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Homework Help: Banked Curve: Finding the normal force with friction

  1. Mar 17, 2010 #1
    This is a five part question, of which I have completed 2 parts, which I will explain below. This is a level 1 physics problem concerning centripetal motion on banked curves and the forces that apply to objects in these scenarios.


    PROBLEM:

    A car travels at a speed of 27m/s around a curve with a radius of 43m (keep in mind that acceleration due to gravity is 9.8m/s2

    What is the net centripetal force needed to keep the car from skidding sideways?
    Answer in units of N.


    38,993.02326N
    My solution to part one ----> Correct


    Were there no friction between the car's tires and the road, what centripetal force could be provided just by the banking of the road?
    Answer in units of N.

    15,782.67791N My solution to part two ------> Correct


    Now suppose the friction force is sufficient to keep the car from skidding. Calculate the magnitude of the normal force (Fn) exerted on the car by the road's surface. Hint: Check the correctness of your answer to the first part before proceeding with this and the following questions.

    Solution to Part three -------> Unknown

    Calculate the magnitude of the friction force.
    Answer in units of N.

    Solution to Part four ---------> Unknown



    Calculate the lowest possible value of the static friction coefficient mus that would prevent the car from skidding.

    Solution to Part five ---------> Unknown


    NOW, here is where I am stuck. I am fairly sure that parts 3-5 deal with the components of the Normal Force and the Force of Static Friction but I keep getting lost with my equations (somehow I end up with far too many sin-cos-tan arrangments with Fn, etc, divided by one another).

    SO,

    Here is my data so far:

    Fc (centripetal force) needed to keep car from skidding sideways: 38,993.02326N
    Fc provided by just the banking of road (without friction): 15,782.67791N
    Magnitude of Normal Force: Unknown
    Magnitude of Ff (friction force): Unknown
    Static friction coefficient mus: Uknown
    Mass of car: 2300kg
    Radius: 43m
    Ac (centripetal acceleration): 16.95348837m/s2
    Velocity: 27m/s
    Angle of Incline: 35 degrees

    Help would be so greatly appreciated! Sorry to inconvenience anyone, I know the problem is quite extensive! Thank you very much!
     
    Last edited: Mar 17, 2010
  2. jcsd
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