# Car driving around a banked curve (with friction)

1. Mar 24, 2008

### TA1068

1. The problem statement, all variables and given/known data
A concrete highway curve of radius 80.0 m is banked at a 13.0 degree angle.

What is the maximum speed with which a 1400 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

2. Relevant equations
$$F_r = \frac{mv^2}{r}$$

$$F_f = \mu N$$

3. The attempt at a solution
I have a few pieces here, but I'm not completely sure how to put them together.

There's a rotational force pulling towards the center of the circle:
$$F_r = \frac{mv^2}{r}$$
Where mass and radius are given.

Also, there is a frictional coefficient:
$$F_f = \mu N$$
Where $$\mu$$ is 1.0 and N is mgcos$$\theta$$ (at least I believe it is... or is it just mg?) where m, g, $$\mu$$, and $$\theta$$ are given.

I had a relatively easy time understanding problems in which there was no friction, but I can't quite figure this out. Anyone have any advice to push me in the right direction? :)

2. Mar 24, 2008

### kkrizka

You already noted that the centripedal force is towards the center of the circle, so all you need to know now is which forces have a component pointing horizontally towards the center. I suggest that you draw a free body diagram with all the forces. This will help you see which contribute (and what components) to the centripetal force.

3. Mar 25, 2008

### physixguru

4. Mar 25, 2008

### TA1068

Awesome... Thank you very much! It all makes sense now. I kept treating centripetal force as a force in itself instead of a net force. Thanks again!