# Circular Motion and coefficient of static friction

1. Dec 4, 2003

### kbrowne29

I've been having trouble with the following problem:

A curve of radius 60 m is banked for a design speed of 100 km/hr. If the coefficient of static friction is .30, at what range of speeds can a car safely make the curve?

Here's what (I think) I know:
We know that there are two forces that are acting towards the center of the circle. One is friction, equal to mu * normal force. The noraml force is equal to mg, and so friction is equal to mu*mg. The other force acting towards the center of the circle is the centripital force, which is equal to mv^2/r.
So...the maximum speed a car could have without skidding out would be given solving for v in the equation mu*mg=mv^2/r. However, I don't know what to do after this, if this is even right (which it probably isn't). I would appreciate any help with this problem. Thanks.

2. Dec 4, 2003

### NateTG

First off, you forgot that the normal force has a component to the inside of the curve since it is banked.

There are two ways that a car can fail to negotiate the turn:
1. The car slides out of the curve from going to fast. In this case, friction is acting with the normal force to provide centripetal acceleration.

2. The car slips into the middle because the curve is too steep. In this case, friction is acting against the normal force which is providing more than the centripetal acceleration.

These two scenarios should give you minimum and maximum values for v.