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Homework Help: Centripetal Acceleration of curved exit ramp

  1. Jul 16, 2007 #1
    Centripetal Acceleration !!!

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

    An Engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the path
    a. Show that for a given speed v and radius r the curve must be banked at an angle [tex]\Theta[/tex] such that tan[tex]\Theta[/tex] = v^2/r * g


    2. Relevant equations

    a_c (centripetal acceleration) = V^2 / r
    [tex]\Sigma[/tex]F_y = m * a = 0

    3. The attempt at a solution

    th_00959_untitled_122_662lo.JPG

    i hope this diag. makes sense to you.....

    According to the question a_c = n * Sin[tex]\Theta[/tex] ---- (1)

    Then

    [tex]\Sigma[/tex]F_y = m * a = 0
    (n * Cos [tex]\Theta[/tex]) - (m * g) = 0
    n = (m * g) / (Cos [tex]\Theta[/tex]) -------- (2)

    substitute 2 in 1 for n

    a_c = (m * g) / (Cos [tex]\Theta[/tex]) * Sin[tex]\Theta[/tex]
    = (m * g) Tan [tex]\Theta[/tex]

    now a_c (centripetal acceleration) = V^2 / r

    therefore (V^2 / r) = (m * g) Tan [tex]\Theta[/tex]

    and Tan [tex]\Theta[/tex] = (V^2) /(m * g * r)

    what am i doing wrong ?.?
     
  2. jcsd
  3. Jul 16, 2007 #2

    PhanthomJay

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    Check your equation (1) again, you have identified the centripetal force, not the centripetal acceleration.
     
  4. Jul 16, 2007 #3
    Thanks!!! worked out right...
     
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