Peoples Physics Book Version-2

7.7. Examples http://www.ck12.org

7.7 Examples

Example 1

Question: You buy new tires for your car in order to take turns a little faster (uh, not advised—always drive slowly).
The new tires double your coefficient of friction with the road. With the old tires you could take a particular turn at
a speed ofvi. What is the maximum speed you can now take the turn without skidding out.

Solution: To find the maximum speed a car can take a corner on a flat road without skidding out, set the force
of friction equal to the centripetal force. This is because the centripetal force pushes the car off the road and the
frictional force keeps the car on the road. Therefore, if the centripetal force and the frictional force were equal, the
car would be going the maximum speed it could go on that turn without sliding off the road.

Fc=

mvi^2

r

=Fk

Then we solve for v.

mvi^2

r =Fk⇒vi

(^2) =Fkr
m ⇒vi=

√

Fkr

m

If we replace the frictional force with twice the frictional force we get the new speed.

vf=

√

2 Fkr

m

The new speed is

√

2 greater than the original speed.