Dispersion-free linear chains

Reinsch, Matthias

doi:10.1119/1.17612

Cited by 13 publications

(16 citation statements)

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“…Instead, the details of the interaction force must be taken into account. The explanation of Newton's cradle is far from being simple and there is an intensive and controversial discussion about this seemingly simple classroom experiment [9][10][11][12][13][14][15][16].…”

Section: A Equations Of Motionmentioning

confidence: 99%

Two-ball problem revisited: Limitations of event-driven modeling

Müller

Pöschel

2011

Phys. Rev. E

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The main precondition of simulating systems of hard particles by means of event-driven modeling is the assumption of instantaneous collisions. The aim of this paper is to quantify the deviation of event-driven modeling from the solution of Newton's equation of motion using a paradigmatic example: If a tennis ball is held above a basketball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimplification, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different final velocity as compared with the velocity resulting from the oversimplified model.

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Section: A Equations Of Motionmentioning

confidence: 99%

Two-ball problem revisited: Limitations of event-driven modeling

Müller

Pöschel

2011

Phys. Rev. E

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“…V based on the mass-spring chain model commonly used to explain the behavior of a crystal lattice and to describe the behavior of Newton's cradle. 8,9,15,16 Another experiment was undertaken by dropping a 1.2-m-long, 12-mm-diam, 96 g wood dowel onto the piezo. The force waveform was similar to that in Fig.…”

Section: Bouncing Rod Experimentsmentioning

confidence: 99%

Differences between bouncing balls, springs, and rods

Cross

2008

American Journal of Physics

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Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.When one hard steel ball collides with another, kinetic energy is conserved, even if the balls have different diameters. Why is kinetic energy conserved in such a collision, given that kinetic energy is not conserved when two unequal length steel springs or rods collide? Experimental results with bouncing balls, springs, and rods are presented, which reveal the answer. For colliding springs and rods a significant fraction of the initial kinetic energy is retained after the collision as vibrational energy in the longer spring and rod. When two hard balls collide, a negligible fraction of the initial energy is converted to vibrational energy because the collision time is much longer than the transit time of an acoustic wave across each ball due to the fact that the contact region of a hard spherical ball is much softer than the rest of the ball.

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“…We believe that a closer examination of Newton's cradle can enhance and extend the pedagogical value of the original demonstration. [8][9][10] Newton's cradle has a long history. In 1662, papers on its underlying physics were presented to the Royal Society by no less than three eminent researchers, 5 John Wallis ͑known for his presentation of as an infinite product͒, Christopher Wren ͑mathematician, astronomer and architect of St. Paul's Cathedral in London͒, and Christiaan Huygens ͑author of a book on the wave theory of light and contributions to probability theory͒.…”

Section: Introductionmentioning

confidence: 99%

“…Only when the masses of the gliders and the spring constants were chosen to achieve a dispersion-free linear relation, did the gliders behave as in the textbook description. 8,10 In a follow-up paper, Herrmann and Seitz 9 re-examined the actual cradle experiment and found in both the experiments and simulations that the first impact of a ball leads to a break-up of the line, contrary to the textbook description. In their simulations, they modeled the interaction between balls as points of mass m that are connected by ͑Hertzian͒ springs.…”

Section: Introductionmentioning

confidence: 99%

Rocking Newton’s cradle

Hutzler

Delaney

Weaire

et al. 2004

American Journal of Physics

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In textbook descriptions of Newton's cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmälzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton's cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton's cradle which displays complex dynamics.

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Dispersion-free linear chains

Cited by 13 publications

References 0 publications

Two-ball problem revisited: Limitations of event-driven modeling

Two-ball problem revisited: Limitations of event-driven modeling

Differences between bouncing balls, springs, and rods

Rocking Newton’s cradle

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