Confused about the Archimedes Principle

[Veritas-in-Caritate]

I'm trying to understand Archimedes principle. I understand that the buoyancy force on a submersed object is equal to the amount of water displaced by the object. But how do you measure these things? How is it that a force can equal a displaced object? How do you measure the buoyancy force and then compare it to an amount of liquid that was displaced? Wouldn't these be two different types of measurements? How then can they equal each other?

[Sensei]

How to measure volume of a thing? Fill glass with water, mark its level. Place something inside, it must be fully submerged, mark water level again. It'll be slightly above the previous mark. Volumes of water plus volume of a thing submerged add together (not always true e.g. some salts + water won't add together).

 

Density of a thing is mass divided by its volume.

[math]d=\frac{m}{V}[/math]

 

ps. You should start from reading Wikipedia page about the subject https://en.wikipedia.org/wiki/Archimedes'_principle

 

[Endy0816]

1 hour ago, Veritas-in-Caritate said:

I'm trying to understand Archimedes principle. I understand that the buoyancy force on a submersed object is equal to the amount of water displaced by the object. But how do you measure these things? How is it that a force can equal a displaced object? How do you measure the buoyancy force and then compare it to an amount of liquid that was displaced? Wouldn't these be two different types of measurements? How then can they equal each other?

The upward force is equal to the weight of the displaced fluid.

If you look at the formula:

 Fb = ρ x g x V.

You'll see density  ρ  which equals some Mass/Volume so the units for volume cancel out. Leaves you Mass times g or just force on both sides.

Edited February 2, 2019 by Endy0816

[Hector1]

On 2/2/2019 at 10:23 AM, Veritas-in-Caritate said:

I'm trying to understand Archimedes principle. I understand that the buoyancy force on a submersed object is equal to the amount of water displaced by the object. But how do you measure these things? How is it that a force can equal a displaced object? How do you measure the buoyancy force and then compare it to an amount of liquid that was displaced? Wouldn't these be two different types of measurements? How then can they equal each other?

Il's a statistical physics problem, you have got interaction with the liquide molecule. Because of the gravity, the interaction will depend on the position of the solide in the liquide. The deeper the surface is the higher the pressure will be. For an homogenous liquide, the difference of pressure will equal the wheight of the object if his  density equal the liquid density.

 

[HallsofIvy]

On ‎2‎/‎2‎/‎2019 at 3:23 AM, Veritas-in-Caritate said:

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I'm trying to understand Archimedes principle. I understand that the buoyancy force on a submersed object is equal to the amount of water displaced by the object. But how do you measure these things? How is it that a force can equal a displaced object?

This is where you are misunderstanding.  Force does NOT "equal a displaced object".  The force is equal to the weight of the water displaced by the object. And "weight" is a force, of course.  The volume of the displaced water is, of course, the same as the volume of the object. 

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How do you measure the buoyancy force and then compare it to an amount of liquid that was displaced?

First, as I said above, it is NOT the "amount of liquid that was displaced", it is the weight of the amount of liquid that was displaced.

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Wouldn't these be two different types of measurements? How then can they equal each other?

Yes, they would, and they don't!

 

Edited March 9, 2019 by HallsofIvy