Coefficient of restitution for elastic disks

We calculate the coefficient of restitution, $\epsilon$, starting from a microscopic model of elastic disks. The theory is shown to agree with the approach of Hertz in the quasistatic limit, but predicts inelastic collisions for finite relative velocities of two approaching disks. The velocity dependence of $\epsilon$ is calculated numerically for a wide range of velocities. The coefficient of restitution furthermore depends on the elastic constants of the material via Poisson's number. The elastic vibrations absorb kinetic energy more effectively for materials with low values of the shear modulus.Comment: 25 pages, 12 Postscript figures, LaTex2

Static coefficient test method and apparatus

The static coefficient of friction between contacting surfaces of a plurality of bodies is determined by applying a load to the bodies in a direction normal to the contacting surfaces. Opposite ends of a flexible filament are connected to a load cell and the first of the bodies. A motor continuously moves the second of the bodies away from the load cell at constant velocity at right angles to the force of the normal load so that the first body moves intermittently relative to the second body across a contact surface between them. The load on the surfaces, the nature of the surfaces, and the speed of the first body relative to the load cell are such that the filament is alternately and cyclically tensioned and relaxed as the movement occurs. The maximum tension occurs at the incipient stages of movement of the first body relative to the second body. The load cell derives a series of measurements which are coupled to an x-y recorder, from which the maximum forces of the filament are determined to enable the static coefficient of friction to be determined. From the maximum forces and the normal force, the coefficient is determined. For determining coefficients of friction where there are large compression loads, the normal load is applied with a calibrated compression spring that is deflected by a predetermined amount determined by a spring load vs. deflection calibration curve