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Circular Motion with static friction

  1. Oct 22, 2011 #1
    1. The problem statement, all variables and given/known data
    In Formula 1 race, the cars approach curves
    from the outside, cut through to the inside, and
    then drift again to the outside (red path AA’ in the
    figure). However, the blue path (BB’) in the figure
    is shorter. Then why do not the drivers follow the
    shortest path? Give answer to this question by
    proving that tred (time to travel red path) is shorter
    than tblue (time to travel blue path). Only given
    values are RA = 32 m and RB = 10 m, and static
    friction coefficient of the road is
    μs =1.2. Assume
    cars make motion with constant speed throughout
    the path.
    Important: The speeds of the cars do not change
    due to static or kinetic frictions. However, only
    static friction acts to the car as a centripetal force when the car makes a circular motion.
    Therefore, first find maximum possible speed of a car while making a circular motion.


    2. Relevant equations
    m.g.μs=m.V2/r
    T= 2∏r/V

    3. The attempt at a solution
    I tried m.g.μs=m.V2/r equation and found V max values for both cars (19,3 for the car on the red path and 10.8 for the blue path)
    and then for T values i used equation 2∏r/V and found T for blue path is shorter. but in the question it wants me to prove that tred is shorter :/
    i attached the picture of question.
    where am i wrong? thanks for helpp!!
     

    Attached Files:

  2. jcsd
  3. Oct 22, 2011 #2

    Delphi51

    User Avatar
    Homework Helper

    This is a very interesting question, hannam. It is a treat to work on it!
    I get your 19.3 and 10.8 (actually I have 19.4, maybe because I use g=9.81). But I conclude the opposite - the red path is quicker. During my calculation I first made a huge mistake, which maybe is why your calc didn't work out. I took the distance to be πr in both cases, but if you look closely at the blue path, the distance is πr PLUS TWO STRAIGHT SECTIONS. Yes, πr not 2πr because its only a half circle.
     
  4. Oct 23, 2011 #3
    i didnt see the straight lines and of course its half circle so it should be πr :) yess i found it thank you so much :smile:
     
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