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. |
For equilibrium... |
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. |
If and
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. |