Reaction force be 0 at top of circular path swing?

[opne]

Homework Statement

Hi, I have a question about a bucket filled with water being swung in a vertical circular path.
I'm wondering why at the top of this swing, the reaction force of the bucket on the water can be 0? (ie. why is the minimum centripetal force required only the weight of the water?)
Then, why can the reaction force only be 0 when the bucket is at the top of its swing?
Further, how else does the reaction force fluctuate throughout a full 360 swing?

Homework Equations

F=mv^2/r
mv^2/r = mg + R
Minimum v^2 = rg

The Attempt at a Solution

R= 0
mv^2/r = mg ... but I have no clue whyThanks.

 

[haruspex]

why is the minimum centripetal force required only the weight of the water?

You have to be careful what you mean by minimum. Minimum with respect to varying what and holding what constant?
For a given constant swing rate, the centripetal force is constant.
For a given total energy, the swing rate is least at the top, so the centripetal force is least there.
If you mean minimum across all energies for which the water does not fall out: If the centripetal force required at the top of the swing were any more than the weight of the water then you could swing the bucket with a little less energy without the water falling out.

why can the reaction force only be 0 when the bucket is at the top of its swing?

At the bottom the reaction force has to counter gravity as well as provide the centripetal force. For any position except top or bottom, the centripetal force is not vertical, so something other than gravity must contribute to it.

how else does the reaction force fluctuate throughout a full 360 swing?

If the energy is fixed, write an expression for the tangential speed as a function of the angle.

 

[opne]

For a given total energy, the swing rate is least at the top, so the centripetal force is least there.

Ah yes! This clears things up thank you.I guess a better question would be, how can the reaction force of the bucket on the water suddenly become 0/stop existing, even though the water is still inside the bucket, and so presumably exerting a force on the bucket?
Or is there no longer a force of the bucket, and the water is in free fall at the top?

Thank you!

 

[haruspex]

the water is in free fall at the top?

Yes.