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Banked Circular Motion without friction

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

    [itex]F_C = \frac{mv^2}{r}[/itex]

    3. The attempt at a solution

    FBD.jpg

    [itex]
    N\sin\beta = \frac{mv^2}{r}
    [/itex]
    [itex]
    mg\cos\beta\sin\beta = \frac{mv^2}{r}
    [/itex]
    [itex]
    2\sin\beta\cos\beta = \frac{2v^2}{rg}
    [/itex]
    [itex]
    \sin(2\beta) = \frac{2(28)(28)}{(190)(9.8)}
    [/itex]

    I got the right answer if I didnt assume [itex]N = mg\cos\beta[/itex]

    Edit : Nevermind, careless mistake I was using different coordinate systems.
     
    Last edited: Sep 27, 2012
  2. jcsd
  3. Sep 27, 2012 #2

    PeterO

    User Avatar
    Homework Helper

    I assume you found that using [itex]
    mg\tan\beta = \frac{mv^2}{r}
    [/itex] was more fruitfull?
     
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