Experimental validation of the brachistochrone curve

We built a simple, cheap and accessible experiment to study the motion of spherical beads through three different curves, one of them being the curve of fastest descent, or brachistochrone. Despite the absence of a no-friction constraint and the rolling of the beads, our experimental findings consistently support the conclusion that the brachistochrone path remains the fastest. We perform a numerical simulation to confront with experiments and obtain that the values are in agreement, with <?CDATA ttheory = 0.237?> t t h e o r y = 0.237 s, and <?CDATA t̄braq = 0.25\,±\, 0.03?> t ‾ b r a q = 0.25 ± 0.03 s. This simple system not only serves as a practical demonstration of minimization principles but can also inspire and engage students in high schools and colleges interested in physics.