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# n5 - F 2 and the unit vector of F 1 29 29 29 29 29 29 29 29...

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2.125 Two cables exert forces on the pipe. Determine the magnitude of the projected component of F 1 along the line of action of F 2 . To compute the unit vector of F 2 , use the identity for direction cosines to find the α angle knowing β and γ . ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 0 0 0 0 1 cos cos cos cos 1 cos cos 1 cos 60 cos 60 0.707 45 or 135 α β γ α β γ = + + = ± - - = - - = ± = From the figure α is 135 0 . Find the components of F 1 . ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 1 0 0 1 0 1 30 lb sin 30 15 lb ' 30 lb cos 30 26.0 lb 26.0 lb sin 30 13.0 lb 26.0 lb cos 30 22.5 lb z x y F F F F = - = - = = = = = =

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The component of the F 2 vector acting along the F 1 vector is the dot product between
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Unformatted text preview: F 2 and the unit vector of F 1 . ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 2 2 1 ˆ ˆ ˆ cos 135 cos 60 cos 60 ˆ ˆ ˆ 0.707 0.5 0.5 ˆ ˆ ˆ 13.0 lb 22.5 lb 15.0 lb * ˆ ˆ ˆ 13.0 lb 22.5 lb 15.0 lb ˆ ˆ ˆ * 0.707 0.5 0.5 13.0 lb 0.707 22.5 lb 0.5 15.0 lb 0.5 5.44 l on u i j k i j k F i j k F F u i j k i j k = + + = -+ + = +-= = +--+ + =-+ + -= uur uur uur ur b...
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n5 - F 2 and the unit vector of F 1 29 29 29 29 29 29 29 29...

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