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You want to design a curve, with a radius of curvature of 35.0 m, so that a car can turn at a velocity of 15 m/s on it without depending on friction. At what angle must the road be banked?

  • physics -

    No tire friction is required if the force on tires at the road surface, Fn, is normal to the surface. That requires
    Fn sinA = M*V^2/R (to provide the centripetal force), and
    Fn cosA = M*g
    (to balance the weight).
    A is the banking angle.
    This leads to
    tanA = V^2/(R*g)

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