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COSMOS: Complete Online <strong>Sol</strong>utions Manual Organization System<br />
Chapter 2, <strong>Sol</strong>ution 106.<br />
See Problem 2.105 for the figure and the analysis leading to the linear algebraic Equations (1), (2), and<br />
(3) below.<br />
11 2<br />
− ⎛ ⎜ ⎞ ⎟FBA<br />
+ ⎛ ⎜ ⎞<br />
⎟FDA<br />
= 0<br />
(1)<br />
⎝14.6 ⎠ ⎝3<br />
⎠<br />
From Equation (1):<br />
⎛ 9.6 ⎞ ⎛4 ⎞ ⎛2<br />
⎞<br />
⎜ ⎟FBA + ⎜ ⎟FCA + ⎜ ⎟FDA<br />
− P = 0<br />
⎝14.6 ⎠ ⎝5 ⎠ ⎝3<br />
⎠<br />
3 1<br />
− ⎛ ⎜ ⎞ ⎟FCA<br />
+ ⎛ ⎜ ⎞<br />
⎟FDA<br />
= 0 (3)<br />
⎝5⎠ ⎝3⎠<br />
F<br />
BA<br />
⎛14.6 ⎞⎛2<br />
⎞<br />
= ⎜ ⎟⎜ ⎟ F<br />
⎝ 11 ⎠⎝3<br />
⎠<br />
⎛5<br />
⎞<br />
From Equation (3): FCA<br />
= ⎜ ⎟ FDA<br />
⎝9<br />
⎠<br />
Substituting into Equation (2) for F and F gives:<br />
BA<br />
⎛ 9.6 ⎞⎛14.6 ⎞⎛2 ⎞ ⎛4 ⎞⎛5 ⎞ ⎛2<br />
⎞<br />
⎜ ⎟⎜ ⎟⎜ ⎟FDA + ⎜ ⎟⎜ ⎟FDA + ⎜ ⎟FDA<br />
− P = 0<br />
⎝14.6 ⎠⎝ 11 ⎠⎝3 ⎠ ⎝5 ⎠⎝9 ⎠ ⎝3<br />
⎠<br />
Since<br />
P = 45 lb<br />
and<br />
and<br />
F BA<br />
F CA<br />
CA<br />
⎛838<br />
⎞<br />
or ⎜ ⎟F<br />
⎝495<br />
⎠<br />
DA<br />
DA<br />
= P<br />
⎛838<br />
⎞<br />
⎜ ⎟F DA = 45 lb<br />
⎝495<br />
⎠<br />
or F DA = 26.581 lb<br />
⎛14.6 ⎞⎛2<br />
⎞<br />
= ⎜ ⎟⎜ ⎟ ( 26.581 lb)<br />
⎝ 11 ⎠⎝3<br />
⎠<br />
⎛5<br />
⎞<br />
= ⎜ ⎟<br />
⎝9<br />
⎠<br />
( 26.581 lb)<br />
or<br />
or<br />
(2)<br />
F = 23.5 lb ⊳<br />
BA<br />
F = 14.77 lb ⊳<br />
CA<br />
and F = 26.6 lb ⊳<br />
DA<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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