Weighted ping-pong balls can fall endlessly through a granular medium (w/ video)

Jun 27, 2011 by Lisa Zyga feature
This partial image taken from the video below shows a projectile near the beginning of its trajectory as it falls through a tube filled with granular matter. Image credit: F. Pacheco-Vázquez, et al. ©2011 American Physical Society

(PhysOrg.com) -- When a meteor impacts a planet or a moon, it always stops at a relatively shallow depth, even when impacting at high speeds. Until now, researchers have assumed that all objects impacting a granular medium – such as sand or beads – rapidly lose energy and stop at a shallow depth. But in a new study, researchers have demonstrated that weighted ping-pong balls impacting a 600-cm (20-ft)-long tube filled with polystyrene beads can reach a terminal velocity, which allows the balls to continue sinking endlessly to an infinite depth.

The team of researchers, Felipe Pacheco-Vázquez, et al., from institutions in Mexico and Cuba, has published their study on the surprising result in a recent issue of . As the scientists explain, their study shows that some granular matter is “no longer safe to walk on.”

“One may safely walk on sand, and also on sugar, rice, and a myriad of dry granular materials,” Pacheco-Vázquez of CINVESTAV-Monterrey in Nuevo Leon, Mexico, told PhysOrg.com. “In this paper, we warn that not all such materials are safe to walk on. In fact, under certain conditions, one can be endlessly swallowed by the medium. We show that, when a spherical ‘intruder’ is deposited on the free surface of a silo of expanded polystyrene beads, it plunges into the ‘granular sea,’ eventually stopping at a certain depth or falling forever, depending on the weight of the intruder.”

As the researchers explain in their study, the possibility of an object reaching a terminal velocity while sinking through a granular medium has never before been observed or predicted, although terminal velocity is well-documented for objects traveling through fluids. Researchers have assumed that all objects impacting a granular medium should eventually come to a stop due to the inelastic properties of granular materials (i.e., the grains do not easily move under an applied stress). In contrast, an object falling in a fluid can reach a terminal velocity because molecules in a fluid move much more easily under an applied stress.

Here, the researchers performed several experiments in which they launched 4-cm-diameter ping-pong balls into a long cardboard tube, which had an inner diameter of 45 cm and was filled with polystyrene beads. Each of the ping-pong balls had a small hole through which the researchers could add steel particles to obtain a desired mass, and then seal the hole. The researchers prepared 18 ping-pong balls with masses ranging from 15 to 182 g. Using a launching pad above the tube, the researchers released the ping-pong balls and tracked their trajectories with a high-speed video camera and a wireless accelerometer as they fell through the tube.

The results showed that the lighter ping-pong balls slowed down and stopped in the middle of the tube, while ping-pong balls with masses greater than about 86 g sank all the way to the bottom. Further, the velocities of the balls that reached the bottom seemed to level off, suggesting that they had reached a constant velocity.

This video is not supported by your browser at this time.
This video shows the trajectory of a projectile with sufficient mass to reach a terminal velocity as it falls through a tube filled with granular matter. Image credit: F. Pacheco-Vázquez, et al. ©2011 American Physical Society. http://prl.aps.org/abstract/PRL/v106/i21/e218001

Through calculations and simulations, the researchers showed that, if the length of the tube were extended, the heavier balls would continue to sink indefinitely. The reason is that the balls reached a terminal velocity when the upward drag force and the downward force of gravity (which depends on the object’s mass) were balanced. At this time, the object’s acceleration is zero, so that it continues sinking at a constant speed.

From a physics perspective, the only way for an object to achieve terminal velocity in a granular medium is if the depth-dependent force of friction felt by the sinking object becomes saturated (constant) before it matches the gravitational force dependent on the object’s weight. Although this reasoning sounds logical, the researchers explain that it goes against intuition, since one would expect the projectile to be stopped due to its high energy dissipation with the grains.

