Shape in translation

neufneufneuf

I study only a translation maybe like that it's easier to resolve or understand. A vacuum object is put in liquid helium, it can move only in translation, for me at right there is more forces from bottom helium than at left. How the vacuum can have sum of forces to 0 ? The left slope can be very long and like attraction is k/d² the force decrease very quickly with distance.

dlouth15

There main forces between the atoms in a liquid aren't k/d^2 forces. They follow a more complicated pattern where they are repulsive at extremely close distances and attractive at slightly larger distances but these attractive forces fall away at a much greater rate than k/d^2 as the atoms move further apart. These forces are called dispersion forces.

Here is a graph for Argon from Wikipedia but others will be similar.



There is the gravitational force between atoms but this force is extremely weak. It only really come into play when you're dealing with large masses of gas at astronomical scales.

However even if you want to model strong attractive forces of a k/d^2 type you need to take into account all the atoms making up the liquid and not merely those in contact with the solid object. These objects will be pushing against each other and so the pressure of the atoms on the solid are not only due to the forces between atoms in contact with the object but also the cumulative effect of all the other atoms pushing against those atoms.

I would recommend you get rid of external gravity in your model as it seems to be only complicating things and not essential.

neufneufneuf

I thought about a big vacuum object, 1 meter for example, repulsive forces don't interact at big distance, it's only at very small distance. And liquid helium can be contain in a recipient, walls block the liquid, it can't move. It's possible to think with theoretical strong attractive forces sure. If liquid can't move up, why object has not net force on it ?

dlouth15

neufneufneuf wrote: »

I thought about a big vacuum object, 1 meter for example, repulsive forces don't interact at big distance, it's only at very small distance.

But the repulsive force of one atom repulses nearby atoms and those in tern repulse further atoms. So distant atoms do have an effect via other atoms.

And liquid helium can be contain in a recipient, walls block the liquid, it can't move.

It's possible to think with theoretical strong attractive forces sure. If liquid can't move up, why object has not net force on it ? And stranger: why liquid at bottom don't move alone ?

I didn't say there would be no net force. If there's an attractive force between the atoms in addition to the dispersion forces then the atoms of the liquid will try to clump in the centre of the container and will therefore push the solid object to the edge.

This is like a submerged object in water. It is being pushed to the surface but another way of looking at it is that the molecules of water are trying to be as close to the centre of gravity as possible, i.e. the centre of the earth. This would be the case even if the earth was made entirely of water. Light objects placed somewhere in this sphere of water would make their way to the edge of the sphere.

Another way of understanding it is in terms of pressure gradients. The reason an object floats is that pressure increases as you descend into water. This means that the pressure on the bottom of an object is greater than the pressure on the top and so the object rises.

In the case of you're diagram, let us assume that the container has finite width. Well then there will be a gradient due to the Earth's gravity as you have indicated. But there will be another gradient due to the gravity of the mass of liquid itself, the atoms themselves attracting one anther.

This second gradient will produce a very small net force on the object away from the centre of the container.

neufneufneuf

In the case of you're diagram, let us assume that the container has finite width.

It can be a torus shape all around Earth, no ?

dlouth15

neufneufneuf wrote: »

It can be a torus shape all around Earth, no ?

No, in that case there would be no preferred direction along the torus. The object would float to the top but would not go along the torus as there's no position along the torus that allows the atoms of the liquid to bunch together under their own gravity. Note that this effect is very small in any case.

neufneufneuf

Could explain more please ? For me, asymetric shape give a net force on object (even the force is very small). When liquid move the potential energy never move and without friction when liquid is moving it don't give or need energy. But if vacuum object has a net force it moves and give energy.

dlouth15

I think the problem is that you are looking only at the atoms immediately in contact with the object. You need to look at all the atoms making up the liquid. Unfortunately I don't think anyone can visualise this without doing a computer model of all the forces.

However it is possible to work out what is going on without this kind of modelling.

If you imagine a liquid helium filled container of some shape out in space. External gravity is negligible. The only gravity is internal gravity caused by the atoms of the liquid. Then the atoms of the liquid will be attracted to the centre of the container. They will not necessarily actually move to the centre, but on each atom there will be a force directed towards the centre due to this internal gravity.

Do you agree with this so far?

Now if you add an object containing a vacuum into the container (you will need to remove some of the helium to make room), then the system will adjust so that the maximum number of helium atoms are as close to the centre as possible. This is the lowest potential energy state of the system. In order to do this the object will move towards the edge of the container. Once there there will be no more movement. The shape of the object in this case doesn't matter.

Do you agree so far?

It is really just the object floating to the edge the same way a balloon floats to the surface of the sea. We don't even have to assume discrete atoms for this; we can just imagine an incompressible continuum of matter and apply the same reasoning.

neufneufneuf

If you imagine a liquid helium filled container of some shape out in space. External gravity is negligible. The only gravity is internal gravity caused by the atoms of the liquid. Then the atoms of the liquid will be attracted to the centre of the container. They will not necessarily actually move to the centre, but on each atom there will be a force directed towards the centre due to this internal gravity. Do you agree with this so far?

Yes, I'm agree.

Now if you add an object containing a vacuum into the container (you will need to remove some of the helium to make room), then the system will adjust so that the maximum number of helium atoms are as close to the centre as possible. This is the lowest potential energy state of the system. In order to do this the object will move towards the edge of the container. Once there there will be no more movement. The shape of the object in this case doesn't matter. Do you agree so far?

I'm not sure to understand.


Look at image please. It's a torus with helium inside, torus has walls like that helium can't move outside. No external gravity. In this case I don't understand why vacuum object don't turn with a net force on it. Could you explain this static study please ?

dlouth15

neufneufneuf wrote: »

Yes, I'm agree.
I'm not sure to understand.

Well feel free to ask questions.

neufneufneuf

Well feel free to ask questions.

you consider the energy with or without helium liquid due to the presence of vacuum object ? for me, it's possible to put liquid helium in a container (walls). You don't consider this possibility ?

dlouth15

neufneufneuf wrote: »

you consider the energy with or without helium liquid due to the presence of vacuum object ? for me, it's possible to put liquid helium in a container (walls). You don't consider this possibility ?

Essentially I consider the potential energy of a container containing liquid helium and also containing an object containing a vacuum. What I predict is that the object will move towards the edge of the container in the same way that an object floats to the surface of the sea. The reason for this is that the system is at lower potential energy when the object is at the edge rather than when the object is somewhere in the middle.

Are you happy that the system is at an overall lower potential energy with the object towards the edge of the container?

neufneufneuf

Yes, I'm agree with you. But if walls prevent the vacuum object to move outside liquid (like cc.png showing). For me there is net force on vacuum object not to up direction but to the left, for you too ?

dlouth15

neufneufneuf wrote: »

Yes, I'm agree with you. But if walls prevent the vacuum object to move outside liquid (like cc.png showing).

The object moves towards the outer edge of the container where it stops due to the walls.

For me there is net force on vacuum object not to up direction but to the left, for you too ?

No, not for me. The reason is that the overall potential energy of the system is the same regardless of where along the torus the object resides.

It is the same as if you had a tube of infinite length filled with liquid. If you put a very light object in that tube, regardless of the object's shape, there's no movement along the tube because there's no position that minimises potential energy.

If on the other hand the tube is of finite length, then the object will move to one or other of the ends of the tube. This allows more of the liquid to exist nearer the middle of the tube and thereby minimise potential energy.

Just to add once again that the effect will be extremely small as gravity is a weak force and won't even be measurable for the sorts of system you might set up in a laboratory.

neufneufneuf

ok, thanks ! like that I understand.