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Sol Cap 02 - Edicion 8

COSMOS: Complete Online

COSMOS: Complete Online Solutions Manual Organization System Chapter 2, Solution 40. (a) Since R is to be vertical, R x = 0 Then, R =Σ F = 0 x x ( ) ( ) ( ) ( ) 600 N cosα + 300 N cos α + 35° − 700 N cosα = 0 Expanding: ( ) 3 cosαcos35°− sinαsin 35° − cosα = 0 Then: tanα = ⎛1 ⎞ cos35°− ⎜ ⎟ ⎝3 ⎠ sin 35° α = 40.265° α = 40.3°! (b) Since R is vertical, R = Ry Then: R = Ry = Σ Fy R = ( 600 N) sin 40.265° + ( 300 N) sin 75.265° + ( 700 N) sin 40.265° R = 1130 N R = 1.130 kN ! 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 41. Selecting the x axis along aa′ , we write (a) Setting R y = 0 in Equation (2): ( ) ( ) R =Σ F = 300 N + 400 N cosα + 600 N sinα (1) x x ( ) ( ) R =Σ F = 400 N sinα − 600 N cosα (2) y y Thus 600 tanα = = 1.5 400 α = 56.3°! (b) Substituting for α in Equation (1): ( ) ( ) R = 300 N + 400 N cos56.3° + 600 N sin 56.3° x R x = 1021.11 N R = R x = 1021 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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