The researchers noted that the two conditions needed for an object to reach a terminal velocity are a critical mass and a complete saturation of the object’s initial pressure. This finding implies that, even if an object has an extremely high initial velocity, it won’t achieve terminal velocity if it does not have the critical mass. So even for a bullet shot from a gun, if the bullet’s mass is less than the critical value, it will eventually come to a stop.

On a final note, the researchers emphasized that the critical mass differs for different granular media due to the different densities of the media. For example, for a ping-pong-ball-sized object to achieve a terminal velocity when impacting sand, the object would have to have a mass of about 14 kg (for a density of 400 g/cm3). No known material on Earth has such a large density.

In the future, the scientists plan to investigate what happens when several objects impact a granular medium simultaneously.

“We would like to study the penetration of a group of projectiles with a mass greater than the critical mass in this particular medium, because maybe we can observe an infinite cooperative dynamics,” Pacheco-Vázquez said. The scientists have previously investigated similar cooperative dynamics in an earlier study.

Explore further: Thermoelectric power plants could offer economically competitive renewable energy

More information: F. Pacheco-Vázquez, et al. “Infinite Penetration of a Projectile into a Granular Medium.” Physical Review Letters 106, 218001 (2011). DOI:10.1103/PhysRevLett.106.218001

4.2 /5 (12 votes)

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User comments : 38

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ArkavianX
not rated yet Jun 27, 2011
Another case of shock liquefaction; sand water ground shaking same effect with entire buildings, doesn't just apply to meteors.
Nik_2213
1 / 5 (1) Jun 27, 2011
This finding could potentially solve the problem of getting a probe (or nuke) deep into an Earth-crossing asteroid or comet...
glene77is
not rated yet Jun 27, 2011
RE: weighted-ping-pong-balls-fall-endlessly.html
May I have permission to verbally "broadcast"
this interesting info to my Table-Tennis Club
at our next game/meeting ?
LuckyBrandon
not rated yet Jun 27, 2011
This finding could potentially solve the problem of getting a probe (or nuke) deep into an Earth-crossing asteroid or comet...


this would only apply if its a rubble pile type of asteroid, and even then, only if its a specific granular material...I doubt this would apply to any type of rock (I would expect those to not only absorb the shock but also crack up themselves potentially causing even more debris to stop any incoming projectile)
Noumenon
4.7 / 5 (57) Jun 27, 2011
Yes, the effect is due to the material shape. The polystyrene pellets are probably spherical, so are intrinsically less likely to "lock into place", forming a "solid". Try is using Nylon pellets which are typically cylindrical.

They just created a model fluid with projectile density greater than the average density of pellets.
Vendicar_Decarian
4.4 / 5 (7) Jun 27, 2011
These ping pong balls are much like the U.S. economy.
Thrasymachus
1 / 5 (2) Jun 27, 2011
I wonder. The friction between the pellets of the medium, and therefore its ability to dissipate the energy of a projectile falling through it, should increase the further down the tube one falls. The friction is a function of the forces pushing the pellets together, and the pellets near the bottom of the tube would have the weight of all the pellets on top compressing them into each other. Eventually, that pressure would be enough to compress all the pellets into a solid mass, preventing any further descent. Still, I wonder. Would it be possible to compress, say, water to such a degree that, though it remains liquid, it is dense enough to "float" a steel ball. If there were a planet the size of Jupiter composed entirely of water with no ice layer, and one dropped an iron ball into it, would that ball eventually come to rest at the center of that planet, or would it come to rest at some higher point? I guess this experiment breaks down where gravity forces phase changes.
Noumenon
4.3 / 5 (66) Jun 27, 2011
These ping pong balls are much like the U.S. economy.

Indeed. And the pellets are much like liberal polices, of redistribution of wealth by gov spending, devaluation of the $, entitlements, etc.
Noumenon
4.6 / 5 (56) Jun 27, 2011
@Thrasymachus,
Interesting thoughts. I think viscosity is independent of pressure,.. but I could be wrong.

