Explanation Given: The magnitude of the resultant force, F R = 600 N . The magnitude of the component force, F 2 = 500 N . The magnitude of the component force, F 3 = 450 N . The angle between the magnitude of component force F 2 and x axes is 60 ° . The angle between the magnitude of component force F 1 and x axes is ϕ = 30 ° . Show the magnitude of component of forces F 1 , F 2 , and F 3 into x and y axis components as in Figure (1). Show the magnitude of resultant force F R into x and y axis components as in Figure (2). Conclusion: Express the magnitude of component force F 1 along the x direction using Figure (1). ( F 1 ) x = F 1 cos ϕ Express the magnitude of component force F 1 along the y direction using Figure (1). ( F 1 ) y = F 1 sin ϕ Express the magnitude of component force F 2 along the x direction using Figure (1). ( F 2 ) x = F 2 cos 60 ° (I) Substitute 500 N for F 2 in Equation (I). ( F 2 ) x = 500 cos 60 ° = 250 N . Express the magnitude of component force F 2 along the y direction using Figure (1). ( F 2 ) y = F 2 sin 60 ° (II) Substitute 500 N for F 2 in Equation (II). ( F 2 ) y = 500 sin 60 ° = 433.01 N . Use Figure (1) and find out the cos θ and sin θ . cos θ = 3 5 sin θ = 4 5 . Express the magnitude of component force F 3 along the x direction using Figure (1). ( F 3 ) x = F 3 cos θ (III) Substitute 450 N for F 3 and 3 5 for cos θ in Equation (III). ( F 3 ) x = ( 450 ) 3 5 = 270 N . Express the magnitude of component force F 3 along the y direction using Figure (1). ( F 3 ) y = F 3 sin θ (IV) Substitute 450 N for F 3 and 4 5 for sin θ in Equation (IV). ( F 3 ) y = ( 450 ) 4 5 = 360 N . Express the magnitude of resultant force F R along the x direction using Figure (2). ( F R ) x = F R cos 30 ° (V) Substitute 600 N for F R in Equation (V). ( F R ) x = 600 cos 30 ° = 519.62 N . Express the magnitude of resultant force F R along the y direction using Figure (2)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.4, Problem 49P

To determine

The magnitude of the component force F1 measured clockwise from the positive x axis and its angle ϕ.

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Chapter 2.4, Problem 48P

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Chapter 2 Solutions

Engineering Mechanics: Statics

Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....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 - Resolve this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 Ch. 2.3 - Determine the magnitude of the resultant force FR...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...Ch. 2.3 - Determine the magnitude of the resultant force FR...

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The magnitude of the component force F 1 measured clockwise from the positive x axis and its angle ϕ .

The magnitude of the component force F1 measured clockwise from the positive x axis and its angle ϕ.

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