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

2024
Views:

74

Pages:

1
Author:

behend6abs

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 53. Free-Body Diagram: (a) Using W = mg: ΣFx = 0: − A cos 45° + B sin 45° = 0 B= A ΣFy = 0: (1) A sin 45° + B sin 45° − mg = 0 A+ B = 2mg (2) From (1) and (2) it follows that 2A = ΣM B = 0: 2 mg and A= 1 mg 2  l    1  mg   cosθ  + M −  mg  [l cos(45° − θ )] = 0 2 2      (3) Using that cos(α − β ) = cos α cos β + sin α sin β , (3) gives  mgl   mgl    cosθ + M −   ( cosθ + sin θ ) = 0  2   2   mgl  M −  sin θ = 0, and  2  sin θ = (b)  2M mgl  2(2.7 N ⋅ m)  = 20.122° 2  (2kg)(9.81 m/s )(0.8 m)  θ = sin −1   2M  or θ = sin −1    mgl  or θ = 20.1°

COSMOS Chapter 4 Solution 53

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