Ping-pong ball floating on a bowl of water

[A.T.]

Here is an experiment I found on youtube:



Here is how I understand the setup:

- A bucket with water spins on a turntable

- The bucket is closed, so the air inside spins with the bucket & water : All three are at rest in the rotating frame (not 100% sure about this, but the ball moves slow, so there can't be wind blowing over the water surface).

- The camera spins with the bucket: It shows what happens in the rotating frame.

Clip 1: A simple ping pong ball placed on the water surface deviates to the edge
Clip 2: A ping pong ball with weight added (so it is mostly submerged) placed on the water surface deviates to the center

What is the explanation?

 

[Sakha]

It could be that because the water forms a bowl-like shape because of the centripetal force (if it is turnining at a considerable rate), then with a heavy ball it will be 'stuck' in the vortex, while a floating ball will be drawn away due to the centripetal too, i.e the centripetal force with the floating ball is enough to 'push' the ball 'uphill'.

 

[A.T.]

It could be that because the water forms a bowl-like shape because of the centripetal force (if it is turnining at a considerable rate), then with a heavy ball it will be 'stuck' in the vortex, while a floating ball will be drawn away due to the centripetal too, i.e the centripetal force with the floating ball is enough to 'push' the ball 'uphill'.

There is no vortex. The water rotates at the same angular velocity everywhere (as does the bucket and the air). And the curved water surface is a stable bowl, which is perpendicular to the vector sum of gravity & centrifugal force, at every point. So the centrifugal force cannot push it uphill.

 

[madhatter106]

thinking about it, I'd say surface tension and gravity.
for the unweighted ball the surface tension of the waters changing topology due to the centrifugal force and that there is going to be 'slip' between the bowl and water which can be seen from the curved path that the ball takes. the weighted ball overcomes this small force since the pull of gravity is stronger.

 

[madhatter106]

the ball appears to travel to the edge however the waters surface topology is changing and 'new' surface area is growing in the center. the weighted ball would then be 'dragging' against the surface due to a stronger pull by Earth's gravity.

 

[patrickd]

The submerged ball has buoyancy. The ball cannot tell that it is on a rotating frame; for all it knows, there is a gravitational field pulling it in the direction of the bucket's wall. It trys to "float" in the opposite direction. There is a similar thought experiment out there involving a helium balloon in an accelerating vehicle (the balloon moves in the direction of acceleration).

 

[A.T.]

The submerged ball has buoyancy. The ball cannot tell that it is on a rotating frame; for all it knows, there is a gravitational field pulling it in the direction of the bucket's wall.

The water surface is equipotential. The effective gravity in the rotating frame (Earth + centrifugal force) is perpendicular to the water surface. The ball is pulled straight into the surface, why does it move along the surface?

There is a similar thought experiment out there involving a helium balloon in an accelerating vehicle (the balloon moves in the direction of acceleration).

If the helium balloon is lighter than air, than it is a different story. The ball is in equilibrium when floating on the water. A neutrally buoyant balloon will not be accelerated within the car.

Also keep in mind that both balls in the experiment are lighter than water, but they move in different directions. So this cannot be the correct explanation.

https://www.youtube.com/watch?v=grJYxdJVTZ4

 

[JeffKoch]

Here is how I understand the setup:

- A bucket with water spins on a turntable

- The bucket is closed, so the air inside spins with the bucket & water : All three are at rest in the rotating frame (not 100% sure about this, but the ball moves slow, so there can't be wind blowing over the water surface).

- The camera spins with the bucket: It shows what happens in the rotating frame.

Clip 1: A simple ping pong ball placed on the water surface deviates to the edge
Clip 2: A ping pong ball with weight added (so it is mostly submerged) placed on the water surface deviates to the center

How do you glean all that from a short soundless youtube clip that says only, "Ping-pong ball floating on the surface of a solid body rotation bowl of water", whatever that broken English means?

 

[xts]

The surface of the water waves - it seems that either turntable had not been leveled properly or the experiments were made too early - before the water in the bucket achieved steady state.

The second experiment - with submerged ball - shows that surface layer of water circulate rim-to-centre. (The water friction must be overwhelming to 2nd order forces, so the the ball just drifts with water) It is pretty explainable by Einstein's circulation (tea leaf paradox) in reverse situation: water spins slower than the bucket.

The first experiment may be explained by waving surface (unleveled turntable)

 

[A.T.]

How do you glean all that from a short soundless youtube clip that says only, "Ping-pong ball floating on the surface of a solid body rotation bowl of water", whatever that broken English means?

See the first comment on YouTube. It seems to be a known problem from Russian physics competitions. A Russian mathematician posted the first case on a different forum.

The surface of the water waves

Where do you see that? Don't get fooled by the nonuniform spinning background and compression artifacts.

The first experiment may be explained by waving surface

I neither see the waves nor do I quite understand how they would explain that the ball moves outwards.

it seems that either turntable had not been leveled properly or the experiments were made too early - before the water in the bucket achieved steady state.

