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

2021
Views:

455

Pages:

2
Author:

Tyshawn Shaffer

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 117. Free-Body Diagram: Express all forces in terms of rectangular components: rA = ( 2.4 m ) i rB = (1.8 m ) j uuur AD = − ( 2.4 m ) i + ( 0.3 m ) j + (1.2 m ) k uuur BE = − (1.8 m ) i + ( 0.6 m ) j − ( 0.9 m ) k WA = − ( 440 N ) j WB = − ( 440 N ) j Then uuur ur AD = TAD T AD = TAD AD uuur ur BE = TBE T BE = TBE BE − 2.4i + 0.3j + 1.2k ( − 2.4 ) 2 2 + ( 0.3) + (1.2 ) 2 −1.8i + 0.6 j − 0.9k ( −1.8) 2 2 + ( 0.6 ) + ( − 0.9 ) 2 8 1 4 = − TADi + TAD j + TADk 9 9 9 6 2 3 = − TADi + TAD j − TADk 7 7 7 continued COSMOS: Complete Online Solutions Manual Organization System ΣM C = 0: or rA × TAD + rB × TBE + rA × WA + rB × WB = 0 i 2.4 8 − 9 j 0 1 9 k i j k 0 TAD + 1.8 0 0 TBE + ( 2.4 ) i × (− 440) j + (1.8 ) i × (− 440) j = 0 4 6 2 3 − − 9 7 7 7 Equating the coefficients of the unit vectors to zero: j: − 9.6 5.4 TAD + TBE = 0 9 7 2.4 3.6 TAD + TBE − 1848 = 0 9 7 k: or TAD = 1890 N TBE = 2610 N Force equations: Cx − 8 6 (1890.00 N ) − ( 2613.3 N ) = 0, 9 7 Cy + 1 2 (1890.00 N ) + ( 2613.3 N ) − 440 N − 440 N = 0, 9 7 Cz + 4 3 (1890.00 N ) − ( 2613.3 N ) = 0, 9 7 or or C x = 3920.0 N or C y = −76.657 N C z = 279.99 N C = ( 3920 N ) i − ( 76.7 N ) j + ( 280 N ) k