The free body diagram approach is still best here. If the cube is solid steel, the force on the bottom is the pressure at the top of the cube times its area plus the weight of the cube of steel. It is in equilibrium and the forces sum to zero,
If the density of the cube is the same as water, the force on the bottom is found the same way -except the result is the same as when just water is present - no cube. It is in equilibrium.
If the density of the cube is less than water, the force on the bottom is now the pressure at the top of the cube times the area plus the weight of the cube, the forces sum to zero. It is in equilibrium and doesn't rise.
If water seeps in below the lighter cube, the force on its bottom is now greater - same as when water was there. It is no longer in equilibrium and it rises to the surface.
Bob at PC
Please excuse spelling - I am writing this on a netbook and my fingers don't fit the keys.
________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Chuck Britton [cvbritton@embarqmail.com]
Sent: Friday, November 05, 2010 3:22 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] A Crude Attempt at Analysis
Assume a cubical volume of water. If we integrate the net force over
the entire surface of that cube, we come up with a total force that
is the weight of the fluid in that cubical volume.
ok so far? (I think I saw this a physics text - so it MUST be right.)
Let's position that cubical, mathematical volume directly ojn the
glass at the bottom of my aquarium, positioned exACTLY such that
there is not one single molecule of water below this mathematical
volume.
It seems to me (naively) that we better come up with exACTLY the same
total force when we integrate force around all SIX sides of this
mathematical volume as we did the first time.
The pseudoContact force of the bottom is supplying exACTLY the same
contribution to the total force as did the layer of water that used
to be there.
Go ahead - shoot me down.
I ain't no theoretician and I CAN take a hit when it's called for.
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