To determine The force vectors in the given figure. Explanation Procedure used: 1. Add the x -component of the given vectors to obtain R x . 2. Add the y -component of the given vectors to obtain R y . 3. Find the magnitude of the resultant R . Use the equation R = R x 2 + R y 2 . 4. Find the standard-position angle θ for the resultant R . Find the reference angle θ r e f for the resultant R by using the equation θ r e f = tan − 1 | R y | | R x | . Then, use the reference angle and the quadrant of R to determine the standard position angle θ . Calculation: The given vector A = 302 is directed at an angle θ A = 180 ° − 45.4 ° = 134.6 ° , B = 155 is directed at an angle θ B = 180 ° + 53 ° = 233 ° and C = 212 is directed at an angle θ C = 30.8 ° . Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the resultant vector is represented as R . Then, the x component of the resultant vector R is, R x = A x + B x + C x = A cos θ A + B cos θ B + C cos θ C = 302 cos 134.6 ° + 155 cos 233 ° + 212 cos 30.8 ° = ( − 212.05 ) + ( − 93.28 ) + 182.10 ≈ − 123 Similarly, the y component of the resultant vector R is, R y = A y + B y + C y = A sin θ A + B sin θ B + C sin θ C = 302 sin 134

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 9.3, Problem 29E

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The force vectors in the given figure.

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

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