Having trouble with friction, incline problems

[bigslowy]

This question was a two parter

A car of mass 422 kg travels around a flat,
circular race track of radius 178 m. The co-
efficient of static friction between the wheels
and the track is 0.135.
The acceleration of gravity is 9:8 m=s2 :
What is the maximum speed v that the car
can go without flying off the track?

I got vmax as 15.3458 m/s

The same car now travels on a straight track
and goes over a hill with radius 200 m at the
top.
What is the maximum speed that the car
can go over the hill without leaving the road?

I'm not sure how to go about tackling that problem, I tried just substituting 200 m in for the radius but that doesn't work.

This one was also a two parter

A civil engineer is asked to design a curved
section of roadway that meets the following
conditions:
With ice on the road, when the coefficient of
static friction between the road and rubber is
0.23, a car at rest must not slide into the ditch
and a car traveling less than 50 km=h must
not skid to the outside of the curve.

At what angle should the road be banked?

I got the angle to be 12.95

What is the minimum radius of curvature of
the curve?

I tried using tan(theta)=v²/rg, but again I was wrong.

Any help would be greatly appreciated.

[Cyclovenom]

Your first problem is correct.

Your second problem requires you to think about the centripetal force, give it some thinking.

(Oh a fellow Civil engineer problem :cool: ) On your third problem the formula you used works only without friction, try solving it with friction.

[bigslowy]

I'm still stuck on both of them, our teacher didn't talk about finding centripetal force with uniform circular motion, can you give another hint?

[Cyclovenom]

I'm still stuck on both of them, our teacher didn't talk about finding centripetal force with uniform circular motion, can you give another hint?

What are the forces acting at the top of the hill??

[bigslowy]

Nevermind, he just used different word, thanks for your help

[RoNiN]

How do you do the 2nd equation?