Stability and Balance

   
The ball hanging from a string is in stable equilibrium.  When displaced the net force of gravity and the string will return the ball to its original position.

If the ball was laying on a horizontal table, it would be in neutral equilibrium.  If move, they would remain in the new position.

The pencil to the left is in an unstable equilibrium.  If the pencil is displaced slightly, the center of gravity will no longer be over the point and the pencil will fall over.

A body whose Center of Gravity is above its base of support will be stable if a vertical line downward from the Center of Gravity falls within the base of support.

The Critical Point is reached when the Center of Gravity is no longer above the base of support.

  

(a)	The Center of Gravity is over the base of the block.  The object is flat on the surface and will remain it this position unless disturbed.  A brick laying on its widest face is most stable because it will take more force to move the Center of Gravity from above the base of the support.
(b)	This block will resume the same position as (a).  If the line was directly over the edge, it would be remain in position but very little force would be required to tip it in either direction.
(c)	This is an unstable situation because the center of gravity is not over the support.  It will fall over unless there is an outside force acting on the block.

Humans are less stable than four-legged animals.  The base of support is much smaller for a human than a four-legged animal of the same size.

Man constantly adjust his stance to keep his Center of Gravity over his base.  Try standing with your heels to a wall and bending over to pick up an object.  It cannot be done because part of the mass must be sent behind the man to remain standing.

The Leaning Tower of Pisa is 55 m tall and about 7.0 m in diameter.  The top is 4.5 m off center.  Is the tower in stable equilibrium?  If so, how much farther can it lean before it becomes unstable?  Assume the tower is of uniform composition.

                     adj                         4.5 m
= Cos ^-1 ( ------- )  =  Cos ^-1 ( --------- )  =  85.3^o
                    hyp                          55 m
  

d = 27.5 m x Cos 85.3^o  =  2.25 m

The radius of the Tower of Pisa is 3.5 m.  The center of gravity is displaced 2.25 m.   Observe that although I worked the problem the long way.  The Center of Gravity is displaced one-half the amount the top is displaced.