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Curved Tracks

Curved Tracks. 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 F c = mv 2 / r directed inward. r.

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Curved Tracks

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  1. Curved Tracks

  2. 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

  3. 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. • The ground pushes back, accelerating the car. Acceleration of the contact point is upward FGW FWG Point in contact doesn’t slip

  4. 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. r Fc

  5. The limit of steering in a curve occurs when the centripetal acceleration equals the maximum static friction. A curve on a dry road (ms = 1.0) is safe at a speed of 90 km/h. What is the safe speed on the same curve with ice (ms = 0.2)? 90 km/h = 25 m/s rdry = v2/ msg = 64 m v2icy = msgr = 120 m2/s2 vicy = 11 m/s = 40 km/h Skidding

  6. 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. next

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