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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 139. The (vector) force in each cable can be written as the product of the (scalar) force and the unit vector along the cable. That is, with uuur AB = i − j+ k ( 32 in. ) ( 48 in. ) ( 36 in. ) ( ) ( ) ( ) 2 2 2 AB = − 32 in. + − 48 in. + 36 in. = 68 in. uuur T AB TAB AB = Tλ AB = TAB = ⎡−( 32 in. ) − ( 48 in. ) + ( 36 in. ) ⎤ AB 68 in. ⎣ i j k ⎦ AB AB ( 0.47059 0.70588 0.52941 ) T = T − i − j + k uuur and AC = ( 45 in. ) − ( 48 in. ) + ( 36 in. ) i j k ( ) ( ) ( ) 2 2 2 AC = 45 in. + − 48 in. + 36 in. = 75 in. uuur T AC TAC AC = Tλ AC = TAC = ⎡( 45 in. ) − ( 48 in. ) + ( 36 in. ) ⎤ AC 75 in. ⎣ i j k ⎦ AC AC ( 0.60 0.64 0.48 ) T = T i − j + k uuur Finally, AD = ( 25 in. ) − ( 48 in. ) − ( 36 in. ) i j k ( ) ( ) ( ) 2 2 2 AD = 25 in. + − 48 in. + − 36 in. = 65 in. 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.

COSMOS: Complete Online Solutions Manual Organization System uuur T AD TAD AD = Tλ AD = TAD = ⎡( 25 in. ) − ( 48 in. ) − ( 36 in. ) ⎤ AD 65 in. ⎣ i j k ⎦ AD AD With W = Wj , at A we have: ( 0.38461 0.73846 0.55385 ) T = T i − j − k Σ F = 0: T + T + T + j = 0 AB AC AD W Equating the factors of i, j, and k to zero, we obtain the linear algebraic equations: i : − 0.47059T + 0.60T − 0.38461T = 0 (1) AB AC AD j : −0.70588T − 0.64T − 0.73846T + W = 0 (2) AB AC AD k : 0.52941T + 0.48T − 0.55385T = 0 (3) AB AC AD In Equations (1), (2) and (3), set T AD = 120 lb, and, using conventional methods for solving Linear Algebraic Equations (MATLAB or Maple, for example), we obtain: T AB = T AC = 32.6 lb 102.5 lb W = 177.2 lb " 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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