An Impossible Equilibrium Situation

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 tensionsandin cables attached to either end of the rod.

Resolving vertically gives

Subtracting these, and using thatgives

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.