Kevin Zhou — Mechanics Review Problem 3 · Kevin Zhou #MRev.3
Physics · mechanics
Problem
Problem 2 (FYKOS 34.1). We model a person’s head as a sphere of radius R, and a beanie as a
circular, massless rubber band of radius r and spring constant k, where r < R. The coefficient of
0 0
friction between the band and head is µ. When is it possible for the person to put the beanie on
with one hand?
That is, find the conditions for which it is possible to stretch the band so that it lies along the
equator of the sphere, by applying forces only at one point at the band, as shown above. Assume
for simplicity that the band is always planar.