# Banked Highway Curve Question

1. Oct 13, 2007

### bikerkid

Hey, I'm really having problems with this question and I don't really know what to do. I'm hoping someone can help me. Thanks in advance.

1. The problem statement, all variables and given/known data
A highway curves to the left with radius of curvature R = 35 m. The highway's surface is banked at 19 degrees so that the cars can take this curve at higher speeds.
Consider a car of mass 907 kg whose tires have static fiction coefficient of .72 against the pavement.
The acceleration of gravity is 9.8 m/s^2.

How fast can the car take this curve without skidding to the outside of the curve? Answer in units of m/s.

2. Relevant equations
(mv^2)/r = Fn Sin(angle)
mg = Fn Cos (angle)
(v^2)/rg = Tan (angle)
Ac = g tan (angle)

2. Oct 14, 2007

### Staff: Mentor

Please show some effort and work.

Consider friction also. Ffriction = $\mu$Fn

To keep the car on the road, the weight component pointing down the curve and the friction must be equal to the inertial force of the car mv2/r.

On a bank/ramp, the weight can be resolved into normal and parallel forces with respect to the plane of the road.

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/carbank.html

3. Oct 14, 2007

### bikerkid

Alright, thanks. I already knew that stuff.

The question was killed anyway, so I don't have to do it. Thanks for your help.