The comfortable roller coaster—on the shape of tracks with a constant normal force
Abstract
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.
- Publication:
-
European Journal of Physics
- Pub Date:
- November 2010
- DOI:
- 10.1088/0143-0807/31/6/001
- arXiv:
- arXiv:1007.1394
- Bibcode:
- 2010EJPh...31.1307N
- Keywords:
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- Mathematical Physics;
- Physics - Classical Physics
- E-Print:
- 10 pages, 4 figures