Why Does a Car Run Off the Road When Going Too Fast on a Curve?

[physicsdude12]

Hey everyone,

I'm having trouble understanding a few aspects in circular motion and specifically in the application of road curves.

Would it possible for someone explain why a car runs off a road when it is going to fast? Basically, i know that a velocity greater than the optimal velocity for a banking angle causes the car to move off in a tangent, but I'm having trouble understanding why this occurs.

Also, the relationship between centripetal force and velocity (centripetal force directly proportional to velocity squared) has confused me even more. Basically, that relationship says that if the velocity doubles, the centripetal force quadruples! This can't be true because when a car is going very fast around a curve, the centripetal force is not enough to keep it in circular motion.

If someone could help me, i would greatly appreciate it.
Thanks,

Also, i am very sorry for my English, it is not the greatest :S

 

[Astronuc]

On a surface, friction between the tires and the road keep allow the car to apply a tractive force. On a curve without banking the frictional force allows the car to be steered (turned) in the curve. With banking (inward), there is a horizontal component of force applied by the road.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/carbank.html

and http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

Since F_centripetal = mv²/r, when v is doubled, F_centripetal is quadrupled.

Similarly, for linear kinetic energy, KE = 1/2mv², when v is doubled, the kinetic energy is quadrupled, but the momentum, mv, only doubles.

 

[physicsdude12]

Thank you very much for your help! :!)
This was really confusing me