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					Banked Curves
Force on a Curve
   A vehicle on a curved track has a centripetal
    acceleration associated with the changing direction.
   The curve doesn’t have to be a complete circle.
    • There is still a radius (r) associated with the curve
    • The force is still Fc = mv2/r directed inward




                             r    Fc
Friction on a Wheel
   A rolling wheel does not slip.
   It exhibits static friction.

   As a car accelerates the tire
    pushes at the point of
    contact.                                     Acceleration of
                                                 the contact point
                                                 is upward
   The ground pushes back,
    accelerating the car.
                                        FWG       FGW


                              Point in contact
                              doesn’t slip
Curves and Friction
   On a turn the force of static friction provides the
    centripetal acceleration.

   In the force diagram there is no other force acting in
    the centripetal direction.


                                           Fc  mv 2 / r
                                           Fc  F f
                          r    Fc
                                           F f   s mg
Skidding
   The limit of steering in a         A curve on a dry road (s =
    curve occurs when the               1.0) is safe at a speed of 90
    centripetal acceleration            km/h.
    equals the maximum static          What is the safe speed on
    friction.                           the same curve with ice (s =
                                        0.2)?
    Fc  mvmax / r  F f   s mg
           2

                                         •   90 km/h = 25 m/s
    v   2
        max   / r  s g                 •   rdry = v2/ s g = 64 m
    vmax   s gr                        •   v2icy = s g r = 120 m2/s2
                                         •   vicy = 11 m/s = 40 km/h
    r  vmax /  s g
         2
Banking
             Curves intended for
              higher speeds are
              banked.

             Without friction a curve
              banked at an angle q can
              supply a centripetal force
              Fc = mg tan q.

             The car can turn without
              any friction.
Using Normal Force
   A car on a curve uses both normal force from
    banking and static friction from the tires to steer the
    curve.


     Fc  FN sin q  F f
     mvmax / r  mg tan q   s mg
       2


     vmax  (  s  tanq ) gr


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posted:8/13/2011
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