Conceptual question

  1. An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the necessary force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. Show that for a given speed v and a radius of r , the curve must be banked at the angle (theta) such that tan(theta)=v^2/r*g
  2. jcsd
  3. What have you tried? think about what tan(theta) is in terms of sine and cosine and what sine and cosine would represent in this case.
  4. this is what i was thinking...

    Fn sin(theta) = mv^2/r
    (mg/cos(theta))sin(theta) = mg tan(theta) = mv^2/r
    tan theta = v^2/(rg)

    does that look right?
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