I once read that a theoretical physicist is someone who will approximate a four-legged table as one with either one or two legs to simplify the problem and will then conclude that it is unstable. I was reminded of that quote when I read the paper by Rostamian et al. in this journal.1 They considered a point mass projectile bouncing up an incline, assuming that the projectile and the surface were both ideal rather than physical objects. It is standard if not universal practice to make simplifying assumptions when developing a physical model, but sometimes it can be taken too far. I tried the experiment using a real ball on a real surface and found that none of their assumptions or conclusions were valid. The time intervals between successive bounces were not equal, the rebound velocity was not equal for all impacts, the angle of incidence to the normal was not equal to the angle of reflection, the friction force was not negligible, the downhill path did not coincide with the uphill path, the ball rolled rather than bounced down the incline, the spin of the ball played a major role, and the number of uphill bounces could not be made arbitrary large. The maximum number of uphill bounces I observed was five. I think that purely mathematical papers published in The American Journal of Physics should come with a warning that any resemblance to the real world is likely to be coincidental.

A. M.
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J. M.
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Bouncing on a slope
Am. J. Phys.