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 curveThere is still a radius (r) associated with the curve The force is still F c = mv 2 /r directed inwardThe force is still F c = mv 2 /r directed inward r FcFc

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. Point in contact doesn’t slip Acceleration of the contact point is upward F WG F GW

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 FcFc

5. Skidding  The limit of steering in a curve occurs when the centripetal acceleration equals the maximum static friction.  A curve on a dry road (  s = 1.0) is safe at a speed of 90 km/h.  What is the safe speed on the same curve with ice (  s = 0.2)? 90 km/h = 25 m/s r dry = v 2 /  s g = 64 m v 2 icy =  s g r = 120 m 2 /s 2 v icy = 11 m/s = 40 km/h

6. Banking  Curves intended for higher speeds are banked.  Without friction a curve banked at an angle  can supply a centripetal force F c = mg tan .  The car can turn without any friction. next