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Maximum and minimum velocity of a moving object on a bank angle

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    A curve of radius 300 m is banked at an angle of 10°. A) At what speed is no friction required? B) If the coefficient of friction is 0.8, what are the maximum and minimum speeds at which the curve can be traveled?


    2. Relevant equations
    F=m*a
    ac=mv2/r

    3. The attempt at a solution

    For part A) I found the velocity needed for no friction is 18.9 m/s. It's B that I am stumped on. I have no idea if I'm even setting it up correctly as determining the angles and perpendicular forces that are related to one another has been problematic for me.

    Here's what I've gotten so far:

    Fx[/SUB=max, ax=mv2/r

    Fx=f cos 10°+N sin10°=ax=mv2/r

    Fy=0

    Fy=-N cos 10°-mg=0

    f = μN

    Is this the correct setup?

    Also, in drawing out the free body diagram, I had a question regarding angle setup. In determining the x coordinate system, it was easy to visually see that friction had an angle of cos θ. In determining the angle for N however, I saw that the angle next to the x coordinate system by f, it corresponded to 90-θ. Since this angle of 90- is next to the angle of for f, someone told me it was opposite sin θ since cos θ was found for f and I did not fully understand that. Otherwise, what is next after setting it up? Any suggestions? Thank you for your time!
     
  2. jcsd
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