In any case I think you're right that eventually the material would compress and change shape so the viscosity would in turn change,.. so still, their statement that the ball would fall indefinitely must be false without correcting assumptions.
krundoloss
not rated yet Jun 27, 2011
I am curious to see if this would also work in a vacuum. It could be possible that the air around the ball creates an air current that assists with moving the very light poly balls out of the way. Just a thought...
antialias_physorg
5 / 5 (3) Jun 27, 2011
Infinite depth is relative here. As the ball 'falls' so does it come closer to the center of gravity of the object it falls through - and hence the force that drives it to fall decreases (e.g. the closer you get to Earth's center the less gravity you experience). However the friction does not decrease so there should be an equilibrium point at which it stops falling.
Noumenon
4.7 / 5 (55) Jun 27, 2011
,... I was wrong above about pressure changing the shape .. would still compress it smaller, so I would think increase in pressure shouldn't increase friction/viscosity, so terminal velocity should be maintained.
Noumenon
4.6 / 5 (58) Jun 27, 2011
Infinite depth is relative here. As the ball 'falls' so does it come closer to the center of gravity of the object it falls through - and hence the force that drives it to fall decreases (e.g. the closer you get to Earth's center the less gravity you experience). However the friction does not decrease so there should be an equilibrium point at which it stops falling.

Terminal velocity means it no longer accelerates, but maintains same velocity. Presumably it could go past the center of earth, decelerate, then begin to fall again reaching terminal velocity once more, though eventually die down, like a pendulum would in practice.
seatco2
4.3 / 5 (3) Jun 27, 2011
Ok! So I will avoid walking on to a small tubular shaped pool of round foam balls. Something tells me that this experiment should be redone with a 20 foot diameter tank instead of a narrow cylinder. In the experiment the ball appears to be 1/6th the diameter of the tank. that leaves very little material on the sides of the tank . This is just a feeling shot from my hip, but I have an idea that the size of all the spheres involved and the width of the tank has something to do with the results.
seatco2
not rated yet Jun 27, 2011
Here is what really bothers me. Why isn't this ball showing some sort of lateral drift? Are all the positions of the beads below it in some sort of perfect non-randomized arrangement? How does the ball fall in a perfectly straight line? Imperfections in the arrangement of the beads should cause the ball to drift or wobble laterally.
Moebius
1 / 5 (4) Jun 27, 2011
Holy cow, this explains what happened to all those rocks I threw in the water. Always wondered what happened to them.
FroShow
not rated yet Jun 28, 2011
@seatco2, the article states that the ping pong ball is 4cm in diameter and the tube is 45cm. My fluid dynamics are rusty, so I'm only comfortable (as opposed to confident) in saying an increase in tube diameter wouldn't affect the results of the experiment. Also, keep in mind the video is not an actual video of the experiment but an image created to convey the results. I'm sure there was some (insignificant) lateral drift in the actual experiments.
FroShow
not rated yet Jun 28, 2011
@Noumenon,
Yes, viscosity and the friction are depth-dependent (7th paragraph).
I think changing the shape of the media is comparable to changing the media's viscosity and thus the friction it applies to the ping-pong.
Unless the media is highly ordered, any irregularity would still give it an opportunity to disperse. (I've wondered about this while reading "Picsou" magazines and watching Scrooge swim through his vault of money.)
FroShow
not rated yet Jun 28, 2011
@Thrasymachus,
If you could compress water to a density greater than that of a steel ball, keep in mind that that force (gravity?) is also acting on the steel ball. The steel ball would then also gain a greater density, greater than that of the water and likely still sink. Can't say I know anything about what those phase states would be like... so really I'm just guessing.
FroShow
5 / 5 (1) Jun 28, 2011
This article gives me the impression that all media can behave fluid-like given proper conditions. It's just that these conditions are so far out from our normal experience that it seems counter-intuitive. I imagine even a solid like steel would behave fluid-like if you have a sufficiently dense particle placed on its surface.
TheGhostofOtto1923
1 / 5 (10) Jun 28, 2011
I wonder. The friction between the pellets of the medium, and therefore its ability to dissipate the energy of a projectile falling through it, should increase the further down the tube one falls. The friction is a function of the forces pushing the pellets together, and the pellets near the bottom of the tube would have the weight of all the pellets on top compressing them into each other. Eventually, that pressure would be enough to compress all the pellets into a solid mass... If there were a planet the size of Jupiter... would that ball eventually come to rest at the center of that planet, or would it come to rest at some higher point? I guess this experiment breaks down where gravity forces phase changes.
-blahblahblah. Reasoned like a true pseudophysicist. I suppose if a real physicist came along and told you your word calcs were inadequate to explain physical phenomena you would try to talk him out of it? With WORDS???
TheGhostofOtto1923
1 / 5 (8) Jun 28, 2011
These ping pong balls are much like the U.S. economy.

