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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 106. See Problem 2.105 for the figure and the analysis leading to the linear algebraic Equations (1), (2), and (3) below. 11 2 − ⎛ ⎜ ⎞ ⎟FBA + ⎛ ⎜ ⎞ ⎟FDA = 0 (1) ⎝14.6 ⎠ ⎝3 ⎠ From Equation (1): ⎛ 9.6 ⎞ ⎛4 ⎞ ⎛2 ⎞ ⎜ ⎟FBA + ⎜ ⎟FCA + ⎜ ⎟FDA − P = 0 ⎝14.6 ⎠ ⎝5 ⎠ ⎝3 ⎠ 3 1 − ⎛ ⎜ ⎞ ⎟FCA + ⎛ ⎜ ⎞ ⎟FDA = 0 (3) ⎝5⎠ ⎝3⎠ F BA ⎛14.6 ⎞⎛2 ⎞ = ⎜ ⎟⎜ ⎟ F ⎝ 11 ⎠⎝3 ⎠ ⎛5 ⎞ From Equation (3): FCA = ⎜ ⎟ FDA ⎝9 ⎠ Substituting into Equation (2) for F and F gives: BA ⎛ 9.6 ⎞⎛14.6 ⎞⎛2 ⎞ ⎛4 ⎞⎛5 ⎞ ⎛2 ⎞ ⎜ ⎟⎜ ⎟⎜ ⎟FDA + ⎜ ⎟⎜ ⎟FDA + ⎜ ⎟FDA − P = 0 ⎝14.6 ⎠⎝ 11 ⎠⎝3 ⎠ ⎝5 ⎠⎝9 ⎠ ⎝3 ⎠ Since P = 45 lb and and F BA F CA CA ⎛838 ⎞ or ⎜ ⎟F ⎝495 ⎠ DA DA = P ⎛838 ⎞ ⎜ ⎟F DA = 45 lb ⎝495 ⎠ or F DA = 26.581 lb ⎛14.6 ⎞⎛2 ⎞ = ⎜ ⎟⎜ ⎟ ( 26.581 lb) ⎝ 11 ⎠⎝3 ⎠ ⎛5 ⎞ = ⎜ ⎟ ⎝9 ⎠ ( 26.581 lb) or or (2) F = 23.5 lb ⊳ BA F = 14.77 lb ⊳ CA and F = 26.6 lb ⊳ DA 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 107. The force in each cable can be written as the product of the magnitude of the force and the unit vector along the cable. That is, with uuur AC = i − j + k ( 18 m) ( 30 m) ( 5.4 m) ( ) ( ) ( ) 2 2 2 AC = 18 m + − 30 m + 5.4 m = 35.4 m uuur T AC TAC AC = Tλ AC = TAC = ⎡( 18 m) − ( 30 m) + ( 5.4 m) ⎤ AC 35.4 m ⎣ i j k ⎦ AC AC ( 0.50847 0.84746 0.152542 ) T = T i − j + k and uuur AB =− i − j + k ( 6 m) ( 30 m) ( 7.5 m) ( ) ( ) ( ) 2 2 2 AB = − 6 m + − 30 m + 7.5 m = 31.5 m uuur T AB TAB AB = Tλ AB = TAB = ⎡−( 6 m) − ( 30 m) + ( 7.5 m) ⎤ AB 31.5 m ⎣ i j k ⎦ AB AB ( 0.190476 0.95238 0.23810 ) T = T − i − j + k uuur Finally AD =−( 6 m) −( 30 m) −( 22.2 m) i j k ( ) ( ) ( ) 2 2 2 AD = − 6 m + − 30 m + − 22.2 m = 37.8 m uuur T AD TAD AD = Tλ AD = TAD = ⎡−( 6 m) − ( 30 m) − ( 22.2 m) ⎤ AD 37.8 m ⎣ i j k ⎦ AD AD ( 0.158730 0.79365 0.58730 ) T = T − i − j − k 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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