COSMOS Chapter 4 Solution 98 - Edubirdie

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

2021
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274

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1
Author:

omiliar74be

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 98. Free-Body Diagram: ΣFx = 0: Dx = 0 ΣM D = 0: ( − 7 in.) i  × C + ( 2 in.) i + ( 3 in.) k  × ( 530 lb ) j + ( − 192 lb ) k  + ( − 3 in.) i + ( 6 in.) j × ( 265 lb ) j + ( − 96 lb ) k  = 0 or − ( 7 in.) C yk + ( 7 in.) Cz j + ( 2 in.)( 530 lb ) k + ( 2 in.)(192 lb ) j − ( 3 in.)( 530 lb ) i − ( 3 in.)( 265 lb ) k − ( 3 in.)( 96 lb ) j − ( 6 in.)( 96 lb ) i = 0 Setting the coefficients of the unit vectors equal to zero: k: j: − C y ( 7 in.) − ( 265 lb )( 3 in.) + ( 530 lb )( 2 in.) = 0, C z ( 7 in.) + ( 96 lb )( 3 in.) + (192 lb )( 2 in.) = 0, or or C y = 37.857 lb C z = − 96.000 lb C = ( 37.9 lb ) j − ( 96.0 lb ) k Then: ΣFy = 0: 37.857 lb + 265 lb + Dy + 530 lb = 0, or Dy = − 832.86 lb ΣFz = 0: − 96 lb + 96 lb + Dz − 192 lb = 0, Dz = 192.000 lb or D = − ( 833 lb ) j + (192.0 lb ) k

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