So I saw this gif the other day, and was wondering, is this real or fake? And supposing there is no energy dissipated by the friction, why does such thing occur?
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9$\begingroup$ Why would you think it is fake? What sort of explanation do you expect? The relation between the shape of a curve and how fast things move along it under gravity is not very intuitive, see e.g. brachistochrone problem $\endgroup$– ACuriousMind ♦Commented Feb 1, 2017 at 23:17
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1$\begingroup$ note, the ball on the bumpy track does not reach the same peak altitude at the far side as the ball on the straight track does. The ball on the bumpy track lost more energy to friction (the track is longer!). So you cant really ignore friction. I believe the way to analyze this is look at the energy. In baseball the rule: keep your eye on the ball. In physics: keep your eye on where energy flows. $\endgroup$– docscienceCommented Feb 2, 2017 at 1:13
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$\begingroup$ Related : What is the position as a function of time for a mass falling down a cycloid curve? $\endgroup$– VoulkosCommented Feb 2, 2017 at 9:27
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$\begingroup$ Possible duplicate of Ball on a slope with hollow. $\endgroup$– sammy gerbilCommented Feb 3, 2017 at 19:49
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$\begingroup$ I think that the answer is given in a amazingly simple way by @Bill N in the link given by sammy gerbil Ball on a slope with hollow. This answer throws away any thought about complex calculations, brachistochrone etc. $\endgroup$– VoulkosCommented Aug 29, 2021 at 18:57
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2 Answers
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Simple. The curvey path drops lower than the straight path, initially, which increases the speed at which it travels the majority of the distance. The straight path drops only slightly, so the ball has to travel the majority of the distance at a lower speed.
The only thing I can think of, as for the reason for the curves, is to limit the speed of the ball, by transfering that motion into gravitational potential energy and then releasing that energy upon the next downslope. Limiting the speed is a good thing, as long as the average speed is still faster than the straight path (notice how the upward slopes do not slope higher than the lowest part of the straight path), because a lower speed ball will lose less momentum due to wind resistance.
It's important to note that lost momentum to wind resistance is lost forever, but lost momentum due to transference to gravitational potential energy is effectively "Stored" in the upward position of the ball.
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Can't say I've done anything as drastic as calculate anything, but a quick intuition for why this might work is to consider all the "free" travel the middle section of the bumpy track gives you.
When the ball rises over the top of the first bump it gets to fall a long way (and speed up again !) and this gives it another gravity boost. So it has a couple of those and gets some extra energy.
All the flat surface gets is those tiny little ramps on the end.
Even though the bumpy path is longer, it's also faster (maybe).
answered Feb 1, 2017 at 23:26