Explanation Given: The magnitude of the component vector force F 1 , F 1 = 350 N . The magnitude of the component vector force F 2 , F 2 = 100 N . The magnitude of the component vector force F 3 , F 3 = 250 N . Angle between F 2 and x -axis is 45 ° Angle between F 2 and y axis is 60 ° . Angle between F 3 and y axis is 45 ° . Angle between F 3 and x -axis is 60 ° . Angle between F 3 and z axis is 60 ° . Angle between F 1 and z axis is 40 ° . Angle between F 2 and z axis is 120 ° . Write the vector force F 1 in Cartesian vector form. F 1 = ( F 1 ) x i + ( F 1 ) y ( + j ) + ( F 1 ) z ( + k ) = 0 i + F 1 sin 40 ° ( + j ) + ( F 1 cos 40 ° ) ( + k ) (I) Here, the unit vectors are i , j , and k . Write the vector force F 2 in Cartesian vector form. F 2 = ( F 2 ) x i + ( F 2 ) y ( + j ) + ( F 2 ) z ( + k ) = ( F 2 cos 45 ° ) i + ( F 2 cos 60 ° ) ( + j ) + ( F 2 cos 120 ° ) ( + 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. Write the vector force F 3 in Cartesian vector form. F 3 = ( F 3 ) x i + ( F 3 ) y ( + j ) + ( F 3 ) z ( + k ) = ( F 3 cos 60 ° ) i + ( F 3 cos 135 ° ) ( + j ) + ( F 3 cos 60 ° ) ( + k ) (III) Here, the component force 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 vector force F 1 , F 2 , and F 3 . F R = F 1 + F 2 + F 3 (IV) Write the magnitude of the resultant force. F R = ( F R ) x 2 + ( F R ) y 2 + ( F R ) z 2 (V) 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 (VI) cos β = ( F R ) y F R (VII) cos γ = ( F R ) z F R (VIII) Conclusion: Substitute 350 N for F 1 in Equation (I). F 1 = 0 i + ( 350 N ) ( 0.6427 ) ( + j ) + ( ( 350 N ) ( 0

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 2.6, Problem 77P

To determine

The expression of each force (F1,F2,F3) in Cartesian vector form.

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

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Chapter 2.6, Problem 76P

Chapter 2.6, Problem 78P

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The expression of each force ( F 1 , F 2 , F 3 ) in Cartesian vector form. The magnitude ( F R ) and coordinate direction angles of the resultant force acting on the screw eye ( α , β , and γ ) .

The expression of each force (F1,F2,F3) in Cartesian vector form. The magnitude (FR) and coordinate direction angles of the resultant force acting on the screw eye (α,β, and γ).

Want to see the full answer?

Chapter 2 Solutions

The expression of each force (F1,F2,F3) in Cartesian vector form.

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