Re: Fluids Physlet

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

At 03:35 PM 8/18/2003 -0400, you wrote:
> Greetings,
>
> Ok, I am stumped by the Physlet on fluids found at (among other places):
>
>
> <http://webphysics.davidson.edu/physletprob/ch8_problems/ch8_11_fluids/fluids_2.html>
>
> The alleged answer is that "B" is the only "physical" animation,



> but I do not see why the block of wood will float higher in this
> animation as oil is drawn away but before the block of wood
> breaks the surface of the oil.
>
> By Archimedes Principle and the equilibrium principle, the
> weight of the block (constant) should equal the weight of
> the fluids displaced;
>  which would be the sum of the (oil displaced)'s weight and
> the (water displaced)'s weight.  Why would the ratio of these



> two weights change when the block is less deep under the oil?
>
> If we calculate the buoyancy force based on the difference
> between the water's pressure pushing up on the bottom
>  surface of the block and the oil's pressure pushing down
> on the top surface, again I do not see why this "difference"
> would be different before the oil no longer covers the top
>  surface of the block.
>
> Animation "A" does not seem physical to me because once
> the block is no longer under the oil, it should sink deeper
>  into the water.
>
> I would appreciate someone else's insight into this.
>
> Thanks,
>
>
> Stuart Leinoff
> Professor of Physics
> Science Division Chair
> ACC


Here's what I have on it Stuart:

the wooden block is acting as a kind of hydrometer.
It is more buoyant than water, and less buoyant than oil.
We easily deduce its relative density is somewhere
between 0.7 and 1.0

 We carefully avoid over extending the simile though, by
supposing the wood has constant density; it probably
 doesn't.  We can expect that if the wood is unsealed,
then water will take up some of the surface pores,
depending on the ambient pressure, and oil will do
 something similar, depending on its pressure.

What forces are acting? There is the buoyancy force
due the water, the sinking force due the oil,
the variable sinking force increment due the absorbed oil,
the variable sinking force increment due the absorbed water
(both of which latter vary with pressure.)

On this basis, you would expect the level of the block to rise
as the oil level (and the hydrostatic pressure) fall, given
the assumption I made. The effect would be much smaller
if the block were sealed. It is a version of the
 "Submariner's Catastrophe".
In that embodiment, it could be rendered as
" What starts sinking [from excess density],
keeps on sinking"



Brian Whatcott    Altus OK    Eureka!