Physics Question #401

Lee Ming Fei, a 20 year old male from the Internet asks on June 22, 1998,

Why does chalk, a cylinder, always break into three pieces when it falls, and not into two or four pieces?

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The answer

Jess Brewer answered on June 22, 1998

Hmmm... I certainly have done this experiment thousands of times, but I neglected to take the data! I know I have seen it happen (that the chalk breaks in 3 pieces) since I recall the frustration (why else do we lunge so desperately to catch the chalk when we drop it in the middle of a lecture, despite how foolish it makes us look?) but it SEEMS that I have also seen 2-piece breaks and also frequently N-piece breaks. Although there may well be some more fundamental theorem, my guess is that, "It depends on the chalk." For a nice fresh batch of chalk with no defects and typical densities, etc. (in which there may be little dispersion, given what is probably a more or less universal manufacturing process) the chalk probably has about the right shear strength that, when dropped from about 4 feet and when hitting the floor at some oblique angle, it will fracture in two places. I am assuming a fresh piece of chalk here; shorter ones will certainly NOT break in the same number of places as long ones. Now, it is clear that when a cylinder fails in this manner, it "wants" to fracture in MANY places, the "ideal" (weakest material) case being a wet noodle with the same aspect ratio; the noodle will "lay itself down" with a whiplike motion, which one could think of as an infinite number of fracture points. A stiffer noodle would "break" in less places, and so on. It just happens that a new, standard size/shape, typically prepared piece of chalk cylinder dropped from about 4 feet usually breaks into 3 pieces. Certainly I will be re-doing this experiment many times over the next few years, so all I have to do is remember to record the results this time.... If it turns out that different sized pieces of chalk dropped from arbitrary heights always break in 3 pieces, I will be amazed and will go talk to a real mechanical engineer!

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