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Re: buoyancy puzzle (long!)



Maybe I'm missing a subtle point, but the buoyancy force it due to the
difference in pressure between the top and bottom of the object. With the
two blocks glued, they become one object of weight W. The buoyancy force
will be -W. The net force is zero and would be at any depth at which you
might place this. I can't see where the two different densities (top and
bottom) matter, once the blocks have been mated. So I say they stay
together, neutral buoyancy, no matter what.

Correct (except see my earlier post which really takes it to the extreme),
but it is dangerous to consider them as one object with a single buoyant
force and a single weight. This is analagous to tidal stresses in gravity -
if you treat a rock as being one object, there is no reason for it to be
torn apart. But if you break it down, you have a force gradient across it
and that will do the job.
Here, the easy breakdown is into two pieces. The upper piece will have a
different force system than the lower piece and there will be a tensile
force between them. The size of that force will not change with depth
(following total submersion). Of course, if you have steel and wood you
could also break it down into crystals and grains, but you do not need to
unless the glue is really strong (the weakest link is the most important).


Back to the original question - the two will break apart when the tensile
force required to hold them together is bigger than the maximum force that
the glue can mediate.

A more interesting question might be to gradually submerge the two blocks.
The force between them will increase from negative (compression) to
positive (tension) as the upper block is submerged more, but following
total submersion it will not change any further (assuming incompressibility)

Rick


----- Original Message -----
From: "Carl E. Mungan" <mungan@USNA.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, May 01, 2002 12:53 PM
Subject: Re: buoyancy puzzle (long!)


John Denker wrote:

In this case, imagine that the glue is a form of rubber cement.
Sticky, but somewhat compressible. When you subject the glued
blocks to great pressure, the glue compresses a bit (decreases
in volume) and exerts a pressure on the glued faces.

Okay, fine. But now back to the original question. Here are two
situations:

1. I hold a block of wood (density = 0.8 g/mL) underwater against the
buoyant force. A small distance beneath it, I hold a block of metal
(density = 1.2 g/mL) in my other hand. I let go. The wood rises and
the metal sinks.

2. Same as above, but this time I completely replace the water in the
gap between the two blocks with rubber cement. I again let go. What
happens? Under what circumstances (if any) would the two break apart?
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/