# Critical speed of a banked curve (with friction.)

1. Nov 5, 2007

### Shipman515

A concrete highway curve of radius 80.0 m is banked at a 14.0$$\circ$$ angle.

What is the maximum speed with which a 1300 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

I was trying v_max = $$\sqrt{}\mu_srg$$
but that didn't seem right because it didn't account for the bank of the curve.

I then tried to determine normal force in the radial direction + the radial component of friction and using that as the net force to find acceleration. F_net = ma. Then using the acceleration to find velocity but i couldn't get the right answer. Any suggestions?

2. Nov 5, 2007

### Kurdt

Staff Emeritus
This approach seems correct, however the force in circular motion is given by,

$$F =\frac{mv^2}{r}$$

3. May 6, 2008

### crash65

Hope it was sorted.

I know this is old but hey...so are a lot of us.

Hope you sorted out the answer by now.....it would be 31 metres per second or 69 mph.

Cheers

4. May 6, 2008

### Kurdt

Staff Emeritus

5. May 6, 2008

### crash65

Thanks for that...will be more aware in future...was looking for some info and wasn't aware.

Perhaps you could guide me..... is there research papers or similar on guidelines for friction values for advisory speed guidelines??

6. May 6, 2008

### Kurdt

Staff Emeritus
Not that I'm aware of personally. You'll be best starting a thread in general physics to gain the maximum attention from other members who may be aware of such things.

7. Sep 8, 2009

### mgazi

(1) S (speed) = 3.87 x SqRt (R x df) "df" (drag factor) + the Super Elevation + the Grade (if any) Negative or Positive. Which is 1.0 + 0.14 = 1.14
(2) Sc = sqRt 15R (E+F)
(3) Baker Text nomograph