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Flat curve
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Ideal speed
Too fast
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W N Ff Fc
v Fc
Flat curve: The normal force acts straight up, balancing gravity.
All of the centripetal force must come from friction between the tyres
and road. If the car goes too fast, friction is not strong enough and the car skids outward.
Banked curve — ideal speed: The road is tilted inward, so the normal force
tilts with it. Its horizontal component points toward the centre and provides
exactly the centripetal force needed. No friction is required.
This is why banked tracks are safer — the banking does the work.
Banked curve — too slow: Less centripetal force is needed, but the
horizontal component of N still points inward. The car tends to slide
down the bank. Friction acts up the slope, partially opposing the
inward push. The car stays on the road, but friction is needed.
Banked curve — too fast: More centripetal force is needed than N alone
provides. The car tends to slide up the bank. Friction acts down the
slope, adding to the inward (centripetal) push. At extreme speeds, even this extra
friction is not enough and the car slides outward.