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Banking of a Road

For getting a centripetal force, a cyclist bends toward the center of circular path, but it is not possible in case of four wheelers. Therefore, the outer bed of the road is raised so that a vehicle moving on it gets automatically inclined toward the center. In Fig. 5(a), reactionR is resolved into two components: the component R cos θ balances the weight of vehicle.
 
 
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and the horizontal component R sin θ provides necessary centripetal force as it is directed toward center of desired circle.
 
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Fig. 5
 
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Dividing (4) by (3), we have
 
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If l = width of the road, h = height of the outer edge from the ground level, then from Fig. 5(b),
 
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From (5), (6), and (7),
 
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Notes:
  • If friction is also present between the tyres and road, then
     
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  • Maximum safe speed on a banked frictional road,
     
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