Iron Ball in Desert: Exploring Equilibrium and Infinity Levels

[mersecske]

Let assume a desert with very deep sand
and an iron ball on the ground level.
Due to small perturbations (wind, small earthquakes, etc.)
the iron ball will sinking down.
Is there an equilibrium level,
or the iron ball will sink down to "negative infinity level"?

 

[NobodySpecial]

The ball will (in an ideal system) sink to the point where it's density is equal to the density of the rock around it.
The density of the Earth's liquid outer Core is around 10-12 g/cc
Iron has a density of around 7.8 g/cc so will sink to this level

 

[mikeph]

I don't know if you mean the sand is "deep" enough that you consider it infinite, since I can't imagine you are referring to the centre of the Earth when you say "negative infinity".The ball should fall until its density is equal to the density of the sand around it, as long as you treat the sand as a fluid. I don't know if an earthquake will move a grain of sand once it becomes so deep that there is 1 metric tonne of sand directly above it.

 

[mersecske]

But it is not an ideal fluid.

 

[HallsofIvy]

No one said anything about an ideal fluid. For the purposes of this problem, sand can be considered as a fluid. Now, if you were to drop something in water, which is only very slightly compressible and so has the same density "all the way down", if you drop an object into water, one of three things can happen. If the density of the object is less than the density of water, it will float on top of the water. If the density of the object is greater than the density of water, it will sink to the bottom. If the density of the object is exactly the same as the density of water, it will float at a height determined by other things (the force with which it hit the water when it was dropped for example).

Now, if you are assuming that your "sand" always has the same density, then the object will sink all the way to the bottom of the sand (to the center of the Earth if the sand goes that far). If you are assuming that the "sand" increases in density as you go deeper, then the object will sink until the density of the "sand" around it is equal to its density as NobodySpecial said.

 

[mersecske]

But it is not fluid.
And I think that density can change in homogeneous gravitational field.

 

[JaredJames]

I recommend you check the definition of a fluid mersecske and also consider effects such as liquefaction which produces quick sand.

It may not be a fluid, but you can certainly consider it a fluid.

EDIT: http://en.wikipedia.org/wiki/Fluid_mechanics#Newtonian_versus_non-Newtonian_fluids explains how you can treat it as a fluid.

 

[mersecske]

maybe "granular fluid" but its only notation

 

[JaredJames]

We aren't saying sand is a fluid, we are describing it as one. The particles of sand react in a similar way to the molecules in a fluid.

You are just nit-picking over semantics.

 

[mersecske]

We aren't saying sand is a fluid, we are describing it as one. The particles of sand react in a similar way to the molecules in a fluid.

I don't think so. Between sand grain there is air and also water can enter into the material.
And also in fluids between molecules there are volume forces, but in sand there are only surface forces I think. Maybe fluid model is a good assumption, but in this situation when we want to study long time scale, i think its not enough.