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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 113. ( ) ( ) 2 2 d = 400 mm + − 600 mm = 721.11 mm DA ( ) ( ) ( ) 2 2 2 d = − 200 mm + − 600 mm + 150 mm = 650 mm DB ( ) ( ) ( ) 2 2 2 d = − 200 mm + − 600 mm + − 150 mm = 650 mm DC T DA = TDAλDA T DA ( 400 mm) i ( 600 mm) = ⎡ − 721.11 mm ⎣ = 0.55470i − 0.83205j T DA T DB = TDBλDB At point D Σ F =0: T + T + T + W 0 i component: j component: k component: 2 Setting ( )( ) DA DB DC = W = 16 kg 9.81 m/s = 156.96 N ( ) T DB And Solving Equations (1), (2), and (3) simultaneously: j ⎤ ⎦ ( 200 mm) ( 600 mm) + ( 150 mm) = ⎡− − ⎤ 650 mm ⎣ i j k ⎦ 4 12 3 = T ⎛ DB ⎜− i − j + k ⎞ 13 13 13 ⎟ ⎝ ⎠ T DC = TDCλDC T TDC DC = ⎡−( 200 mm) − ( 600 mm) − ( 150 mm) ⎤ 650 mm ⎣ i j k ⎦ ⎛ 4 12 3 ⎞ = T DC ⎜− i − j − k 13 13 13 ⎟ ⎝ ⎠ W = Wj 4 4 0.55470TDA − TDB − TDC = 0 (1) 13 13 12 12 −0.83205TDA − TDB − TDC + W = 0 (2) 13 13 3 3 TDB − TDC = 0 (3) 13 13 T = 62.9 N ! DA T = 56.7 N ! DB T = 56.7 N ! DC 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 114. ( ) ( ) 2 2 d = 400 mm + − 600 mm = 721.11 mm DA ( ) ( ) ( ) 2 2 2 d = − 200 mm + − 600 mm + 200 mm = 663.32 mm DB ( ) ( ) ( ) 2 2 2 d = − 200 mm + − 600 mm + − 200 mm = 663.32 mm DC T DA = TDAλDA T DA ( 400 mm) i ( 600 mm) = ⎡ − 721.11 mm ⎣ T DA ( 0.55470i 0.83205j ) = − T DB = TDBλDB T DB j ⎤ ⎦ ( 200 mm) ( 600 mm) + ( 200 mm) = ⎡− − ⎤ 663.32 mm ⎣ i j k ⎦ T DB ( 0.30151i 0.90454 j + 0.30151k ) = − − T DC = TDCλDC T DC ( 200 mm) ( 600 mm) − ( 200 mm) = ⎡− − ⎤ 663.32 mm ⎣ i j k ⎦ T DC At point D Σ F =0: T + T + T + W 0 DA DB DC = ( 0.30151i 0.90454j 0.30151k ) = − − − i component: 0.55470T − 0.30151T − 0.30151T = 0 (1) DA DB DC j component: −0.83205T − 0.90454T − 0.90454T + W = 0 (2) DA DB DC k component: 0.30151T − 0.30151T = 0 (3) 2 Setting ( )( ) W = 16 kg 9.81 m/s = 156.96 N And Solving Equations (1), (2), and (3) simultaneously: DB T = 62.9 N ! DA T = 57.8 N ! DB DC T = 57.8 N ! DC 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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