COSMOS Chapter 4 Solution 95 - Edubirdie

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

2022
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301

Pages:

1
Author:

diamundgalx45p

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 95. Free-Body Diagram: The forces acting on the three-force member intersect at D. (a) From triangle ACO  r  −1  1   = tan   = 18.4349°  3r  3 θ = tan −1  tan θ = (b) From triangle DCG ∴ DC = and or θ = 18.43° r DC r r = = 3r tan θ tan18.4349° DO = DC + r = 3r + r = 4r  yDO    x AG  α = tan −1  where yDO = ( DO ) cosθ = ( 4r ) cos18.4349° = 3.4947r and x AG = ( 2r ) cosθ = ( 2r ) cos18.4349° = 1.89737r  3.4947r  ∴ α = tan −1   = 63.435°  1.89737r  where 90° + (α − θ ) = 90° + 45° = 135.00° Applying the law of sines to the force triangle, mg R = A sin 90° + (α − θ )  sin θ ∴ RA = ( 0.44721) mg Finally, P = RA cos α = ( 0.44721mg ) cos 63.435° = 0.20000mg or P = mg 5

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