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Experimental demonstration of the Brachistochrone property of the cycloid

Abstract:

In the present work, the Brachistochrone property of the cycloid is tested experimentally. For this purpose, comparative tracks are built, sensors are placed at the end of the track to measure the travel time of the test object in each track. Mathematically, it is reaffirmed that the fastest curve an object can travel when falling by its own weight from the highest point to the lowest located not on the same vertical line of the first is a cycloid. Although it would be thought that the fastest curve is a straight line between the two points, in the experiment the object takes less time to move in the cycloid due to the property of the Brachistochrone. This curve is subject only to the gravitational force in which friction does not act. A cycloid is only an approximation of the optimal trajectory if there are forces other than gravity and the support reaction. The Brachistochrone theory was experimentally demonstrated with three types of curves and three types of objects. The constructed model can be useful for educational purposes.