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2/9 Two forces are applied to the construction bracket as shown. Determine the angle @ which makes the resul- tant of the two forces vertical. Determine the magni- tude R of the resultant. F = 800 lb y F = 425 lb 70%

2/9 Two forces are applied to the construction bracket as shown. Determine the angle @ which makes the resul- tant of the two forces vertical. Determine the magni- tude R of the resultant. F = 800 lb y F = 425 lb 70%

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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ONLY ANSWER 1, 2 & 3!!!!!!!!!!!!!!!!!

1.The problem sketch shows _____ loads. 

2.The moment load (the couple) has a magnitude of _____ N*m.

3.The resultant moment induced by all of the loads has a magnitude of _____ N*m.

 
## Problem 2/9 **Problem Description:** Two forces are applied to the construction bracket as shown in the diagram. The problem requires determining the angle θ which makes the resultant of the two forces vertical. Additionally, the magnitude \( R \) of the resultant needs to be determined. **Given:** - Force \( F_1 = 800 \) lb - Force \( F_2 = 425 \) lb **Objective:** 1. Determine the angle θ that makes the resultant of the two forces vertical. 2. Determine the magnitude \( R \) of the resultant force. ### Explanation of Diagram: - **Forces:** - \( F_1 \) is applied at an angle θ from the vertical axis \( y \). - \( F_2 \) is applied at an angle of 70° counterclockwise from the horizontal axis \( x \). - **Coordinate Axes:** - The diagram shows \( x \), \( y \), and \( z \) axes for spatial orientation. - **Construction Bracket:** - The forces are applied to the bracket, which is fixed to a base on a surface. - **Resultant Force:** - The goal is to find a specific angle \( θ \) such that the sum of the forces \( F_1 \) and \( F_2 \) results in a vertical line of action, meaning no resultant horizontal component. ### Solution Outline: To solve this problem, we need to: 1. Resolve each force into its horizontal and vertical components. 2. Sum the horizontal components of \( F_1 \) and \( F_2 \) to be zero (since the resultant force must be vertical). 3. Use trigonometric relationships to solve for angle θ. 4. Calculate the magnitude \( R \) using the vertical components of the forces. ### Equations: - \( F_1 \) components: - \( F_{1x} = F_1 \sin(\theta) \) - \( F_{1y} = F_1 \cos(\theta) \) - \( F_2 \) components: - \( F_{2x} = F_2 \cos(70^\circ) \) - \( F_{2y} = F_2 \sin(70^\circ) \) - Resultant vertical and horizontal component equations: - \( R_x =
Transcribed Image Text:## Problem 2/9 **Problem Description:** Two forces are applied to the construction bracket as shown in the diagram. The problem requires determining the angle θ which makes the resultant of the two forces vertical. Additionally, the magnitude \( R \) of the resultant needs to be determined. **Given:** - Force \( F_1 = 800 \) lb - Force \( F_2 = 425 \) lb **Objective:** 1. Determine the angle θ that makes the resultant of the two forces vertical. 2. Determine the magnitude \( R \) of the resultant force. ### Explanation of Diagram: - **Forces:** - \( F_1 \) is applied at an angle θ from the vertical axis \( y \). - \( F_2 \) is applied at an angle of 70° counterclockwise from the horizontal axis \( x \). - **Coordinate Axes:** - The diagram shows \( x \), \( y \), and \( z \) axes for spatial orientation. - **Construction Bracket:** - The forces are applied to the bracket, which is fixed to a base on a surface. - **Resultant Force:** - The goal is to find a specific angle \( θ \) such that the sum of the forces \( F_1 \) and \( F_2 \) results in a vertical line of action, meaning no resultant horizontal component. ### Solution Outline: To solve this problem, we need to: 1. Resolve each force into its horizontal and vertical components. 2. Sum the horizontal components of \( F_1 \) and \( F_2 \) to be zero (since the resultant force must be vertical). 3. Use trigonometric relationships to solve for angle θ. 4. Calculate the magnitude \( R \) using the vertical components of the forces. ### Equations: - \( F_1 \) components: - \( F_{1x} = F_1 \sin(\theta) \) - \( F_{1y} = F_1 \cos(\theta) \) - \( F_2 \) components: - \( F_{2x} = F_2 \cos(70^\circ) \) - \( F_{2y} = F_2 \sin(70^\circ) \) - Resultant vertical and horizontal component equations: - \( R_x =
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