Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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



At 1:12 PM -0700 11/5/10, John Mallinckrodt wrote:
I don't see anything to shoot down here other than the needless term "pseudoContact force."

--------------------

Going forward ....

Now if you replace the cubical volume of water with a physical cube of identical shape but smaller mass:

1. The gravitational force (which is, of course, downward) gets smaller;

2. the integral over the five exposed sides is still the same as it was above (and also obviously downward), and thus;

3. the integrated force over the remaining (bottom) side of the cube (which is obviously upward since the others are ALL downward) need not be as large as it used to be due to the reduction of the gravitational force.

I still don't see why there should be any confusion.

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.

ok - when the physical cube is just a tad off the bottom - we agree that the mathematical summation of forces over all six sides must be identical to the Archemedian Lift force. This summation really doesn't care what's inside the defining surface. When does the summation begin to care what's inside the surface.
If it's water inside the surface we get one answer - might we not expect to get the same mathematical sum if something else is inside the surface. When does the Stokes Theorem begin to care about what's inside the volume.

The mathematical cube can have one surface on the glass and if it has water in it - it better still have the right upward force coming from the underside. True - that underside force is now 'called' a contact force since there is no 'fluid' there to exert pressure. But the force has gotta be the same. (seems to me).