dorsal/arxiv
View SchemaA Billiard-Theoretic Approach to Elementary 1d Elastic Collisions
| Authors | S. Redner |
|---|---|
| Categories | |
| ArXiv ID | physics/0402048 |
| URL | https://arxiv.org/abs/physics/0402048 |
| DOI | 10.1119/1.1738428 |
| Journal | Am. J. Phys. 72, 1492-1498 (2004) |
Abstract
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier at x=0, the corresponding billiard system is an infinite wedge. The collision history of the two particles can be easily inferred from the corresponding billiard trajectory. This connection nicely explains the classic demonstrations of the ``dime on the superball'' and the ``baseball on the basketball'' that are a staple in elementary physics courses. It is also shown that three elastic particles on an infinite line and three particles on a finite ring correspond, respectively, to the motion of a billiard ball in an infinite wedge and on on a triangular billiard table. It is shown how to determine the angles of these two sets in terms of the particle masses.
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"abstract": "A simple relation is developed between elastic collisions of freely-moving\npoint particles in one dimension and a corresponding billiard system. For two\nparticles with masses m_1 and m_2 on the half-line x\u003e0 that approach an elastic\nbarrier at x=0, the corresponding billiard system is an infinite wedge. The\ncollision history of the two particles can be easily inferred from the\ncorresponding billiard trajectory. This connection nicely explains the classic\ndemonstrations of the ``dime on the superball\u0027\u0027 and the ``baseball on the\nbasketball\u0027\u0027 that are a staple in elementary physics courses. It is also shown\nthat three elastic particles on an infinite line and three particles on a\nfinite ring correspond, respectively, to the motion of a billiard ball in an\ninfinite wedge and on on a triangular billiard table. It is shown how to\ndetermine the angles of these two sets in terms of the particle masses.",
"arxiv_id": "physics/0402048",
"authors": [
"S. Redner"
],
"categories": [
"physics.ed-ph",
"physics.class-ph"
],
"doi": "10.1119/1.1738428",
"journal_ref": "Am. J. Phys. 72, 1492-1498 (2004)",
"title": "A Billiard-Theoretic Approach to Elementary 1d Elastic Collisions",
"url": "https://arxiv.org/abs/physics/0402048"
},
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