NAME: ____________________________________
ME 270 – Fall 2012
PROBLEM 2. (20 points)
GIVEN: Plate ABC is held up by three cables attached to ring D. An upward force, F, pulls on ring D.
You may treat ring D as a particle. The tension in cable DA is given by
TDA = 96iˆ - 64jˆ -192kˆ N
FIND:
a) On the axes provided below, draw a free body diagram of ring D. (4 pts)
b) Write vector expressions for the forces in cables DB and DC in terms of their unknown
magnitudes and their known unit vectors. (6 pts)
c) Using your equations of static equilibrium, determine the magnitude of the forces in cables DB and
DC, and the magnitude of the upward force, F. (10 pts)
Free Body Diagram
b)
 6iˆ  3 ˆj  6kˆ 
TDB  TDB 
 62  32  62 


 6iˆ  3 ˆj  6kˆ 
 TDB 


9


2 
 2 1
TDB  TDB   iˆ  ˆj  kˆ 
3 
 3 3
c)
F
x
2
 0  96  0TDC  TDB
3
TDB  144 N
4
1

0


64

T

TDB
y
DC
5
3
4
1
0  64  TDC  144 
5
3
F
TDC  140 N
3
2
 0  192  TDC  TDB  F
5
3
3
2
F  192  140   144 
5
3
F
z
F  372 N
 8 ˆj  6kˆ 
TDC  TDC 
 82  62 


 8 ˆj  6kˆ 
 TDC 
 10 


3 
4
TDC  TDC  ˆj  kˆ 
5 
5