Banked Curves (finding smallest & largest speed)

  1. Hello, thank you for helping.

    My Question:
    On a banked race track, the smallest circular path on which cars can move has a radius r1 = 107 m, while the largest has a radius r2 = 163. The height of the outer wall is 18 m.
    Find the smallest speed and largest speed at which cars can move on this track without relying on friction.

    I already solved the problem but I was wondering if it was correct.

    r2-r1 = 163m-107m= 56m.
    tan(theta) = 18/56

    tan(theta) = v^2 / (rg)
    v = sqrt(tan(theta)rg)

    for smallest speed:
    v = sqrt(tan(18/56)107*9.8) = 2.45 m/s

    for largest speed:
    v = sqrt (tan(18/56)163*9.8) = 2.99 m/s

    Thanks again!
     
  2. jcsd
  3. Fermat

    Fermat 876
    Homework Helper

    tan(@) = 18/56 = 0.34143

    But you used tan(18/56)!

    which = 5.61x10^-3

    That's why your answers are so low.

    If you use tan@ = 0.34143, you will get the correct answers.
     
  4. oooo.. makes sense. Thank you!
     
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