**Title: Analyzing the Resultant of Forces****Description:**To determine the resultant of three given forces, we first need to understand how the angles and magnitudes of the forces relate to each other. In this scenario, we are given three forces with their magnitudes and a diagram showing their directions.**Text on Diagram:**1. **Forces:** - \( F_1 = 2550 \, \text{N} \) - \( F_2 = 3150 \, \text{N} \) - \( F_3 = 3680 \, \text{N} \)2. **Angles:** - Angle between \( F_2 \) and the positive x-axis is \( 120^\circ \). - Angle between \( F_2 \) and \( F_3 \) is \( 42^\circ \).**Instructions:**- To find the resultant, first note the angle given for \( F_3 \) is the angle between \( F_2 \) and \( F_3 \). For calculating \( F_3 \)'s x and y components, you should add the given angles together.**Diagram Explanation:**- The diagram is presented in the first quadrant of an x-y coordinate system.- \( F_1 \) acts along the positive x-axis.- \( F_2 \) forms an angle of \( 120^\circ \) with the positive x-axis and extends into the second quadrant.- \( F_3 \), with a given angle of \( 42^\circ \) to \( F_2 \), also extends into the second quadrant.To solve for the resultant force, decompose each force into its x and y components using trigonometric functions, sum up the components, and use these sums to calculate the magnitude and direction of the resultant force.**Educational Objective:**- This exercise helps in understanding vector addition, specifically resolving forces into components and calculating resultant vectors using angles and magnitudes.

Answered: Image /qna-images/answer/916ca886-054c-45fc-86ca-cf91a6d0d7ca.jpg

Find the resultant of these three forces. Note the angle give for F3 is the angle between F2 and F3; to find the angle to use to get F3's x and y components, add the given angles ogether. F₂ = 3150 N F3 = = 3680 N 42.0° 120.0° F₁ = 2550 N X

Find the resultant of these three forces. Note the angle give for F3 is the angle between F2 and F3; to find the angle to use to get F3's x and y components, add the given angles ogether. F₂ = 3150 N F3 = = 3680 N 42.0° 120.0° F₁ = 2550 N X

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Title: Analyzing the Resultant of Forces**

**Description:**

To determine the resultant of three given forces, we first need to understand how the angles and magnitudes of the forces relate to each other. In this scenario, we are given three forces with their magnitudes and a diagram showing their directions.

**Text on Diagram:**

1. **Forces:**
- \( F_1 = 2550 \, \text{N} \)
- \( F_2 = 3150 \, \text{N} \)
- \( F_3 = 3680 \, \text{N} \)

2. **Angles:**
- Angle between \( F_2 \) and the positive x-axis is \( 120^\circ \).
- Angle between \( F_2 \) and \( F_3 \) is \( 42^\circ \).

**Instructions:**

- To find the resultant, first note the angle given for \( F_3 \) is the angle between \( F_2 \) and \( F_3 \). For calculating \( F_3 \)'s x and y components, you should add the given angles together.

**Diagram Explanation:**

- The diagram is presented in the first quadrant of an x-y coordinate system.
- \( F_1 \) acts along the positive x-axis.
- \( F_2 \) forms an angle of \( 120^\circ \) with the positive x-axis and extends into the second quadrant.
- \( F_3 \), with a given angle of \( 42^\circ \) to \( F_2 \), also extends into the second quadrant.

To solve for the resultant force, decompose each force into its x and y components using trigonometric functions, sum up the components, and use these sums to calculate the magnitude and direction of the resultant force.

**Educational Objective:**

- This exercise helps in understanding vector addition, specifically resolving forces into components and calculating resultant vectors using angles and magnitudes.

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