Here's a cute problem I came across recently.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose you have a rubber band with spring constant k, mass m and unstretched radius r. Now suppose you have a frictionless cone and the angle of the peak is [itex]2 \theta [/itex] (that is, if you project the shape of the cone onto a plane it looks like a triangle and the top angle is [itex] 2 \theta [/itex]. If you were to gently slide the rubber band down the cone (so it doesn't have any appreciable momentum, but you're not forcing it either) it will come to rest at some point on the cone where it will be at equilibrium (we're assuming that the cone is big enough so the rubber band doesn't go all the way to the bottom). What is the radius of the rubber band at this point of equilibrium?

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# A cute problem

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