Abstract
In this section, we finally return to the Newton’s cradle shown in Fig. 1 and Fig. 28a. When the chain of balls is struck at one end, the ball on the opposite end is ejected from the chain, providing a nice illustration of the principle of conservation of momentum. In reality, not all of the energy is transferred to the ejected particle (Hutzler S, Delaney G, Weaire D, MacLeod F (2004) Rocking Newton’s cradle. Am J Phys 72:1508–1516 [1]). While dissipation will account for some energy loss, it is also important to account for forces between the particles due to their elastic deformation. In other words, the Hertzian contact between the particles plays an important role in the dynamics of the Newton’s cradle. As we have seen throughout this volume, the dynamics of a chain of particles interacting through Hertzian contact is extremely rich and complex. We already have a model accounting for the Hertzian contact in Eq. (3).
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Notes
- 1.
Since these will affect the dynamics in the direction of the wave propagation along the array (i.e., the vertical direction when considering the orientation in Fig. 6.3a).
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Chong, C., Kevrekidis, P.G. (2018). Media with Onsite Forces: The Newton’s Cradle and Beyond. In: Coherent Structures in Granular Crystals. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-77884-6_6
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