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COSMOS: Complete Online <strong>Sol</strong>utions Manual Organization System<br />
Chapter 2, <strong>Sol</strong>ution 137.<br />
( 500 lb)[ cos30 sin15 sin 30 cos30 cos15 ]<br />
( 500 lb)[ 0.2241i 0.50j 0.8365k<br />
]<br />
( 112.05 lb) i ( 250 lb) j ( 418.25 lb)<br />
k<br />
( 600 lb)[ cos 40 cos 20 sin 40 cos40 sin 20 ]<br />
( 600 lb)[ 0.71985i 0.64278j 0.26201k<br />
]<br />
( 431.91 lb) i ( 385.67 lb) j ( 157.206 lb)<br />
k<br />
( 319.86 lb) ( 635.67 lb) ( 261.04 lb)<br />
P = − ° ° i + ° j + ° ° k<br />
= − + +<br />
=− + +<br />
Q = ° ° i + ° j − ° ° k<br />
= + −<br />
= + −<br />
R = P + Q = i + j + k<br />
( ) ( ) ( )<br />
2 2 2<br />
R = 319.86 lb + 635.67 lb + 261.04 lb = 757.98 lb<br />
R = 758 lb !<br />
Rx<br />
319.86 lb<br />
cosθ x = = = 0.42199<br />
R 757.98 lb<br />
θ = 65.0°!<br />
Ry<br />
635.67 lb<br />
cosθ y = = = 0.83864<br />
R 757.98 lb<br />
θ = 33.0°!<br />
Rz<br />
261.04 lb<br />
cosθ z = = = 0.34439<br />
R 757.98 lb<br />
θ = 69.9°!<br />
x<br />
y<br />
z<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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