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What angle should the curve be banked at?

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    A 162kg car rounds a curve with a radius of 267 m at 43 m/s. The acceleration of gravity is 9.8 m/s2

    a. (already solved) - What force must the road exert on the road to keep the car on the curve.

    1121.864 Newtons

    b. - At what angle must the curve be banked to give a passenger the most comfortable ride?

    2. Relevant equations

    Centripetal force = mass x velocity2/radius
    Centripetal acceleration = velocity2/radius

    3. The attempt at a solution

    I have no attempt. I do not understand what part "b" of the problem is asking or how to solve for it.

    I don't even really want a solution, I just need someone to explain to me how to solve what angle the curve should be banked at, and I'll solve it myself.
  2. jcsd
  3. Jan 21, 2010 #2


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    Homework Helper

    The centripetal force should be the same as the component of the weight for a comfortable ride.
  4. Jan 21, 2010 #3


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    Homework Helper

    If R is the normal reaction of the road on the car, for comfortable driving, R*cosθ must balance the weight of the car mg, and R*sinθ must provide necessary centripetal force m*v^2/r. Using these hints solve for θ.
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