COSMOS Chapter 3 Solution 119 - Edubirdie

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

2024
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1
Author:

descorrer7yy

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 119. (a) Duct AB will not have a tendency to rotate about the vertical or y-axis if: ( ) R M By = j ⋅ ΣM RB = j ⋅ rF /B × FF + rE/B × FE = 0 where rF /B = (1.125 m ) i − ( 0.575 m ) j + ( 0.7 m ) k rE/B = (1.35 m ) i − ( 0.85 m ) j + ( 0.7 m ) k FF = 50 N ( sin α ) j + ( cos α ) k  FE = − ( 25 N ) k ∴ ΣM RB i j k i j k = ( 50 N ) 1.125 m −0.575 m 0.7 m + ( 25 N ) 1.35 m −0.85 m 0.70 0 sin α cos α 0 0 −1 = ( −28.75cos α − 35sin α + 21.25 ) i − ( 56.25cos α − 33.75 ) j + ( 56.25sin α ) k  N ⋅ m R M By = −56.25cos α + 33.75 = 0 Thus, cos α = 0.60 α = 53.130° or α = 53.1° (b) R = FE + FF where FE = − ( 25 N ) k FF = ( 50 N )( sin 53.130° j + cos 53.130°k ) = ( 40 N ) j + ( 30 N ) k ∴ R = ( 40 N ) j + ( 5 N ) k and M = ΣM RB = −  28.75 ( 0.6 ) + 35 ( 0.8 ) − 21.25 i − 56.25 ( 0.6 ) − 33.75 j + 56.25 ( 0.8)  k = − ( 24 N ⋅ m ) i − ( 0 ) j + ( 45 N ⋅ m ) k or M = − ( 24.0 N ⋅ m ) i + ( 45.0 N ⋅ m ) k .

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