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) Replace the loading on the member by an equivalent resultant force (indicate the magnitude and direction of the force) and a couple moment (indicate the magnitude and direction of the moment) acting at point A. 200 lb 150 L

) Replace the loading on the member by an equivalent resultant force (indicate the magnitude and direction of the force) and a couple moment (indicate the magnitude and direction of the moment) acting at point A. 200 lb 150 L

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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### Problem Description: Replace the loading on the member by an equivalent resultant force (indicate the magnitude and direction of the force) and a couple moment (indicate the magnitude and direction of the moment) acting at point **A**. ### Diagram Explanation: The diagram depicts a mechanical member with multiple forces acting upon it. These forces and distances are: - **Forces:** - **200 lb** force acting upwards with an angle of **30°** from horizontal at a distance of **3 ft** from point **A**. - **150 lb** force acting upwards, at point **B** with the direction forming a **3:4:5** right triangle. - **100 lb** force acting downwards with an angle of **30°** from horizontal at a distance of **4 ft** from point **A**. - **120 lb** force acting upwards with the direction forming a **3:4:5** right triangle. - A couple moment of **200 lb·ft** acting clockwise at point **A**. - **Distances:** - The entire horizontal length from point **A** to point **B** is **4 ft** with an additional **3 ft** extending beyond point **B**. - The vertical distance from point **B** down to the horizontal extension is **4 ft**. ### Steps to Find Equivalent Resultant Force and Moment: 1. **Determine Resultant Force Vector:** - Resolve all forces into their horizontal (x) and vertical (y) components. - Sum up all the x-components to get the resultant force in the x-direction, \( F_{Rx} \). - Sum up all the y-components to get the resultant force in the y-direction, \( F_{Ry} \). 2. **Calculate the Magnitudes:** - Resultant force magnitude, \( F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} \). - Resultant force direction, \( \theta = \tan^{-1}(\frac{F_{Ry}}{F_{Rx}}) \). 3. **Calculate Resultant Moment:** - Sum the moments about point **A** considering the force and their respective perpendicular distances to **A**. The specific calculations depend on the detailed set of equations set up for each force component and their corresponding distances. ### Summary: Replacing these forces with an equivalent
Transcribed Image Text:### Problem Description: Replace the loading on the member by an equivalent resultant force (indicate the magnitude and direction of the force) and a couple moment (indicate the magnitude and direction of the moment) acting at point **A**. ### Diagram Explanation: The diagram depicts a mechanical member with multiple forces acting upon it. These forces and distances are: - **Forces:** - **200 lb** force acting upwards with an angle of **30°** from horizontal at a distance of **3 ft** from point **A**. - **150 lb** force acting upwards, at point **B** with the direction forming a **3:4:5** right triangle. - **100 lb** force acting downwards with an angle of **30°** from horizontal at a distance of **4 ft** from point **A**. - **120 lb** force acting upwards with the direction forming a **3:4:5** right triangle. - A couple moment of **200 lb·ft** acting clockwise at point **A**. - **Distances:** - The entire horizontal length from point **A** to point **B** is **4 ft** with an additional **3 ft** extending beyond point **B**. - The vertical distance from point **B** down to the horizontal extension is **4 ft**. ### Steps to Find Equivalent Resultant Force and Moment: 1. **Determine Resultant Force Vector:** - Resolve all forces into their horizontal (x) and vertical (y) components. - Sum up all the x-components to get the resultant force in the x-direction, \( F_{Rx} \). - Sum up all the y-components to get the resultant force in the y-direction, \( F_{Ry} \). 2. **Calculate the Magnitudes:** - Resultant force magnitude, \( F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} \). - Resultant force direction, \( \theta = \tan^{-1}(\frac{F_{Ry}}{F_{Rx}}) \). 3. **Calculate Resultant Moment:** - Sum the moments about point **A** considering the force and their respective perpendicular distances to **A**. The specific calculations depend on the detailed set of equations set up for each force component and their corresponding distances. ### Summary: Replacing these forces with an equivalent
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