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Circular motion problem please help no idea what's going wrong ><

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data

    A highway curve of radius 560m is designed for traffic moving at a speed of 73.0km/hr (1216m/s). What is the correct banking angle of the road?


    2. Relevant equations

    a=v^2/r
    F=ma


    3. The attempt at a solution

    Forces in t direction:
    Fnet=Fncos[tex]\vartheta[/tex]-Fg=0
    Fn=mg/cos[tex]\vartheta[/tex]=0


    Forces in r direciton:

    Fnetr=Fnsin[tex]\vartheta[/tex]=mv^2/r
    mgsin[tex]\vartheta[/tex]/cos[tex]\vartheta[/tex]=mv^2/r
    tan[tex]\vartheta[/tex]=v^2/r*g
    [tex]\vartheta[/tex]=tan-1(1216^2/(9.81*560))
    [tex]\vartheta[/tex]= 90 degrees?

    which is wrong..... = (
     
  2. jcsd
  3. Oct 13, 2009 #2
    double check the way you're assigning your forces, is the Fny component which is cancelling vertical gravity the hypotenuse of the triangle? I find it helpful in these cases to rotate the coordinate system so that the x axis is actually the sloped road. That way your Fn has only 1 component, and you break down gravity into y & x where x points towards the center of the turn.
     
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