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Homework Help: Energy work

  1. Oct 6, 2004 #1
    hi, im having a little trouble with the last part of this problem.

    A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where i am holding it. Initially the particle is moving in a circle of radius R_0 with angular velocity w_0, but i now pull the string down through the hole until length R remains between the whole and the particle. (a) whats the particles angular velocity now? (b) assuming that I pull the string slowly that we can approximate the particles path by a circle of slowly shrinking radius, calculate the work i did pulling the string.

    i was able to get part a by using conservation of angular momentum and i got

    w= (R_0/R)^2*w_0

    for part b i know that to find the work done i need to take the integral of F.dr, but i and not really sure how i would set that up.


    thanks
     
  2. jcsd
  3. Oct 6, 2004 #2

    NateTG

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    If you know the work energy theorem, there's an easy answer.

    Otherwise:
    What is the tension in the string when the mass is at radius [tex]r_i[/tex]?
    What force do you need to pull at to pull the mass in?
     
  4. Oct 6, 2004 #3
    ok I got the tension to be
    (m*v^2)/r_0 = m*r_0*w_0^2 = F

    so the i took the intagral of (F*dr) evaluated at r_0 to r and got (1/2)*m*w_0^2(r^2 - r_0^2)

    is this right? because change in KE = work and for change in KE i get

    (1/2)*m[ (r*w)^2 - (r_0 *w_0) ^2] , which is close to the formula i was expecting to get.
     
  5. Oct 7, 2004 #4

    NateTG

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    Looks good to me.
     
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