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

2019
Views:

340

Pages:

2
Author:

imophulebf7

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 108. Free-Body Diagram: Note that: xC = L 1 − zC 2 3 (a) Setting: TA = TB = T ΣM O = 0: or rOA × TA + rOB × TB + rOC × TC + rOH × W + rOF × WBD + rOG × WAD = 0 − L L i × TA j + i × TB j + 2 2 ( ) 3  L L  3   − 4  i + Lk  × TC j 4   2 tan 60°     L   1   L   1  3 3 Lk  ×  − Wj  +  − i + Lk  ×  − Wj  + ( xC i + zC k ) × ( − Wj) = 0 +  i + 4 4 4   3   4   3  or ( ) 3 L  L L L 3  T k + LTC i − TAk + TAk +  − 4  2 tan 60°  C 2 2 4   − 1L 1 3 1L 1 3 Wk + LWi + Wk + LWi − xCWk + zCWi = 0 34 3 4 34 3 4 continued COSMOS: Complete Online Solutions Manual Organization System Equating the coefficients of the unit vectors to zero: i: W 3 W 3 3L L+ L − TC + WzC = 0 3 4 3 4 4 (1) or, using the relation between xC, and zC:  L  3 3 − LTC +  +  − 3 xC + 4 2  2 3  k:  L   W = 0   (2) 1 L L 3 1 1 LW + LW − xCW = 0 − T + T + L  −  TC − 2 2 2 4 12 12   1 3 L  −  TC = xCW 4  2 (3) Substituting (3) into (2) − 3 4 C  1 3 + +  2 3 2    1 3  − 3 L  −  TC  = 0 2 4     4 W 3 4 ΣFy = 0: 2T + W − 2W = 0 3 W T = 3 TC = TA = TB = Therefore: TC = (b) Using TC in (1): W 3 4 W 3 W 3 W 3 4 3 L+ L −  W  L + WzC = 0 3 4 3 4 3 4  1  zC = 1 − L 2 3  and from geometry xC = L 1 1 − zC = 2 − 3 L 2 3 3 ( ) Therefore: xC = 1 2− 3 L 3 ( )  1  zC = 1 − L 2 3 