Explanation Given: The magnitude of the resultant force, F R = 50 lb . The magnitude of component force, F 3 = 52 lb . The magnitude of component force, F 1 = 80 lb . The angle between the magnitude of component force F 1 and u is 25 ° . The angle between the magnitude of component force F 2 and u axes is θ . Show the magnitude of component forces into x and y axis components as in Figure (1). Show the magnitude of resultant force F R into x and y axis components as in Figure (2). Conclusion: Use Figure (1) and find out the cos θ and sin θ . cos θ = 5 13 sin θ = 12 13 Express the magnitude of resultant force directed along the positive u axis using Figure (1). + → ( F R ) x = ∑ F x ( F R ) x cos 25 ° = F 1 + F 3 cos θ + F 2 cos ( θ + 25 ° ) (I) Substitute 50 lb for ( F R ) x , 80 lb for F 1 , 5 13 for cos θ , and 52 lb for F 3 in Equation (I). 50 cos 25 ° = 80 + [ ( 52 ) 5 13 ] + F 2 cos ( θ + 25 ° ) 45.315 = 80 + 20 + F 2 cos ( θ + 25 ° ) F 2 cos ( θ + 25 ° ) = − 54.68 lb (II) Express the magnitude of resultant directed along the positive u axis using Figure (1). + ↑ ( F R ) y = ∑ F y − ( F R ) y sin 25 ° = F 3 sin θ − F 2 sin ( θ + 25 ° ) (III) Substitute 50 lb for ( F R ) y , 52 lb for F 3 , and 12 13 for sin θ in Equation (III)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 2.4, Problem 56P

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The magnitude and its direction θ of the component force F2 directed along the positive u axis.

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Chapter 2.4, Problem 55P

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Chapter 2 Solutions

Engineering Mechanics: Statics

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The magnitude and its direction θ of the component force F 2 directed along the positive u axis.

The magnitude and its direction θ of the component force F2 directed along the positive u axis.

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Chapter 2 Solutions