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Circular motion with friction

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m moves in a horizontal circle of radius R on a rough table. It is attached to a horizontal string fixed at the center of the circle. The speed of the particle is initially v0. After completing one full trip around the circle, the speed of the particle is v0/2.


    a) Find the energy dissipated by friction during one revolution in terms of m, v0, and R.

    b) What is the coefficient of kinetic friction?

    c) How many revolutions will the particle make before coming to rest?

    d) Suppose the experiment is repeated with one slight modification: the initial speed of the particle is doubled. How many revolutions does the particle make in this case?


    2. Relevant equations



    3. The attempt at a solution

    I need some help withthe friction part

    .5Iwo2 = .5Iw2 - Friction energy

    is the friction energy F = umg

    .5Iwo2 = .5Iw2 - umg
     

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  3. Dec 7, 2009 #2

    ideasrule

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    umg would be the force. Work done is W=Fd.
     
  4. Dec 7, 2009 #3
    part a)

    so the energy would be .5Iwo2 = 1/8Iwo2 + Wfriction... at one rotation it is half the velocity

    Wf = 3/8Iwo2

    is this the energy dissipated
     
    Last edited: Dec 7, 2009
  5. Dec 7, 2009 #4
    and for part b i use umgRQ. where Q is theta in radians as the Work of friction

    and then i would solve it for u.

    and part c i just solve for RQ

    part d i would just double initial velocity and solve for RQ again

    should i be solveing for RQ because of the distance it travels around teh circle, or should the answer be in simply Q in radians
     
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