COSMOS Chapter 4 Solution 97 | Michigan State University - Edubirdie

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Michigan State University
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ERG 160 | Success in Science, Technology, Engineering, and Mathematics
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2024
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COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 97. Free-Body Diagram: ΣFx = 0: ΣM D = 0: Dx = 0 ( − 7 in.) i  × C + ( 2 in.) i + ( 3 in.) k  × ( 530 lb ) j + ( −192 lb ) k  + ( −3 in.) i + ( 6 in.) j × ( −96 lb ) j + ( 265 lb ) k  = 0 or − ( 7 in.) C yk + ( 7 in.) C z j + ( 2 in.)( 530 lb ) k + ( 2 in.)(192 lb ) j − ( 3 in.)( 530 lb ) i + ( 3 in.)( 96 lb ) k + ( 3 in.)( 265 lb ) j + ( 6 in.)( 265 lb ) i = 0 Setting the coefficients of the unit vectors to zero: k: − C y ( 7 in.) + ( 96 lb )( 3 in.) + ( 530 lb )( 2 in.) = 0, or C y = 192.571 lb j: C z ( 7 in.) + ( 265 lb )( 3 in.) + (192 lb )( 2 in.) = 0, or C z = −168.429 lb C = (192.6 lb ) j − (168.4 lb ) k Then: ΣFy = 0: 192.571 lb − 96 lb + Dy + 530 lb = 0, ΣFz = 0: −168.429 lb + 265 lb + Dz − 192 lb = 0, or Dy = −626.57 lb or Dz = 95.429 lb D = − ( 626 lb ) j + ( 95.4 lb ) k

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