Motion and force along a curved path-angle of curves?

[a18c18]

Homework Statement

An automobile club plans to race a 740 kg car at the local racetrack. The car needs to be able to travel around several 175 m radius curves at 85 km/h. What should the banking angle of the curves be so that the force of the pavement on the tires of the car is in the normal direction? (Hint: What does this requirement tell you about the frictional force?)

Homework Equations

a=v^2/r
Tcos(theta)=mv^2/r
F=ma

The Attempt at a Solution

Friction must equal 0?

 

[Mattowander]

Correct. So draw a free body diagram for the situation.

Here is a hint : Resolve the normal force into x and y components. One of these components should equal the weight of the car, the other should provide the required centripetal force towards the center of the track.