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

2022
Views:

76

Pages:

2
Author:

drvnomyhv

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 136. First reduce the given force-couple system to an equivalent force-couple system ( R, M B ) at point B. d BD = ( − 480 mm )2 + ( 560 mm )2 + ( − 480 mm )2 = 880 mm FBD = FBDλBD = 132 N ( − 480i + 560 j − 480k ) 880 = (12 N )( − 6i + 7 j − 6k ) d EB = ( 240 mm )2 + ( − 220 mm )2 + ( 480 mm )2 = 580 mm FEB = FEBλEB = 145 N ( 240i − 220 j + 480k ) 580 = ( 5 N )(12i − 11j + 24k ) ΣF : R = FBD + FEB = (12 N )( − 6i + 7 j − 6k ) + 5 N (12i − 11j + 24k ) = − (12 N ) i + ( 29 N ) j + ( 48 N ) k d BF = ( 340 mm )2 + ( 240 mm )2 + ( − 60 mm )2 = 20 442 mm Then MB = = . 20 N ⋅ m ( 340i + 240 j − 60k ) 20 442 20 N ⋅ m (17i + 12 j − 3k ) 442 COSMOS: Complete Online Solutions Manual Organization System Now determine whether R and M B are perpendicular R ⋅ M B = ( −12 j + 29 j + 48k ) ⋅ 20 (17i + 12 j − 3k ) 442 20 ( −12 × 17 + 29 × 12 − 48 × 3) 442 = =0 ∴ R and M B are perpendicular so that ( R, M B ) can be reduced to the single equivalent force R = − (12.00 N ) i + ( 29.0 N ) j + ( 48.0 N ) k Now require M B = rB/P × R or j: 20 × 12 = −12 ( z − 0.480 ) + 0.480 ( 48 ) 442 or k: i j k 20 N ⋅ m (17i + 12 j − 3k ) = − 0.480 y z − 0.480 ( N ⋅ m ) 442 −12 29 48 z = 1.449 m − 20 × 3 = − 0.480 ( 29 ) + 12 y 442 or y = 0.922 m ∴ The point of intersection is defined by y = 0.922 m z = 1.449 m .

COSMOS Chapter 3 Solution 136

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