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Banked Curve

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  1. Apr 10, 2016 #1
    1. The problem statement, all variables and given/known data
    A car is making a turn on a wet highway ramp. The coefficient of static friction between the tires and the road is 0.25. Determine the maximum speed at which the car can safely negotiate a turn of radius 200m with a banking angle of 20 degrees.
    radius= 200m
    μs=0.25
    angle(θ)=20°


    2. Relevant equations

    Fs=μs(Fn)

    Fc=mv/r
    3. The attempt at a solution
    I tried solving this by drawing an FBD. I drew my x and y axes so they could follow the incline and the normal and friction forces would run along the axes. The only force I broke down into components was Fg. I used the first formula to solve for Fs by plugging in the given coefficient of static friction and plugging in +mgcosθ for Fn. I got Fs=0.25(mucosθ). Then, I plugged that into the second formula with all other given values. I divided out my 'm' variables, and then isolated for 'v'. The answer I got was 22.14609185m/s. The correct answer is 36m/s. I don't know what I did wrong.
     
  2. jcsd
  3. Apr 10, 2016 #2

    ehild

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    Gold Member

    The second formula is wrong, check.
     
  4. Apr 10, 2016 #3
    I typed it wrong, but in solving the problem, i used mv^2/r
     
  5. Apr 10, 2016 #4

    ehild

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    Homework Helper
    Gold Member

    Without seeing your FBD and work in detail, we can not help you. The car goes along a horizontal circle, so the centripetal force is horizontal, while the friction acts along the slope. They are not equal. And friction is not the only force that keeps the car on track.
     
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