# Homework Help: Having trouble with friction, incline problems

1. Sep 28, 2004

### 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.

2. Sep 28, 2004

### Pyrrhus

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 ) On your third problem the formula you used works only without friction, try solving it with friction.

3. Sep 28, 2004

### 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?

4. Sep 28, 2004

### Pyrrhus

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

5. Sep 28, 2004

### bigslowy

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

6. Oct 12, 2006

### RoNiN

How do you do the 2nd equation?

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