Indeed. And the pellets are much like liberal polices, of redistribution of wealth by gov spending, devaluation of the $, entitlements, etc.
Yah except that theyre entirely different.

Philos.
pcapp
not rated yet Jun 28, 2011
If you had a bowling ball rolling on an incline plane of infinite length, with one bowling pin every foot, would the ball roll forever? Would the bowling pins count as granular material like the polystyrene?
pcapp
not rated yet Jun 28, 2011
All material has an elastic property. The polystyrene moved out of the way because the rest of the material compressed to some extent or other to allow enough space for the grains under the ball to move aside. After the ball dropped past the point, the compression was released and the material moved back to the location that was previously help be the ball. Keep in mind that the material that was 'in the way' when it was under the ball is now 'on top of' the ball and providing weight that is helping push the ball down.
If the tube was more narrow the sides of the container may not have allowed for an accumulated deformation of the polystyrene, and it would not have been able to move out of the way.
At terminal velocity, The force of gravity on the ball = the acculmulated force to deform and move the polystyrene. Keep in mind that the ball was already moving at this time, so it keeps moving.
fmfbrestel
not rated yet Jun 28, 2011
http://www.physor...06-.html

water at -130c at super high pressure and indeed an increase in density. However the increase in density is not linear. Water at the bottom of the ocean is not appreciably more dense then water at the surface. In fact, the article i linked to is the first time super dense water has been observed. to get there they had to freeze the water, compress it until it changed into an amorphous solid, and then raise the temperature while maintaining pressure. So just squeezing water will not get you there.
xponen
1 / 5 (1) Jun 29, 2011
Maybe this finding could improve bunker-busting-missile? Perhaps the missile could be made dense/small enough so that it can penetrate deeper underground and also improve its fuse timer (to be more precise). -What this mean is: underground bunker should be reinforced with more concrete, and caves is not safe.
hush1
5 / 5 (1) Jul 02, 2011
"Another case of shock liquefaction; sand water ground shaking same effect with entire buildings, doesn't just apply to meteors." - ArkavianX

Incompressibility does not allow shock or sound waves.
Incompressible fluids do not exist.

"...viscosity is independent of pressure..." - Noumenon
Agreed.

"...without correcting assumptions..."
One (unstated) assumption is that the individual pellets' density never changes, regardless of pressure.

Presence or absence of air will have no appreciable effects.
Initial position effects terminal velocity.
The ping pong ball will always move. (Incompressible flow)
(Assuming the density of the ping pong ball is constant)

MorituriMax
not rated yet Jul 02, 2011
I hope the Earth never gets hit by a ping pong asteroid.
FroShow
not rated yet Jul 02, 2011
@hush1;
Incompressibility does not allow shock or sound waves.
Incompressible fluids do not exist.
False; water (considered an incompressible fluid) is known to transmit sound in everyday experience. (Granted that nothing is truly incompressible in extreme situations such as black holes.)

...viscosity is independent of pressure...
False; I again refer to paragraph 7 of the article, or check the wikipedia page on viscosity, or even consider the difference between gaseous oxygen and liquid oxygen at the same temperature (different pressures).

