Anomalous Frictional Behavior in Collisions of Thin Disks

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Abstract
We report on two-dimensional collision experiments with nine thin Delrin disks with variable axisymmetric mass distributions. The disks floated on an air table, and collided at speeds of about 0.5 to 1.0 m/s with a flat-walled stationary thick steel plate clamped to the table. The collision angle was varied. The observed normal restitution was roughly independent of angle, consistent with other studies. The frictional interaction differed from that reported for spheres and thick disks, and from predictions of most standard rigid-body collision models. For “sliding” two-dimensional collisions, most authors assume the ratio of tangential to normal impulse equals μ (friction coefficient). The observed impulse ratio was appreciably lower: roughly 0.5 μ slightly into the sliding regime, approaching μ only for nearly grazing collisions. Separate experiments were conducted to estimate μ check its invariance with force magnitude; and check that the anomalies observed are not strongly dependent on velocity magnitude. We speculate that these slightly anomalous findings are related to the two-dimensional deformation fields in thin disks, and with the disks being only “impulse-response” rigid and not “force-response” rigid.

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