# The Naked Scientists Forum

### Author Topic: Why does water remain inside an inverted swinging bucket?  (Read 27646 times)

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« on: 16/02/2009 18:30:02 »
Konstantin Tretjakov  asked the Naked Scientists:

Dear Chris

In the course of my attempts to explain my opinion of the airplane problem (Why doesn't a glass of water in an aeroplane spill when the airplane turns?), I have discovered one other thing which is either a global conspiracy or just me being stupid, namely, the "swinging bucket" experiment, which has even been on your kitchen science:

The classical way of explaining why the water does not spill is by referring to the centrifugal force, that supposedly "cancels out the gravity acting on water that would otherwise make the water spill". And then they show you a picture with an inverted bucket and two forces acting on water: gravity and centrifugal.

But in fact, there is *nothing to do with centrifugal force* here. If the
bucket would stop on the highest point, it would *fall together with the water inside it*, so technically, water would stay inside the bucket.

Another easy way to understand the *real* magic of the experiment is not to swing the bucket in full circles, but rather let it swing as a pendulum. One will then observe that on the highest points, where the bucket is at its steepest angle, but the centrifugal force is at its lowest, the water *is still parallel to the bucket*, as if no gravity would act upon it.

And I do seem to understand why it's so (the explanation is the same as for the airplane), but I'm confused because it all looks as some kind of a "great spinning bucket conspiracy", and as I tend to believe what Google tells me, it is tearing me apart.

Cheers,
Konstantin.

PS: You see, I do need this answer to sleep normally... :)

What do you think?

#### lightarrow

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##### Why does water remain inside an inverted swinging bucket?
« Reply #1 on: 16/02/2009 20:26:51 »
Konstantin Tretjakov  asked the Naked Scientists:

Dear Chris

In the course of my attempts to explain my opinion of the airplane problem (Why doesn't a glass of water in an aeroplane spill when the airplane turns?), I have discovered one other thing which is either a global conspiracy or just me being stupid, namely, the "swinging bucket" experiment, which has even been on your kitchen science:
http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/inverted-bucket/

The classical way of explaining why the water does not spill is by referring to the centrifugal force, that supposedly "cancels out the gravity acting on water that would otherwise make the water spill". And then they show you a picture with an inverted bucket and two forces acting on water: gravity and centrifugal.

But in fact, there is *nothing to do with centrifugal force* here. If the
bucket would stop on the highest point, it would *fall together with the water inside it*, so technically, water would stay inside the bucket.

Another easy way to understand the *real* magic of the experiment is not to swing the bucket in full circles, but rather let it swing as a pendulum. One will then observe that on the highest points, where the bucket is at its steepest angle, but the centrifugal force is at its lowest, the water *is still parallel to the bucket*, as if no gravity would act upon it.

And I do seem to understand why it's so (the explanation is the same as for the airplane), but I'm confused because it all looks as some kind of a "great spinning bucket conspiracy", and as I tend to believe what Google tells me, it is tearing me apart.
The trick is not to accelerate the bucket much, so that the difference between the bucket's and the water's accelerations is little enough; then the water doesn't spill out of the bucket, because they stay in (quite) the same frame of reference.
This said, the fact a bucket, or water or whatever else, doesn't fall down when you rotates them in a vertical circle, is of course due to centripetal force (in your frame of reference) or centrifugal force (in the bucket's frame of reference).

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #2 on: 17/02/2009 21:04:57 »
The link doesn't actually mention centrifugal force until the very end, as a way of looking at things from the bucket's point of view.  It never tries to explain the phenomenon as using the centrifugal force from the point of view of an inertial frame (which would, of course, be incorrect)

One of the problems with your characterization, "If the bucket would stop on the highest point, it would *fall together with the water inside it*" is that you have described a physically impossible situation.  Without some other force, the bucket won't stop at its highest point — it can't do that, because to be moving in a circle, it must have a speed dictated by the centripetal force equation.  To stop the bucket at the highest point, then, means that the water will fall out of the bucket, during the period of time that the centripetal force equation is not satisfied by the water, because of the other force acting on the bucket and/or the inertia of the water.

#### lyner

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##### Why does water remain inside an inverted swinging bucket?
« Reply #3 on: 17/02/2009 22:55:39 »

One of the problems with your characterization, "If the bucket would stop on the highest point, it would *fall together with the water inside it*" is that you have described a physically impossible situation.  Without some other force, the bucket won't stop at its highest point — it can't do that, because to be moving in a circle, it must have a speed dictated by the centripetal force equation.  To stop the bucket at the highest point, then, means that the water will fall out of the bucket, during the period of time that the centripetal force equation is not satisfied by the water, because of the other force acting on the bucket and/or the inertia of the water.
The speed of the bucket is not the same at all times. 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.
For the water to stay in the bucket, it is only necessary for the centripetal acceleration at the top to be greater than, or equal to the acceleration due to Gravity - that will make the bucket ' overtake the falling water'.

