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Note that the angles start from zero and increase to 360°. By convention, angles are given relative to the positive x-axis. For this purpose, choose the positive x-axis as pointing toward 0°, and the negative x-axis as pointing towards 180°, the positive y-axis at 90° and the negative y-axis at 270°. (a) A: 200 g along +x axis B: 100 g 45° above -x axis II: (a) A: 150 g 60° along +y axis B: 200 g 45° above -x axis C: 100 g 30° below -x axis COMPONENT METHOD: (b) A: 100 g 30° above -x axis B: 150 g along -y axis (b) A: 150 g 30° below +x axis B: 200 g 60° above +x axis C: 150 g 60° above -x axis For both parts I and II, use the component method to find the resultants and their directions Using the component method (for two given vectors), we can write Ax+ Bx = Rx; Ay + By = Ry For three given forces in Part II, this can be rewritten as Ax + Bx + Cx = Rx; Ay + By + Cy = R₂ The magnitude of R in each case, is found using Pythagoras theorem: R = √ (R² + R₂²) and the direction (the angle q that R makes with the positive x-axis) can be found from q=tan ¹ [R, /R] Rewrite the angle as measured counterclockwise from the positive x-axis. Make sure to indicate what quadrant R is by noting the signs (+ or -) on R, and Ry.

Note that the angles start from zero and increase to 360°. By convention, angles are given relative to the positive x-axis. For this purpose, choose the positive x-axis as pointing toward 0°, and the negative x-axis as pointing towards 180°, the positive y-axis at 90° and the negative y-axis at 270°. (a) A: 200 g along +x axis B: 100 g 45° above -x axis II: (a) A: 150 g 60° along +y axis B: 200 g 45° above -x axis C: 100 g 30° below -x axis COMPONENT METHOD: (b) A: 100 g 30° above -x axis B: 150 g along -y axis (b) A: 150 g 30° below +x axis B: 200 g 60° above +x axis C: 150 g 60° above -x axis For both parts I and II, use the component method to find the resultants and their directions Using the component method (for two given vectors), we can write Ax+ Bx = Rx; Ay + By = Ry For three given forces in Part II, this can be rewritten as Ax + Bx + Cx = Rx; Ay + By + Cy = R₂ The magnitude of R in each case, is found using Pythagoras theorem: R = √ (R² + R₂²) and the direction (the angle q that R makes with the positive x-axis) can be found from q=tan ¹ [R, /R] Rewrite the angle as measured counterclockwise from the positive x-axis. Make sure to indicate what quadrant R is by noting the signs (+ or -) on R, and Ry.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 7CQ
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Note that the angles start from zero and increase to 360°. By convention, angles are given relative to the positive x-axis. For this purpose, choose the positive x-axis as pointing toward 0°, and the negative x-axis as pointing towards 180°, the positive y-axis at 90° and the negative y-axis at 270°. (a) A: 200 g along +x axis B: 100 g 45° above -x axis II: (a) A: 150 g 60° along +y axis B: 200 g 45° above -x axis C: 100 g 30° below -x axis COMPONENT METHOD: (b) A: 100 g 30° above -x axis B: 150 g along -y axis (b) A: 150 g 30° below +x axis B: 200 g 60° above +x axis C: 150 g 60° above -x axis For both parts I and II, use the component method to find the resultants and their directions Using the component method (for two given vectors), we can write Ax + Bx = Rx; Ay + By = Ry For three given forces in Part II, this can be rewritten as Ax + Bx + Cx = Rx; Ay + By + Cy = R₂ The magnitude of R in each case, is found using Pythagoras theorem: R = √ (R₂²+R₂²) and the direction (the angle q that R makes with the positive x-axis) can be found from q=tan ¹ [R, /R] Rewrite the angle as measured counterclockwise from the positive x-axis. Make sure to indicate what quadrant R is by noting the signs (+ or -) on Rx and Ry.
Transcribed Image Text:Note that the angles start from zero and increase to 360°. By convention, angles are given relative to the positive x-axis. For this purpose, choose the positive x-axis as pointing toward 0°, and the negative x-axis as pointing towards 180°, the positive y-axis at 90° and the negative y-axis at 270°. (a) A: 200 g along +x axis B: 100 g 45° above -x axis II: (a) A: 150 g 60° along +y axis B: 200 g 45° above -x axis C: 100 g 30° below -x axis COMPONENT METHOD: (b) A: 100 g 30° above -x axis B: 150 g along -y axis (b) A: 150 g 30° below +x axis B: 200 g 60° above +x axis C: 150 g 60° above -x axis For both parts I and II, use the component method to find the resultants and their directions Using the component method (for two given vectors), we can write Ax + Bx = Rx; Ay + By = Ry For three given forces in Part II, this can be rewritten as Ax + Bx + Cx = Rx; Ay + By + Cy = R₂ The magnitude of R in each case, is found using Pythagoras theorem: R = √ (R₂²+R₂²) and the direction (the angle q that R makes with the positive x-axis) can be found from q=tan ¹ [R, /R] Rewrite the angle as measured counterclockwise from the positive x-axis. Make sure to indicate what quadrant R is by noting the signs (+ or -) on Rx and Ry.
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