Sol Cap 02 - Edicion 8

COSMOS: Complete Online Solutions Manual Organization System
Chapter 2, Solution 139.
The (vector) force in each cable can be written as the product of the
(scalar) force and the unit vector along the cable. That is, with
uuur
AB = i − j+
k
( 32 in. ) ( 48 in. ) ( 36 in. )
( ) ( ) ( )
2 2 2
AB = − 32 in. + − 48 in. + 36 in. = 68 in.
uuur
T AB TAB
AB = Tλ
AB = TAB
= ⎡−( 32 in. ) − ( 48 in. ) + ( 36 in. ) ⎤
AB 68 in.
⎣ i j k ⎦
AB
AB
( 0.47059 0.70588 0.52941 )
T = T − i − j + k
uuur
and AC = ( 45 in. ) − ( 48 in. ) + ( 36 in. )
i j k
( ) ( ) ( )
2 2 2
AC = 45 in. + − 48 in. + 36 in. = 75 in.
uuur
T AC TAC
AC = Tλ
AC = TAC
= ⎡( 45 in. ) − ( 48 in. ) + ( 36 in. ) ⎤
AC 75 in.
⎣ i j k ⎦
AC
AC
( 0.60 0.64 0.48 )
T = T i − j + k
uuur
Finally, AD = ( 25 in. ) − ( 48 in. ) − ( 36 in. )
i j k
( ) ( ) ( )
2 2 2
AD = 25 in. + − 48 in. + − 36 in. = 65 in.
continued
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr.,
Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell
© 2007 The McGraw-Hill Companies.