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1-Three chains act on the bracket such that they create a resultant force having a magnitude of 520 lb. If
two of the chains are subjected to known forces, as shown, determine the angle θ of the third chain
measured clockwise from the positive x axis, so that the magnitude of force F in this chain is a minimum.
All forces lie in the x-y plane. Hint: First find the resultant of the two known forces.
Do not use calculus.
2- The ends of the three cables are attached to a ring at A and to the edge of a uniform 150-kg plate.
3- Determine the moment of the force
F  (50iˆ  40 ˆj  20kˆ)lb about the AB axis. Express the result as
a Cartesian vector.
Solution: First find the moment of the force about A.


M A  (2kˆ)  (50iˆ  40 ˆj  20kˆ)lb. ft  80iˆ  100 ˆj lb. ft
Next find the unit vector for axis AB:
4
3
uˆ   iˆ  ˆj
5
5
Now find the component of the moment along AB:



3
 4
M AB   80iˆ  100 ˆj    iˆ 
5
 5

ˆj   4 iˆ  3

5
 5
ˆj lb. ft    16 iˆ  12
5

 5
ˆj lb. ft
