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Radius from Radial Acceleration

  1. Nov 6, 2006 #1
    An unbanked circular highway curve on level ground make a turn of 90 degree. The highway carries traffic at 60 mph, and the centripetal force on a vehicle is not to exceed 1/10 of its weight. What is the minimum length of the curve in miles?

    I am working towards the arc contained within the angle theta which is 90 degrees. I have easily determined that of course, that arc is 25% of the circumference. I am trying then to find the radius. I have worked backwards here, fiddling with Ar=V^2/R as well as MA = mv^2/r. I am stuck though. Not really looking for the answer, just a shove in the right direction as that I would REALLY like to get this one on my own. I just dont have the physics brain.
  2. jcsd
  3. Nov 6, 2006 #2
    Youre on the right track. Fc < MG/10. R must be greater than something
  4. Nov 6, 2006 #3
    With Fc being the centripetal force = Mass(Gravity)/10? Thats assuming a mass then, since I don't know it, right?
  5. Nov 6, 2006 #4
    Right, but it will cancel out as you suspect
  6. Nov 6, 2006 #5
    Because of the force of friction.. I seem to be getting more lost than I was now.
  7. Nov 6, 2006 #6
    They ask for centripetal force, which is a sum of forces. You don't need to split it up any further. Like I said, mv^2/r < mg/10. Note the mass on both sides. No arc length, no friction, but make sure to convert to SI
  8. Nov 6, 2006 #7
    Ah. Told you I have no capacity for physics. Or sleep these days.
  9. Nov 6, 2006 #8
    I figure a curve (arc) length of no less than 7.36 miles based on my work. Wow. There is no way that is right. Thats a heckuva curve. (the problem calls for the old british system. I would rather work SI, trust me.)
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