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Centripetal acceleration of a vehicle on banked circular arc

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data
    A van is moving on a horizontal circular bend in the road of radius 75m. The bend is banked at arctan(1/3) to the horizontal. The maximum speed at which the van can be driven around the bend without slipping is 25m/s. Calculate the coefficient of friction between the road surface and the tyres of the van.

    2. Relevant equations
    centripetal force = mv2/r
    Friction ≤ μR

    3. The attempt at a solution
    See attached diagram. At the maximum speed F=μR. Resolving perpendicular to the plane gives:

    R = mgcosθ
    ∴ F = μmgcosθ

    Resolving in a direction perpendicular to the weight gives:

    Rsinθ + Fcosθ = mv2/r
    mgsinθcosθ + μmgcos2θ = mv2/r

    Solving for μ gives:

    μ = [(v2/r)-gsinθcosθ]/[gcos2θ]

    And substituting the values gives μ=0.61. This is apparantly incorrect (the answer should be μ=0.40). I cannot see what I have done wrong.

    Any hints would be greatly appreciated!
     

    Attached Files:

  2. jcsd
  3. Feb 3, 2013 #2

    haruspex

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    That would be true if there were no net acceleration perpendicular to the surface. But you know there is a net centripetal acceleration, and that is not parallel to the surface, therefore it has a component perpendicular to the surface.
    Try resolving vertically instead.
     
  4. Feb 3, 2013 #3
    Ah, yes that makes sense. I got 0.40 now.

    Thank you!
     
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