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Find coefficient of friction

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data

    The car's wheel with mass 1kg and radius 0.3m has initial speed 40rad/s.
    When braked, the force push to the center of the wheel is 10N.
    The car stops after 2s.
    Find coefficient.


    2. Relevant equations



    3. The attempt at a solution

    This is what I did
    Fc= Us.N= Us*m*g
    so Us= Fc/mg

    But why the problem gives so many information..about velocity..?
     
  2. jcsd
  3. Oct 28, 2007 #2
    you have "initial speed", find final velocity

    you must convert 40rad/s to m/s

    then from there, plug in

    your equations are wrong unless i screwed up

    i have

    [tex]\mu_{k}=\frac{1}{g}(\frac{v^{2}}{R}-\frac{F}{m})[/tex]

    i simplified it so yours may look different.

    EDIT: well i confirmed my equation by simplifying the units and all the units cancel out so seems like it's good, so i hope that helps.
     
    Last edited: Oct 29, 2007
  4. Oct 29, 2007 #3
    why they the time and final velocity, when stop?
     
  5. Oct 29, 2007 #4
    How did you derive such relation? Would you mind explaining your steps?

    @ camherokid:
    I have a different line of thought:
    Let initial angular speed be w = 40rad/s, radius of the wheel be r = 0.3m, mass of the wheel be M = 1kg, push-force be P = 10N, time be t = 2sec.

    Speed of the centre of the wheel, v = w*r = 12m/s. {Assuming, no slipping.}

    It has to stop in t = 2sec. Thus, final speed is zero.
    Assuming uniform deceleration, a = (0 - v)/t = -v/t = -6m/s^2.

    This deceleration will require an average force of magnitude, F = M*a = -M*v/t = -6N .

    Now assuming this force comes only by friction, µ*P = -F. (As friction is in opposite direction; considering P to be positive.)

    Thus, µ = M*v/(P.t) = (M*w*r)/(P*t) = 0.6

    Therefore coefficient of friction, µ = 0.6
     
  6. Oct 29, 2007 #5
    actually, it should have been. sign was backwards.

    [tex]\mu_{k}=\frac{1}{g}(\frac{F}{m}-\frac{v^{2}}{R})[/tex]

    drew a force body diagram to get Normal force, but i never plugged in numbers.

    gotta go to class, i'll check in 3-4 hrs.
     
    Last edited: Oct 29, 2007
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