|ES-115 Three Force Equilibrium|
|If three forces are applied to a body they must be coplanar
and concurrent or parallel for equilibrium to be possible.|
Let us apply three forces to a body:
|Since two lines define a plane, let us let and define the x-y plane. is then the only force with a z component.|
|Since the third force has no z component the forces must be coplanar. Let us assume that intersect at 0. If we take moments about 0...|
|Since is not equal to zero,
d must be zero or parallel to .
If it is zero, the three forces are concurrent, meaning they all pass though the same point.
are parallel, they define an axis, let us say the x-axis.
then, is the only force with a y component,
hence the equation shown to the left...|
Therefore the three forces are parallel.