Three tracks are straight, parabolic and cycloid. All three paths have the same initial and final states. When the balls race down the curves the cycloid path arrives first. The parabola is a very close second. The straight line is a distant third although many students think the straight path should have the fastest time.
Set up time
Physics and Science Concepts
Motion in Two Dimensions
Place balls of equal mass and size at the top of the tracks, one at the cycloid, one at the parabola, and one at the straight track. Let the balls roll down, the cycloid ball will arrive first. Then, place two balls on the cycloid track, one at the top and one a little ways down. The two balls will reach the end at the same time.