The Two-Fork Toothpick Trick, Explained

Last week, GrrlScientist posted a cool video showing a trick with two forks and a toothpick:


http://view.break.com/410281 – Watch more free videos

It’s a nifty demonstration of some physics principles, so I thought I would explain how it works, with a couple of pictures (several of her commenters have the right idea, btw).

The key concept here is the idea of the “center of mass” of a system, which is basically the point at which you consider all the mass to be concentrated if you need to treat an extended object as a point particle. If you’re going to throw it through the air, for example, the center of mass will trace out a nice, simple parabolic path, regardless of what sort of tumbling or flailing motion is going on with the rest of the object.

A quick-and-dirty way to locate the center of mass of a given object is to try to balance it on your finger. The balance point for an extended object will be directly below the center of mass of that object. Using that trick, I located the center of mass for a couple of forks, shown here:

i-d82b8519aa6e7cbb3ac750afd27e8bdc-sm_forks.jpg

The toothpick in that picture is roughly at the position of the center of mass.

Now, when you wedge the two forks together with the toothpick, you can treat the resulting thing as a single extended object, with its own center of mass. The two forks stick together to form a sort of very broad horseshoe shape, as seen here:

i-84c8810a54b54fe84cc1a8a041fad312-sm_forks_toothpick.jpg

The center of mass of an object is found by breaking the mass of the object down into lots of little pieces, and multiplying each piece by its distance from some reference point. Then, you add all those terms together, and divide by the total mass of the object, which will give you a position. Notice that nothing in that recipe requires the center of mass of an object to be inside the object– it can perfectly well be a point floating out in space, and in fact it is for any horseshoe-shaped object.

In the case of our wedged-together forks, you can estimate the position of the center of mass by saying that it ought to be at about the midpoint of a line connecting the centers of mass of the two individual forks, which is the dotted line shown in the diagram. The midpoint of that would be about halfway out the toothpick.

This is the reason why it’s possible to balance the two forks on the rim of the glass in the first place. If you place that bit of the toothpick on the rim of the glass, and eveything is wedged together securely, then you’re supporting the forks-and-toothpick object from a point directly under its center of mass, and it should balance there happily.

So shouldn’t burning half of the toothpick away shift the center of mass? Yes, but by a trivial amount. Each of those forks has a mass of about 35 grams, while the toothpick has a mass of less than one gram. Losing half of the toothpick probably shifts the center of mass toward the tines of the forks by a hundred microns or so, but that’s almost certainly less than the width of the rim on the glass, so it won’t make a difference in the balance.

It really doesn’t depend on the burning, other than the fact that burning away the toothpick is a smoother way of eliminating the mass than most other things you could do. You could snip the end of the toothpick away with scissors, though, and you’d still be able to balance the forks at the very end of the toothpick.

So, you see, it’s just physics, not magic. This is a cute demonstration, though, and I may crib this for the next time I teach intro mechanics– “explain how this video works” would be a great conceptual homework question…

Comments

  1. #1 Gordon
    December 17, 2007

    I thought the question was why does the toothpick stop burning when it reaches the glass.

  2. #2 Emory Kimbrough
    December 17, 2007

    I remember from way back in 9th grade being taught another excellent example of the center of mass not always being inside the object: When a pole-vaulter or high-jumper clears the bar at a track meet, that athlete’s center of mass actually passes _below_ the bar. To a high-school student, this at first sounds outrageously impossible, but it’s true because the jumper curves his or her body rather like how the forks form a curve in this video.

    Years later I used this example myself when teaching introductory physics – the students are surprised by it and can really relate to it as a real-world example – It’s quite a useful tidbit for any physics teacher.

  3. #3 Chad Orzel
    December 17, 2007

    I remember from way back in 9th grade being taught another excellent example of the center of mass not always being inside the object: When a pole-vaulter or high-jumper clears the bar at a track meet, that athlete’s center of mass actually passes _below_ the bar. To a high-school student, this at first sounds outrageously impossible, but it’s true because the jumper curves his or her body rather like how the forks form a curve in this video.

    Yep.
    I use this one all the time in intro mechanics. I found a pretty good graphic showing the center-of-mass position for a high jumper, and that works nicely.

    You can also explain “hang time” in basketball (for those who appear to have any, that is) in terms of the center of mass– Michael Jordan could appear to hang in the air because of the way he moved his legs around, shifting his center of mass within his body.

  4. #4 Ahcuah
    December 17, 2007

    I’m reminded of another center-of-mass trick you can do with dominoes, which is to stack them so that the topmost one
    is not over the base one in the least. It’s a bit tricky to place them properly, but if the second one down half overlaps
    the top one (plus just a little bit), and you keep doing that
    (if I remember correctly, the next one should be a 2/3 overlap, plus just a little bit, then 3/4, 4/5, etc.) eventually you can extend it out as far as you want (since 1/2 + 1/3 + 1/4 + 1/5 . . . never converges). You just have to make sure that the center of mass of the top two combined is
    over the edge of the third, etc.

  5. #5 agm
    December 17, 2007

    I agree with Gordon. Center-of-mass bar tricks are the prerequisite for this, not the exclusive point of the video. One commenter provides some explanation:

    When the flame reaches the rim of the metal cup, the metal absorbs so much of the heat that the toothpick cannot continue to burn. The same thing happens if you try to burn a piece of paper held with pliers. There will typically be a little bit of charred but unburned paper sticking out from the jaws.

  6. #6 Eric
    December 18, 2007

    I had heard of a variant of this trick where instead of balancing the toothpick on the rim of a glass, you balance it, stacked tip-to-tip on another toothpick. I tried it a few times, but could never get two forks to stick together like that.

  7. #7 Dave S.
    December 18, 2007

    I disagree with the proffered explanation as to why the flame goes out. For one thing, the cup need not be metal. A glass will work as well. I think what happens is that while the (wooden) toothpick is burning, the flame surrounds the entire pick and sufficient heat is generated to ignite the next bit of toothpick in line. But when the flame contacts the glass air cannot get under the toothpick, and so the underside does not burn. This diminishes the total heat at that point to such an extent that the nearby wood does not reach ignition temperature. Once the local fuel is used up, the flame simply goes out.

    Or, I could be wrong about that.

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