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Re: [Phys-l] Finishing up with that Dead Horse.

(Why oh why can't I leave this alone? Thank goodness it's time for Sunday practice with the Out-Laws!)

1. Take a cubical aquarium with (inner) sides of length H filled with water of density rho. The total force on the bottom of the aquarium is

F = rho*H^3*g

and the flexion reflects the fact that that force is uniformly spread over the bottom.

2. Now take a solid cube of side H/2 and density rho/2 push it under water (using a very narrow pusher that displaces a negligible amount of water. A volume of water (H/2)^3 spills over the side and is lost. As long as the solid cube is at rest and completely surrounded by water, the pusher will apply a force to the cube equal to F/16, down balancing the other two forces on the cube: the gravitational force = F/16, down and the buoyant force = F/8, up. There is NO difference in the flexion of the bottom because the total force on the bottom is the same (same pressure, same area, still uniformly distributed.

3. Now arrange for that same cube to be put in direct contact with the floor of the aquarium so that no water is allowed between the bottom of the cube and the floor of the aquarium and note the following:

THE CUBE
a) The gravitational force on the cube is F/16, down
b) The force on the cube due to contact with the water is F/8 down
c) The force on the cube due to contact with the floor of the aquarium is 3/16 F, up.

THE FLOOR OF THE AQUARIUM
d) The force exerted by the water on the floor of the aquarium is 3/4 F, down
e) The total force exerted on the floor of the aquarium is 15/16 F, down AND it is distributed non uniformly.
f) The flexion is different than in cases 1 and 2 reflecting BOTH a smaller total force AND a nonuniform distribution.

It will help to draw careful free body diagrams for each of these cases.

John Mallinckrodt
Cal Poly Pomona

On Nov 7, 2010, at 9:11 AM, Chuck Britton wrote:

Will the amount by which the aquarium bottom flexes - depend on
whether there is water under the lead cube or not? Or, perhaps, does
it depend on what specific mechanism is used to exclude the water??