Bar ABC rests against a smooth surface at end C and is supported at end A with a ball-and-socket joint. The cable at B is attached midway between the ends of the bar. Determine the tension in the cable BD. Draw the free body diagram of bar АВС. 600 mm 600 mm 800 N 400 mm 400 mm 400 mm 400 mm 800 mm Determine the tension in cable BE and the reactions at A and C.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem Statement**

Bar \( ABC \) rests against a smooth surface at end \( C \) and is supported at end \( A \) with a ball-and-socket joint. The cable at \( B \) is attached midway between the ends of the bar. Determine the tension in the cable \( BD \).

1. **Free Body Diagram and Setup:**

   - The bar \( ABC \) is positioned with end \( A \) elevated and supported by a ball-and-socket joint.
   - End \( C \) is resting on a smooth surface, allowing no frictional forces.
   - A cable \( BD \) is connected at point \( B \).

2. **Visual Diagrams:**

   - **Diagram 1 (on the left):** 
     - Shows the bar \( ABC \) in isolation. 
     - Ends are labeled, with \( A \) at the top, \( B \) at the midpoint, and \( C \) at the bottom resting on the surface.
  
   - **Diagram 2 (on the right):**
     - A three-dimensional representation.
     - \( A \) is positioned above the surface along the z-axis, at a height of 1200 mm (600 mm + 600 mm).
     - \( C \) is on the x-y plane.
     - The cable joins the bar at \( B \) and extends to \( D \), a distance of 400 mm from both the x and y axes’ origin at \( C \).
     - The bar \( ABC \) is inclined, with an 800 N force acting vertically downward at point \( B \).

3. **Tasks:**

   - Draw the free body diagram of the bar \( ABC \).
   - **Determine the tension in cable \( BE \)** and analyze the reactions at points \( A \) and \( C \).

This setup requires resolving the forces acting on the structure considering equilibrium conditions.
Transcribed Image Text:**Problem Statement** Bar \( ABC \) rests against a smooth surface at end \( C \) and is supported at end \( A \) with a ball-and-socket joint. The cable at \( B \) is attached midway between the ends of the bar. Determine the tension in the cable \( BD \). 1. **Free Body Diagram and Setup:** - The bar \( ABC \) is positioned with end \( A \) elevated and supported by a ball-and-socket joint. - End \( C \) is resting on a smooth surface, allowing no frictional forces. - A cable \( BD \) is connected at point \( B \). 2. **Visual Diagrams:** - **Diagram 1 (on the left):** - Shows the bar \( ABC \) in isolation. - Ends are labeled, with \( A \) at the top, \( B \) at the midpoint, and \( C \) at the bottom resting on the surface. - **Diagram 2 (on the right):** - A three-dimensional representation. - \( A \) is positioned above the surface along the z-axis, at a height of 1200 mm (600 mm + 600 mm). - \( C \) is on the x-y plane. - The cable joins the bar at \( B \) and extends to \( D \), a distance of 400 mm from both the x and y axes’ origin at \( C \). - The bar \( ABC \) is inclined, with an 800 N force acting vertically downward at point \( B \). 3. **Tasks:** - Draw the free body diagram of the bar \( ABC \). - **Determine the tension in cable \( BE \)** and analyze the reactions at points \( A \) and \( C \). This setup requires resolving the forces acting on the structure considering equilibrium conditions.
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