# Buoyancy of a pail of water problem

I have a question, if a hung object is submerged in a pail of water, does the weight of the pail with water increase. The object is still hung and no water spills.

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Doc Al
Mentor

What do you think?

Well, I think it does not add. Since the object is hung? Am I correct?

Doc Al
Mentor

Well, I think it does not add. Since the object is hung? Am I correct?
No. Ask yourself: Before the object is in the water, what's the tension in the string? Does that tension change when the object is submerged?

before, the tension is the weight of the object. when submerged, the tension change since there is a bouyant force that acts on the object. Am I correct?

Doc Al
Mentor

before, the tension is the weight of the object. when submerged, the tension change since there is a bouyant force that acts on the object. Am I correct?
Exactly.

And if the water exerts a buoyant force on the object, the object must exert an equal and opposite force on the water. (Newton's 3rd law.) So the water is being pushed down by the object.

So it adds weight. The weight added will be the weight of the object when in air, since buoyant force will be cancelled?

Doc Al
Mentor

Yes.
The weight added will be the weight of the object when in air, since buoyant force will be cancelled?
No. The buoyant force isn't cancelled. But a force equal to the buoyant force will be added to the 'weight' of the pail plus water.

So buoyant force will be added? I got it. How about if water spills? The spilled water will be the buoyant force that will be out of the pail. However, the object exerts a force equal but opposite of the buoyant force, so it adds weight? correct?

Doc Al
Mentor

So buoyant force will be added? I got it. How about if water spills? The spilled water will be the buoyant force that will be out of the pail. However, the object exerts a force equal but opposite of the buoyant force, so it adds weight? correct?
If the pail starts out full to the brim, then the weight of the spilled water will exactly equal the buoyant force on the submerged object. (See Archimedes' principle.)

Ok. I got it now. Thanks a lot.