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ERIC Number: EJ1162311
Record Type: Journal
Publication Date: 2017-Jan
Pages: 12
Abstractor: As Provided
ISSN: ISSN-0031-9120
Approaching the Brachistochrone Using Inclined Planes--Striving for Shortest or Equal Travelling Times
Theilmann, Florian
Physics Education, v52 n1 Article 015009 Jan 2017
The classical "brachistochrone" problem asks for the path on which a mobile point M just driven by its own gravity will travel in the shortest possible time between two given points "A" and "B." The resulting curve, the cycloid, will also be the "tautochrone" curve, i.e. the travelling time of the mobile point will not depend on its starting position. We discuss three similar problems of increasing complexity that restrict the motion to inclined planes. Without using calculus we derive the respective optimal geometry and compare the theoretical values to measured travelling times. The observed discrepancies are quantitatively modelled by including angular motion and friction. We also investigate the correspondence between the original problem and our setups. The topic provides a conceptually simple yet non-trivial problem setting inviting for problem based learning and complex learning activities such as planing suitable experiments or modelling the relevant kinematics.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A