Experiments on the duration of impacts, mainly of bars with rounded ends, in elucidation of the elastic theory

Abstract

The general theory of impact enunciated by Newton divides bodies into two classes, "perfectly elastic" and "imperfectly elastic." In the former class, no sensible dissipation of energy occurs during impact, while in the latter a certain proportion of the energy of the relative motion is always dissipated ultimately into heat. Many actual bodies are not far from being perfectly elastic in the Newtonian sense. For the theoretical discussion of the problem, we have at our disposal two distinct mathematical theories applicable mainly under different conditions, due to Hertz and St. Venant. The Hertz theory, which regards impact as a statical effect, rests on the foundation that when two bodies are pressed steadily together, they come into contact over a small area and that intense stress is developed in the bodies locally around it, rapidly falling off at a distance. The creation of a state of strain is accomplished by wave propagation, but each stage of the compression is so slow that infinitesimal waves have time to adjust it locally without drawing away any sensible fraction of the energy.