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Friction problem with banked curve given static friction coefficient

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the maximum speed with which a 1200 rubber-tired car can take around a banked curve with radius of 80.0 meters an angle of 19.0 degrees? (static friction coefficient is 1.0)


    2. Relevant equations
    Fs=mu*F(normal)
    F(netxdirection)/m=acceleration
    acceleration=velocity2/radius


    3. The attempt at a solution
    I tried answering this problem several times and I failed at each; although I swear my first answer was correct (31.6 m/s). My professor's answer was 40.1 m/s and I have no idea how he got that.

    Please help....
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 19, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Show how you solved it. What are your vertical and horizontal force equations?
     
  4. Sep 20, 2009 #3
    Hey....sorry for being so short. I was in a hurry to just get the question asked. I spent all day on homework and no time to fully explain.

    Here are my notes on this problem:

    Known:
    incline angle=19.0 degrees
    Radius of turn=80.0 m
    Mass of car=1200 kg
    mu(s) tire on cement road=1.0

    Forces:
    Normal
    Weight
    Friction

    Find:
    Max velocity without slipping on cement

    Steps:
    1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
    2. Enter Normal in Friction equation (F=mu*N) to get Friction force.
    3. Enter Friction force in F(netx)=ma for x-axis to solve for acceleration in the x direction which is also the radial/centripetal direction btw.
    4. Use a=v^2/r to find the velocity.

    Maybe this velocity is not the maximum? Am I missing something conceptual?
     
  5. Sep 20, 2009 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Careful! The acceleration is horizontal, so you cannot say that the acceleration is zero normal to the incline.

    Instead, analyze vertical and horizontal force components. Set up two equations and solve them together.
     
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