COSMOS Chapter 4 Solution 99 | Michigan State University - 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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COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 99. Free-Body Diagram: ( ) Note that W = mg = (18 kg ) 9.81 m/s 2 = 176.580 N Moment equilibrium: ΣM A = 0: ( ) rB/ A × By j + Bz k + rC/ A × C zk + rG/ A × ( −176.580 N ) j = 0 or i j k i j k i j k 1.5 0 0 + 1.2 1.2sin 60° −1.2cos 60° + 0.6 0.6sin 60° − 0.6cos 60° = 0 0 B y Bz 0 0 Cz 0 −176.580 0 or ( ) 1.2C z sin 60° − (105.948 N ) cos 60° i + ( −1.5Bz − 1.2C z ) j + 1.5By − 105.948 N k = 0 Solving the equation one component at a time: From i component: 1.2C z sin 60° − (105.948 N ) cos 60° = 0, From j component: −1.5Bz − 1.2C z = 0, From k component: 1.5By − 105.948 N = 0, or or C z = 50.974 N Bz = − 0.8 ( 50.974 N ) = − 40.779 N or By = 70.632 N Force equations: ΣFy = 0: Ay − 176.580 N + 70.632 N = 0, or Ay = 105.948 N ΣFz = 0: Az + 50.974 N − 40.779 N = 0, or Az = −10.195 N Therefore: A = (105.9 N ) j − (10.20 N ) k B = ( 70.6 N ) j − ( 40.8 N ) k C = ( 51.0 N ) k

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