Banked Curves Physics 12

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)

Aircraft Banked Turn  The lift force acts perpendicularly to the wings and in a bank, can be broken into components  The x-component of the lift force provides the centripetal acceleration and turns the aircraft in a circle

 eXCdI eXCdI

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?

FBD

Like the plane, the normal (lift) force turns the vehicle

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.

Practice Problems  Page

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.

FBD FgFg FLFL

Consider y-direction first

Consider x-direction

Find the “G-Force”  How many g’s would the pilot experience if they turned in a circle of radius 1.00km while travelling at the speed of sound?