Q.Why are curved roads banked?
On a FLAT (unbanked) curved road, the entire centripetal force needed for a vehicle to turn must come from static friction between the tyres and the road, . This is a poor long-term solution for two reasons: friction has a hard upper limit (), which caps the maximum safe turning speed, and in real conditions is far from constant -- it drops sharply on a wet, oily, dusty, or otherwise non-uniform road surface, making the safe speed limit unpredictable and potentially dangerously low exactly when it matters most (e.g. in rain). By tilting the road surface at an angle (banking), the normal reaction N -- which is always present regardless of friction -- now has a HORIZONTAL component that points towards the centre of the curve and can, by itself (at the 'most safe speed' ), supply the ENTIRE centripetal force needed, with zero reliance on friction at all. For other speeds in a realistic range around , friction still contributes, but only up to its safe (well below limiting) capacity, giving the road a much wider genuinely safe speed range ( to ) than an unbanked road ever could.
Curved roads are banked so that the road's own normal reaction -- not just friction -- can safely provide the centripetal force needed for vehicles to turn, over a whole range of speeds.
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