Will Two Identical Spherical Cavities in Free Space Attract or Repel Each Other?

[zd1899]

Suppose that in free space , dust particles are evenly distributed all around.
Amidst the dust particles , there are two identical spherical cavities at some distance from each other. Do you think they will attract each other or repel or just be as they were??

 

[Vanadium 50]

They repel. (Wrong...see below)

 

[zd1899]

And may i know how? I always think that they would attract each other as the mass around the spheres would try and close on in , i was thinking of going about this by using the principle of superposition but still couldn't get a conclusion.

 

[A.T.]

I think this is similar to this:
https://www.physicsforums.com/showthread.php?t=290667&p=2068605
So I say they attract:
https://www.physicsforums.com/showthread.php?t=290667&p=2073542

 

[Vanadium 50]

Oops...sign error.

Hold one bubble fixed. Consider the force on the second bubble. If the first bubble didn't exist, there would be no force on the second. Since there is a gap, the gravitational force points away from the bubble. So the dust moves in that direction, away from the bubble, which means that the void moves towards it.

 

[zd1899]

Hey thanks that cleared a lot up.

 

[Vanadium 50]

Another way you can think of it is to treat the dust as massless, and the bubbles as having negative mass. The force points in the opposite direction, so the acceleration points in the same direction: the bubbles attract.

 

[DaveC426913]

Amidst the dust particles , there are two identical spherical cavities at some distance from each other. Do you think they will attract each other or repel or just be as they were??

What are these cavities composed of? Are they simply voids in the distribution of the particles? Is there anything holding them rigid? Is there anything holding the particles from filling them?

 

[zd1899]

What are these cavities composed of? Are they simply voids in the distribution of the particles? Is there anything holding them rigid? Is there anything holding the particles from filling them?

Yes , they are simply voids. The Dust particles are distributed uniformly and there are two nearby spherical voids.

 

[DaveC426913]

Yes , they are simply voids. The Dust particles are distributed uniformly and there are two nearby spherical voids.

Then it is folly to pretend they act as an object. The particles will uniformaly distribute themselves within them.

 

[A.T.]

Then it is folly to pretend they act as an object. The particles will uniformaly distribute themselves within them.

Even if all particles are initially at rest?

 

[Danger]

Won't all of the dust particles attract each other into a assemblage, thus merging the voids into one huge one that surrounds the object? (No offense, Vanadium, but the original question didn't assume the dust to be massless.)

 

[A.T.]

Yeah, I guess dust particles with empty space between are quite different from a fluid, which cannot be compressed or vaporize. How would they behave with only one spherical cavity, when initially all are at rest?

 

[DaveC426913]

Even if all particles are initially at rest?

They cannot be at rest; they must have some thermal energy.

 

[A.T.]

They cannot be at rest; they must have some thermal energy.

Why?

 

[theneedtoknow]

Why?

Because if they lacked thermal energy, and they were at rest, you would pretty much know everything about them with certainty (position, velocity, energy) which violates the uncertainty principle

 

[A.T.]

Because if they lacked thermal energy, and they were at rest, you would pretty much know everything about them with certainty (position, velocity, energy) which violates the uncertainty principle

I was thinking more in terms of larger particles so I omitted this. How would they behave classically without quantum effects, just gravity.

 

[DaveC426913]

I was thinking more in terms of larger particles so I omitted this. How would they behave classically without quantum effects, just gravity.

OK, I see where you're going.

The particles adjacent to the voids feel an imbalanced gravitational pull. The net effect is that they are pulled away from the voids, causing the voids to grow. The particles between the two voids have this imbalance ... uh ... balanced. They feel no pull towards or ways from the two voids, but they do feel a very small pull outward, as if being squeezed out from between the two voids.

The net effect is that the voids will grow until they are separated by a thin filament of particles.


If we expanded the model to include multiple voids in a 3D volume, we would see all voids grow until they were separated only by thin, dense filaments. Ultimately, the volume would be less "voids in a sea of particles" and more "empty space shot through with filaments", like a cobweb in a box.

Interestingly, this is exactly what is http://images.google.com/images?q=g...oe=utf8&rlz=&um=1&ie=UTF-8&sa=N&hl=en&tab=wi".

 

[vin300]

Surface tension has a role?

 

[zd1899]

Hey! I just found out that its an ex Physics olympiad problem.
The dust configuration remains constant , won't move in. So we can do this using the potential energy concept for the sphere's i.e. they would try and reduce their respective energies.