Tap the cradle (or press Space) to release it.
Force carried by each contact, one lane per contacting pair, oldest on the left. The pulse arrives at each lane in turn: that delay is the wave speed. Measured wave speed: —
What this is
An independent reimplementation of Newton’s cradle — the desk toy of five suspended steel balls. The device is public domain: papers on its physics were presented to the Royal Society in 1662 by John Wallis, Christopher Wren and Christiaan Huygens, a quarter of a century before Newton’s Principia. There is no author, publisher or year to credit for the object itself, and no rights are claimed over it here.
Nothing on this page is copied from any existing simulator. The contact model, the
integrators, the renderer and the conservation-manifold algebra were all written for
this app. What is owed to others is the physics, and it is credited below and
in CREDITS.txt, which ships with the app.
Credit for the physics
- S. Hutzler, G. Delaney, D. Weaire and F. MacLeod, “Rocking Newton’s cradle”, American Journal of Physics 72(12), 1508–1516 (2004), DOI 10.1119/1.1783898 — the equations of motion, the Hertzian stiffness, the dissipation model, the apparatus constants, and the observation that two conservation laws cannot determine N velocities.
- E. J. Hinch and S. Saint-Jean, “The fragmentation of a line of balls by an impact”, Proc. R. Soc. Lond. A 455, 3201–3220 (1999).
- F. Hermann and P. Schmälzle, Am. J. Phys. 49(8), 761 (1981); F. Hermann and M. Seitz, Am. J. Phys. 50(11), 977 (1982).
- V. F. Nesterenko, Dynamics of Heterogeneous Materials (Springer, 2001); A. N. Lazaridi and V. F. Nesterenko, J. Appl. Mech. Tech. Phys. 26, 405 (1985); reviewed in C. Chong, M. A. Porter, P. G. Kevrekidis and C. Daraio, arXiv:1612.03977.
- L. Landau and E. Lifshitz, Theory of Elasticity, for the Hertz contact law.
What differs from a real cradle
- The chain is reduced to one dimension, valid for small swing angles. A real cradle is two-dimensional and its contacts go off-centre at large amplitude.
- Strings are inextensible and massless; there is no air resistance unless damping is switched on, no rotation, no friction between balls, and no sound.
- The default ball is deliberately soft, so the contact is long enough to watch. The “Steel” preset uses the documented stiffness of the apparatus in Hutzler et al., and then runs in slow motion because a steel contact lasts about a tenth of a millisecond.
- Gravity is modelled as a linear restoring spring of constant mg/L, the small-angle reduction used in the source paper.
Controls
- Space, the Release button, or a tap on the cradle releases it. P pauses and resumes.
- Everything is computed in your browser. There is no account, no network request, no tracking, and no cost. Your settings are kept in this browser only.