Explanation Given information: The component force, F 1 = 200 N . The component force, F 2 = 150 N . The angle between the component forces, F 1 and y axis , θ = 45 ° . The angle between the component forces, F 2 and x axis , θ = 30 ° . Calculation : Show the component of forces F 1 and F 2 into x and y axis components as in Figure 1. Show the magnitude of the resultant force using Figure 1 as in Figure 2. Express the magnitude of the resultant force acting along the positive x axis measured counterclockwise. + → F R x = ∑ F x F R x = F 1 sin 45 ° − F 2 cos 30 ° Substitute 200 N for F 1 and 150 N for F 2 . F R x = ( 200 N ) sin 45 ° − ( 150 N ) cos 30 ° = ( 200 × 0.707 ) − ( 150 × 0.866 ) = 11.5 N → Express the magnitude of the resultant force acting along the positive y axis measured counterclockwise. + ↑ F R y = ∑ F y F R y = F 1 cos 45 ° − F 2 sin 30 ° Substitute 200 N for F 1 and 150 N for F 2 . F R y = ( 200 N ) cos 45 ° + ( 150 N ) sin 30 ° = ( 200 × 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.4, Problem 32P

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Determine the magnitude of the resultant force measured counterclockwise from the positive x axis, FR and the direction of the resultant force measured counterclockwise from the positive x axis, θ.

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Chapter 2.4, Problem 31P

Chapter 2.4, Problem 33P

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Determine the magnitude of the resultant force measured counterclockwise from the positive x axis, F R and the direction of the resultant force measured counterclockwise from the positive x axis, θ .

Solution Summary: The author determines the magnitude and direction of the resultant force measured counterclockwise from the positive x axis, F_R, and the angle between the component forces.

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Determine the magnitude of the resultant force measured counterclockwise from the positive x axis, FR and the direction of the resultant force measured counterclockwise from the positive x axis, θ.

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Chapter 2 Solutions