# Car on unbanked curve

1. Jul 5, 2004

### akatsafa

I'm setting this problem up, but I'm now stuck.

A car is safely negotiating an unbanked circular turn at a speed of 17m/s. The maximum static frictional force act on the tires. Suddenly a wet patch in the road reduces the maximum static friction force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?

I made a free body diagram and came up with f net equations. I have fnetx=1/3usg=v^2/r. I have fnety=N-mg. For fnetx, I further get 3.267m/s^2us=v^2/r. And this is where I get stuck. I'm not sure what I do to find the speed without knowing the radius.

2. Jul 5, 2004

### arildno

The magnitude of the initial frictional force satisfies:
$$F=m\frac{v_{0}^{2}}{R}$$

Afterwards, we have:
$$\frac{1}{3}F=m\frac{v_{1}^{2}}{R}$$

By division, we get:
$$\frac{1}{3}=(\frac{v_{1}}{v_{0}})^{2}$$