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Add the following Forces analytically to find the resultant vector, the magnitude of the resultant vector and the direction the resultant vector is going. F1= 350 N @ 105° F2= 450 N @ 203º F3= 350 N @ -36° Fa= 250 N i - 300 Nj Fs= -150 N i- 350 N j

Add the following Forces analytically to find the resultant vector, the magnitude of the resultant vector and the direction the resultant vector is going. F1= 350 N @ 105° F2= 450 N @ 203º F3= 350 N @ -36° Fa= 250 N i - 300 Nj Fs= -150 N i- 350 N j

College Physics
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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I need help with question 4

**Question 4: Vector Addition Problem** Add the following forces analytically to find the resultant vector. Determine the magnitude of the resultant vector and the direction in which the resultant vector is going: - \( F_1 = 350 \, \text{N} \, @ \, 105^\circ \) - \( F_2 = 450 \, \text{N} \, @ \, 203^\circ \) - \( F_3 = 350 \, \text{N} \, @ \, -36^\circ \) - \( F_4 = 250 \, \text{N} \, \mathbf{i} - 300 \, \text{N} \, \mathbf{j} \) - \( F_5 = -150 \, \text{N} \, \mathbf{i} - 350 \, \text{N} \, \mathbf{j} \) **Analysis:** To solve this problem, break each force into its x and y components. Use trigonometric functions for those with given angles and the unit vector notation for those with specified i and j components. For example: \[ F_1 = (350 \cos 105^\circ) \, \mathbf{i} + (350 \sin 105^\circ) \, \mathbf{j} \] Repeat this process for each force vector, sum the x-components and y-components separately, and then recombine them to determine the resultant vector. **Resultant Vector:** - Calculate the magnitude using the Pythagorean theorem. - Determine the direction using the inverse tangent function of the y-component over the x-component. This process illustrates vector addition and helps in understanding vector components' role in determining overall direction and magnitude on a coordinate plane.
Transcribed Image Text:**Question 4: Vector Addition Problem** Add the following forces analytically to find the resultant vector. Determine the magnitude of the resultant vector and the direction in which the resultant vector is going: - \( F_1 = 350 \, \text{N} \, @ \, 105^\circ \) - \( F_2 = 450 \, \text{N} \, @ \, 203^\circ \) - \( F_3 = 350 \, \text{N} \, @ \, -36^\circ \) - \( F_4 = 250 \, \text{N} \, \mathbf{i} - 300 \, \text{N} \, \mathbf{j} \) - \( F_5 = -150 \, \text{N} \, \mathbf{i} - 350 \, \text{N} \, \mathbf{j} \) **Analysis:** To solve this problem, break each force into its x and y components. Use trigonometric functions for those with given angles and the unit vector notation for those with specified i and j components. For example: \[ F_1 = (350 \cos 105^\circ) \, \mathbf{i} + (350 \sin 105^\circ) \, \mathbf{j} \] Repeat this process for each force vector, sum the x-components and y-components separately, and then recombine them to determine the resultant vector. **Resultant Vector:** - Calculate the magnitude using the Pythagorean theorem. - Determine the direction using the inverse tangent function of the y-component over the x-component. This process illustrates vector addition and helps in understanding vector components' role in determining overall direction and magnitude on a coordinate plane.
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