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Experimental analysis of the brachistochrone using a kinematical approximation method Liht, Enrique; Yang, Hans

Abstract

The solution to the brachistochrone – the curve of fastest descent – for a spherical steel bearing sliding and rolling down a low-friction plastic track is determined from experimental data and numerical analysis. It is hypothesized that the curve of fastest descent will be closely correlated to the cycloid. Analysis involves a spreadsheet simulation of model curves where the times of descent are predicted by an approximation formula derived using basic kinematics. Results display a positive correlation between a model curve’s deviation from the cycloid and the time of descent.

Item Metadata

Title
Experimental analysis of the brachistochrone using a kinematical approximation method
Creator
Liht, Enrique; Yang, Hans
Date Issued
2011-03
Description
The solution to the brachistochrone – the curve of fastest descent – for a spherical steel bearing sliding and rolling down a low-friction plastic track is determined from experimental data and numerical analysis. It is hypothesized that the curve of fastest descent will be closely correlated to the cycloid. Analysis involves a spreadsheet simulation of model curves where the times of descent are predicted by an approximation formula derived using basic kinematics. Results display a positive correlation between a model curve’s deviation from the cycloid and the time of descent.
Genre
Report
Type
Text
Language
eng
Series
University of British Columbia. Science One Research Projects
Date Available
2011-06-07
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0107227
URI
http://hdl.handle.net/2429/35252
Affiliation
Science, Faculty of
Campus
UBCV
Peer Review Status
Unreviewed
Scholarly Level
Undergraduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International