# Homework Help: Banked road, find radius

1. Feb 26, 2013

### x86

1. The problem statement, all variables and given/known data
you want to design a curve with a radius of curvature of 350 m, so a car can turn at a velocity of 15 m/s without relying on friction. Find the angle at which the road must be banked.

2. Relevant equations
I've derived this equation via free body diagram, x component is gravity pushing the car into the curvature

Fn sinx = mv^2/r
Fn cosx = mg

tanx = v^2 / (gr) where r = radius, g = gravity, v = velocity

I've used it before so I know its correct.

3. The attempt at a solution

tanx = 15^2 m^2/s^2 / (9.8 m/s^2 * 350 m)

x = 3.75 degrees.

The book says this answer is incorrect, and I'm not sure where I went wrong. (The book got around 30 degrees)

2. Feb 27, 2013

### ehild

Youe solution is correct, but have you copied the data correctly?

350 m for the radius is a bit too great. Was not it 35 m instead?

ehild

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