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Banked Curve

  1. Feb 20, 2014 #1
    1. The problem statement, all variables and given/known data
    A curve with a 140m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction between tires and road needed to prevent skidding?

    2. Relevant equations
    F_fr = MkN
    N = mgcosθ
    ∑F = ma
    ∑F_net-x = mv^2/r = Nsinθ

    3. The attempt at a solution
    I have drawn my xy coordinate system so that the x component is parallel to the curve, and , and found that the normal force is mgcosθ. However, I don't know how to combine my equations together to find an angle theta. Is finding an angle here even the proper approach if the problem does not ask for it? Should I be doing something else instead?
     
  2. jcsd
  3. Feb 20, 2014 #2

    collinsmark

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    Hello PhysicsDerp,

    Welcome to Physics Forums! :smile:

    Not sure what that equation is. Oh, wait. I get it: The force of friction, Ffr = μkN, where N is the normal force. Okay, that's good. :approve:

    Not so fast (see below).

    Yes, Newton's second law is important for this one. :smile:

    Be careful there. It's not quite that simple.

    That should work out. Personally, I would have simply stuck with the x-axis on the horizontal direction and the y-axis on the vertical.

    I don't think changing the coordinate system such that the x-axis is parallel to the ramp will make the problem any easier. But whatever the case, it should still allow you to find the correct answer.

    Something is not quite right there.

    The normal force would be mgcosθ if the car were just sitting there at rest. But it's not; it's accelerating around the curve. The normal force is more complicated than that (regardless of the choice of coordinates).

    You might want to take another look at your free body diagram. Make sure that you have the following forces outlined on it:
    • The force due to gravity
    • The normal force
    • The force of friction
    • The resultant force (i.e., the net force)
    The resultant (net) force is equal to ma. This is the force equal to the centripetal force.
     
    Last edited: Feb 20, 2014
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