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Banked curve angle w/no friction - teacher's work differs

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data

    At what angle should the roadway on a curve with a 50m radius be banked to allow cars to make the curve at 12 m/s even if friction is 0?

    2. Relevant equations



    3. The attempt at a solution

    All of the centripetal acceleration comes from normal force from the road on the car.

    I choose to represent the road as being along the y axis and Fn as being along +x axis. Then gravity is directed at angle theta to the left of the -yaxis.

    Normal force must equal the component of gravity along -xaxis, which is mgsin(theta),

    Since the required centripetal force is mv^2/r, this is 2.88m, mgsin(theta) = 2.88m

    gsin(theta) = 2.88

    theta = 17.09

    My professors work seems to be similar, but at the end she says that:
    gtan(theta) = 2.88

    theta = 16.37

    why?
     
  2. jcsd
  3. Mar 11, 2012 #2

    BruceW

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    Homework Helper

    Just to check I understand your axes correctly: so the instantaneous velocity of the car is in the z-direction? And the y-direction is like the direction a pedestrian would walk along to cross the road as quick as possible? And the x-direction is the direction of the normal force?

    In this case, gravity will not be directed at angle theta from the y-axis. And the normal force should not equal the component of gravity along the x-axis. I think you should draw the diagram again. I would advise making one of the axis go opposite to the direction of gravity. (Although your method should work too, but I think it makes it a bit more complicated).
     
  4. Mar 12, 2012 #3

    ehild

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    Gold Member


    You calculated N instead of the centripetal force, which is Nsin(phi). The angle gravity encloses with the negative x axis is not the banking angle. It is phi in the figure.

    ehild
     

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