## The Bottle Balancer

by:  Ron Perkins

The bottle balancer is a fascinating conversation piece that illustrates the principle of center of gravity!  A small hole in an oak board allows you to balance a 2-liter soda bottle at an angle that appears to defy gravity. This can be used as a teaching tool or a centerpiece at your next party!  Hold the special angle cut of the wooden, bottle balancer board against a flat horizontal surface.   When a full, sealed, 2-Liter soda bottle is inserted into the wooden hole from above, it will catch the bottle flange and the wood/bottle assembly balances at a surprising angle.

Explanation:

In order for an object at rest to NOT tip over, its center of gravity, or its center of mass must be directly over its base.   A goose-necked desk lamp is usually quite stable, unless it is configured so that the lamp part is stretched horizontally, far from the large base.  Then, it becomes less stable and often tips over.   The wood/bottle assembly example is more complicated than the lamp example because if the bottle is moved, the flowing liquid results in a change of its center of mass.

Consider a thought experiment!  To simplify the Soda Bottle Balance, consider the soda in the bottle frozen and the bottle super-glued to the wooden board so that everything balances on the angled edge of the board.  Balancing will only occur if the center of mass is directly above the flat angled edge of the wood.    How do you find the center of mass?  Loosely tie a string to your forefinger with a hanging weight tied to the other end of the string, e.g. a large metal nut or a bunch of washers.  Balance the object (in this case, the glued and frozen bottle balancer) on your forefinger above the string.    The center of mass will be somewhere along the straight line that includes the string.    Then, balance the wood/bottle assembly on your forefinger at a different point.    Again, the center of mass will be somewhere along the straight line that includes the string.    Where the two lines intersect is the center of mass.   This imaginary point must be directly above the object’s base in order for the object to be stable and not tip over.   Sometimes the center of mass is within the object and sometimes it is a point in space outside the object, as in the wood/bottle assembly.

What happens when you release the carbon dioxide gas from a balanced 2-liter soda bottle?   A sealed 2-liter soda bottle has a mass of more than 2000 grams of material and contains about 10 grams of carbon dioxide under pressure (Wikipedia).   If the bottle is opened and the gas released, the mass of the bottle becomes less by about 0.5%.   However, approximately half of this decrease in mass is to the left of the center of mass and half to the right. The release of gas results in very little change in the center of mass.   In trying the experiment, one must find a method of slowly releasing the gas in the bottle without disturbing its balance.   One method would be to make an extremely small hole in the balanced bottle by pressing a small hot needle into the bottle, allowing gas to slowly escape without losing liquid. This way the bottle assembly stays balanced as the gas begins to slowly leak from the bottle.   Observe what occurs!  Sounds like an interesting experiment!    Please let Educational Innovations know the results!

Note:

As the pressure is released, the bottle may sag causing the soda to flow, drastically changing the center of mass of the bottle.   Also, if the gas is released too quickly, foaming will occur as dissolved gas quickly comes out of solution, resulting in loss of liquid.