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Re: [Phys-l] Definition of upthrust or buoyancy

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?

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Thursday, October 21, 2010 12:45 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Definition of upthrust or buoyancy

On 10/21/2010 11:29 AM, Philip Keller wrote in part:
2. The argument that "if you cut off the piling it floats so it
must be in tension" had me convinced for a while.

That's a worthwhile Gedankenexperiment. It has some simple
points and some tricky points, all of which are instructive.

Or the reverse argument that if you wanted to add another layer to
your piling, you would need glue. But you wouldn't need glue -- you
would just need to have smooth enough surfaces to push out all the
water.....

But you would need glue, or chemical bonds, or a suction pump,
or something; just setting the slice into place would not
suffice, as we now discuss:

Scenario: We are working in deep water, where there is tremendous
pressure. We are building a piling out of two slices, using the
following fancy structure:

XXXXXXX
XXX XXX
OXX XXO

XXX XXX
XXX XXX
XXX >
XXXXXXX

The piling material is buoyant, i.e. it wants to float up.
The bottom piece is anchored to the bottom somehow. The
diagram is a slice along the axis of a cylinder.

Basic structure is indicated by X. There is an O-ring seal
at location O. When we gently push the top slice into place
atop the bottom slice, at first it just sits there loosely,
with water in the empty core region, and a thin film of water
between the two slices. We pump out the water using the pump
at location >.

As we pump out the water, a tremendous suction-cup effect is
created. The top slice is no longer sitting there loosely;
it is firmly pressed down onto the lower piece. The piling
as a whole is under tremendous compression.

Conversely, if we then switch off the pump and allow water
to flow backwards through the pump, the suction-cup effect
will be released. Water will weasel its way in and create
a thin film between the two slices. The top slice will
float away, because it is buoyant.

So we see that both answers are possible: For a piling
made of slices of buoyant material, each individual slice
is under compression, and:
A) If water can get in between the slices, the structure
as a whole is under tension, in the sense that the
individual slices will float away, unless they are held
together by some explicit tensile force.
B) If water cannot get in between the slices, then a
suction-cup effect is produced, and the structure as a
whole is under compression.

Whether simply pushing two flat surfaces together suffices
to create the suction-cup effect is not clear. I still
consider this a pathological case. It would not work easily
or quickly (because of viscosity among other things) and it
might not work at all. It would raise all sorts of questions
about the chemical nature of the surfaces, blah, blah, blah,
and I don't want to get into it.

The two cases that arise in practice are relatively easy to
understand
-- the "sitting there loosely" limit, and
-- the "suction-cup" limit.
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