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# Sol Cap 02 - Edicion 8

## COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 122. See Problem 2.121 for the analysis leading to the linear algebraic Equations (1), (2), and (3) below: i component: 0.087704T + 0.107415T − 0.119806T = 0 (1) BE CF DG j component: 0.99226 T + 0.99226 T + 0.99226 T − W = 0 (2) BE CF DG k component: − 0.087704T + 0.062016T − 0.032102T + P = 0 (3) BE CF DG Setting W = 10.5 N and P = 0.5 N, and solving (1), (2), (3) simultaneously: T = 4.84 N ! BE T = 1.157 N ! CF T = 4.58 N ! DG Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 123. At D ΣF = 0: Σ F x = Σ F z = 0: 0: uuur DA =− i + j + k ( 8ft) ( 40ft) ( 10ft) ( ) ( ) ( ) 2 2 2 DA = − 8ft + 40ft + 10ft = 42ft T TADB DA = ⎡− ( 8ft) + ( 40ft) + ( 10ft) ⎤ 42 ft ⎣ i j k ⎦ = T ADB − 0.190476i + 0.95238j + 0.23810k uuur DB = 3ft i + 36ft j − 8ft k ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 DB = 3ft + 36ft + − 8ft = 37ft T TADB DB = ⎡( 3ft) + ( 36ft) − ( 8ft) ⎤ 37 ft ⎣ i j k ⎦ = T ADB 0.081081i + 0.97297j − 0.21622k uuur DC = a − 8ft i − 24ft j − 3ft k ( ) ( ) ( ) ( ) 2 ( a 8ft) ( 24ft) ( 3ft) 2 2 DC = − + − + − ( a ) ( a ) 2 = − 8 + 585 ft TDC TDC = ⎡( a 8ft) ( 24ft) ( 3ft) ⎤ 2 ⎣ − i − j − k ⎦ − 8 + 585 ( a − 8) ( a − ) 2 + − 0.190476TADB + 0.081081TADB + TDC = 0 8 585 3 0.23810TADB − 0.21622TADB − TDC = 0 − 8 + 585 ( a ) 2 (1) (2) Dividing equation (1) by equation (2) gives ( a − ) 8 0.190476 − 0.081081 = −3 − 0.23810 + 0.21622 or a = 23 ft Substituting into equation (1) for a = 23 ft and combining the coefficients for T ADB gives: Σ F x = 0: − 0.109395TADB + 0.52705TDC = 0 (3) continued Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.

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