Banked Circular Motion without friction

[hqjb]

Homework Statement

A roadway is designed for traffic moving at a speed of 28 m s . A curved section of the
roadway is a circular arc of 190 m radius. The roadway is banked so that a vehicle can go
around the curve with the lateral friction forces equal to zero

Homework Equations

F_C = \frac{mv^2}{r}

The Attempt at a Solution

<br /> N\sin\beta = \frac{mv^2}{r}<br />
<br /> mg\cos\beta\sin\beta = \frac{mv^2}{r}<br />
<br /> 2\sin\beta\cos\beta = \frac{2v^2}{rg}<br />
<br /> \sin(2\beta) = \frac{2(28)(28)}{(190)(9.8)} <br />

I got the right answer if I didnt assume N = mg\cos\beta

Edit : Nevermind, careless mistake I was using different coordinate systems.

 

[PeterO]

Homework Statement

A roadway is designed for traffic moving at a speed of 28 m s . A curved section of the
roadway is a circular arc of 190 m radius. The roadway is banked so that a vehicle can go
around the curve with the lateral friction forces equal to zero

Homework Equations

F_C = \frac{mv^2}{r}

The Attempt at a Solution

<br /> N\sin\beta = \frac{mv^2}{r}<br />
<br /> mg\cos\beta\sin\beta = \frac{mv^2}{r}<br />
<br /> 2\sin\beta\cos\beta = \frac{2v^2}{rg}<br />
<br /> \sin(2\beta) = \frac{2(28)(28)}{(190)(9.8)} <br />

I got the right answer if I didnt assume N = mg\cos\beta

Edit : Nevermind, careless mistake I was using different coordinate systems.

I assume you found that using <br /> mg\tan\beta = \frac{mv^2}{r}<br /> was more fruitfull?