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:
 10.1088/01430807/31/6/001
 arXiv:
 arXiv:1007.1394
 Bibcode:
 2010EJPh...31.1307N
 Keywords:

 Mathematical Physics;
 Physics  Classical Physics
 EPrint:
 10 pages, 4 figures