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COSMOS: Complete Online <strong>Sol</strong>utions Manual Organization System<br />
Chapter 2, <strong>Sol</strong>ution 107.<br />
The force in each cable can be written as the product of the magnitude of<br />
the force and the unit vector along the cable. That is, with<br />
uuur<br />
AC = i − j + k<br />
( 18 m) ( 30 m) ( 5.4 m)<br />
( ) ( ) ( )<br />
2 2 2<br />
AC = 18 m + − 30 m + 5.4 m = 35.4 m<br />
uuur<br />
T AC TAC<br />
AC = Tλ<br />
AC = TAC<br />
= ⎡( 18 m) − ( 30 m) + ( 5.4 m)<br />
⎤<br />
AC 35.4 m<br />
⎣ i j k ⎦<br />
AC<br />
AC<br />
( 0.50847 0.84746 0.152542 )<br />
T = T i − j + k<br />
and<br />
uuur<br />
AB =− i − j + k<br />
( 6 m) ( 30 m) ( 7.5 m)<br />
( ) ( ) ( )<br />
2 2 2<br />
AB = − 6 m + − 30 m + 7.5 m = 31.5 m<br />
uuur<br />
T AB TAB<br />
AB = Tλ<br />
AB = TAB<br />
= ⎡−( 6 m) − ( 30 m) + ( 7.5 m)<br />
⎤<br />
AB 31.5 m<br />
⎣ i j k ⎦<br />
AB<br />
AB<br />
( 0.190476 0.95238 0.23810 )<br />
T = T − i − j + k<br />
uuur<br />
Finally AD =−( 6 m) −( 30 m) −( 22.2 m)<br />
i j k<br />
( ) ( ) ( )<br />
2 2 2<br />
AD = − 6 m + − 30 m + − 22.2 m = 37.8 m<br />
uuur<br />
T AD TAD<br />
AD = Tλ<br />
AD = TAD<br />
= ⎡−( 6 m) − ( 30 m) − ( 22.2 m)<br />
⎤<br />
AD 37.8 m<br />
⎣ i j k ⎦<br />
AD<br />
AD<br />
( 0.158730 0.79365 0.58730 )<br />
T = T − i − j − k<br />
continued<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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