Secrets of the 'Levitating' Slinky: Viral web videos trigger physicists to explore a striking phenomenon

Dec 22, 2011 By Ben P. Stein
Credit: InfoMofo via flickr

While holiday shoppers search frantically for the Moshi Monsters, LeapPad Explorers, or Lalaloopsy Silly Hair dolls atop their children's wish lists, many physicists remain engrossed in the properties of a simple 1940s-era toy -- the Slinky.

Spurred by a wave of recent Web videos showing the bottom of a dropped Slinky hovering dramatically in midair , physicists have provided new insights into this phenomenon, from the existence of shock waves in the falling Slinky, to a remarkably universal "levitation" time for a Slinky on other planets or moons despite their different gravitational fields.

In February 2000, the late science writer Martin Gardner posed a simple question intended for physics students, but also triggering a new round of papers and videos on the much-studied toy. Gardner wrote: "If you hold one end of a Slinky, letting it hang down and then drop it, what happens?"

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"It turns out the bottom stays suspended, levitating in air for some period in time," said Shimon Kolkowitz, a physics graduate student at Harvard University in Cambridge, Mass. As an undergraduate at Stanford University in Palo Alto, Calif. in 2007, Kolkowitz wrote a paper now posted online for a class taught by his professor, physics Nobel Laureate Robert Laughlin.

And recently, Bill Unruh, a physics professor at the University of British Columbia, in Vancouver, heard some colleagues in the faculty lounge discussing a video of the levitating Slinky. As a result, Unruh, a world expert in black hole radiation, became captivated with Slinky physics.

Making calculations over a couple of days, Unruh wrote and posted a paper on the falling Slinky at the website arXiv.

Inspired by Gardner's riddle and earlier Slinky studies while putting together his paper, Kolkowitz calculated that the bottom of his metal Slinky would remain suspended for approximately three-tenths of a second. And only recently he made a surprising realization: the levitation time of the toy would be exactly the same if it were dropped on the moon, Jupiter or Mars, even with their vastly different gravitational fields.

Unruh found that the falling Slinky creates a shock wave through the toy, analogous to the blast wave of a bomb or a sonic boom created by aircraft. 

What in the world is going on?

"A Slinky is a simple spring, with the unique attribute that the spring in its natural resting state has all the coils touching one another," Unruh said.

"It's what's called a pretensioned spring," Kolkowitz added. "If you just leave it sitting on a desk on its side it'll actually be fully compressed."

Held from midair, the Slinky stretches out, quickly reaching a condition known as "equilibrium." in which the downward force of gravity is balanced by the upward tension of the coils above it.  When the top is released, the bottom stays suspended. The top of the Slinky collapses, so that the coils slam into each other. That collapse travels down as a wave through the Slinky. The bottom coils remain at rest until the top crashes into them.

And that's the key to understanding how the bottom of the Slinky remains suspended in midair for a short while.

"The bottom part of the Slinky hasn't deformed in any way," Kolkowitz explained. "Until that compression reaches the very bottom it won't move."

This levitation time -- approximately 0.3 seconds for Kolkowitz's own Slinky  -- would be the same on any planet or moon. Gravity and tension of the spring effectively cancel each other out.

Kolkowitz  said that one way of understanding this is that on the moon, the weaker gravitational field wouldn't stretch the Slinky as much, so the spring would compress more gently towards the bottom when dropped, taking the same 0.3 seconds to travel there. On Jupiter, the stronger gravitational field would stretch the suspended Slinky to a greater degree, so that the spring would have a larger distance to compress. But the more stretched-out top would snap back faster toward the bottom, resulting in the same levitation time.

As Kolkowitz pointed out, however, the Slinky's center of mass -- which shifts, but is always located somewhere in between the top and bottom of the toy -- still accelerates according to gravity all the way down to the ground from the moment it's released. So there's no violation of any of Newton's laws or Galileo's observations about falling objects.

The levitation time would only increase with a heavier Slinky and decrease if the coils were stiffer. The spring's mass and stiffness, Kolkowitz said, are the only two factors that affect the duration of levitation.

Kolkowitz pointed out this levitation effect would occur when any other spring or other elastic, nonrigid object is dropped -- and no object is completely rigid. "It's just that the Slinky is an especially easy system" in which to observe the effect, he said.

