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Maximum velocity at the top of a roller coaster?

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data

    A roller-coaster car has a mass of 509 kg when fully loaded with passengers.
    -The radius of the circle is 15m. (See picture below)

    What is the maximum speed the vehicle can have at point B and still remain on the track?
    _________m/s


    2. Relevant equations

    Sum of forces in the radial direction = -m(v^2)/R



    3. The attempt at a solution
    There would be a normal force pointing up and mg pointing down
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Oct 14, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Right. And what will the normal force become just before the car leaves the track? Use that to calculate the maximum speed. (You already know the radius of the curve at point B.)
     
  4. Oct 14, 2007 #3
    So I set the normal force equal to zero just before it would leave the track and use..

    normal - mg = m(v^2)/r masses would cancel.
    0 + g = (v^2)/r
    gr = (v^2)
    sqrt(gr) = v

    when i take the sqare root of 9.8*15 I'm getting 12.1244m/s which sounds reasonable.
     
  5. Oct 14, 2007 #4

    Doc Al

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    Staff: Mentor

    Sounds good to me.
     
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