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Banked road, find radius

  1. Feb 26, 2013 #1
    1. The problem statement, all variables and given/known data
    you want to design a curve with a radius of curvature of 350 m, so a car can turn at a velocity of 15 m/s without relying on friction. Find the angle at which the road must be banked.


    2. Relevant equations
    I've derived this equation via free body diagram, x component is gravity pushing the car into the curvature

    Fn sinx = mv^2/r
    Fn cosx = mg

    tanx = v^2 / (gr) where r = radius, g = gravity, v = velocity

    I've used it before so I know its correct.


    3. The attempt at a solution

    tanx = 15^2 m^2/s^2 / (9.8 m/s^2 * 350 m)

    x = 3.75 degrees.

    The book says this answer is incorrect, and I'm not sure where I went wrong. (The book got around 30 degrees)
     
  2. jcsd
  3. Feb 27, 2013 #2

    ehild

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    Homework Helper
    Gold Member

    Youe solution is correct, but have you copied the data correctly?

    350 m for the radius is a bit too great. Was not it 35 m instead?

    ehild
     
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