Shung-Yuan Sean Lee
Fu-Shing Junior High School of Yilan County Student Student
Email：sean7777@smail.ilc.edu.tw
LIN JHIH-YU
Fu-Shing Junior High School of Yilan County Student Student
Email：kiki115@smail.ilc.edu.tw
Abstract
A brachistochrone curve is lying on a plane, from a given point to the other not directly below the former, along which a bead slides frictionlessly under the influence of a uniform gravitational field in the shortest time. The solution, in theory, to the problem of searching for the curve is an inverted cycloid.
However, for a brachistochrone curve in theory, it is based on the assumption of a particle under the unique influence of gravitational field without friction. It is unrealistic to have such frictionless environment, therefore it is to investigate how much the deviation is for a brachistochrone curve to be affected by friction.
Experimental data includes measuring descent times of a spherical steel rolling down along different curved surfaces and video shooting in slow motion. The results of the loci for the particle motion under gravitational force with friction are further analyzed in comparison with the cycloid. It is concluded that the brachistochrone curve under the influence of friction is approximately 1/2 period of cycloid, far from the solution proposed by the theory. Moreover, acrylic-surfaced tracks is difficult to maintain constant reliable data due to its bouncy texture. It is suggested that better material is needed to optimize the experimental condition.
Keywords :brachistochrone curve, friction, cycloid