4. **Vertical Load (W):** - Shown as a weight hanging from point C downward. ### Equilibrium Conditions: To solve for the forces, express the equilibrium conditions along the x and y axes, considering the geometry and dimensions provided. \[ \Sigma F_x =
Transcribed Image Text:### Equilibrium of a Particle **Principles:** For a particle to be in equilibrium, the sum of the forces acting on it must be zero. This requires that the sum of the forces in the x-direction (ΣFx) and the sum of the forces in the y-direction (ΣFy) are both equal to zero. 1. **ΣFx = 0** 2. **ΣFy = 0** **Given Data:** - Height \( h \) = 2.5 ft - Distance \( d_1 \) = 4.75 ft - Distance \( d_2 \) = 3 ft - Load \( W \) = 50 lb **Problem Statement:** Determine the numeric force values with three significant figures for the system shown in the diagram. The load \( W \) is 50 lb. **Diagram Analysis:** The diagram depicts a particle C, which is in equilibrium under the action of: - A horizontal member connected at points A and B. - Two slanted members forming angles \( \alpha \) and \( \beta \) with the horizontal member. - A vertical load \( W \) hanging from point C. - \( A \) and \( B \) are points where the horizontal member is supported. - \( h \) is the vertical distance from the horizontal member to the point C. - \( d_1 \) is the horizontal distance from point A to C. - \( d_2 \) is the horizontal distance from point C to B. ### Detailed Description of Diagram: 1. **Horizontal Member (AB):** - Positioned horizontally with a total length \( d_1 + d_2 \). - Ends labeled A and B. 2. **Vertical Distance (h):** - Shown as a vertical line from the horizontal member down to C. 3. **Angles (\( \alpha \) and \( \beta \)):** - \( \alpha \) is the angle between the horizontal member and the left slanted member. - \( \beta \) is the angle between the horizontal member and the right slanted member. 4. **Vertical Load (W):** - Shown as a weight hanging from point C downward. ### Equilibrium Conditions: To solve for the forces, express the equilibrium conditions along the x and y axes, considering the geometry and dimensions provided. \[ \Sigma F_x =
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