There is no point in choosing an awkward frame of reference to solve the problem.

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##### Why does water remain inside an inverted swinging bucket?
« Reply #4 on: 17/02/2009 23:08:18 »
Thanks for this, I often get wet when I try to demonstrate the swinging bucket. I often wonder why I sometimes get it wrong.

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #5 on: 18/02/2009 15:51:39 »
Hello, I'm the author of the question.

It's been some time since I asked the question, and the question was asked in relation to the airplane case, so by now I believe to have figured out an newbielink:http://"http://phd.kt.pri.ee/2009/02/12/the-great-swinging-bucket-conspiracy/" [nonactive]that satisfies me personally. And I do find the answer somewhat surprising and slightly contrary to what they teach at school.

The answer to the “conspiracy” probably lies in the following observation:

If you rotate the bucket that is attached to a fixed-length stick with constant angular speed, then it is indeed the case that water will not spill only if the rotation is fast enough. In this case the bucket and water are in different positions. The bucket is supported by the stick, that rigidly resists both the gravitational and the centrifugal forces acting on the bucket. Water is not supported, so it has to rely on centrifugal acceleration to fight gravity and stay inside.

However, most people show (or, most importantly, explain) this experiment as a “bucket on a string”, which completely changes the whole point. And most of them don’t seem to realize that. That’s where I see a problem.

For example, if you take a bucket that is heavy enough, then even when you hold it in your hand (i.e. not on a string) you will tend to let it rotate according to its "own" will and inertia rather than apply force necessary for it to keep a constant angular velocity. And in this case the water won't spill due to the strain of your hand being the only force acting on the bucket rather than centrifugal force being "strong enough".
Of course, an explanation of the whole thing that refers to the notion of centrifugal force is also possible, but then you have to note that as long as the bucket is operated "via" the flexible string, the centrifugal force magically adapts itself so that water not only stays in the bucket, but is also parallel to the bottom as long as there is any strain on the string.

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #6 on: 18/02/2009 16:00:21 »
Thanks for this, I often get wet when I try to demonstrate the swinging bucket. I often wonder why I sometimes get it wrong.

To demonstrate a much more astonishing experiment take a tray, tie 4 ropes to the corners. Tie them together in the middle and attach a string there so that the tray could hang freely on the string.
Put one or two glasses with water/wine on the tray so that the tray would keep its balance. Now hold the end of the string and start swinging it. If you do it smoothly you might be able to make a full circle with glasses still on the tray (it looks heartstopping!).
The experiment seems to fail only when the glasses are too light and get blown away by the relative wind when you reach certain velocity, so pour more water in them.

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #7 on: 18/02/2009 17:14:22 »
[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.

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #8 on: 18/02/2009 18:49:08 »
[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.

What you are talking about here is a bucket performing uniform circular motion. You can't perform it on a string, indeed: the motion will be circular, but not uniform.
And it is indeed possible to make it stop right on the top and fall down.

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #9 on: 18/02/2009 21:23:08 »

What you are talking about here is a bucket performing uniform circular motion. You can't perform it on a string, indeed: the motion will be circular, but not uniform.
And it is indeed possible to make it stop right on the top and fall down.

Try it.  The drawback of a thought experiment is that you can make a mental construct that is wrong.

The motion is not uniform circular motion, because v is not constant, but at any point, the centripetal acceleration equation must be satisfied if the motion is circular.  What we can conclude is that the tension in the string is not constant because v is changing.

The experiment will fail for another reason.  The bucket has a velocity in the x direction at its apex.  Without a force in the -x direction — which can't be supplied by the tension — there's no way for the bucket to stop at the apex.  That force can be supplied by a rigid rod, but not a string.  And this means that we are relying on the bucket to follow a ballistic trajectory to land in our hands, which is a parabola, not a circle.

#### lyner

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##### Why does water remain inside an inverted swinging bucket?
« Reply #10 on: 18/02/2009 22:06:47 »
[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.
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.

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.

#### paul.fr

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##### Why does water remain inside an inverted swinging bucket?
« Reply #11 on: 18/02/2009 22:14:21 »
Thanks for this, I often get wet when I try to demonstrate the swinging bucket. I often wonder why I sometimes get it wrong.

Perhaps this is because you are swinging it both ways!

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #12 on: 18/02/2009 22:17:25 »
Try it.  The drawback of a thought experiment is that you can make a mental construct that is wrong.

The motion is not uniform circular motion, because v is not constant, but at any point, the centripetal acceleration equation must be satisfied if the motion is circular.  What we can conclude is that the tension in the string is not constant because v is changing.

