What angle should the curve be banked at?

  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. rock.freak667

    rock.freak667 6,228
    Homework Helper

    The centripetal force should be the same as the component of the weight for a comfortable ride.
     
  4. rl.bhat

    rl.bhat 4,435
    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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