### 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

Answered: Image /qna-images/answer/320fe748-91aa-4498-89b6-61a53b9e40b6.jpg

) 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

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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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

### 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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