Explanation Given: The magnitude of the component vector force F 1 , F 1 = 80 N . The magnitude of the component vector force F 2 , F 2 = 100 N . The magnitude of the resultant force, F R = 120 N . Angle between F ′ and F R is 45 ° Angle between F ′ and y axis is 30 ° . Show the magnitude of component of forces F 1 , F 2 , and F 3 into x , y , and z axis components as in Figure (1). Write the vector resultant force F R in Cartesian vector form. F R = ( F R ) x i + ( F R ) y ( + j ) + ( F R ) z ( + k ) = F ′ sin 30 ° i + F ′ cos 30 ° j + ( F R sin 45 ° ) k = F R cos 45 ° sin 30 ° i + F R cos 45 ° cos 30 ° j + F R sin 45 ° k (I) Here, the unit vectors are i , j , and k ; the magnitudes of resultant force F R in x , y , and z axes are F R x , F R y , and F R z respectively Write the vector force F 1 in Cartesian vector form. F 1 = ( F 1 ) x i + ( F 1 ) y ( + j ) + ( F 1 ) z ( + k ) = F 1 cos θ i + 0 j + F 1 sin θ k (II) Here, the component forces of F 1 in x , y , and z axes are F 1 x , F 1 y , and F 1 z respectively. Write the vector force F 2 in Cartesian vector form. F 2 = ( F 2 ) x i + ( F 2 ) y ( + j ) + ( F 2 ) z ( − k ) = 0 i + 0 ( + j ) − ( F 3 ) ( k ) = − F 2 k (III) Here, the component forces of F 2 in x , y , and z axes are F 2 x , F 2 y , and F 2 z respectively. Write the vector force F 3 in Cartesian vector form. F 3 = ( F 3 ) x i + ( F 3 ) y ( + j ) + ( F 3 ) z ( + k ) Here, the component forces of F 3 in x , y , and z axes are F 3 x , F 3 y , and F 3 z respectively. Express the resultant force of F 1 , F 2 , and F 3 . F R = F 1 + F 2 + F 3 (IV) Write the magnitude of the force F 3 . F 3 = ( F 3 ) x 2 + ( F 3 ) y 2 + ( F 3 ) z 2 (V) Determine the coordinate direction angles. cos α = ( F 3 ) x F 3 (VI) cos β = ( F 3 ) y F 3 (VII) cos γ = ( F 3 ) z F 3 (VIII) Conclusion: Substitute 120 N for F R in Equation (I). F R = 120 N cos 45 ° sin 30 ° i + 120 N cos 45 ° cos 30 ° j + 120 N sin 45 ° k = { 42

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ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.6, Problem 78P

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The magnitude (F3) and coordinate direction angles of the force F3 (α,β, and γ).

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Chapter 2.6, Problem 77P

Chapter 2.6, Problem 79P

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Chapter 2 Solutions

Engineering Mechanics: Statics

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The magnitude ( F 3 ) and coordinate direction angles of the force F 3 ( α , β , and γ ) .

The magnitude (F3) and coordinate direction angles of the force F3 (α,β, and γ).

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