Well, I guess you will have to do that experiment yourself to be sure. But aside from that particular video:

What would one expect to happen in the two cases, if the experiment is done correctly, as I described in the first post: everything (vessel, water, air, ball) initially spins at exactly the same angular velocity around the center?

 

[JeffKoch]

See the first comment on YouTube. It seems to be a known problem from Russian physics competitions. A Russian mathematician posted the first case on a different forum.

People can comment whatever they like on youtube. I'd consider all this a waste of time without a reference describing the problem setup and the experiment results, with or without a youtube video.

 

[xts]

The surface of the water waves
Where do you see that? Don't get fooled by the nonuniform spinning background and compression artifacts.

Why "fooled"? So, if the bucket is covered, the light source and camera are installed in the cover: what is a possible explanation to rotating pattern we see?
And what is an explanation to small scale rotating movement of the ball, other than surface movement synchronous with rotation?

nor do I quite understand how they would explain that the ball moves outwards.

They may cause both movement inwards and outwards - depending how they propagate. If they propagate on the outward spiral, they'll move a ball with the same mechanism as Hawaian waves move a surfer. This effect works for a ball on surface, but not for submerged one.

Well, I guess you will have to do that experiment yourself to be sure.

It is not that easy as it seems to. You have to use well stabilised turntable rotating at constant speed and camera+lighting+ball release mechanism operating wireless. Well - you may use glass caserole pot instead of the bucket and watch it from lab frame, but you still need wireless ball releaser.
The old gramophone is designed to carry a vinyl record, but not a bucket nor even 3kg pot.

What would one expect to happen in the two cases, if the experiment is done correctly, as I described in the first post: everything (vessel, water, air, ball) initially spins at exactly the same angular velocity around the center?

Lemma: in a rotating frame there is no circulation of the water. That is due to conservation of energy and angular momemtum. (elaborated proof on request)

Submerged ball filled with water: does not move: the surface of the ball just delimits some amount of water. Virtual surface of the same shape delimits identical "ball" of water in other place. Neither of them moves.

Ball on the surface: falls to the centre. The equipotential surface is tilted toward centre. Thus the centre of ball mass lies closer to the rotation axis than the point it touches the surface - centrifugal acceleration acting on the ball is thus smaller than the one acting at the point of contact.

Submerged ball (empty, with lead weight attached) - floats towards rim. The same effect as previously, just opposite direction: centre of mass lies further from rotation axis than centre of displaced water.

 

[A.T.]

I'd consider all this a waste of time without a reference describing the problem setup and the experiment results, with or without a youtube video.

I described what the setup is supposed to be. You should be able to tell what is supposed to happen, with or without a youtube video.

 

[A.T.]

what is a possible explanation to rotating pattern we see?

It is the ceiling of the room. The vessel and the lid are transparent. The camera looks upwards trough them.

And what is an explanation to small scale rotating movement of the ball, other than surface movement synchronous with rotation?

Coriolis force?

Ball on the surface: falls to the centre. The equipotential surface is tilted toward centre. Thus the centre of ball mass lies closer to the rotation axis than the point it touches the surface - centrifugal acceleration acting on the ball is thus smaller than the one acting at the point of contact.

Submerged ball (empty, with lead weight attached) - floats towards rim. The same effect as previously, just opposite direction: centre of mass lies further from rotation axis than centre of displaced water.

This is consistent with the video, based on the description in the first comment on youtube. (In the OP I described the clips the other way around, sorry for that!)

Life would be weird in a gravity field with a strong gradient. This is one of the problems with all those rotating space ship/station ideas.

 

[xts]

(rotating pattern we see?) It is the ceiling of the room. The vessel and the lid are transparent. The camera looks upwards trough them.

Then we should see the weight attached to the ball (unless they were smart to paint it white, but not smart enough to cover the lid with dark rug). The shadows would look differently.

(small scale rotating movement of the ball) Coriolis force?

Having the same effect on submerged ball, subjected to friction of water and to ball floating on the surface with very little friction?

Hard to believe...
But if their results are consistemt with simple model predictions - we may believe that we see real effect, not only poor experimental metodology artifact.

 

[A.T.]

A very nice related video. Unfortunately no ball inside

https://www.youtube.com/watch?v=Zip9ft1PgV0

 

[Cantab Morgan]

Clip 1: A simple ping pong ball placed on the water surface deviates to the edge
Clip 2: A ping pong ball with weight added (so it is mostly submerged) placed on the water surface deviates to the center

According to the Youtube comment, you have it backwards. The weighted ball moves out, and the floating ball moves in. What to believe?

 

[A.T.]

According to the Youtube comment, you have it backwards. The weighted ball moves out, and the floating ball moves in. What to believe?

Yes I pointed this out in post #14, but I cannot edit the OP anymore. The YT comment is consistent with simple considerations based on the effective gravity gradient in the rotating frame (explained by xts in post #12).