Faster than gravity accelerations and the resulting trajectories in a sliding particle and wedge system

Abstract

An analysis is given of the mathematical model of a system from the mechanics of rigid bodies, in which a wedge slides smoothly along a horizontal surface under the influence of a particle sliding along the (smooth) sloping surface of the wedge. It is shown that, for certain values of the wedge angle, the acceleration of a wedge with a given mass can be made larger than the gravitational “ g”, and indeed arbitrarily large, by choosing a particle of sufficiently large mass. Various properties of the particle's parabolic path are then derived. In particular, a bifurcation in the particle's horizontal range is shown to occur for a certain critical value of the wedge angle and the particle-wedge mass ratio.