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1. A control rod AB is fixed with a pin connection at B. The rod is 26 in long and is at an angle of 600 from the positive x-axis. A 11.9 lb force F is applied to the end of the control rod (point A) down and to the right, at an angle of a from the rod. Knowing that it creates a 253.4 in lb clockwise moment about point B, determine angle a and the perpendicular distance between the line of action of force F and point B.

1. A control rod AB is fixed with a pin connection at B. The rod is 26 in long and is at an angle of 600 from the positive x-axis. A 11.9 lb force F is applied to the end of the control rod (point A) down and to the right, at an angle of a from the rod. Knowing that it creates a 253.4 in lb clockwise moment about point B, determine angle a and the perpendicular distance between the line of action of force F and point B.

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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Answer should be 1. α = 55o, d⊥ = 21.3 in
### Example Problem on Control Rods and Mechanical Moments **Problem Statement:** 1. A control rod \( AB \) is fixed with a pin connection at \( B \). The rod is 26 inches long and is oriented at an angle of 60 degrees from the positive x-axis. A force \( F \) of 11.9 lbs is applied to the end of the control rod (point \( A \)), directed downwards and to the right, forming an angle \( \alpha \) with the rod. - Knowing that this force creates a 253.4 in-lb clockwise moment about point \( B \), determine the angle \( \alpha \) and the perpendicular distance between the line of action of force \( F \) and point \( B \). **Detailed Explanation:** - **Control Rod Orientation:** - Rod AB is 26 inches in length. - Positioned at an angle of 60 degrees from the positive x-axis. - **Applied Force:** - Force \( F \) = 11.9 lbs. - Acts at point \( A \) in a direction down and to the right. - Forms an angle \( \alpha \) with the rod \( AB \). - **Conditions Given:** - Creates a moment of 253.4 in-lb (clockwise) about point \( B \). - **Objectives:** - Determine the angle \( \alpha \). - Determine the perpendicular distance between the line of action of force \( F \) and point \( B \). **Steps to Solve:** 1. **Identify known quantities:** - Length of rod \( AB \) = 26 inches. - Force \( F \) = 11.9 lbs. - Moment \( M \) = 253.4 in-lb (clockwise). 2. **Decompose the Force:** - Formulate the components of the force in terms of angle \( \alpha \), particularly since the force is always decomposed along and perpendicular to the rod for simplicity in moment calculations. 3. **Utilize Moment Equation:** - Use the torque (moment) equation: \( M = F \cdot d \) - Here, \( d \) is the perpendicular distance from the line of action of \( F \) to point \( B \). 4. **Calculate \( \alpha \):** - Relate the
Transcribed Image Text:### Example Problem on Control Rods and Mechanical Moments **Problem Statement:** 1. A control rod \( AB \) is fixed with a pin connection at \( B \). The rod is 26 inches long and is oriented at an angle of 60 degrees from the positive x-axis. A force \( F \) of 11.9 lbs is applied to the end of the control rod (point \( A \)), directed downwards and to the right, forming an angle \( \alpha \) with the rod. - Knowing that this force creates a 253.4 in-lb clockwise moment about point \( B \), determine the angle \( \alpha \) and the perpendicular distance between the line of action of force \( F \) and point \( B \). **Detailed Explanation:** - **Control Rod Orientation:** - Rod AB is 26 inches in length. - Positioned at an angle of 60 degrees from the positive x-axis. - **Applied Force:** - Force \( F \) = 11.9 lbs. - Acts at point \( A \) in a direction down and to the right. - Forms an angle \( \alpha \) with the rod \( AB \). - **Conditions Given:** - Creates a moment of 253.4 in-lb (clockwise) about point \( B \). - **Objectives:** - Determine the angle \( \alpha \). - Determine the perpendicular distance between the line of action of force \( F \) and point \( B \). **Steps to Solve:** 1. **Identify known quantities:** - Length of rod \( AB \) = 26 inches. - Force \( F \) = 11.9 lbs. - Moment \( M \) = 253.4 in-lb (clockwise). 2. **Decompose the Force:** - Formulate the components of the force in terms of angle \( \alpha \), particularly since the force is always decomposed along and perpendicular to the rod for simplicity in moment calculations. 3. **Utilize Moment Equation:** - Use the torque (moment) equation: \( M = F \cdot d \) - Here, \( d \) is the perpendicular distance from the line of action of \( F \) to point \( B \). 4. **Calculate \( \alpha \):** - Relate the
**Representation of Force on an Inclined Arm:** In this diagram, we have a mechanical setup consisting of an inclined arm, a pivot point, and an applied force. Understanding the elements of this setup can aid in learning about angles and the resolution of forces in mechanics. ### Key Elements: 1. **Pivot Point B:** - The inclined arm is fixed at the base or pivot point labeled as B. - The angle between the inclined arm and the horizontal baseline at this pivot is denoted to be 120 degrees. This is shown in blue on the left side of the diagram. 2. **Inclined Arm AB:** - The arm labeled AB is extending from the pivot point B upwards to point A. - At point A, an external force is applied. 3. **Applied Force F:** - The force is denoted by the red vector labeled F, which is acting at point A. - The direction of the force is shown pointing downwards and to the right. 4. **Angle Alpha (α):** - The angle between the force vector (F) and the arm AB at point A is denoted as α in the diagram. This angle is highlighted in red. ### Applications: This diagram can be used to explain the following concepts in an educational setting: - **Resolution of Forces:** Understanding how a force can be broken down into components along different axes, which is crucial for analyzing mechanical systems. - **Mechanics of Rigid Bodies:** Demonstrating how an external force acting on a body can create rotational effects considering different angles and pivots. - **Angles in Mechanics:** The significance of internal angles and how they relate to the movement and stability of structures. ### Conclusion: Grasping the relationship between the applied force, the inclined arm, and the angles involved will lay a foundation for further studies in physics and engineering mechanics, particularly in understanding how forces cause movement and how structures respond to these forces.
Transcribed Image Text:**Representation of Force on an Inclined Arm:** In this diagram, we have a mechanical setup consisting of an inclined arm, a pivot point, and an applied force. Understanding the elements of this setup can aid in learning about angles and the resolution of forces in mechanics. ### Key Elements: 1. **Pivot Point B:** - The inclined arm is fixed at the base or pivot point labeled as B. - The angle between the inclined arm and the horizontal baseline at this pivot is denoted to be 120 degrees. This is shown in blue on the left side of the diagram. 2. **Inclined Arm AB:** - The arm labeled AB is extending from the pivot point B upwards to point A. - At point A, an external force is applied. 3. **Applied Force F:** - The force is denoted by the red vector labeled F, which is acting at point A. - The direction of the force is shown pointing downwards and to the right. 4. **Angle Alpha (α):** - The angle between the force vector (F) and the arm AB at point A is denoted as α in the diagram. This angle is highlighted in red. ### Applications: This diagram can be used to explain the following concepts in an educational setting: - **Resolution of Forces:** Understanding how a force can be broken down into components along different axes, which is crucial for analyzing mechanical systems. - **Mechanics of Rigid Bodies:** Demonstrating how an external force acting on a body can create rotational effects considering different angles and pivots. - **Angles in Mechanics:** The significance of internal angles and how they relate to the movement and stability of structures. ### Conclusion: Grasping the relationship between the applied force, the inclined arm, and the angles involved will lay a foundation for further studies in physics and engineering mechanics, particularly in understanding how forces cause movement and how structures respond to these forces.
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