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At what angle should a curve of 200 m radius be banked so that no friction is required when a car travels at 60 kilometers per hour around the curve?

For a banked curve with no friction, the only forces acting on a car are the normal force and the weight. We have just looked at this situation. The centripetal force must be supplied by the horizontal component of the normal force. We have just analyzed this situation in arriving at

tan = v2 / g r

While it is easier to think of an automobile travelling at 60 km/h, it will be easier to use velocity in our calculations in terms of m/s, so we begin by changing units,

km 1000 m h v = 60 -- [------] [------] h km 3600 s
v = 16.7 m/s

Now we can directly apply

tan = v2 / g r = (16.7 m/s)2 / (10 m/s2)(200 m)

= 7.91o

(c) 2000, Doug Davis; all rights reserved.