The experiment will fail for another reason.  The bucket has a velocity in the x direction at its apex.  Without a force in the -x direction — which can't be supplied by the tension — there's no way for the bucket to stop at the apex.  That force can be supplied by a rigid rod, but not a string.  And this means that we are relying on the bucket to follow a ballistic trajectory to land in our hands, which is a parabola, not a circle.

Wow, this is a rather insightful observation! Experiment easily confirms that if the string loses tension somewhere halfway to the top, the bucket then indeed seems to continue along something like a ballistic trajectory, not just "stop there and fall down". So it must probably be indeed the case that it is impossible to have the bucket "stop" right on the top.

However, I should note that this discussion has now left the realm of the original question/complaint, which was, in other words, the following: There is no point in putting *water* into the bucket if we just want to illustrate centrifugal force. And speaking about water staying inside the bucket due to centrifugal force is misleading. It would be somewhat more correct to spin the bucket without water and say that it does not fall down due to centrifugal force. But then, there would be nothing spectacular in a spinning empty bucket...

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #13 on: 18/02/2009 22:29:20 »
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.

I got confused in exactly the same way as you when I read that reply and was close to posting the same type of reply, but then I figured out what swansont meant in fact. What he meant was that it is impossible to have the bucket stop right on the top of a circular trajectory and then fall down (although this counterexample does not, to my mind, ruin the logic of the original question).

Consider three cases:
1) The tension of the string achieves zero slightly before the top. In this case, it is clear that the bucket won't make a perfect half-arc to the top.
2) The bucket makes a perfect half-arc to the top and the tension of the string is >0 there. Clearly, the bucket must continue moving on along the circle.
3) The bucket makes a perfect half-arc to the top and achieves zero string tension on the top. In this case there must be some centrifugal force acting on the bucket that is exactly cancelling gravity. Thus, the bucket can not be completely at rest there, and will move on along the circle.

It's amazing how much can one discover about a simple bucket, even an empty one :)

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #14 on: 19/02/2009 11:04:21 »
[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.
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.

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.

#### lyner

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##### Why does water remain inside an inverted swinging bucket?
« Reply #15 on: 19/02/2009 22:51:48 »
Who said it comes to a stop? It won't work unless the speed is greater than that limit. There wouldn't be any phenomenon to discuss unless that condition is met.
« Last Edit: 19/02/2009 22:55:00 by sophiecentaur »

#### konstantin

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##### Why does water remain inside an inverted swinging bucket?
« Reply #16 on: 20/02/2009 07:49:13 »
Who said it comes to a stop? It won't work unless the speed is greater than that limit. There wouldn't be any phenomenon to discuss unless that condition is met.

I said something like that in the example of "accidentally taking away all of the centrifugal force". Swansont remarked that it is impossible to achieve with just a string.
Note, though, that even if you fail to make a full circle with the bucket and it "falls" inbetween, you won't spill all of the water once you catch the bucket (using your string) again. In fact, most if it would stay in the bucket. That's still a phenomenon to discuss, isn't it :)

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #17 on: 20/02/2009 13:45:54 »
Who said it comes to a stop? It won't work unless the speed is greater than that limit. There wouldn't be any phenomenon to discuss unless that condition is met.

Konstantin did in the OP ("If the bucket would stop on the highest point") and you did in your first post ("If you give it just the right velocity at the bottom, it will be stationary when it reaches the top")

#### Vern

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##### Why does water remain inside an inverted swinging bucket?
« Reply #18 on: 20/02/2009 16:52:36 »
Quote from: konstantin
I said something like that in the example of "accidentally taking away all of the centrifugal force". Swansont remarked that it is impossible to achieve with just a string.
Just release the string; when I do that the water still mostly stays in the bucket.

#### swansont

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##### Why does water remain inside an inverted swinging bucket?
« Reply #19 on: 20/02/2009 21:53:32 »
As t the OP, I think the short answer is that as long as the water and bucket feel the same acceleration, the water will stay inside the bucket.  Gravity acts on both of them, so that doesn't matter.  As long as the force on the bucket and the force the bucket exerts on the water are in the same direction and the same magnitude — which is what you must get with a rope — the water remains inside.  But a rigid support can exert a lateral force or a compression force.

#### lyner

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##### Why does water remain inside an inverted swinging bucket?
« Reply #20 on: 21/02/2009 00:01:34 »
Who said it comes to a stop? It won't work unless the speed is greater than that limit. There wouldn't be any phenomenon to discuss unless that condition is met.

Konstantin did in the OP ("If the bucket would stop on the highest point") and you did in your first post ("If you give it just the right velocity at the bottom, it will be stationary when it reaches the top")
Yes I did but that was apropos of the speed changing according to the height. I sort of assumed that the string would go slack and you would get wet.

#### The Naked Scientists Forum

##### Why does water remain inside an inverted swinging bucket?
« Reply #20 on: 21/02/2009 00:01:34 »