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Wouldnt the bucket on the drop create a vacume drawing the water upwards towards the outer edges and spilling over the sides in a matter of speaking. in said vacume it would displace the water and the cork would be left where it is.
The original question asks whether the cork will float to the top of the bucket normally, slower than normal, faster than normal, or not at all. It is immaterial whether the cork moves a tenth of a millimeter then stops or never moves at all.
With water of sufficient depth (more than the length of the cork), no, the cork won't make it to the top.
Variation in density? There is none. And, that's NOT what causes bouyancy.
Ummm...then why would a submarine be crushed at extreme depths of the ocean? Water is denser at the bottom than the top of whatever container it is in. It's true of any fluid, or gas for that matter. That's why the atmosphere gets thinner the farther away from Earth you are. THIS IS THE POINT YOU ARE FAILING TO REALIZE. Restudy your fluid mechanics.
Look at the bucket at rest with water in it. Insert cork. Water level goes up. The amount of water displaced by the cork is what gives the cork bouyancy. Any object that weighs less than the amount of water it displaces will float. Any object that weighs more than the amount of water it displaces sinks.
No disagreements here with that statement. You just described how densities of dissimilar materials causes them to interact.
Since gravity is what is working on the water to produce the bouyancy, as soon as the gravity is gone (or at least, it's effect in free-fall), there is no bouyancy.
Again, due to the density gradient in the water, and the water has mass, it takes time for that gradient to go away once the free-fall starts. In other words, for that gradient to go away, the water has to expand in order to assume a uniform density. Think of it like this: before the drop, the water is like a spring compressed somewhat by its own weight. Since it is compressed, its length is reduced. Put it in free-fall, and it will relax to its natural length. This transition from a compressed state to a relaxed state will take some amount of time.
Never mind, I give up.
I'm a painter by trade, so I've got lots of buckets sitting around. I also like wine and have a camera. Don't make me go there.
Or, I could send all this to an old physics prof of mine....
"Fluid pressure from gravity At any depth in a fluid, the pressure in all directions is proportional to that depth. Thus, the water pressure at 10 meters is twice the pressure at 5 meters.
An object under the water will have a downward pressure on its top proportional to the depth of its top, and it will have an upward pressure on its bottom, proportional to the depth of the bottom."
The second paragraph explains buoyancy, which does depend on the pressure (and therefore, density) gradient in water. Like I've been saying it will take time for the water to transition from this state (when it's at rest) to a state of equal pressure and density throughout the mass of the water (when it's falling). It is in this time that buoyancy still exists and will cause the cork to rise.
I think the real question here is why are you throwing a perfectly good bucket off a building and how much will the fine be when you get caught?
Or how much jail time if it hits someone?