Another way to think about the levitation problem is that "the wave velocity in that Slinky is all that matters," Kolkowitz said. The wave velocity dictates "the length of time it takes information to reach the bottom of the Slinky," he said.  Once that wave slams into the bottom, the bottom no longer levitates.

In his analysis, Unruh observed that the collision of the upper part of the Slinky with the motionless lower coils is an example of a shock wave, analogous to a sonic boom that occurs in aircraft traveling faster than the speed of sound. Moreover, the wave that moves through the toy travels parallel to the compression of the Slinky, making it a "longitudinal" wave, the same type of wave as a sound wave. The normal speed of this wave in a Slinky is best measured by how many loops per second the wave passes through, about 50-100 loops per second for a typical Slinky, depending on such things as the thickness of the coils.

But in a falling Slinky, the coils crash into each other, creating a shock wave.

According to Unruh, the velocity of the shock wave, when it reaches the bottom, is notably higher than the normal velocity of the Slinky wave, breaking a sort of "sound barrier" in the Slinky.

"This behavior of is typical," he wrote in an email to Inside Science. "The blast wave of a bomb gets to you faster than the sound of a bomb would if it were very small."

A shock wave is simply a statement that something in a physical system changes abruptly, in this case, the velocity of the lower coils in the Slinky.

"There is a lot of interesting physics in a very, very simple system," said Unruh.

Kolkowitz said that this is an easy experiment for anyone to duplicate: use a stopwatch to time the fall when a friend drops a Slinky. This technique depends on the reflexes of the person running the stopwatch and therefore could introduce some error. 

Filming the falling Slinky with a video camera that captures a known number of frames per second and then counting the number of frames in which the bottom of the Slinky stays still would allow experimenters to more accurately calculate how long the Slinky's bottom stays suspended. 

"It's just such an easy experiment to do and it's kind of fun," Kolkowitz said.

Though Kolkowitz doesn't use Slinky experiments in his quantum physics work, he said the surprising insights on the levitating Slinky shows how studying and measuring even everyday objects can provide results that are "counterintuitive and not what you expect."

Explore further: Tiny magnetic sensor deemed attractive

Source: Inside Science News Service

4.5 /5 (23 votes)

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User comments : 44

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Nanobanano
1 / 5 (13) Dec 22, 2011
See, this is why I think we've still got gravity and "DM" misunderstood.

We can see here that certainly for some classes of problems, gravity and tension are identical.

The naive "sling" with a string and a weight on the end behaves exactly like gravity, AND it even behaves like DM.

Now we have a formula for propagation of gravity explaining how gravity weakens with distance, but whatever "DM" is does not weaken with distance.

Yet both of them can be equated to Tension on a string or rubberband balancing "centrifugal force" from the rotating body, be it a planet, star, solar system, galaxy, or galaxy cluster.

Reference frames in the real universe ultimately coincide with "Epicycles", whether or not you like it, since all reference frames in the real universe are rotating with respect to at least one other reference frame.

While a common string and weight does not simulate the "strength" of the gravity or DM attraction with distance, it still models this accurately.
Doug_Huffman
2 / 5 (4) Dec 22, 2011
Nice demo.

The stationary Slinky end is as counter-intuitive as the balance of normal and tension forces making a tension-spoked wheel "stand on the bottom spoke."
antialias_physorg
4.1 / 5 (9) Dec 22, 2011
On Jupiter, the stronger gravitational field would stretch the suspended Slinky to a greater degree, so that the spring would have a larger distance to compress.

I'm surprised that Unruh, being an expert on black hole physics, didn't takethis to a higher degre by calculating what would happen in the vicinity of a balck hole event horizon.
I.e. a situation in which the gravity isn't (to first order approximation) constant between top and bottom of the slinky, but at which we have a significant gravity differential between the two ends.

In that case the tension is not uniformely distributed over the slinky - but the average acceleration on each part should be identical (as that non-uniform tension is always offset by an identical, non-uniform gravity force)

Hmm..the more I think about it: should behave the same way as in any of the other cases mentioned.

Weird.
Isaacsname
not rated yet Dec 22, 2011
Hhhmm. What about if it were held in the middle and spun horizontally ? Would both ends collapse towards the center at the same time ?

