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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 109. At A Σ F = 0 Substituting for !!!" AB =− i − j + k ( 6.5 ft) ( 8 ft) ( 2 ft) ( ) ( ) ( ) 2 2 2 AB = − 6.5 ft + − 8 ft + 2 ft = 10.5 ft T TAB AB = ⎡−( 6.5 ft) − ( 8 ft) + ( 2 ft) ⎤ 10.5 ft ⎣ i j k ⎦ T AB ( 0.61905i 0.76190j 0.190476k ) = − − + !!!" AC = i − j + k ( 1ft) ( 8ft) ( 4ft) ( ) ( ) ( ) 2 2 2 AC = 1ft + − 8ft + 4ft = 9ft T TAC AC = ⎡( 1ft) − ( 8ft) + ( 4ft) ⎤ 9ft⎣ i j k ⎦ ( 0.111111 0.88889 0.44444 ) = T i − j + k AC !!!" AD = i − j − k ( 1.75 ft) ( 8 ft) ( 1 ft) ( ) ( ) ( ) 2 2 2 AD = 1.75 ft + − 8 ft + − 1 ft = 8.25 ft T TAD AD = ⎡( 1.75 ft) − ( 8 ft) − ( 1 ft) ⎤ 8.25 ft ⎣ i j k ⎦ T AD ( 0.21212i 0.96970j 0.121212k ) = − − Σ F = 0: − 0.61905T + 0.111111T + 0.21212T = 0 (1) x AB AC AD Σ F = 0: −0.76190T − 0.88889T − 0.96970T + W = 0 (2) y AB AC AD Σ F = 0: 0.190476T + 0.44444T − 0.121212T = 0 (3) z AB AC AD W = 320 lb and Solving Equations (1), (2), (3) simultaneously yields: T = 86.2 lb ! AB T = 27.7 lb ! AC T = 237 lb ! AD 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 110. See Problem 2.109 for the analysis leading to the linear algebraic Equations (1), (2), and (3) shown below. − 0.61905T + 0.111111T + 0.21212T = 0 (1) AB AC AD −0.76190T − 0.88889T − 0.96970T + W = 0 (2) AB AC AD 0.190476T + 0.44444T − 0.121212T = 0 (3) AB AC AD Now substituting for T = 220 lb Gives: AD Solving Equations (4) and (6) simultaneously gives − 0.61905T + 0.111111T + 46.662 = 0 (4) AB AC −0.76190T − 0.88889T − 213.33 + W = 0 (5) AB AC 0.190476T + 0.44444T − 26.666 = 0 (6) AB AC T = 79.992 lb and T = 25.716 lb AB Substituting into Equation (5) yields W = 297 lb ⊳ AC 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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