Saturday, 27 July 2019

newtonian mechanics - What is the third law action pair of buoyancy?


Consider a block floating in a fluid. The force due to gravity balances the buoyant force exerted on the block. But there must be a third-law action pair to the buoyant force. If the block exerts a force on the fluid, that would mean that the pressure in fluid just below the block is more than that in other places that are on the same horizontal level.


enter image description here


I do not believe that to be the case, since it doesn't conform to real world observations.


Also, if the block has a $m$ and density $\rho$, and the fluid + the container has a mass $M$. What is the mass of the block + container + fluid (as in the picture), as measured by a weighing machine underneath the container.


According to my common sense, since the buoyant force is internal, the measured mass of the system should be $m + M$. Am I right?



Answer



The buoyant block does exert a force on the water, it's force is equal to the mass of the displaced water, so the pressure of the water immediately beneath the block is exactly the same as the pressure of the water at that height in the rest of the container.


Indeed, the mass of the system is just the mass of container with water + mass of block


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