Hydrostatics - Why is the pressure force the same?

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Homework Help Overview

The discussion revolves around hydrostatics, specifically examining why the pressure force at the bottom of a cone and a cylinder filled with liquid is perceived to be the same despite their differing weights. Participants explore the relationship between pressure, force, and area in the context of these shapes.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between pressure and force, noting that pressure is defined as force per unit area. They question how the pressure force can be the same when the weights of the containers differ. Some express confusion about the implications of pressure acting in all directions and the role of contact forces.

Discussion Status

The discussion is active, with participants raising questions about the assumptions underlying the problem. Some have offered insights into the nature of pressure and its effects, while others are seeking clarification on specific points, indicating a productive exploration of the topic.

Contextual Notes

There is an acknowledgment that the weights of the containers differ, which raises questions about the relationship between weight and contact forces at the bottom. Participants are grappling with the implications of pressure being uniform across different shapes and the forces acting on the surfaces of the containers.

theBEAST
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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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