Banked Curves

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Banked Curves

• Physics 12

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What are banked turns?

• Using a slope/ hill/angle to help us turn
  safely.
• Why do we use banked turns?
• To allow us to not rely on friction for turning
  on a road.
• To allow planes to turn (as they dont have
  friction).
• To allow race cars to go at faster speeds.
• To help with the wear and tear of your tires.

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Banked Turns

• Banked turns are used when building roads and
  highways in order to increase safety (and not
  have to rely on friction for this)
• Banked turns are used in NASCAR racing to
  increase the speed at which drivers can safely
  navigate a turns
• In flight, airplanes must bank (tilt) in order to
  use the lift force to turn the aircraft (as there
  is no friction)

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Aircraft Banked Turn

• The lift force acts perpendicularly to the wings
  and in a bank, can be broken into components
• How do we get the centripetal force then?
• The x-component of the lift force provides the
  centripetal acceleration and turns the aircraft
  in a circle

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So how do we determine maximum speed???
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• https//www.youtube.com/watch?v5sULOQeXCdI

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Road Design with a Banked Turn

• Consider the car and turn from the unbanked turn.
  The radius of the turn is 55m and the turn is
  banked at a 25 angle (we will assume that there
  is no frictional component helping turn the car)
• Find the maximum speed at which a vehicle can
  safely navigate the turn
• If the bank is changed to 45, how does the
  maximum speed change?

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FBD
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Like the plane, the normal (lift) force turns the
vehicle
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Maximum speed for 45

• You can see that the maximum speed to negotiate
  this turn (in the absence of friction) is faster
  than an unbanked turn with a coefficient of .90.

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Practice Problems

• Page 566
• 20-23

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Example

• An aircraft that is flying at the speed of sound
  (343m/s) is turning in a circle. If the pilot
  experiences a G-force of 2 (meaning they
  experience a lift force twice that of gravity)
  solve for the radius of the circle.

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FBD
FL
Fg
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Consider y-direction first
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Consider x-direction
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Find the G-Force

• How many gs would the pilot experience if they
  turned in a circle of radius 1.00km while
  travelling at the speed of sound?