Re: [Phys-l] A Crude Attempt at Analysis

[John Mallinckrodt <ajm@csupomona.edu>]

Maybe we need to go microstep by microstep through the thought experiment I proposed at the end of my last message:  

1. Position the box JUST above the bottom so that the two surfaces are JUST BARELY in contact and the water is excluded.  Make sure you understand what "just barely in contact" means on an atomic scale and that you, therefore, understand that there will be NO significant force DUE to that contact.

2. Note, therefore that you will have to provide an upward force of support on the box since there are NO other upward forces.

3. Release the box and note that it will accelerate downward due to the fact that you have removed the upward force that kept it in place.

4. Notice that the box is now being driven into more substantial contact with the surface.  Make sure you understand what "more substantial contact" means on an atomic scale and that you, therefore, understand that the surface will be put into compression.

5. Because of that increasing compression, the surface will apply an increasingly strong upward force to the bottom of the box.

6. At some point that upward force will balance the downward force so the acceleration will fall to zero. However, because the box is now MOVING downward, it will continue downward, thereby compressing the surface and increasing the upward force even more. 

7. With the now upward NET force, the box slows, stops, and then begins moving back up.

8. The process may repeat itself with additional "overshoots," but the oscillations are damped and the box quickly (and I mean QUICKLY!!!!) comes to rest at JUST the right position such that the upward compressive force of contact at the bottom of the box JUST balances the downward forces on the box due to gravity and fluid contact on the exposed sides.

This is what happens EVERY time an object is placed on a surface so there's nothing remarkable or unique to the case of having nearby fluids.  The only remarkable thing (and it WOULD be remarkable!) is the idea that you could have surfaces that are SO flat that they would exclude the water while being barely in contact.

If this doesn't do it for you I'm afraid I can't be clearer and really have to move on to other things.

John Mallinckrodt
Cal Poly Pomona

On Nov 5, 2010, at 1:50 PM, Chuck Britton wrote:

> Confusion - what confusion might you be referring to? ;-)
>
> Any mathematically defined volume that is 'under water' (perhaps also 
> in contact with the bottom my aquarium) must experience a NET upward 
> force that is equal to the weight of the displaced water.
>
> Sounds simple enough to me.
>
> uh, I was thinking that the total SIX sided integral would have to be 
> the same for the same volume.
> (regardless of what was filling up that volume.)
>
> I guess I AM still confused.
>
> I was thinking that he mathematical integral didn't depend on silly 
> details like what was contained within the volume. Or whether it was 
> a micron or so above the glass.
>
> Straighten me out here please.
>
>
> > ... Just a thought that might help.  Imagine that you place the physical 
> > cube JUST in contact with the bottom so that all fluid is excluded, 
> > but the bottom exerts NO significant force on the cube.  Hopefully 
> > you see that the cube will be DRIVEN downward into MORE significant 
> > contact with the bottom.   It is the resulting compression of the 
> > bottom that results in it exerting a greater--and ultimately 
> > balancing--upward force.  The same mechanism explains how horizontal 
> > surfaces always manage to exert JUST the right amount of upward 
> > force on whatever sits on them.