Or would it be impossible to find the exact middle :P ?
rawa1
1 / 5 (8) Dec 22, 2011
This behavior of shock waves is typical," he wrote in an email to Inside Science. "The blast wave of a bomb gets to you faster than the sound of a bomb would if it were very small."
It's the result of momentum conservation laws and it's the principle of Astroblaster toy, the water splashes and supernova jets, anti-Stokes dispersion, Raman spectra and Mossbauer effect. And it applies in explanation of cold fusion and/or anomalous behaviour of water clusters for example.

http://www.4physi...gate.htm
El_Nose
5 / 5 (9) Dec 22, 2011
@nano

-- what??

either you didn't understand the article or you don't understand physics to draw that conclusion from the article -- you never wrote a complete thought - you just jumped from one half point to another half point with out even attempting to be cohesive.

antialias_physorg
3.4 / 5 (5) Dec 22, 2011
What about if it were held in the middle and spun horizontally ? Would both ends collapse towards the center at the same time ?

As long as the rotation continues the spring will not collapse at all. It's remain in equilibrium. Only when you slow it down will the spring start to collapse. But there will (obviously) not be a 'levitation' effect.

(Unless we are talking zero-g...in which case 'horizontal' makes no sense and you DO get a 'levitating' effect ;-) )

Or would it be impossible to find the exact middle

Nope. Since it will spin about one point in equilibrium.

If you add a longitudinal disturbance, however, then you will have a mass wave travelling back and forth along the spinning slinky. In this case you'd get an eccentric horizontal spin (or probably something much more chaotic unless you do this in space.)
Ddoodle
not rated yet Dec 22, 2011
i always knew it, there is a Slinky band between me and the earth.
So the only thing i have to do to levitate is to cut it off. yess

Vendicar_Decarian
3.1 / 5 (9) Dec 22, 2011
This is nothing but a new world order conspiracy.

The Work of the Global Warming Illuminati is never done.
Ddoodle
not rated yet Dec 22, 2011
Or i just change the center of my mass to the center of the earth, and leave the slinky there.
haha, and i already have some clues on how to do that. http://www.youtub...UTOxHoto
antialias_physorg
4 / 5 (8) Dec 22, 2011
i always knew it, there is a Slinky band between me and the earth.

That is actually more true than you think. The atoms that make up you are mostly empty space. The electrostatic forces between them (and between the electrons and the nuclei they whizz around) allow for SOME movement of atoms relative to one another depending on outside forces...and also for deformations of the probability functions of electrons around the atomic nuclei they belong to.
The system is not TOTALLY rigid. Just very, very stiff. So the 'slinky effect' is near (but not totally) instantaneous. As noted in the article: The effect depends on the mass (your mass being more than a slinky lengthens the effect) and on the stiffness (which is vastly greater for electromagnetic forces than for a spring, which lowers the effect)

So the only thing i have to do to levitate is to cut it off

You have to hang yourself and then cut the rope. There will be a levitation effect. It will just be short.
Isaacsname
4 / 5 (1) Dec 22, 2011
So then there's a brief instant where the volumetric mass(?) of a falling object actually is falling through it's own center of gravity ? Loool, sorry for all the bonehead questions.
antialias_physorg
3.7 / 5 (6) Dec 22, 2011
Erm? What?

The center of gravity falls as per Newton (or Einstein...whichever you prefer...but Newton is good enough for this). It doesn't levitate.
Isaacsname
not rated yet Dec 22, 2011
Erm? What?

The center of gravity falls as per Newton (or Einstein...whichever you prefer...but Newton is good enough for this). It doesn't levitate.


Why does a falling raindrop deform ?
Nik_2213
1 / 5 (1) Dec 22, 2011
"Why does a falling raindrop deform ?" Air friction vs gravity & surface tension, yes ? Don't forget the images from space of water blobs that are spherical at rest...
Moebius
3.4 / 5 (5) Dec 22, 2011
It isn't levitating, it's contracting towards the center but the force of gravity negates the rise of the bottom forcing the top to go down because the spring was originally stretched by gravity to exact equilibrium before it was dropped.
Isaacsname
not rated yet Dec 22, 2011


