Two balls are released simultaneously on the straight and curved tracks. The straight track can be positioned at many places along the curved track. Which ball wins?
Brachistochrone
The brachistochrone is a classic problem in classical mechanics and the calculus of variations. The goal is to find a curve that connects two points such that an object sliding on this curve under the action of gravity will slide from the higher point to the lower point in the least amount of time. At first it jangles intuition somewhat that this curve is not simply a straight line! I built a simple demonstration activity for our annual Physics Department Open House that illustrates this.