Archimedes Principle and Buoyancy

[charistivity]

I have been trying to fully wrap my head around Archimedes' principle and buoyancy but I have one question that I haven't been able to resolve. For some reason, i believe that I might be over-thinking it.

So I know that when an object is fully submerged (sinks) in a fluid, the volume of fluid displaced is the same as the volume of the entire object. Now what if a object is partially submerged (floats)? What is the significance of the volume of the fluid displaced? is it the same as the weight of the object or is it the same as the volume of the fraction of the object submerged?

Some sources say it is the former but I have one source that states it is the latter

Any help clearing this up (in plain language ) would be greatly appreciated!

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[Odi]

The volume displaced is equal to the relative densities of the object and the medium multiplied by the volume of the object. I know you said plain language, but that is the answer, and it's actually much easier than it sounds once you check the math:

A floating object is stationary, therefore according to the free body diagram:

Weight - Buoyant Force = 0

Rewritten:

Weight = Buoyant Force

Rewritten with units:

m*g = D(medium)*V(displaced)*g

Gravity cancels on each side and we can rewrite the mass of the object as a product of its density and volume:

D(object)*V(object) = D(medium)*V(displaced)

Solve for V(displaced) to get your answer:

V(displaced) = [D(object) / D(medium)] * V(object)

This^ is what I wrote in the first sentence expressed mathematically.

The relative densities as shown above [D(object) / D(medium)] is the most important thing to understand here.This ratio is dimensionless and always less than 1 because the denominator is always greater than the numerator for floating objects--it's why the object floats in the first place.

As an example with actual numbers; the same way you get a 90 points out of 100 points on a test, you can get densities of 90g/ml for an object out of 100g/ml for the medium to give you 0.9. This means that 90% of the objects volume (irregardless of how massive it is) will be submerged thanks to the relative densities.

 

[Thoroughbred_Med]

The volume displaced is equal to the relative densities of the object and the medium multiplied by the volume of the object. I know you said plain language, but that is the answer, and it's actually much easier than it sounds once you check the math:

A floating object is stationary, therefore according to the free body diagram:

Weight - Buoyant Force = 0

Rewritten:

Weight = Buoyant Force

Rewritten with units:

m*g = D(medium)*V(displaced)*g

Gravity cancels on each side and we can rewrite the mass of the object as a product of its density and volume:

D(object)*V(object) = D(medium)*V(displaced)

Solve for V(displaced) to get your answer:

V(displaced) = [D(object) / D(medium)] * V(object)

This^ is what I wrote in the first sentence expressed mathematically.

The relative densities as shown above [D(object) / D(medium)] is the most important thing to understand here.This ratio is dimensionless and always less than 1 because the denominator is always greater than the numerator for floating objects--it's why the object floats in the first place.

As an example with actual numbers; the same way you get a 90 points out of 100 points on a test, you can get densities of 90g/ml for an object out of 100g/ml for the medium to give you 0.9. This means that 90% of the objects volume (irregardless of how massive it is) will be submerged thanks to the relative densities.

That was a great explanation.

Thank you so much!

 

[charistivity]

@Odi, this makes so much sense. Thank you very much for taking the time to explain this so succinctly! I greatly appreciate it!