🚀 go-pugleaf

EUREKA ! PERHAPS WE NOW KNOW HOW TO DEAL WITH TILTED EQUILIBRIUM ? BUT ...

I like the idea of Malcolm Davis who suggested that total buoyancy can be
subdivided into two parts, one supporting the inner water and another
supporting the weight of the empty can. Since the walls are very thin the
center of the first part coincides with the center of liquid inside the
container. No torque is created by two large forces (weight of the inner
liquid and the buoyant force which supports it). Malcolm suggests we
"consider only the volume above the contained water." He is right, the weight
of the empty can is supported by that part of the displaced volume which is
between the levels of inner and outer water. The terms "partial buoyant force"
and "partial displacement" may be appropriate here. The center B of partial
buoyant force (equal and opposite to the weight of the empty container) happens
to be on the axis of symmetry, even when the can is tilted. This simplifies
mathematics.

Unfortunately, my reasoning through the problem leads to a conclusion which
does not agree with what really happens. This means something is wrong with
the reasoning but I do not know what. My prediction is that an axially
symmetric container with a fluid load should capsize when its horizontal
immersion puts the center of mass C, of the empty can, above the center of
partial displacement, B. As I see it, the axial locations of B and C do not
change when the container is tilted. The vertical thickness of the layer of
partial displacement is directly proportional to the cosine of the tilt angle.
It decreases with the the tilt angle but the location of its center, B (with
respect to the bottom of the can), does not change. DO YOU AGREE WITH THIS
PARADOXIAL SITUATION? Walls were assumed to be negligibly thin. A can whose
mass can also be neglected would not create a layer of partial displacement
and would be in neutral equilibrium at any tilt angle.

My wife, who is not a physicist, asked why I refused to look for a correct
solution in an appropriate textbook. My answer was "I do not want to deprive
myself of the pleasure of thinking", at least for the time being. A fameous
philosopher once stated that the process of looking for a solution is more
important to him than the solution itself. I would not agree with him if I
were a practicing engineer, but as a teacher I can permit myself the luxury.
A note received yesterday ended with the quotation: "Those who know how to do,
do, those who understand teach". Was it a compliment or an insult?

            Ludwik Kowalski        kowalski@apollo.montclair.edu