Sol Cap 02 - Edicion 8

COSMOS: Complete Online Solutions Manual Organization System
Chapter 2, Solution 113.
( ) ( )
2 2
d = 400 mm + − 600 mm = 721.11 mm
DA
( ) ( ) ( )
2 2 2
d = − 200 mm + − 600 mm + 150 mm = 650 mm
DB
( ) ( ) ( )
2 2 2
d = − 200 mm + − 600 mm + − 150 mm = 650 mm
DC
T DA = TDAλDA
T DA
( 400 mm) i ( 600 mm)
= ⎡ −
721.11 mm ⎣
= 0.55470i
− 0.83205j
T DA
T DB = TDBλDB
At point D Σ F =0: T + T + T + W 0
i component:
j component:
k component:
2
Setting ( )( )
DA DB DC =
W = 16 kg 9.81 m/s = 156.96 N
( )
T DB
And Solving Equations (1), (2), and (3) simultaneously:
j ⎤
⎦
( 200 mm) ( 600 mm) + ( 150 mm)
= ⎡− −
⎤
650 mm ⎣ i j k ⎦
4 12 3
= T ⎛ DB ⎜− i − j + k
⎞
13 13 13
⎟
⎝
⎠
T DC = TDCλDC
T TDC
DC = ⎡−( 200 mm) − ( 600 mm) − ( 150 mm)
⎤
650 mm ⎣ i j k ⎦
⎛ 4 12 3 ⎞
= T DC ⎜− i − j − k
13 13 13
⎟
⎝
⎠
W = Wj
4 4
0.55470TDA − TDB − TDC
= 0
(1)
13 13
12 12
−0.83205TDA − TDB − TDC
+ W = 0
(2)
13 13
3 3
TDB
− TDC
= 0
(3)
13 13
T = 62.9 N !
DA
T = 56.7 N !
DB
T = 56.7 N !
DC
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.