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If you will put up with me talking to myself here, let me extend your
example to clarify something for myself. If I slightly revise your
example to, say, two cups put together rim to rim with an O-ring
between the rims and plunge them under water, they will stay together
because of the net compression pushing the two halves together. But
if I glue a string to the bottom of one of the cups, the pair will
float upward because they are less dense overall than water, but the
string stopping them from rising will be under tension - even though
the O-ring is in compression.
If the bottom of one of the cups is glued to the botton of the pond
with no water between the cup and the pond, the cups are still under
net compression along the O-ring. If I am following the arguments
being made correctly, the claim would be that the glue is actually
under compression as well.
I guess the question I am wrestling with is how small can I make the
glob of glue so it no longer covers the bottom of the cup completely
and now starts acting like a string and becomes under tension. What
is the essence of that transition from compression to tension?