Velcro$^{\mbox{{\textregistered}}}$ as a Mesoscopic Model System for Stick-Slip Motion

The Amontons-Coulomb (AC) laws of friction, established during the 18$^{th}$ Century, serve to explain many of the phenomenological observations of friction in the macroscopic world. The AC laws for friction do not adequately explain certain systems, which undergo stick-slip motion, however. The hook-and-loop system (Velcro), in particular, exhibits easily observed stick-slip motion. Velcro evinces clear evidence of stick-slip dynamics that is independent of sliding velocity in accordance with Coulomb but, the maximum static friction force $F_s^{\max } $ and kinetic friction $F_k $ are keenly dependent on ``area of contact'' (hook number) in contrast to accepted law, but consistent with recent studies of frictional dynamics in nanoscopic systems. Both the $F_s^{\max } $ and $F_k $ as a function of area follow power law dependences with an exponent of approximately 2/3. Moreover, the fluctuations of the kinetic friction $F_k $ also follow a power law dependence with an exponent of approximately 1/2 in accordance with random walk theory. On the other hand, the $F_s^{\max } $ and $F_k $ both follow a linear dependence with applied load in accordance with the classical theory of AC.