# Banked Curves - PowerPoint

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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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```
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 views: 10 posted: 8/13/2011 language: English pages: 7