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:

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:

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…