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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 125. ( ) ( ) ( ) 2 2 2 d = − 2.7 m + 2.4 m + − 3.6 m = 5.1 m AB ( ) ( ) 2 2 d = 2.4 m + 1.8 m = 3 m AC ( ) ( ) ( ) 2 2 2 d = 1.2 m + 2.4 m + − 0.3 m = 2.7 m AD ( ) ( ) ( ) 2 2 2 d = − 2.4 m + 2.4 m + 1.2 m = 3.6 m AE T AB = TABλAB T AB ( 2.7 m) ( 2.4 m) ( 3.6 m) = ⎡− + − ⎤ 5.1 m ⎣ i j k ⎦ 9 8 12 = T ⎛ AB ⎜− i + j − k ⎞ 17 17 17 ⎟ ⎝ ⎠ T AC = TACλAC T T AC ( 2.4 m) j ( 1.8 m) = ⎡ + 3m ⎣ T AC ( 0.8j 0.6k ) = + = 2T λ AD ADE AD T ADE k ⎤ ⎦ 2 = ⎡( 1.2 m) + ( 2.4 m) − ( 0.3 m) ⎤ 2.7 m ⎣ i j k ⎦ ⎛ 8 16 2 ⎞ = T ADE ⎜ i + j − k 9 9 9 ⎟ ⎝ ⎠ 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 T AE = TAEλAE T ADE ( 2.4 m) ( 2.4 m) ( 1.2 m) = ⎡− + + ⎤ 3.6 m ⎣ i j k ⎦ ⎛ 2 2 1 ⎞ = T ADE ⎜− i + j + k 3 3 3 ⎟ ⎝ ⎠ W =−Wj At point A: ΣF = 0: T + T + T + T W = 0 i component: j component: k component: Simplifying (1), (2), (3): AB AC AD AE + 9 8 2 − TAB + TADE − TADE = 0 (1) 17 9 3 8 16 2 TAB + 0.8 TAC + TADE + TADE − W = 0 (2) 17 9 3 12 2 1 − TAB + 0.6 TAC − TADE + TADE = 0 (3) 17 9 3 − 81T + 34T = 0 (1) ′ AB ADE 72T + 122.4T + 374T = 153 W (2) ′ AB AC ADE − 108T + 91.8T + 17T = 0 (3) ′ AB AC ADE Setting W = 1400 N and solving (1), (2), (3) simultaneously: T = 203 N " AB T = 149.6 N " AC T = 485 N " ADE 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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