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Roller coaster in a circular loop problem

  1. Sep 4, 2009 #1
    1. The problem statement, all variables and given/known data
    A roller coaster car is on a track that forms a circular loop of radius R in the vertical plane.

    (a) If the car is to maintain contact with the track at the top of the loop, what is the minimum speed v that the car must have at the bottom of the loop? Ignore air resistance and rolling friction.
    (b) If the car has a speed 6v/5 at the bottom of the loop, then what will be force vector acting on the car by the track when it reaches the top of the loop? [v is the minimum speed calculated in (a).]
    (c) If the car has a speed 4v/5 at the bottom of the loop, locate the point on the track where the car ceases to maintain contact with the track.


    2. Relevant equations
    0.5mv12 + mg(2R) - 0.5mv22 - mg(0) = 0.
    Fc = N - mg


    3. The attempt at a solution
    For a), i just used the first eqn, sub in all the known datas, i got v = 2sqrt(gR) as the min speed needed.

    For b), i assumed force vector needed is normal force. So at the top, i used the 2nd eqn, and i got N = Fc - mg = mv2/R - mg.

    For c), i dunno how to attempt the qn. Hope you guys can help thx!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 4, 2009 #2
    Your answer for (a) looks dubious; recheck your working.
    For (c), consider how the centripetal force on the car varies with its position on the track (hint: use an angle approach). Then find the point where N = 0.
     
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