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# Physics/Buoyancy

Question
QUESTION: If a body is at the bottom of a liquid filled container and i assume that there is no liquid film between container and body's bottom . So now what will be the force on body except for weight . Problem is that at bottom of container no pressure will be there at bottom of the container so buoyancy=P(below)*AREA-P(above)*AREA=-P(above)*AREA . So is buoyancy -ve there and body has tendency to sit at the bottom of the container only??

ANSWER: There will be pressure at the bottom of the container, force of the body divided by contact area.  The force downward from the body will be counteracted by the normal force upward.  The total force downward will be mg-F_b, where m is the mass, g is the gravitational constant, and F_b is the buoyant force.  That force is given by the weight of the fluid displaced, as always, which is given by the density multiplied by the volume multiplied by the gravitational constant.

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QUESTION: Thanx for the reply sir but I would like to add and ask more about the same - Byoyancy is the difference between the pressure forces of water on the bottom and top surface of the cube . So since there is no water on the lower side of the cube there must not be any upward buoyant force on the cube ?? So the body will have tendency to remain at the bottom .( Force is acting on the top surface)

You never mentioned it was a cube, but that's not relevant to the problem at hand.  Assuming absolutely no molecules of liquid squeeze underneath then you're talking about adhesion-levels of smooth contact with the bottom of the container.  That would complicate matters enormously, as I'd have to ask about the adhesive properties of those surfaces.  However, there is still a buoyant force acting on the block in the system.  If you measured just the force between the block's bottom and the bottom of the container with the container empty, you'd find the pressure due to the weight of the block divided by its area.  If you fill it with liquid with no block, you'd find the pressure due to the depth of the liquid.  If you fill it up so the liquid is pressing down on the top of the block, you'd find that the weight in just that contact section (block to container) would be the weight of the block plus the top-pressure*area of the liquid at the top, as you would expect...but you would not find the weight of the block plus the bottom-pressure*area.  That difference is the buoyant force.

Physics

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#### Dr. Stephen O. Nelson

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