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?
[Physics] Curved Slope faster than linear
brachistochrone-problemenergy-conservationnewtonian-mechanicsrotational-dynamics
Best Answer
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.