Hydrostatics - Why is the pressure force the same?

AI Thread Summary
In hydrostatics, the pressure force at the bottom of different shaped containers, such as a cone and a cylinder, can be the same due to equal depth and area, despite differing weights of the liquid. The pressure at the bottom is determined by the formula pressure = force/area, leading to equal forces when both area and depth are constant. However, the overall weight of the containers differs, creating a paradox where the contact force equals the weight of the liquid. The discussion raises questions about forces acting on the conical surface and their directions, highlighting the complexity of pressure distribution in different geometries. Understanding that pressure acts in all directions helps clarify these concepts.
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Homework Statement


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The Attempt at a Solution


So for the cone there is the weight of the liquid (W), the upward force (F_y), and the pressure force acting on the bottom (F_v):
F_v = W - F_y

For the cylinder there is only the weight of the liquid and the pressure force acting on the bottom:
F_v = W

So how are they the same?
 
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Pressure = force/area
so
force = pressure * area

At the bottom of each container the depth of water is the same so the pressure must be the same. The area is the same so the force must be the same.

If they were placed on scales they would obviously weigh differently yet the force on the bottom is the same, hence the paradox.

To resolve it remember that pressure acts in all directions.
 
sorry,but a doubt of my own from here.

i know that these 2 containers should weigh different.but shouldn't the contact force be equal to the weight of the body and since the force at the bottom is the same ,shouldn't the weight be same?
i think that i might be wrong somewhere but can't figure out what.
 
In the case of the cone, is there a force acting on the conical surface? What is the direction of this force? Is the conical surface of the cone exerting a force on the water? What is the direction of this force?
 

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