COSMOS Chapter 4 Solution 136 - Edubirdie

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

2021
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483

Pages:

2
Author:

omiliar74be

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 136. Free-Body Diagram: ΣFx = 0: Bx + C x = 0, or Bx = − C x (1) ΣFy = 0: Ay + By + C y = 0 (2) ΣFy = 0: Az − P = 0, or Az = P = 40.0 lb (3) ΣM O = 0: or rOA × A + rOB × B + rOC × C + M Ai − M C k = 0 ( ) ( ) ( ) ai × Ay j + Azk + bj × Bxi + By j + ck × C x i + C y j + M Ai − M C k = 0 or a Ayk − a Az j − bBx j + cCx j − cC y i + M Ai − M C k = 0 continued COSMOS: Complete Online Solutions Manual Organization System Equating the coefficients of the unit vectors to zero: i : − cC y + M A = 0 Cy = j: (4) − a Az + cC x = 0, or using (3) Cx = k: MA 36 lb ⋅ ft = = 36.0 lb c 1 ft a 9 in. P= ( 40 lb ) = 30.0 lb c 12 in. (5) a Ay − b Bx − M C = 0, or, using (1) and (5) b M 6 in. 0 Ay = − P + C = − = − 20.0 lb ( 40 lb ) + c a 12 in. 9 in. (6) Finally substituting into (1) and (2) gives: Βx = −30.0 lb By = − Ay − C y = 20.0 lb − 36.0 lb = −16.00 lb Therefore: A = − ( 20.0 lb ) j + ( 40.0 lb ) k B = − ( 30.0 lb ) i − (16.00 lb ) j C = ( 30.0 lb ) i + ( 36.0 lb ) j

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