How to fall infinitely deep in sand or grain

When you drop something onto sand you are used to seeing it crater the sand a little and stop with a thud. New research shows that if an object dropping is dense enough then it will reach a terminal velocity in the granular material and keep going forever. It’s a highly unexpected and nonintuitive result but has been shown by dropping metal balls into polystyrene beads.

A computer simulation of metal balls dropping into a granular material. The simulations matched the actual experiments conducted to show that a sufficiently dense ball can fall infinitely deeply in a granular material.

A computer simulation of metal balls dropping into a granular material. The simulations matched the actual experiments conducted to show that a sufficiently dense ball can fall infinitely deeply in a granular material.

The researchers dropped ping pong balls filled with metal of different masses into a 5 meter deep silo of polystyrene balls. They attached a thread with marks along it to the ping pong ball so that a high speed camera could capture the movement as the ping pong ball dropped. With this setup, the researchers could achieve 2 millimeter precision with their depth measurements.

Above a certain mass, the ping pong balls continued to fall all the way to the bottom of the tube and had reached a constant (terminal) velocity. In this regime, the polystyrene beads seemed to be acting just like a fluid.

The researchers answer the question of how massive/dense a ping pong ball sized object would need to be to continue falling infinitely deeply in sand and they get an answer of about 14 kg or a density of 400 g/cm^3. That is about 400 times the density of water and there is nothing on Earth known of that density. So unless you discover some crazy new material, have no fear about dropping your keys at the beach and having them continue to sink until they hit bedrock.

Ref: Phys. Rev. Lett. 106, 218001 (2011)

Posted June 1st, 2011 in Uncategorized.

One comment:

  1. Barry Herchenroder:

    Good stuff… This result could be used to make a great experiment to get high school and other students interested in science, especially physics!

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