# Car on circular turn with friction; finding max. velocity

awertag

## Homework Statement

A car of mass 1800 kg rounds a circular turn of radius 10 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.40, how fast can the car travel without skidding?

## The Attempt at a Solution

I thought to do Fnet(c) = (mv^2)/r
Fn-mg= (mv^2)/r
but i thought that for max speed without going off road is when Fn=0
so it would just be mg= (mv^2)/r
which gave me v=9.998 m/s

Was wrong...I dont know what else to do and how to include friction. Any good help will be greatly appreciated. --awe.g

irycio
Imagine your car taking a turn. It can, as long as force of the friction serves as a centripetal force (this is indeed the force that makes your car turn ;)). Hence they both have to be equal. Now, the force of the friction is the force that the car applies to the surface of the road multiplied by the coefficient of the friction.

awertag
ok so then my frictional force is equal to Fn-mg?
but how does that help exactly?

irycio
Why would your frictional force be equal to Fn-mg? your friction force is lesser than or equal to $$\mu F_n$$, $$\mu$$ being friction coefficient. In our case we want our friction force to be as big as it can, hence $$F_f = \mu F_n$$.

awertag
oh right. but I thought I want Fn to be 0 because you want to go as fast as possible without going off the road?

irycio
Yep, but your car ain't gonna fly :P. I mean, increasing velocity increases force neaded for a car to turn and it works only in XY plane. Fn is constant all the time.

awertag
lol too bad... I got the question now, thanks for all your help!!