Re: buoyancy puzzle (long!)

["Carl E. Mungan" <mungan@USNA.EDU>]

2. 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?

Let me remind you of the 3 proposed solutions:

A. They can break apart. The likelihood of this happening depends on
the depth of immersion of the blocks because the force between the
blocks is purely tensile and has no compressive component.

B. They cannot break apart. It is invalid to talk about a buoyant
force on each block individually so there is no tendency for the
blocks to fly apart.

C. They can break apart. The likelihood of this happening only
depends on the difference in densities of the two blocks and not on
the depth of immersion. The physics is the same if we replace the
glue with a bunch of strings.

Rick wrote:

> 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.

I take that as a vote for B.

John Denker wrote:

> Let's consider the case where the glue goes in as a liquid and
> then hardens to a slightly squishy solid.
>
> a) While it is liquid, it comes into hydrostatic equilibrium
> with the water it is replacing.
>
> b) You continue to hold on while the glue hardens.  During
> this time, you don't notice any difference in the force
> equation.  Water at pressure P behaves just like liquid
> glue at pressure P.
>
> c) As the glue hardens, if you absolutely don't move your hands,
> you won't notice any change in the force.  If you do move
> your hands, after the glue has hardened you will discover that
> the spring constant dF/dx increased radically.  In fact, an
> imperceptible dx suffices to create enough force to overcome
> the difference in weight and hold the blocks together.
>
> To repeat:  It would be completely unphysical to think of
> the insertion of the glue as causing an important change in
> the pressure or force.  The hardening of the glue causes
> a radical change in dF/dx, which is something else entirely.

I take that as a vote for C.

Who else would like to argue a case? Can anyone think of a simple,
decisive experiment to settle the issue? Carl
--
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/