Anomalous behavior of normal kinematic restitution in the oblique impacts of a hard sphere on an elastoplastic plate

We observe oblique impacts of a hard aluminum oxide sphere on a thick elastoplastic polycarbonate plate by recording stroboscopic photographs of the sphere trajectory and spin. The apparent kinematic coefficient of normal restitution grows monotonically with the magnitude of the tangent of the angle of incidence, and the apparent coefficient of friction decreases with increasing normal impact velocity. Although every collision dissipates the total kinetic energy of the sphere, we observe restitution coefficients exceeding unity for the most grazing impacts. We exploit this example to confirm that, although an apparent kinematic coefficient of normal restitution below one is sufficient to guarantee dissipation of kinetic energy in any collision, this condition is not necessary for oblique impacts of spheres on a plate.