# Circular Curve of a Highway problem

## Homework Statement

A circular curve of highway is designed for traffic moving at 95 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 110 m, what is the correct angle of banking of the road?

## Homework Equations

F_y = N sin(theta) = (mv^2)/r
F_x = N cos(theta) = mg

## The Attempt at a Solution

I assumed that if N = mg then I could cancel out m from either equation since I don't know it initially.
Then I would be left with:
sin(theta) = ((mv^2)/r)/N
cos(theta) = (mg)/N

I used my sin equation. With v = 26.38 m/s and r = 110 m and g = 9.8 m/s^2
I ended up with: sin(theta) = .64589 which is the coefficient of friction.
Doing the inverse sin of that equation, I got an angle of 40.23 degrees.
It was incorrect. What am I doing wrong?

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tiny-tim
Homework Helper
Hi mossfan563! … sin(theta) = ((mv^2)/r)/N
cos(theta) = (mg)/N

I used my sin equation. With v = 26.38 m/s and r = 110 m and g = 9.8 m/s^2
I ended up with: sin(theta) = .64589 which is the coefficient of friction.
Doing the inverse sin of that equation, I got an angle of 40.23 degrees.
It was incorrect. What am I doing wrong?
sin(theta) ? friction?? and what happened to g?

Hint: tan(theta) = … ? There is no friction.

tiny-tim
Homework Helper
There is no friction.
i know!! you mentioned it!

try the tan(theta) thing i know!! you mentioned it!

try the tan(theta) thing Sorry I thought LowlyPion replied to my question. I got an email with his response asking if there was friction or not.

Thanks for the hint! It worked!

LowlyPion
Homework Helper
Sorry I thought LowlyPion replied to my question. I got an email with his response asking if there was friction or not.

Thanks for the hint! It worked!
Sorry. I withdrew my post when I saw someone else was helping you already. Too many cooks and all that. You found the Cosθ term ... so carry on.