Sunday, September 20, 2009

On Google Part VIII: A Pencil's Kinetic Energy


A Google search that somehow lead to this blog (I have no idea how) was “kinetic energy of a pencil landed on the carpet”. I’m quite proud of this, since it’s a scientific topic (probably from a 10 year old, but still). The answer is quite simply zero. Once it has landed, it has no kinetic energy. If we change the question slightly, and consider a pencil an instant before it lands on the carpet, things become a bit more interesting. Neglecting air friction, and assuming an average sized wooden pencil dropped from an average table, you’re looking at about 30 mJ, or in imperial units, 0.007 cal. If you’re looking at the explosive energy (as in kiloton explosive), it’s about 7 millionths of a gram. Not very worthwhile, if you ask me. If you want to drop a decent amount of kinetic energy on your carpet, consider dropping a truck off a cliff.

Taking air resistance into account (since I have no excuses), you’ll have a Reynold’s number of about 2000 (at sea level on a slightly warm day), nowhere near enough to cause turbulence in the boundary layer, and lose about 0.7 mJ if the pencil falls sideward. If the pencil falls point down, then your Reynold’s number is a bit higher at 40000, which means you’ve got slightly less skin friction. Not to mention that the pressure drag is way down. If that happens, you only lose about 0.1 mJ of kinetic energy.

I bet your Google search didn’t tell you that… all you would have found, if you fixed up your search, was the good old Ek = ½.m.v^2 and Ep = m.g.h formulae.
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