🚀 go-pugleaf

TILTED EQUILIBRIUM PROBLEM
> I am not quite sure this analytically answers your question...
> Wouldn't the horizontal surface area be increased with the tilt? This
> seems to me that although Pascal's law says the pressure will be exerted
> equally throughout a liquid, that if there is more HORIZONTAL surface
> area, it would produce greater surface tension and hence more stability.

An interesting idea but .... Surface tension plays a role when objects are
so small that surface/volume ratios become very large. For large objects,
such as cans or boats, their effect is probably negligible. But it may be
true that when large forces (weight and buoyancy) cancel little forces
become important. I will keep this explanation as a last resort ...
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Charles Shirkey brought to my attention a reference from The Physics
Teacher (April 1990, page 210) which shows how a similar problem was solved
in a very elegant way. The article reminded me that the general condition for
equilibrium is the existence of a minimum of potential energy. I wish I knew
how to demonstrate that such a minimum indeed exists at the tilt angle of
50 degrees when the liquid load is 200 grams (in the previously described
problem). If somebody can prove the case then, it would be, in my opinion, a
piece worth publishing. The problem may be trivial for a naval engineer but
not for a typical physics teacher. Use the above reference as a model for your
publication.

I am still thinking about how to solve the problem and waiting for helpful
suggestions. NOTE THAT BOTH WEIGHT AND BUOYANT FORCE ARE DUE TO GRAVITY.
GRAVITY WORKING DOWN (ATTRACTION) AND GRAVITY WORKING UP ("REPULSION"). TWO
FORCES ARE EQUAL AND OPPOSITE, AS OBSERVED BY ARCHIMEDES.

        Ludwik Kowalski          kowalski@apollo.montclair.edu