[Phys-L] Re: Buoyancy question

[turner at MORNINGSIDE.EDU (Gary Turner)]

> I found this to be an interesting description of the skin effect-assisted
> buoyancy effect.  I had difficulty justifying the assertion that the rate
> of surface PE increases with increasing displacement.
>
> If I take a model used elsewhere in this thread, of a long thin cylinder,
> vertically plunged into the water, the surface's rate of PE increase seems
> to be constant with displacement increase. Or did I miss something?

Ahh, this is a slightly different situation.  Now we have broken the surface
membrane, it is no longer being "stretched" in the same way.  Indeed, the
meniscus will probably (let's assume we have water) bend the wrong way,
indicating a negative PE, or a preference for adhesion rather than cohesion.

Note that if the cylinder is removed, the system will not return to its
original state, water will remain attached to the cylinder.

Until the surface breaks, it is acting as an elastic sheet.  If you remove
the needle, that surface will naturally spring back to its original form, so
must be at a positive PE w.r.t. that original (undisplaced - is this a word?
 double negative?) configuration.


> > Suppose though that the combined grav PE fell more rapidly than the PE of
> > the surface rose, even up to the point where the needle was entirely below
> > the water "level".  Suppose further that the  surface does not close in on
> > itself - like dropping a cannonball onto a loose sheet of polythene - that
> > is trivial, it's going to sink!.
>
> Hmmm...I seem to be finding Devil's Advocate counter-models:
> A cannonball sinks a loose sheet of polythene floating on the surface:
> but a cannonball does not sink a circular sheet of polythene fixed at its
> perimeter to a wooden hoop. Or at least I can visualize circumstances where
> the cannonball does not sink for this arrangement.

Exactly correct.  When it is connected to a hoop, it will be put under
tension, stretched under tension, and therefore store PE - just as the water
surface does, for pretty much the same reasons.  The unattached polythene
sheet cannot be placed under significant tension because it has nothing
significant to hold it.  It therefore cannot store significant PE (w.r.t.
original configuration), so the system PE will continue to fall - the
cannonball will sink and drag the sheet with it.

Wherever you find forces, there are energy gradients at some level.  Balance
of forces occurs when system PE has a gradient of zero.  Otherwise, the
system will try to relax in such a way that system PE falls.

> This would be comparable to an inflatable whose bottom skin is attached to
> an inflated perimeter ring.
> I would enjoy more on this balanced rate model that Gary laid out.
>
> Brian Whatcott    Altus OK    Eureka!