Forces applied to bucket We have two similar buckets of equal weight submerged in water, the first up and the second down.

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*Calculation of the weight of each bucket (Can the weight of the water inside each bucket be considered an additional weight, or can it be considered in one case without the other)


*Are the forces applied to each bucket the same?

 A: IMO there are a number of issues with the wording of the problem.
First, the beginning statement says the buckets are of "equal weight". But part 1 asks to calculate the weight of the bucket. It makes no sense. The true weight of the bucket doesn't change inside or outside the water. It's not clear whether the parenthetical comment is yours or in the problem statement.  Perhaps they're talking about the apparent weight in water(?).
Then, is said that the two buckets are "similar". That is not sufficient to determine the volume of water displaced and thus the buoyant force. You would need to either say they are identical, or that the volume of each bucket is the same which would then mean they have the same density.
Regarding the pressure difference between the top and bottom of each bucket,  assuming these are ordinary size buckets you can probably disregard any water pressure difference between the top and bottom parts of each bucket. In any case, for what it's worth, for approximately every meter in water depth the water pressure increases by about 0.1 atmosphere.
Hope this helps.