Huh,..." The center of mass is not attached to the slink at the center of mass. "

http://www.exo.ne...nky.html
Riff
1 / 5 (2) Dec 22, 2011
Looks to me like plain old inertia.
350
5 / 5 (6) Dec 22, 2011
The simplest way to explain this is that the bottom is being supported by the tension. I would venture to guess that the top falls faster than 9.8 meters per second, compensating the bottom.
Riff
not rated yet Dec 22, 2011
@350. That sounds like the most plausible explanation yet.
Osiris1
1 / 5 (2) Dec 22, 2011
Just draw the force vectors over a drawing of it and do the calculus of the moving c.g., etc. It is NOT levitation per se at all. The 'spell checker' here is maddening. It should get a better spell vocabulary.... doesn't like 'per se'!
antialias_physorg
3.7 / 5 (6) Dec 22, 2011
It is NOT levitation per se at all

I would draw your attention to the quotes around 'levitating' in the title.
Mahal_Kita
1 / 5 (1) Dec 22, 2011
@nano

-- what??

either you didn't understand the article or you don't understand physics to draw that conclusion from the article -- you never wrote a complete thought - you just jumped from one half point to another half point with out even attempting to be cohesive.


Let there be glue..

Mwah.. Just trolling a little, huh :-)

Is there space for that? I know there is time for that. Virtual spacetime.. There's nothing here, but does that mean you're not there? Like a movie; actors are already rich and famous, and we've just seen the CD version. Kind of like those darn stars out there. You were there, now you're not. Therefore Nano.. You're not here. So happy with that.. Hooyaa!
Mahal_Kita
1 / 5 (1) Dec 22, 2011
Erm? What?

The center of gravity falls as per Newton (or Einstein...whichever you prefer...but Newton is good enough for this). It doesn't levitate.


Damn righ it doesn't.. The UnRuh guy is cool.
Tachyon8491
1 / 5 (3) Dec 23, 2011
Slink, slank, slunk - you know a slunk slinky slank some time ago due its static condition, it will dynamically slink again when given the chance - question is, does it slink already during preparation for slinking, or only when it when it classically slinks after release...
LarsKristensen
1 / 5 (4) Dec 23, 2011
What happens when Slinky will be sent in rotation in gravitational empty space and after the balance is released?
mlinuxk
1 / 5 (2) Dec 24, 2011

When the slinky is released two events occur simultaneously, the first being the slinky begins to fall and the other is the release of the energy stored in the spring. At the instant of release, the forces would be equal i.e. F1 = F2. The bottom of the slinky is not levitating in motion. The spring is falling and is contracting at an equal rate. The bottom of the spring is falling as fast as it retracting upward toward equilibrium hence the two motions approximately cancels. The top of the spring is falling at the same rate as the bottom of the spring and is retracting at the same rate as the bottom, but both vectors are in the same direction and hence the motions sum, apparently doubling the rate at which the spring is moving toward the ground. The time it takes for this to occur has nothing to do with magnitude of force of gravity either more or less but is entirely dependent on the physical properties of the spring (slinky) such as mass, length and elasticity of the spring.
Isaacsname
not rated yet Dec 24, 2011
...so exactly how long of a slinky can you do this with ?

...I'm curious.
Manitou
1 / 5 (1) Dec 24, 2011
If we optimize material and number of coils, what is the longest "levitation" time we can get?
TheZunz
1 / 5 (1) Dec 24, 2011
.3 sec.
Would this time be different with a shorter or longer slinky?
Isaacsname
not rated yet Dec 24, 2011
...so say hypothetically, the slinky were also a piezoelectric material, and at the exact time it were dropped, you use pulsed inductive coupling ( I admit that might sound strange, I don't even know if it's possible :P) to to prevent the material from attempting to reach an equilibrium position, but pulsed on and off rapidly, would the slinky appear to drop to the ground in little hops ?

antialias_physorg
3.7 / 5 (6) Dec 24, 2011
..so exactly how long of a slinky can you do this with ?

For an infinitely thin slinky and one in which the shockwave does not travel faster than the spring contracts (this is dependent on the material) the longest time you could get is the time it takes of the center of mass to fall to the level of the lowest point of the slinky.
gwrede
2.3 / 5 (3) Dec 24, 2011
There is a blatant error in the video. They state that the ball is half way to the net before the hitter can feel the hit. Now, tennis bats are made from hardwood, aluminum, or glass. The speed of the hit is the same as the speed of sound in that material, which should be 4km/s, 6.4, and 4, respectively. So, let's just say 4km/s to really be safe. The racket is half a meter long, and to again be safe, we assume that the player hits the ball with the far end and not the sweet spot. Thus, 0.0001 seconds later the player feels the hit.

