Verticle Banking on a circular track

  • #1
[SOLVED]If fast enough, a car can be driven on a track that is banked vertically. In the view of the 2008 formula one race in Singapore, the government has decided to build one such track. Given that the diameter of the track is 100m, and the coefficient of static friction between the rubber tires and the track is 1.0, calculate the minimum speed that a vehicle can drive along the track without slipping.

Okay so i know that the normal force will be providing all of the centripetal force now, i am just not sure how to play around with friction.

Without friction,

N = mv^2/r
mg = mv^2/r
100g = v^2
v = sqrt(100g)

But what about friction? I know that the friction keeps the car from coming back down on a straight path. So theres friction acting upwards, parallel to the race track.

How would i work with it after that?

Thanks loads
 
Last edited:

Answers and Replies

  • #2
Kurdt
Staff Emeritus
Science Advisor
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The normal force on the car will be the centrifugal force from circular motion. The friction will be stopping the car sliding down the vertical track. Set the friction force equal to the weight of the car and substitute in for the normal force to find v. You actually have the right answer without friction but since the coefficient is 1 that is no surprise.

EDIT: be careful with diameter and radius. I often make the same mistake.
 
  • #3
Thanks a lot!
 

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