Explanation Given: The magnitude of component force, F 1 = 300 N . The angle between the magnitude of component force F 1 and x ′ axis, θ = 10 ° . The angle between the magnitude of component force F 2 and x ′ axis is 60 ° . Illustrate the component of forces F 1 and F 2 into x and y axis components as shown below in Figure (1). Using Figure (1), find the cos θ and sin θ . cos θ = 12 13 sin θ = 5 13 Express the magnitude of resultant force acting along the positive x ′ axis. + → F R x = ∑ F x F R x = F 1 [ sin ( 60 ° + θ ) ] − F 3 cos θ (I) Express the magnitude of resultant force acting along the positive x ′ axis. + ↑ F R y = ∑ F y F R y = F 1 ( cos 60 ° + θ ) + F 2 + F 3 sin θ (II) Calculate the magnitude of the resultant force F R measured counterclockwise from the positive x ′ axis. F R = ( F R x ) 2 + ( F R y ) 2 (III) Calculate the directional angle ϕ ′ measured counterclockwise from positive x ′ axis. ϕ ′ = [ tan − 1 F R y F R x ] − ( 90 ° − 60 ° ) (IV) Conclusion: Substitute 300 N for F 1 , 180 N for F 3 12 13 for cos θ and 10 ° for θ in Equation (I). F R x = 300 [ sin ( 60 ° + 10 ° ) ] − ( 180 ) 12 13 = 300 sin 70 ° − 166

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Two forces act on the hook. Determine the...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - The force F = 450 lb acts on the frame. Resolve...Ch. 2.3 - If force F is to have a component along the u axis...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

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The magnitude and direction of the resultant force measured counterclockwise from the positive x ′ axis.

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