Explanation Given data: The force | F 1 | = | F 2 | = | F 3 | = 54 , 600 N Refer to figure 1: The x - component of vector F 1 is 54,600 N. Since, force is along the x -axis. ∴ F 1 x = 54 , 600 N The y- component of vector F 1 is 0 N. Since, force is acting along the x -axis. ∴ F 1 y = 0 N The x -component of vector F 2 is 0 N. Since, force is acting along the x -axis. ∴ F 2 x = 0 N The y -component of vector F 2 is 54,600 N. Since, force is acting along the y -axis. ∴ F 2 y = 54 , 600 N Formula to determine the x- component of vector F 3 . F 3 x = F 3 sin α (1) Here, α is the angle between F 3 and negative x -axis. Substitute 45.0 ° for α and 54,600 N for F 3 in equation (1). F 3 x = 54 , 600 N × cos ( 45.0 ° ) = 38 , 608.03 N ≅ 38 , 600 N Since the force is towards the negative x -component. F 3 x = − 38 , 600 N Formula to determine the y -component of vector F 2 . F 3 y = F 2 sin α (2) Substitute 45.0 ° for α and 54,600 N for F 3 in equation (2). F 3 y = 54 , 600 N × sin ( 45.0 ° ) = 38 , 608.03 N ≅ 38 , 600 N The resultant vector F R x of the x -component. F R x = F 1 x + F 2 x + F 3 x (3) Substitute 54 , 600 N for F 1 x , 0 N for F 2 x and − 38 , 600 N for F 3 x in equation (3). F R x = 54 , 600 N+ 0 N + ( − 38 , 600 N ) = 16 , 000 N The resultant vector F R y of the y -component

11th Edition

ISBN: 9780134159386

Author: Dale Ewen, Neill Schurter, Erik Gundersen

Publisher: PEARSON

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Chapter 7, Problem 5RP

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To find: The sum of the set of vectors and the angle in standard position of the resultant vectors.

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Chapter 7, Problem 4RP

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Chapter 7 Solutions

Applied Physics (11th Edition)

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The sum of the set of vectors and the angle in standard position of the resultant vectors.

Solution Summary: The author explains the formula to determine the x- component of vector F_3.

To find: The sum of the set of vectors and the angle in standard position of the resultant vectors.

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Chapter 7 Solutions