Regarding the article “Skateboarders rock at physics” (SN: 12/3/11, p. 10), the skateboarders’ “intuitive” conclusion that the ball will roll faster down the blue ramp (which is longer but has two steeper sections compared with the shorter red ramp with a single shallower section) depends on the particular geometries chosen for the two ramps.
I’ve programmed the solution for a point particle sliding (so no rolling) without friction down the two ramps and find that for certain ratios of the heights and lengths of the various ramps, it can actually be faster to slide down the red (single) ramp. Intuition can only go so far in such problems.
A full examination of the problem requires analysis and calculation to aid intuition. Nowadays, this means using a computer to explore all the possibilities.
Don Polvani, Arnold, Md.