Equilibrium is not always possible. Forces may balance vertically and horizontally, but there may still be a turning motion preventing equilibrium. The floowing diagram shows a uniform rod of weight 100 N purporting to be held horizontal by tensions
and
in cables attached to either end of the rod.
Resolving vertically gives
Subtracting these, and using that
gives
Then
Taking moments about A gives
so the road will swing clockwise about A and cannot be in equiliubrium.
It is however, possible for the system to be in equilibrium if the rod is non – uniform.