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Archived Rolling Motion, Pebble stuck in a Tire by Static Friction

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data

    A 1.2 g pebble is stuck in a tread of a 0.76 m diameter automobile tire, held in place by static friction that can be at most 3.6 N. The car starts from rest and gradually accelerates on a straight road. How fast is the car moving when the pebble flies out of the tire tread? I know the answer is 17 m/s however I don't know how to get it.

    2. Relevant equations

    v=(2*[itex]\pi[/itex]*R)/T
    v=ωR
    [itex]\alpha[/itex]=τ/I
    I=1/2*M*R2
    Fc=(m*v2)/2

    3. The attempt at a solution

    I tried using the centripetal force equation and rearranged for velocity, using the maximum static friction as my force. I then divided that number by 2 to get the speed in the centre of the wheel (since the speed at the top of the wheel is twice the speed of the vehicle).
     
    Last edited: Mar 4, 2013
  2. jcsd
  3. Feb 25, 2016 #2

    CWatters

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    Science Advisor
    Homework Helper

    I believe the approach suggested by the OP gives the correct answer.

    F=(mv^2)/r
    Rearrange for v...
    V=SQRT(Fr/m)
    = SQRT(3.6*0.38/0.0012)
    = 33.76m/S

    This is the Velocity of the top of the wheel. The Velocity of the car is half that..

    33.76/2=16.88m/S

    Book answer 17m/S.
     
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