COSMOS Chapter 4 Solution 17 - Edubirdie

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

2020
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280

Pages:

1
Author:

Hundebuchesn

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 17. Free-Body Diagram: Equations of equilibrium: − ( 330 N )( 0.25 m ) + B sin α ( 0.3 m ) + B cos α ( 0.5 m ) = 0 ΣΜ Α = 0: (1) Ax − B sin α = 0 ΣFx = 0: (2) Ay − ( 330 N ) + B cos α = 0 ΣFy = 0: (3) (a) Substitution α = 0 into (1), (2), and (3) and solving for A and B: B = 165.000 N, Ax = 0, Ay = 165.0 N or A = 165.0 N , B = 165.0 N (b) Substituting α = 90° into (1), (2), and (3) and solving for A and B: B = 275.00 N, Ax = 275.00 N, Ay = 330.00 N A= Ax2 + Ay2 = θ = tan −1 Ay Ax (275)2 + (330) 2 = 429.56 N = tan −1 330 = 50.194° 275 ∴ A = 430 N 50.2°, B = 275 N (c) Substituting α = 30° into (1), (2), and (3) and solving for A and B: B = 141.506 N, Ax = 70.753 N, Ay = 207.45 N, ⇒ A= Ax2 + Ay2 = θ = tan −1 Ay Ax (70.753)2 + (207.45) 2 = 219.18 N = tan −1 207.45 = 71.168° 70.753 ∴ A = 219 N 71.2°, B = 141.5 N 60°

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