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COSMOS: Complete Online <strong>Sol</strong>utions Manual Organization System<br />
Chapter 2, <strong>Sol</strong>ution 84.<br />
2 2<br />
2<br />
x y z<br />
(a) We have ( θ ) ( θ ) ( θ )<br />
cos + cos + cos = 1<br />
2<br />
2<br />
( θ ) = − ( θ ) − ( θ ) 2<br />
or cos 1 cos cos<br />
z x y<br />
Since F z < 0 we must have cosθ z < 0<br />
2 2<br />
Thus cosθ =− 1 − ( cos113.2° ) − cos( 78.4°<br />
)<br />
z<br />
cosθ z =− 0.89687<br />
θ = 153.7°!<br />
z<br />
(b) Then:<br />
F<br />
Fz<br />
−35 lb<br />
= =<br />
cosθ<br />
− 0.89687<br />
z<br />
F = 39.<strong>02</strong>5 lb<br />
And<br />
F = Fcosθ<br />
x<br />
x<br />
( )<br />
F = 39.<strong>02</strong>5 lb cos113.2°<br />
x<br />
F =− 15.37 lb !<br />
x<br />
F = Fcosθ<br />
y<br />
y<br />
( )<br />
F = 39.<strong>02</strong>5 lb cos78.4°<br />
y<br />
F = 7.85 lb !<br />
y<br />
F = 39.0 lb !<br />
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,<br />
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell<br />
© 2007 The McGraw-Hill Companies.
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