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Physics, Astronomy & Cosmology / Why does water remain inside an inverted swinging bucket?
« on: 19/02/2009 11:04:21 »You have made one fatal error in your calculation. The motion will be circular as long as the speed is high enough (i.e. > or greater than root gr). It can be any speed you like as long as it's bigger than that. That way, the string will stay taught and the water will stay in there. There is no way that it will be uniform motion - it is bound to gain and lose KE on the way round unless you have super strength.[If you give it just the right velocity at the bottom, it will be stationary when it reaches the top - when the gravitational potential energy is the same as the Kinetic Energy at the bottom. The water will fall out and the string will go slack.
No, it won't. For the bucket to move in a circle, the centripetal acceleration must be v^2/r (this is a geometric requirement) and you can't do this with a string. The requirement for circular motion and no tension at the apex is g=v^2/r. You'd need a rigid support to allow v to go to zero, and the water will fall out before then, since it would not be supported.
Of course, to make the rotation to occur with a floppy string you need to move your hand in a small circle, slightly ahead in phase of the bucket, in order to accelerate it. Once you have go enough speed, you can hold your hand rigid and it can spin in a circle until friction slows it down. There is no need for a rigid rod if the string is under tension at all times. Where is your objection to that? There's Physics involved as well as Geometry.
Are you saying this is only a thought experiment? I have done it on several occasions. It works - of course. I recommend that anyone who doubts it should try with an almost empty bucket for a start - and work up.
My objection is that this requirement (v> sqrt gr) is incompatible with coming to a stop at the apex of the circle, in which case v=0. They cannot both be true.
And Konstantin is right, this is peripheral to the main discussion, but it's also important to be looking at a realistic model of the phenomenon when you are discussing it.