Time required for a sphere to fall through a funnel

We experimentally test a recently proposed theory of the behavior of a single frictional, inelastic, spherical particle falling under gravity through a symmetric funnel. We find that, while many qualitative results of the theory are supported by the data, the quantitative behavior of a real sphere falling through a real funnel differs from the predictions. The behavior above a 45∘ funnel angle, the duration, and the dependence of the duration on the initial horizontal position all show significant deviations from the predicted results. In particular, for drop positions near the gap, the duration of the fall is often significantly less than predicted for 50∘ and 60∘ funnel angles; and at a 60∘ funnel angle, where the data best matches the model, the R2 goodness of fit is only 0.27. The fit can be significantly improved for 60∘ funnel angle by relaxing the most stringent approximation of the theory, which asserts that the transition from slipping to rolling is governed by a single constant parameter, β, independent of impact speed and angle. We conclude that, although the theory captures most of the key features of the dynamics of a ball falling through a funnel, it does not do so with quantitative accuracy, indicating that for commonly encountered balls and drop heights, a more realistic model of particle collisions is required.

Abstract licence: CC BY

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