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Find the resultant Force and direction of adding the three vectors shown

Find the resultant Force and direction of adding the three vectors shown

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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 Find the resultant Force and direction of adding the three vectors shown

### Understanding Vector Addition Using Force Diagram The diagram shown illustrates multiple vectors, each representing a force with different magnitudes and directions. This is a common type of diagram used in physics to study the resultant force and equilibrium conditions. #### Diagram Analysis: 1. **Vectors and Their Magnitudes:** - **Vector A:** Directed to the left, labeled as "4k". - **Vector B:** Directed upwards, forming a 50-degree angle with the horizontal axis, labeled as "10k". - **Vector C:** Directed downwards at an angle, labeled as "8k". Additionally, small lines labeled "2" and "3" form a right-angled triangle indicating the horizontal and vertical components of this vector. 2. **Angles:** - There is an angle of 50 degrees between Vector B (10k) and the horizontal axis. 3. **Vector Components:** - For Vector C: It's broken down into horizontal (2k) and vertical (3k) components. It is common to decompose a vector into components when calculating the resultant vector or when analyzing equilibrium. #### Concepts Illustrated: - **Vector Addition:** To find the resultant force vectors acting on a point, use vector addition. This can be done using graphical methods (triangle or parallelogram rule) or analytical methods (using components). - **Equilibrium:** If forces are in equilibrium, the sum of all forces will be zero. This diagram can be used to visualize and calculate whether forces are balanced and the system is in equilibrium. - **Trigonometry in Vectors:** Angles are used to resolve vectors into their horizontal and vertical components using trigonometric functions (sine and cosine). ### Practical Applications: - **Engineering:** Understanding how to add and resolve forces is crucial in structural engineering, mechanical systems, and any field where force analysis is needed. - **Physics:** Fundamental in studying mechanics, particularly in statics and dynamics. ### Calculation Process: To determine the resultant vector or to check for equilibrium: 1. **Resolve Vector B and Vector C into their components.** 2. **Sum the horizontal components** of all vectors. 3. **Sum the vertical components** of all vectors. 4. **Check for equilibrium** by ensuring the net horizontal and vertical components are zero. This breakdown simplifies complex vector problems into manageable calculations, making it easier to analyze forces acting on a point.
Transcribed Image Text:### Understanding Vector Addition Using Force Diagram The diagram shown illustrates multiple vectors, each representing a force with different magnitudes and directions. This is a common type of diagram used in physics to study the resultant force and equilibrium conditions. #### Diagram Analysis: 1. **Vectors and Their Magnitudes:** - **Vector A:** Directed to the left, labeled as "4k". - **Vector B:** Directed upwards, forming a 50-degree angle with the horizontal axis, labeled as "10k". - **Vector C:** Directed downwards at an angle, labeled as "8k". Additionally, small lines labeled "2" and "3" form a right-angled triangle indicating the horizontal and vertical components of this vector. 2. **Angles:** - There is an angle of 50 degrees between Vector B (10k) and the horizontal axis. 3. **Vector Components:** - For Vector C: It's broken down into horizontal (2k) and vertical (3k) components. It is common to decompose a vector into components when calculating the resultant vector or when analyzing equilibrium. #### Concepts Illustrated: - **Vector Addition:** To find the resultant force vectors acting on a point, use vector addition. This can be done using graphical methods (triangle or parallelogram rule) or analytical methods (using components). - **Equilibrium:** If forces are in equilibrium, the sum of all forces will be zero. This diagram can be used to visualize and calculate whether forces are balanced and the system is in equilibrium. - **Trigonometry in Vectors:** Angles are used to resolve vectors into their horizontal and vertical components using trigonometric functions (sine and cosine). ### Practical Applications: - **Engineering:** Understanding how to add and resolve forces is crucial in structural engineering, mechanical systems, and any field where force analysis is needed. - **Physics:** Fundamental in studying mechanics, particularly in statics and dynamics. ### Calculation Process: To determine the resultant vector or to check for equilibrium: 1. **Resolve Vector B and Vector C into their components.** 2. **Sum the horizontal components** of all vectors. 3. **Sum the vertical components** of all vectors. 4. **Check for equilibrium** by ensuring the net horizontal and vertical components are zero. This breakdown simplifies complex vector problems into manageable calculations, making it easier to analyze forces acting on a point.
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