Explanation Given: The magnitude of the component vector force F 1 , F 1 = 600 N . The magnitude of the component vector force F 2 , F 2 = 450 N . Angle between F ′ and x -axis is 30 ° . Angle between F 2 and y axis is 45 ° . Show the magnitude of the components forces F 1 and F 2 in x , y , and z directions as in Figure (1). Show the direction angles with magnitude of component forces F 1 and F 2 as in Figure (2). Write the vector force F 1 in Cartesian vector form using Figure 1. F 1 = ( F 1 ) x i + ( F 1 ) y ( − j ) + ( F 1 ) z ( + k ) = ( F ′ cos 30 ° ) i + ( F ′ sin 30 ° ) ( − j ) + ( F 1 sin θ ) ( + k ) = ( F 1 cos θ cos 30 ° ) i − ( F 1 cos θ sin 30 ° ) j + ( F 1 sin θ ) k (I) Here, the unit vectors are i , j , and k , and the sum of forces F x and F y is F ′ . Write the vector force F 2 in Cartesian vector form using Figure 2. F 2 = ( F 2 ) x i + ( F 2 ) y ( + j ) + ( F 2 ) z ( + k ) = 0 i + ( F 2 cos 45 ° ) ( + j ) + ( F 2 sin 45 ° ) ( + k ) (II) Here, the component force F 2 in x , y , and z axes are F 2 x , F 2 y , and F 2 z , respectively. Express the resultant force of vector force F 1 and F 2 . F R = F 1 + F 2 (III) Write the magnitude of the resultant force. F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (IV) Here, the magnitude of the resultant force measured along x , y , and z axes is ( F R ) x , ( F R ) y , and ( F R ) z . Determine the coordinate direction angles. cos α = ( F R ) x F R (V) cos β = ( F R ) y F R (VI) cos γ = ( F R ) z F R (VII) Conclusion: Substitute 600 N for F 1 , 3 / 5 for sin θ , and 4 / 5 for cos θ in Equation (I)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 2.6, Problem 76P

To determine

The magnitude (FR) and coordinate direction angles of the resultant force acting on the eyebolt (α,β, and γ).

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Chapter 2.6, Problem 75P

Chapter 2.6, Problem 77P

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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