COSMOS Chapter 3 Solution 149 | Answer Key - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2019
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1
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calidancer42q7j

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 149. Require the equivalent forces acting at A and C be parallel and at an angle of α with the vertical. Then for equivalence, ΣFx : ( 250 lb ) sin 30° = FA sin α + FB sin α (1) ΣFy : − ( 250 lb ) cos 30° = − FA cos α − FB cos α (2) Dividing Equation (1) by Equation (2), ( 250 lb ) sin 30° − ( 250 lb ) cos 30° = ( FA + FB ) sin α − ( FA + FB ) cos α Simplifying yields α = 30° Based on ΣM C : ( 250 lb ) cos 30° (12 ft ) = ( FA cos 30° )( 32 ft ) ∴ FA = 93.75 lb or FA = 93.8 lb 60° Based on ΣM A : − ( 250 lb ) cos 30° ( 20 ft ) = ( FC cos 30° ) ( 32 ft ) ∴ FC = 156.25 lb or FC = 156.3 lb . 60°

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