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Determine the horizontal and vertical components of reactions at the pin at A and the reaction of the roller at B on the lever.

Determine the horizontal and vertical components of reactions at the pin at A and the reaction of the roller at B on the lever.

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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I a bit confused on the process can you please be detailed.

### Problem R5-4 (14th Edition) **Problem Statement:** Determine the horizontal and vertical components of reactions at the pin at \( A \) and the reaction of the roller at \( B \) on the lever. **Diagram Explanation:** The figure illustrates a lever system with the following components and dimensions: - The lever is anchored to a fixed pin at point \( A \). - The lever extends horizontally with point \( B \) being supported by a roller. - A force \( F = 50 \, \text{lb} \) is applied at an angle of \( 30^\circ \) from the horizontal. - The vertical distance from the line of action of the force to the base level of point \( A \) is \( 14 \, \text{in.} \). - The horizontal distance from point \( A \) to the point where the force is applied is \( 20 \, \text{in.} \). - The horizontal distance from point \( A \) to the roller at point \( B \) is \( 18 \, \text{in.} \). ### Key Points to Determine: 1. **Reactions at Pin \( A \):** - Horizontal component (\( A_x \)). - Vertical component (\( A_y \)). 2. **Reactions at Roller \( B \):** - Reaction force at \( B \) (\( B_y \)). To solve this problem, the following principles of static equilibrium will be applied: - \(\sum F_x = 0\): The sum of all horizontal forces must be zero. - \(\sum F_y = 0\): The sum of all vertical forces must be zero. - \(\sum M_A = 0\): The sum of moments about point \( A \) must be zero. These equations will help in determining the values of \( A_x \), \( A_y \), and \( B_y \).
Transcribed Image Text:### Problem R5-4 (14th Edition) **Problem Statement:** Determine the horizontal and vertical components of reactions at the pin at \( A \) and the reaction of the roller at \( B \) on the lever. **Diagram Explanation:** The figure illustrates a lever system with the following components and dimensions: - The lever is anchored to a fixed pin at point \( A \). - The lever extends horizontally with point \( B \) being supported by a roller. - A force \( F = 50 \, \text{lb} \) is applied at an angle of \( 30^\circ \) from the horizontal. - The vertical distance from the line of action of the force to the base level of point \( A \) is \( 14 \, \text{in.} \). - The horizontal distance from point \( A \) to the point where the force is applied is \( 20 \, \text{in.} \). - The horizontal distance from point \( A \) to the roller at point \( B \) is \( 18 \, \text{in.} \). ### Key Points to Determine: 1. **Reactions at Pin \( A \):** - Horizontal component (\( A_x \)). - Vertical component (\( A_y \)). 2. **Reactions at Roller \( B \):** - Reaction force at \( B \) (\( B_y \)). To solve this problem, the following principles of static equilibrium will be applied: - \(\sum F_x = 0\): The sum of all horizontal forces must be zero. - \(\sum F_y = 0\): The sum of all vertical forces must be zero. - \(\sum M_A = 0\): The sum of moments about point \( A \) must be zero. These equations will help in determining the values of \( A_x \), \( A_y \), and \( B_y \).
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