Explanation Given information: The magnitude of component vector force F 1 , F 1 = 300 N . The magnitude of component vector force F 2 , F 2 = 500 N . The angle between F 1 and F ′ is 60 ° . The angle between F ′ and y axis is 45 ° . The angle between F 2 and x axis is 60 ° . The angle between F 2 and y axis is 45 ° . The angle between F 2 and z axis is 120 ° . Calculation: Illustrate the magnitude of components force F 1 in x , y , and z direction as shown below in Figure 1. Illustrate the direction angles with magnitude of component force F 1 as shown below in Figure 2. Use trigonometry to calculate the magnitude of the components from Figure 1. F z = ( F 1 sin 60 ° ) N Substitute 300 N for F 1 . F z = ( 300 sin 60 ° ) N = 300 × 0.866 = 259.8 N F ′ = ( F 1 cos 60 ° ) N Substitute 300 N for F 1 . F ′ = ( 300 cos 60 ° ) N = 300 × 0.5 = 150 N F x = ( F ′ cos 45 ° ) N Substitute 150 N for F ′ . F x = ( 150 cos 45 ° ) N = 150 × 0.7071 = 106.065 N F y = ( F ′ sin 45 ° ) N Substitute 150 N for F ′ . F y = ( 150 sin 45 ° ) N = 150 × 0.7071 = 106.065 N Here, the component forces in x , y , and z axes are F x , F y , and F z respectively, and the sum of forces, F x and F y is F ′

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2.6, Problem 44P

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Determine the coordinate direction angles of the vector force F1 (α1,β1,γ1).

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Chapter 2.6, Problem 43P

Chapter 2.6, Problem 45P

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Determine the coordinate direction angles of the vector force F 1 ( α 1 , β 1 , γ 1 ) .

Solution Summary: The author illustrates the coordinate direction angles of the vector force F_1 in x, y, and z direction.

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Determine the coordinate direction angles of the vector force F1 (α1,β1,γ1).

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