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Roller coaster loop problem

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data
    A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop. The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure that the cars remain on the track. The biggest loop is 40.0 m high, with a maximum speed of 31.0 m/s (nearly 70 mph) at the bottom. Suppose the speed at the top is 12.0 m/s and the corresponding centripetal acceleration is 2g.

    What is the radius of the arc of the teardrop at the top?

    2. Relevant equations
    Fr= n+mg

    3. The attempt at a solution
    I think n + mg = mv^2/r, but I don't know what to do with the given value Ac=2g or how to go any further from here. Any help is greatly appreciated.
  2. jcsd
  3. Nov 3, 2008 #2
    nvm, I got it.
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