Explanation Given: The magnitude of a component force, F 2 = 650 N . The magnitude of a component force, F 3 = 500 N . The angle between the magnitude of the component force F 3 and x axes is 45 ° . The angle between the magnitude of the component force F 1 and x axes is ϕ . The angle between the u and x axes is 45 ° . The magnitude of the resultant force, F R = 600 N . 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). Use Figure (1) and find out the cos θ and sin θ . cos θ = 3 5 sin θ = 4 5 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 θ . (I) Substitute 650 N for F 2 and 3 5 for cos θ in Equation (I). ( F 2 ) x = ( 650 ) 3 5 = 390 N Express the magnitude of component force F 2 along the y direction using Figure (1). ( F 2 ) y = F 2 sin θ (II) Substitute 650 N for F 2 and 4 5 for sin θ in Equation (II). ( F 2 ) y = ( 650 ) 4 5 = 520 N Express the magnitude of component force F 3 along the x direction using Figure (1). ( F 3 ) x = F 3 cos 45 ° (III) Substitute 500 N for F 3 in Equation (III). ( F 3 ) x = 500 cos 45 ° = 353.55 N Express the magnitude of component force F 3 along the y direction using Figure (1). ( F 3 ) y = F 3 sin 45 ° (IV) Substitute 500 N for F 3 in Equation (IV). ( F 3 ) y = 500 sin 45 ° = 353.55 N Express the magnitude of resultant force F R along the x direction using Figure (2). ( F R ) x = F R cos 45 ° (V) Substitute 600 N for F R in Equation (V). ( F R ) x = 600 cos 45 ° = 424.26 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 46P

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The magnitude of the component vector force F1 and its direction ϕ.

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Chapter 2.4, Problem 45P

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The magnitude of the component vector force F 1 and its direction ϕ .

The magnitude of the component vector force F1 and its direction ϕ.

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