Buoyancy Confusion

[betterfuture]

So I just had a quick question and hope someone can clear it up.

If an object i.e. a cork is submerged in two different liquids, liquid A and liquid B, of different densities, will the bouyant force for the object be the same for both cases? I'd appreciate all the help. Thanks!

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[theonlytycrane]

density = mass / volume. let's say liquid A has densityA and liquid B has densityB.

Fb in liquid A = densityA * volume (of the cork) * g and Fb in liquid B = densityB * volume (of the cork) * g.

The buoyant force will be greater in the liquid with higher density.

 

[BerkReviewTeach]

Great to the point answer theonlytycrane. The weight of the cork remains constant, but the buoyant force varies with density of the medium and volume submerged.

One point to pay extra close attention to here is that fully submerged objects will have different buoyant forces acting on them. However, if the object is only partially submerged (i.e., floating), then the buoyant force equals the weight, and thus the buoyant force is the same for both systems. The difference is that it will be more submerged in the less dense solution (float lower) and less submerged in the more dense solution (float higher). The fact you said that it was submerged is significant here.

I'm not sure if you are referring to our Passage 2 on Physics Review Exam 1.4, but that is a key theme throughout the questions associated with that passage.

 

[betterfuture]

density = mass / volume. let's say liquid A has densityA and liquid B has densityB.

Fb in liquid A = densityA * volume (of the cork) * g and Fb in liquid B = densityB * volume (of the cork) * g.

The buoyant force will be greater in the liquid with higher density.

Don't you mean Volume submerged AND NOT Volume of the cork.

 

[betterfuture]

Great to the point answer theonlytycrane. The weight of the cork remains constant, but the buoyant force varies with density of the medium and volume submerged.

One point to pay extra close attention to here is that fully submerged objects will have different buoyant forces acting on them. However, if the object is only partially submerged (i.e., floating), then the buoyant force equals the weight, and thus the buoyant force is the same for both systems. The difference is that it will be more submerged in the less dense solution (float lower) and less submerged in the more dense solution (float higher). The fact you said that it was submerged is significant here.

I'm not sure if you are referring to our Passage 2 on Physics Review Exam 1.4, but that is a key theme throughout the questions associated with that passage.

Aha! I just figured it out. This is what you said but I could not follow through until I plugged in some random numbers in on a scratch piece of paper.

When an object floats, it is in static equilibrium thus Fb=Fw. Since weight did not change the Fb should not change.

In the case off the different densities, say density of liquid A and density of liquid B, if the density of liquid A is less than liquid B, that same object, the cork, will have its Volume submerged to a greater degree in liquid A but have less of its Volume submerged in liquid B. And this is all because the object does not change its weight, Fw. So to equal Fb due to the different densities the Volume submerged should also be different that way Fb=Fw.

 

[theonlytycrane]

@betterfuture I took submerged to mean totally in the fluid (not floating). So the volume of fluid displaced = volume of the cork.

 

[betterfuture]

@betterfuture I took submerged to mean totally in the fluid (not floating). So the volume of fluid displaced = volume of the cork.

Right! Like you and BerkReviewTeach said, in the case where the object is fully submerged, then you would take the Volume of the object into consideration and plug it in for the equation for Fb. Here, the bouyant forces will be different since one only considers the densities of the liquid now that all other variables are the same.