Moments and Equilibrium
It is not enough fro all the forces in each direction to equal each other to keep a body in equilibrium.
The bar on the left below is balanced. The upwards forces equal the downwards forces. The bar on the right is not balanced. The bar on the right will turn in the direction of the arrows.
There is another condition that must be satisfied for equilibrium.
The Principle of Moments
For a body to remain in equilibrium, the sum of the clockwise moments (Force*Distance) must be equal to the sum of the anticlockwise moments about each pivot point. In the diagram above, the pivot points are shown as circles on the plank.
The Principle of Moments can be used to find unknown forces of unknown distances.
Take moments about C