Now, where is the ball at that time? Let's say that a good hitter hits the ball to a velocity of 160 kph, which is 44 m/s. In 0.0001 seconds, the ball moves half a centimeter.

Of course, if we add for the time it takes for the hit information to travel from our hand to our brain (estimated at 100m/s by several sources), then we add .01 seconds, giving 0.0101 seconds for the ball to move, which is slightly less than half a meter. (About 18 inches.)
Hengine
not rated yet Dec 25, 2011
Haa it's almost exactly how I expected it to be. When it is held in his hand there are two points on the ends of the spring undergoing different accelerations.

bottom of the spring has -gravity vs spring constant fighting

top has -gravity -spring constant vs hand

When released there is a spring constant AND gravity moving the top of the spring in the down direction.

The bottom of the spring is in perfect equilibrium! The energy in the spring constant is exactly what gravity did to it to stretch it. It stays in the exact position until spring length returns to 0.

:D
Isaacsname
not rated yet Dec 25, 2011
Did anybody understand what I was asking, or was it so moronic it doesn't warrant an answer ?

If the material the slinky were made of could be forced to suddenly become stiff, while it were falling, since it wouldn't be collapsing to it's " equilibrium position " the entire slinky would start to fall to the ground.

What if you could rapidly flip the slinky back and forth between the state of collapsing and the state of falling ?

phyzzi
1 / 5 (1) Dec 26, 2011
It's the inverse of an explosion where the center of mass follows a trajectory even though the pieces fly apart. For the slinky the center of mass falls with constant gravitational acelleration. As the "pieces come together" the bottom of the slinky is eventually included and starts moving.
Cynical1
1 / 5 (1) Dec 27, 2011
Liked your Dec 22 explanation, Antialias Physorg. It gave a valid explanation why all things are in balance - but only for a short while. Hmmm. A lot like life.
antialias_physorg
4.3 / 5 (6) Dec 27, 2011
The thing to remember is that the electromagnetic force is incredibly strong. (A million million million million million million times stronger than gravity). This results in electrons and protons forming a very intimate mixture under ordinary circumstances, so that they balance each other out with great precision.

What happens when that kind of electrostatic energy from but a relatively few atoms is liberated can be seen in the atomic bomb.
Burnerjack
1 / 5 (2) Dec 27, 2011
IMNSHO, any professional who spent working time on this should have their budget frozen until such time a thorough review as to how the resources afforded them can be shown to be used in a productive and professional manner. Any tuition and/ot taxpayer funds dispersed for this (if any) is an affront to the payees and further proof to the squandering of said funding.
antialias_physorg
4.3 / 5 (6) Dec 27, 2011
MNSHO, any professional who spent working time on this should have their budget frozen until such time a thorough review as to how the resources afforded them can be shown to be used in a productive and professional manner.


IMNSHO you should really read the article (and the paper*) before commenting on whether this is worthless for a few days of work or not.

This does have applications in the material sciences (shockwave vs. inertial forces). At the very least it'll make a nasty question for exams.

Good thing you're not in charge of who gets tuition/grant money.

*Though there is one big faux-pas in the paper. It cites a wikipedia entry.
Wikipedia entries are not cite-worthy in scientific papers.
CHollman82
2 / 5 (4) Dec 27, 2011
The spring is stretched and wants to return to its rest position, gravity prevents this. When you let go of the top it is accelerated toward the bottom by both gravity AND the tension of the spring, but the bottom is also accelerated toward the top by the tension of the spring. This acceleration is cancelled by gravity, just as it had been when it was suspended, until the top slams into it.

Pretty obvious.
ubavontuba
1 / 5 (4) Dec 27, 2011
Interesting. So few comments on the acceleration rate of the top coil.

CHollman82 seems to understand. Conservation must be satisfied.
erenberg
5 / 5 (1) Dec 28, 2011
@burnerjack
I thought science was about studying how and why things work. Understanding a simple system like a slinky can help understand more complex problems. Additionally it is nice to see people thinking about problems that at first pass seem trivial.
Moebius
1 / 5 (2) Dec 30, 2011
@350. That sounds like the most plausible explanation yet.


Except I said it first, if you can understand what I said.

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