The comfortable roller coaster -- on the shape of tracks with constant normal force

Details The comfortable roller coaster -- on the shape of tracks with constant normal force The comfortable roller coaster -- on the shape of tracks with constant normal force

2010-07-08

arxiv.org/abs/1007.1394v1

Eur. J. Phys. 31 (2010) 1307-1317

Physics

Mathematical Physics

10 pages, 4 figures

Scientific paper

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.

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