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where N is normal reaction
the explanation is that whenever we take sharp turns at high speed, we need greater centripetal force which friction cant provide and the vehicle may skid off. so to reduce dependance on friction and avoid wear and tear of tyres road are banked.
if ' W ' be the angle of banking then the foll happens
N cos W = mg
N sin w= mv^2/r
this reduces dependence on friction and hence we can safely turn our vehicles even at higher speeds.
The road is banked to reduce the sideways friction force between the tyres and the road.
This force is needed to make the vehicle turn in a circle.
The angle chosen will provide the correct friction at a mathematically determined speed.
One might choose a steeper angle for a turn on a motorway (freeway?) to that of a rural lane, but the angle also depends on the radius of the bend.
At the correct speed the sideways friction force will be zero.
Many people mistakenly believe that the vehicle weight affects the angle and in fact this is not the case.
If the tyres are rubber and the road surface is concrete the the same ideal angle will be true for a large truck and a small motorcycle (honest!)
If you like the maths of these things then why not have a look in wikkipedia.
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