Explanation Given: The magnitude of component force, F 3 = 500 N . The magnitude of component force, F 2 = 650 N . The angle between the u and x axis is 45 ° . The angle between the magnitude of component force F 3 and x axis is 45 ° . The angle between the magnitude of component force F 1 and x axis is ϕ . Show the summing of magnitude of component forces into x and y axis components as in Figure (1). Show the free body diagram of the resultant force 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 θ (III) Substitute 500 N for F 3 and 45 ° for θ 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 θ (IV) Substitute 500 N for F 3 and 45 ° for θ 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 θ (V) Substitute 45 ° for θ in Equation (V). ( F R ) x = F R cos 45 ° = 0.7071 F R Express the magnitude of resultant force F R along the y direction using Figure 2. ( F R ) y = F R sin θ (VI) Substitute 45 ° for θ in Equation (VI). ( F R ) y = F R sin 45 ° = 0.7071 F R Express the magnitude of resultant force from the positive x axis using Figures 1 and 2. + → ( F R ) x = ∑ F x ( F R ) x = ( F 1 ) x − ( F 2 ) x + ( F 3 ) x (VII) Substitute 0 .7071 F R for ( F R ) x , F 1 cos ϕ for ( F 1 ) x , 390 N for ( F 2 ) x and 353

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.4, Problem 45P

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The magnitudes of the resultant force FR and component force F1.

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Chapter 2.4, Problem 44P

Chapter 2.4, Problem 46P

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Chapter 2 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

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 magnitudes of the resultant force F R and component force F 1 .

The magnitudes of the resultant force FR and component force F1.

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