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ERIC Number: EJ963900
Record Type: Journal
Publication Date: 2011-Nov
Pages: 18
Abstractor: As Provided
Reference Count: 6
ISBN: N/A
ISSN: ISSN-0143-0807
Mechanical Paradox: The Uphill Roller
Cortes, Emilio; Cortes-Poza, D.
European Journal of Physics, v32 n6 p1559-1576 Nov 2011
We analyse in detail the dynamics of a mechanical system which is a rigid body with the geometry of a double cone. This double cone is apparently able to spontaneously roll uphill along inclined rails. The experiment has been known for some centuries, and because of its peculiar behaviour, it has been named "mechanical paradox". Although this instrument is well known today, we have not found in the literature a dynamical study like the one we are presenting. A deeper analysis of this mechanical object will allow us to go further than explaining the apparent paradox in the system; it will show interesting features of the dynamics that are not evident or intuitive. In this work, we follow a complete study of the geometry, the kinematic variables and the Lagrangian dynamics of the problem for any set of the angular parameters and initial values, and obtain as a result a full description of the dynamic variables of this mechanical device. In addition to studying the dynamics of the system with the angles that yield the typical paradoxical behaviour, we study carefully what we call the constant potential geometry regime, where the centre of mass maintains its height, and found in this particular case some features of the dynamics which are not common in rolling objects. We believe that this work can offer the student good material to review some fundamental concepts of analytical mechanics. (Contains 16 figures.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers: N/A