I understanding Archimedes' principle.

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Discussion Overview

The discussion revolves around understanding Archimedes' principle, specifically why the buoyant force equals the weight of the fluid displaced and how this relates to free-floating objects. Participants explore the conceptual and mathematical aspects of buoyancy and fluid displacement.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants seek to understand why the buoyant force equals the weight of the fluid displaced and how this relates to the weight of the object for floating objects.
  • One participant explains that the buoyant force is the upward force exerted by the fluid, which must equal the downward force (weight of the object) for the object to float.
  • A mathematical explanation is provided, suggesting that the buoyant force can be calculated based on the weight of the displaced water and the volume of the object submerged.
  • Another participant emphasizes that the fluid displaced exerts an upward force that must balance the weight of the object for it to float, noting the mechanics of fluid displacement.
  • Further clarification is offered that the surrounding fluid applies the same distribution of forces to the object as it did to the water that was previously present.

Areas of Agreement / Disagreement

Participants express a common understanding of the relationship between buoyant force and weight of displaced fluid, but there remains uncertainty about the underlying reasons for this relationship. Multiple viewpoints and explanations are presented without a consensus on the conceptual clarity of the principle.

Contextual Notes

Some participants express confusion about the reasoning behind the equality of buoyant force and weight of displaced fluid, indicating that further assumptions or clarifications may be needed to fully grasp the concept.

threy
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I want to know why does the buoyant force equal to the weight of fluid displaced and how the weight of water displaced is equal to the weight of object for free floating objects? What's buoyant force by the way?
 
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The weight of the object is the downward force. Buoyant force is the upward force exerted by the fluid on the object. (Just like, for example, if you have a book on a table, the table exerts a normal force on the book) . For objects to float the downward force which is the weight should be equal to the upward force which is the buoyant force.

I hope you get the idea.
 
Yeah, I get this but I still have no idea why does the buoyant force equal to the weight of fluid displaced?
 
Since I think you want some mathematical explanation.

Buoyant Force = (weight of displaced water ÷ volume of displaced water) * depth * (surface area in contact with water)

depth * (surface area in contact with water) = volume of the object that is under water.

Buoyant Force = (Weight of displaced water ÷ volume of displaced water) * (volume of the object that is under water)

The volume of the object that is under water = volume of displaced water, because the object displaced the water.

Buoyant Force = (Weight of displaced water ÷ volume of displaced water) * (volume of displaced water)

Buoyant Force = Weight of displaced water
 
threy said:
Yeah, I get this but I still have no idea why does the buoyant force equal to the weight of fluid displaced?

The fluid is displaced upwards - take a bowl of water, float something in it, and the water level will rise slightly. It takes some force to push that water up, and that force has to exactly balance the weight of the object if it's going to float at the surface.
 
threy said:
Yeah, I get this but I still have no idea why does the buoyant force equal to the weight of fluid displaced?
Because the fluid surrounding the object does not know that the object has replaced the water that was there previously. The surrounding fluid was supporting the weight of the water that was there previously. So now it is applying the very same distribution of forces to the object.
 

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