Which is the fastest way?
Move the balls along the inclined plane and the brachistochrone curve into the top position. Start the machine and watch the balls move. Then move both balls into different positions in the two same brachistochrone curves. Let them go and watch how fast they reach the bottom.
How it works
A cycloid is a curve drawn by a point on the circumference of a disk rolling without slipping along a straight line. A brachistochrone curve (curve of the fastest descent) is a suitably selected and a suitably mounted fragment of a cycloid. The time that a ball takes to move between two points (the way it moves in the experiment) is the shortest along with a brachistochrone curve and not along a straight line, which is the shortest path between two points. If the brachistochrone curves are identical, the sliding time to a finishing-line established in a suitable place is the same regardless of the starting point.
Brachistochrone curves are used in planning tracks of space shuttle flights.