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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 105. BA 2 2 ( 11 in. ) ( 9.6 in. ) 14.6 in. 2 2 ( 9.6 in. ) ( 7.2 in. ) 12.0 in. 2 2 2 ( ) ( ) ( ) FBA ( 11 in. ) ( 9.6 in. ) d = − + = d = + − = CA d = 9.6 in. + 9.6 in. + 4.8 in. = 14.4 in. DA F BA = FBAλBA = ⎡ − + ⎤ 14.6 in. ⎣ i j ⎦ 11 9.6 F ⎡ ⎛ ⎞ ⎛ ⎞ = ⎤ BA ⎢− ⎜ ⎟i + ⎜ ⎟j ⎥ ⎣ ⎝14.6 ⎠ ⎝14.6 ⎠ ⎦ F FCA CA = FCAλCA = ⎡( 9.6 in. ) − ( 7.2 in. ) ⎤ 12.0 in. ⎣ j k ⎦ 4 3 F ⎡ ⎛ ⎞ ⎛ ⎞ = ⎤ CA ⎢⎜ ⎟j − ⎜ ⎟k ⎥ ⎣⎝5⎠ ⎝5⎠ ⎦ F FDA DA = FDAλDA = ⎡( 9.6 in. ) + ( 9.6 in. ) + ( 4.8 in. ) ⎤ 14.4 in. ⎣ i j k ⎦ 2 2 1 F ⎡ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ = ⎤ DA ⎢⎜ ⎟i + ⎜ ⎟j + ⎜ ⎟k ⎥ ⎣⎝3⎠ ⎝3⎠ ⎝3⎠ ⎦ P =−P j At point A: Σ F = 0: F + F + F + P = 0 BA CA DA i component: 11 2 − ⎛ ⎜ ⎞ FBA + ⎛ ⎞ FDA = 0 14.6 ⎟ ⎜ 3 ⎟ ⎝ ⎠ ⎝ ⎠ (1) j component: ⎛ 9.6 ⎞ ⎛4 ⎞ ⎛2 ⎞ ⎜ FBA FCA FDA P 0 14.6 ⎟ + ⎜ + − = 5 ⎟ ⎜ 3 ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (2) k component: 3 1 − ⎛ ⎜ ⎞ FCA + ⎛ ⎞ FDA = 0 5 ⎟ ⎜ 3 ⎟ ⎝ ⎠ ⎝ ⎠ (3) 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 From Equation (1) ⎛14.6 ⎞⎛2 ⎞ FBA = ⎜ F 11 ⎟⎜ 3 ⎟ ⎝ ⎠⎝ ⎠ ⎛14.6 ⎞⎛2 ⎞ 29.2 lb = ⎜ 11 ⎟⎜ 3 ⎟ ⎝ ⎠⎝ ⎠ DA F DA or F = DA 33lb Solving Eqn. (3) for F CA gives: F CA ⎛5 ⎞ = ⎜ F 9 ⎟ ⎝ ⎠ DA F CA ⎛5 ⎞ = ⎜ 9 ⎟ ⎝ ⎠ ( 33 lb) Substituting into Eqn. (2) for FBA, FDA, andF CA in terms of F DA gives: ⎛ 9.6 ⎞ ⎛4 ⎞⎛5 ⎞ ⎛2 ⎞ ⎜ ( 29.2 lb) ( 33 lb) ( 33 lb) P 0 14.6 ⎟ + ⎜ + − = 5 ⎟⎜ 9 ⎟ ⎜ 3 ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ∴ P = 55.9 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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