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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 140. 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 ( 0.48 m) ( 0.72 m) ( 0.16 m) ( ) ( ) ( ) 2 2 2 AB = − 0.48 m + 0.72 m + − 0.16 m = 0.88 m uuur T AB TAB AB = Tλ AB = TAB = ⎡− ( 0.48 m) + ( 0.72 m) − ( 0.16 m) ⎤ AB 0.88 m ⎣ i j k ⎦ AB AB ( 0.54545 0.81818 0.181818 ) T = T − i + j − k and uuur AC = i + j − k ( 0.24 m) ( 0.72 m) ( 0.13 m) ( ) ( ) ( ) 2 2 2 AC = 0.24 m + 0.72 m − 0.13 m = 0.77 m uuur T AC TAC AC = Tλ AC = TAC = ⎡( 0.24 m) + ( 0.72 m) − ( 0.13 m) ⎤ AC 0.77 m ⎣ i j k ⎦ AC AC ( 0.31169 0.93506 0.16883 ) T = T i + j − k At A: Σ F = 0: T + T + P + Q + W = 0 AB AC Noting that T AB = T AC because of the ring A, we equate the factors of i, j,andk to zero to obtain the linear algebraic equations: ( ) i : − 0.54545 + 0.31169 T + P = 0 or P = 0.23376T ( ) j : 0.81818 + 0.93506 T − W = 0 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 With W = 1200 N: or W = 1.75324T ( ) k : −0.181818 − 0.16883 T + Q = 0 or Q = 0.35065T 1200 N T = = 684.45 N 1.75324 P = 160.0 N ! Q = 240 N ! 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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