Initial position [a]ffects terminal velocity.
Look at paragraph 6: "...the balls reached a terminal velocity when the upward drag force and the downward force of gravity... were balanced."
hush1
5 / 5 (2) Jul 03, 2011
@FroShow
"...nothing is truly incompressible ..." - FroShow
Had that in mind when I stated incompressible fluids do not exist.

"False; I again refer to paragraph 7 of the article,..." - FroShow
Well, what is definition of "critical mass" used by the authors? (next paragraph.)

"Look at paragraph 6:..." - FroShow
Place the ping pong ball at the location where the upward drag force and downward force of gravity are balanced. What will happened?

FroShow
not rated yet Jul 03, 2011
Place the ping pong ball at the location where the upward drag force and downward force of gravity are balanced. What will happened?
If the ball is not moving, there is no 'upward drag force'. Friction (drag) is a function of speed. So, there is no 'place' where your 'upward' drag can equal gravity's pull.

Well, what is definition of "critical mass" used by the authors?
It might be more useful to read this as "critical density" (because in their experiment the ping-pong balls maintained constant volume). "Critical mass" is that minimal density where gravity's pull matches the combined force of buoyancy and friction. If you'd like me to try and explain in more detail, with examples, PM me as 1000 characters won't be enough for what I'd say.

...Had that in mind when I stated incompressible fluids do not exist.
You know what they say about assuming.
If it's not explicitly stated, it's not obvious.
TheGhostofOtto1923
1 / 5 (8) Jul 03, 2011
I hope the Earth never gets hit by a ping pong asteroid.
Its called a mini black hole. There is already one swimming around in the core courtesy of Fermilab. Its causing earthquakes and global warming (lots of it) as the planet very slowly implodes.

This is what I hear.
FroShow
not rated yet Jul 03, 2011
This is getting off topic... but it is possible that there are billions of mini black holes zipping through you right now. Only that they're so small that their event horizons never come in contact with any matter and so they grow extremely slowly. It could take longer than the universe has been in existence for one to swallow the earth.
http://news.natio...science/
The earthquakes and global warming you speak of are more likely related to other things.
TheGhostofOtto1923
1 / 5 (9) Jul 03, 2011
This is getting off topic... but it is possible that there are billions of mini black holes zipping through you right now. Only that they're so small that their event horizons never come in contact with any matter and so they grow extremely slowly. It could take longer than the universe has been in existence for one to swallow the earth.
http://news.natio...science/
The earthquakes and global warming you speak of are more likely related to other things.
I suppose youre right. Yakuza zero point energy weapons maybe?
http://www.cheniere.org/

-Im just yankin ya... or not -?
hush1
5 / 5 (2) Jul 04, 2011
"If you'd like me to try and explain in more detail, with examples, PM me as 1000 characters won't be enough for what I'd say." - FroShow

The example you gave is sufficient. Thks.

.1)
"If the ball is not moving, there is no 'upward drag force'. Friction (drag) is a function of speed. So, there is no 'place' where your 'upward' drag can equal gravity's pull." - FroShow
.2)
""Critical mass" is that minimal density where gravity's pull matches the combined force of buoyancy and friction." - FroShow

Thks - minimal density makes sense.
Is there an initial position I can place the ping pong ball in the cylinder (the length is unrestricted) where buoyancy alone matches gravity's pull?
FroShow
not rated yet Jul 04, 2011
s there an initial position I can place the ping pong ball in the cylinder (the length is unrestricted) where buoyancy alone matches gravity's pull?

So long as the ping pong ball and the 'fluid' have dissimilar densities, no. http://en.wikiped...Buoyancy
(It's a little more complicated in this case of a granular 'fluid', but the principles are comparable.)
hush1
5 / 5 (2) Jul 04, 2011
lol
The authors are too kind to us. (By not adding fluid of any kind to the cylinder of 'quicksand'.)
Thks for the exchange of thoughts.
FroShow
5 / 5 (1) Jul 04, 2011
Except air (of course). :P

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