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The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A.

The bent rod ACDB is supported by a sleeve at A and a ball-and-socket joint at B. Determine the components of the reactions and the tension in the cable. Neglect the mass of the rod and any moment reactions at A.

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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The problem presented involves a bent rod ACDB supported by a sleeve at point A and a ball-and-socket joint at point B. The task is to determine the components of the reactions at the supports and the tension in the cable. It is specified to neglect the mass of the rod and any moment reactions at point A. ### Diagram Description: The diagram shows a rod with the following segments and dimensions: - **Segment AC:** 0.7 meters along the x-axis - **Segment CD:** 0.4 meters along the x-axis - **Segment DB:** 0.4 meters along the z-axis **Cable:** The cable stretches from point D to point E, at an elevation of 0.5 meters in the z-direction from point O. **Weights and Forces:** - A mass of 82 kg is hanging at point C, producing a gravitational force. **Coordinate System:** - A coordinate system is depicted with axes labeled as x, y, and z, providing a spatial reference for measurements. ### Points of Interest: - **Point A:** Location of the sleeve support, along the x-axis, fixed. - **Point B:** Location of the ball-and-socket joint, able to rotate. - **Point C and D:** Points along the rod influencing geometry and tension in the system. - **Point E:** Attachment point of the cable influencing tension and reaction forces. ### Objective: Calculate the support reactions at A and B, and the tension in the cable, ensuring a static equilibrium of the system.
Transcribed Image Text:The problem presented involves a bent rod ACDB supported by a sleeve at point A and a ball-and-socket joint at point B. The task is to determine the components of the reactions at the supports and the tension in the cable. It is specified to neglect the mass of the rod and any moment reactions at point A. ### Diagram Description: The diagram shows a rod with the following segments and dimensions: - **Segment AC:** 0.7 meters along the x-axis - **Segment CD:** 0.4 meters along the x-axis - **Segment DB:** 0.4 meters along the z-axis **Cable:** The cable stretches from point D to point E, at an elevation of 0.5 meters in the z-direction from point O. **Weights and Forces:** - A mass of 82 kg is hanging at point C, producing a gravitational force. **Coordinate System:** - A coordinate system is depicted with axes labeled as x, y, and z, providing a spatial reference for measurements. ### Points of Interest: - **Point A:** Location of the sleeve support, along the x-axis, fixed. - **Point B:** Location of the ball-and-socket joint, able to rotate. - **Point C and D:** Points along the rod influencing geometry and tension in the system. - **Point E:** Attachment point of the cable influencing tension and reaction forces. ### Objective: Calculate the support reactions at A and B, and the tension in the cable, ensuring a static equilibrium of the system.
### Transcription for Educational Use The image presents a list of forces measured in newtons (N) as follows: - **\(A_y = 573.99 \, \text{N}\)** - **\(A_z = 351.42 \, \text{N}\)** - **\(B_x = 328 \, \text{N}\)** - **\(B_y = 573.996 \, \text{N}\)** - **\(B_z = 351.42 \, \text{N}\)** - **\(T = 1673.46 \, \text{N}\)** Each force component is associated with a direction in a three-dimensional space, denoted by the subscripts \(x\), \(y\), and \(z\). The total force, \(T\), is also listed. **Explanation:** - The values represent vector components of forces acting in different directions. - The notation suggests that these may be components related to two different vectors (\(A\) and \(B\)) projected in a 3D coordinate system. - \(T\) likely represents the resultant or total force obtained from a combination of these components. This type of data might be used in studies related to physics or engineering, focusing on force analysis or vector resolution.
Transcribed Image Text:### Transcription for Educational Use The image presents a list of forces measured in newtons (N) as follows: - **\(A_y = 573.99 \, \text{N}\)** - **\(A_z = 351.42 \, \text{N}\)** - **\(B_x = 328 \, \text{N}\)** - **\(B_y = 573.996 \, \text{N}\)** - **\(B_z = 351.42 \, \text{N}\)** - **\(T = 1673.46 \, \text{N}\)** Each force component is associated with a direction in a three-dimensional space, denoted by the subscripts \(x\), \(y\), and \(z\). The total force, \(T\), is also listed. **Explanation:** - The values represent vector components of forces acting in different directions. - The notation suggests that these may be components related to two different vectors (\(A\) and \(B\)) projected in a 3D coordinate system. - \(T\) likely represents the resultant or total force obtained from a combination of these components. This type of data might be used in studies related to physics or engineering, focusing on force analysis or vector resolution.
Expert Solution
Step 1

To Find : 

The component of the reactions and the tension in the cable .

Given : 

The weight of block is

 w=mg=82·9.81=804.42 N

Free body diagram :

The F.B.D is :

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