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Homework Help: Banked curve problem

  1. Mar 5, 2006 #1
    http://img138.imageshack.us/img138/2042/untitled15mr.jpg [Broken]

    theta = 21 degrees
    Mu = 0
    radius = 150 meters
    a = radial acceleration of uniform circular motion

    a = v^2 / r

    The sum of all forces = m*a

    Since the car is at an angle and Fn is always perpendicular I split it into X and Y components.

    Fn in the x direction = Fn sin theta
    Fn in the y direction = Fn cos theta

    X direction: Fn sin theta = m (v^2 / r)

    Y direction: no acceleration so Fn cos theta - Fg = 0
    Fn = (mg / cos theta)

    By substitution into the equation for the x direction:

    ( mg / cos theta ) * sin theta = m (v^2 / r)

    mg tan theta = m (v^2 / r)

    cancelling m and re-arranging...

    tan theta = ( v^2 / rg )

    v^2 = tan 21 / (150 * 9.8)
    v^2 = 564.28

    v = 23.75 meters per second


    Is this answer correct?
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 5, 2006 #2

    Fermat

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    Homework Helper

    Yes.
    Your working is pefectly correct and the answer is correct.

    There's just a little typo. You used a '/'-sign instead of a '*'-sign between the tan21 and the 150*9.8
     
  4. Mar 5, 2006 #3
    Yes you are correct with the equations tan(theta) = v^2/rg.
     
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