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I'm wondering how classical physics (i.e., using Newtonian Gravity) would explain why it is that objects are sorted by density in the presence of a gravitational field?

Qmechanic
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Feynmanfan85
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1 Answers1

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It can be pretty straightforward: classical physics predicts that the lowest energy configuration is the most stable. If a lot of objects of different density but the same size and shape are placed in a container, and the gravitational potential energy of the objects is calculated, the lowest total potential energy configuration will usually have the highest-density objects at the bottom.

If the objects have different sizes and shapes, the problem can be much more complicated - but still, the configurations that have the lowest potential energy will be most likely in any experiment that permits the objects to move and settle in gradually.

If the objects fall through a fluid, their falling speed depends on their size and density, so it's pretty easy to construct a device to separate the objects according to their size and density. For example, they can fall onto a belt that's moving north, through a fluid that's moving east, to separate them into streams of objects of equal falling speed; then further separated according to size through a series of graduated screens or according to density by putting them in containers and shaking. Again, nothing but classical physics comes into play.

By the way, separation according to density is extremely important in, for example, gold mining. Panning for gold employs both the differences in density and size between particles of gold and particles of sand.

S. McGrew
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  • Thanks, this is helpful. The way I thought about it is as follows:

    If we have two objects, one more dense than the other, then the more dense object, by definition, has more mass per unit of volume. So for any given volume, there's a greater gravitational force on the more dense object.

    Therefore, gravity exerts a greater local force on the more dense object, causing it to push harder, locally, on whatever medium it's in.

    Intuition suggests this would cause the more dense object to reach a lower point in the medium, thereby sorting objects according to density within the medium.

     – Feynmanfan85 Jul 07 '19 at 17:01