### Finding the Magnitude and Direction of the Resultant Force**Problem Statement:**The particle shown below is at rest, where \( F_1 = 6.95 \, \text{N} \) and \( F_2 = 10.4 \, \text{N} \). Find the magnitude and direction of the resultant force \( F \).**Given:**- \( F_1 = 6.95 \, \text{N} \)- \( F_2 = 10.4 \, \text{N} \)**Diagram Description:**In the provided diagram:- There is a coordinate system with the \( y \)-axis oriented vertically and the \( x \)-axis oriented horizontally.- A particle is positioned at the origin.- There are two forces acting on the particle, \( F_1 \) and \( F_2 \): 1. \( F_1 \): This force is applied at an angle of \( 30.0^\circ \) counterclockwise from the negative \( x \)-axis. 2. \( F_2 \): This force is applied at an angle of \( 45.0^\circ \) clockwise from the positive \( x \)-axis.**Graphical Representation:**The diagram features arrows representing the forces:- \( F_1 \) is directed towards the left, slanting upward from the horizontal line.- \( F_2 \) is directed towards the left, slanting downward from the horizontal line.- The resultant force \( F \) is indicated, but its magnitude and direction are unknown.**Calculations:**To find the magnitude and direction of \( F \), you would typically resolve \( F_1 \) and \( F_2 \) into their vector components, sum these components, and then determine the magnitude and direction of the resulting vector.**Magnitude Calculation:**\[ F = \sqrt{(F_{1x} + F_{2x})^2 + (F_{1y} + F_{2y})^2} \]**Direction Calculation:**\[ \theta = \text{atan2}(F_{1y} + F_{2y}, F_{1x} + F_{2x}) \]Where \( F_{1x}, F_{1y}, F_{2x}, \) and \( F_{2y

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Answered: The particle shown below is at rest,…

The particle shown below is at rest, where F₁ = 6.95 N, and F₂ = 10.4 N. Find the magnitude and direction of F. magnitude direction F₁ 30.0° 45.0° counterclockwise from the +x-axis F 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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