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Rotational motion roller coaster problem

  1. Oct 21, 2012 #1
    1. The problem statement, all variables and given/known data

    7KWPp.png

    2. Relevant equations
    ƩF = ma = (mv2) / r


    3. The attempt at a solution

    For part A:
    Fn - Fg = (mv2) / r
    Fn = ((mv2) / r ) + mg
    Fn = (500x20^2) / 10 + 500x9.8
    Fn = 24900

    This seems too high to be true. But I'm unsure of what I did wrong. I know the normal force is the force of which the track is acting on the car.

    For part B:
    I think it is just 20m/s but I'm not sure. I know an object traveling in a circle has the most speed when it's at the bottom of the circle.

    Thanks for the help in advance!
     
  2. jcsd
  3. Oct 21, 2012 #2

    TSny

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    Part A looks correct.

    For part B, set up equations similar to part A and think about what happens to the value of Fn when the vehicle leaves the track.
     
  4. Oct 21, 2012 #3
    Hmm...

    I think Fn would equal 0 when the vehicle leaves the track. So I use the same equation as part A except I set Fn to 0 and solve for v?
     
  5. Oct 21, 2012 #4

    TSny

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    Yes Fn will be zero. Good. But if you use the same equation you will end up taking the square root of a negative number (oops). Set up a correct similar equation using a new free body diagram for point B
     
  6. Oct 21, 2012 #5
    Fg - Fn = (mv2) / r
    (mgr / m)1/2 = v
    (500x9.8x15 / 500)1/2 = 12.1

    V = 12.1
     
  7. Oct 21, 2012 #6

    TSny

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    Good! (minus 1 point for not including units :devil:)
     
  8. Oct 21, 2012 #7
    Haha thank you so much! I got the units on my paper :P
     
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