Question

You are an automotive engineer in Western Colorado designing a horizontal curve on a twisty mountain road. This curve has a radius of curvature of 100 meters.

(a) Suppose you want to slope this curve such that no frictional force is required to keep a vehicle on the road if it drives at a speed of 50 kilometers per hour. Calculate the required banking angle to do this.

(b) I have a friend in Western Colorado who rides her motorcycle on such curves much faster than this. She hasn’t ridden off the side of the mountains yet, so clearly she’s pretty good at physics! If the coefficient of static friction between her motorcycle tires and the pavement is 0.8, how fast can she ride around one of these curves?

Hint: There are two possible choices for a coordinate system in this problem: one aligned with the road (tilted), and one aligned with Earth’s gravity and the plane of the curve (the usual one). Think carefully about which one will make your life easier. What direction is the bike accelerating in?

Answer 1

Sorry to use images, there is a problem with the equation editor.

A.

B.

The radius and angle are taken from part A