Impact-induced acceleration by obstacles

Abstract

We explore a surprising phenomenon in which an obstruction accelerates, rather than decelerates, a moving flexible object. It has been claimed that the right kind of discrete chain falling onto a table falls faster than a free-falling body. We confirm and quantify this effect, reveal its complicated dependence on angle of incidence, and identify multiple operative mechanisms. Prior theories for direct impact onto flat surfaces, which involve a single constitutive parameter, match our data well if we account for a characteristic delay length that must impinge before the onset of excess acceleration. Our measurements provide a robust determination of this parameter. This supports the possibility of modeling such discrete structures as continuous bodies with a complicated constitutive law of impact that includes angle of incidence as an input.

Understanding how a falling ball chain can be speeded up by impact onto a surface

“…The analytical solution predicts only a small increase of Δy/y 0 over this range, about 16%, in agreement with the data in Ref. [15].…”

“…[15] that the transition from coiling (a type of buckling) to "smooth" flow for the incoming chain is stated as occurring for θ in the range 45° to 37.5 degrees, and with videos in Ref. [15] showing that rebounding spheres collide with the incoming spheres at 37.5 degrees, but do not come near the sphere above at the next smallest angle where a video is given, 22.5°. The critical angle is indicated in Fig.…”

“…In order to determine the critical inclination angles corresponding to the conditions in Eqs. (15) and (16), the velocity of the chain just after the collision with the surface must be known. As a first approximation, we shall calculate the velocity of the sphere just leaving the collision point with the surface assuming that it is free, with no external forces acting on it besides those associated with the interaction with the inclined surface during the collision.…”

“…(17) to the lab reference frame, where the inclined surface is at rest, and then substituting them into Eq. (15). We again specialize to the measurements of Ref.…”

Acquiring momentum: simple strategies by simple objects

“…In their paper, 'Impact-induced acceleration by obstacles', Hanna et al [1] discuss observations of such a process. They report the first observation of a most remarkable phenomenon: when two identical extended ball chains are dropped simultaneously, one onto a table and the other onto a distant floor, the chain dropped onto the table falls faster.…”