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

2024
Views:

67

Pages:

2
Author:

hekeldigzjbz

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 148. Free-Body Diagram: Express forces in terms of their rectangular components: ( ) ( ) ( ) WAB = − (1.25 kg/m ) 9.81 m/s 2 ( 0.9 m ) j = − (11.0363 Ν ) j WBC = − (1.25 kg/m ) 9.81 m/s 2 ( 0.3 m ) j = − ( 3.6788 Ν ) j WCD = − (1.25 kg/m ) 9.81 m/s 2 (1.35 m ) j = − (16.5544 Ν ) j uuur FE =T T=T FE −0.6i + 0.9 j − 1.35k ( − 0.6 ) 2 2 + ( 0.9 ) + ( −1.35 ) 2 = T ( −2i + 3j − 4.5k ) 33.25 continued COSMOS: Complete Online Solutions Manual Organization System λ AD uuur AD = = AD 0.9i − 0.3j − 1.35k ( 0.9 ) 2 2 + ( −0.3) + ( −1.35 ) 2 = 6 2 9 i− j− k 11 11 11 rG/ A = ( 0.45 m ) i rF / A = ( 0.6 m ) i rB/ A = ( 0.9 m ) i rH/A = ( 0.9 m ) i − ( 0.3 m ) j − ( 0.675 m ) k Now, ΣM AD = 0: ( ) ( ) ( ) ( ) λ AD ⋅ rG/ A × WAB + λ AD ⋅ rF / A × T + λ AD ⋅ rB/ A × WBC + λ AD ⋅ rH / A × WCD = 0 −2 −9 −2 −9 6 6 − 2 −9 6 T 1 1 + 0.9 0.45 0 0   + 0.6 0 0 0 0   11 11 33.25    11  − 2 3 − 4.5 0 −11.0363 0 0 − 3.6788 0 6 −2 −9 1 + 0.9 − 0.3 − 0.675   = 0  11  0 −16.5544 0 4.0634 − 0.34054T + 2.7089 + 6.0950 = 0 Solving for T: TBG = 37.785 N or TBG = 37.8 N