### Problem Statement**Q.1) Use the Parallelogram law and the laws of sine and cosine to find the resultant of the two forces shown below. Also, determine its orientation from the x-axis.**### Diagram ExplanationThe given diagram is an x-y coordinate system showing two forces acting at an angle from a common origin point. The forces are:1. A force of 170 N that points upwards and to the left, making an angle with the y-axis.2. A force of 210 N that points downwards and to the right, making an angle with the x-axis.The two vectors form a parallelogram with the x-axis and y-axis. The dimensions below the x-axis indicate the horizontal (12 units along the x-axis) and vertical (5 units along the y-axis) components necessary to form the parallelogram, creating a right triangle with a base of 12 units and a height of 5 units. ### Solution Steps1. **Determine the angle between the forces:** - Use the given horizontal and vertical components to find the internal angle, θ, between the 170 N and 210 N forces. - Using trigonometric ratios, \( \tan^{-1} \left(\frac{5}{12}\right) \) can be used to find part of the angle.2. **Find the magnitude of the resultant force (R):** - Use the Parallelogram law. The magnitude of the resultant force \( R \) can be found using the law of cosines. \[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)} \] - Here, \( F_1 = 170 \text{ N} \) and \( F_2 = 210 \text{ N} \).3. **Determine the direction of the resultant force:** - Use vector components or trigonometric identities (law of sines) to find the angle of the resultant vector relative to the x-axis.### Detailed Calculation Explanation**Step 1: Find the internal angle, θ:**\[ \theta = \tan^{-1}\left(\frac{5}{12}\right) \approx 22.62^\circ \]Since the diagram implies an angle greater than the calculated internal angle, the included angle between the two vectors is:\[

Given data: - The force 1 is F1 = 170 N. The force 2 is F2 = 210 N.

Answered: Q.1) Use the Parallelogram law and the…

Q.1) Use the Parallelogram law and the laws of sine and cosine to find the resultant of the two forces shown below. Also determine its orientation from x- axis. 170 N 5 12 210 N

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

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

### Problem Statement

**Q.1) Use the Parallelogram law and the laws of sine and cosine to find the resultant of the two forces shown below. Also, determine its orientation from the x-axis.**

### Diagram Explanation

The given diagram is an x-y coordinate system showing two forces acting at an angle from a common origin point. The forces are:

1. A force of 170 N that points upwards and to the left, making an angle with the y-axis.
2. A force of 210 N that points downwards and to the right, making an angle with the x-axis.

The two vectors form a parallelogram with the x-axis and y-axis. The dimensions below the x-axis indicate the horizontal (12 units along the x-axis) and vertical (5 units along the y-axis) components necessary to form the parallelogram, creating a right triangle with a base of 12 units and a height of 5 units.

### Solution Steps

1. **Determine the angle between the forces:**
- Use the given horizontal and vertical components to find the internal angle, θ, between the 170 N and 210 N forces.
- Using trigonometric ratios, \( \tan^{-1} \left(\frac{5}{12}\right) \) can be used to find part of the angle.

2. **Find the magnitude of the resultant force (R):**
- Use the Parallelogram law. The magnitude of the resultant force \( R \) can be found using the law of cosines.
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)} \]
- Here, \( F_1 = 170 \text{ N} \) and \( F_2 = 210 \text{ N} \).

3. **Determine the direction of the resultant force:**
- Use vector components or trigonometric identities (law of sines) to find the angle of the resultant vector relative to the x-axis.

### Detailed Calculation Explanation

**Step 1: Find the internal angle, θ:**

\[ \theta = \tan^{-1}\left(\frac{5}{12}\right) \approx 22.62^\circ \]

Since the diagram implies an angle greater than the calculated internal angle, the included angle between the two vectors is:

\[

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