# Car turning round

1. Dec 16, 2004

### Clari

A car is turing round a bend of radius 100m and banking angle 15 degrees. If the coefficient of static friction between the tyres and the road is 0.1, determine the range of speeds within which the car can turn safely round the bend.

Here is what I have done:

$$R sin \theta + f >= \frac{mv^2}{r}$$
$$R sin \theta + \mu R >= \frac{mv^2}{r}$$
$$R (sin \theta + \mu) >= \frac{mv^2}{r}$$
$$mg cos \theta ( sin \theta + \mu) >= \frac{mv^2}{r}$$
$$v<= \sqrt{rgcos\thata (sin\theta +\mu)}$$
$$v<= 18.6 ms^{-1}$$

2. Dec 16, 2004

### Staff: Mentor

To solve this problem, do this:

First identify all the forces acting on the car. I see three forces: weight, normal force (perhaps that's what you call R), and friction.

Now apply Newton's 2nd law: The net horizontal force on the car will produce the centripetal acceleration, while the net vertical force will be zero.

The range of speeds is obtained by realizing that at one extreme the friction points down the incline, while at the other it points up the incline.