Equilibrium of the Balance (from Class Notes 100830)

The balance is in equilibrium with the total of the upward and downward forces acting on it is zero, and when the total of the torques is zero. 

We haven't really defined torque, but think about this:  If we change the position of a paperclip, the upward and downward forces don't change.  The force on the clip changes position.  If we move it further from the balance point the system will tip in the corresponding direction.  It has more leverage. 

Torques are a way of taking account of forces and their leverage.  We will define torque at a later time, so as not to get too confusing now.

The water in which a paper clip is immersed exerts pressure-related forces on all points of the clip, some upward, some downward, and some horizontal.  The pressure increases with depth, with the result that the total of the upward pressure-related forces on the clip is greater than the total of the downward pressure-related forces.  So the total force exerted by the water on the clip is in the upward direction  This is the force we call the buoyant force.

The more of the clip is submerged, the greater the upward buoyant force. 

If we add a mass to the 'clip end' of the beam, the paper clip will descend, increasing the upward buoyant force until it counterbalances the weight of the added mass.