🚀 go-pugleaf

A suggested homework activity.

Take a cylindrical glass and try to place it standing in water, for example,
in a large pot or sink. It will flip because the center of gravity is too high.
But the glass will float after some water is poured into it to lower the
center of gravity. Ask your students to perform the experiments at home and to
describe their observations. The challenging part is that the liquid-loaded
glass floats tilted, even when its initial position is vertical. The tilt
angle can be estimated; it decreases with the amount of water added. This can
be contrasted with essentially vertical floating of the same glass loaded with
a uniform layer of sand rather than with water. What is the cause of this
difference?

Hint: vertical equilibrium is still unstable (small deviations from symmetry
reinforce themselves) while the tilted equilibrium configuration is stable.
See what happens when the amount of water added is rather small, then when it
is barely sufficient to assure floating. The water inside the container is free
to flow and the center of mass shifts accordingly. You can place a small iron
ball into the glass to simulate the behavior of inner water.

Obvious? Yes, but not for those who learn the subject for the first time.

                   Ludwik Kowalski  kowalski@apollo.montclair.edu