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Homework Help: Mechanics question - help please?

  1. May 11, 2008 #1
    [SOLVED] Mechanics question - help please?

    Hey, I've just signed up here, and not entirely sure if I'm posting in the right place. But I have a Mechanics question, which has confused me, so here goes:

    1. The problem statement, all variables and given/known data

    A bead of mass m is threaded onto a horizontal wire. When moving with speed u, the retarding force of air resistance is known to be ku^2 where k is a constant. Write down an equation of motion for the bead that describes the speed u in terms of the time t, and hence show that:

    (m/u) = (m/u0) + kt

    if u = u0 when t = 0.

    2. Relevant equations

    I guess F = ma ?

    3. The attempt at a solution

    Since the retarding force is given by ku^2 I tried letting a = (F/m) = (-ku^2)/m and then writing that u = u0 - (ktu^2)/m, because the speed should be the initial speed plus (acceleration x time) right? But when I re-arrange this equation to get something in terms of (m/u) it doesn't give me the right answer. Am I even on the right lines?
  2. jcsd
  3. May 11, 2008 #2


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    Staff Emeritus
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    Gold Member

    Welcome to PF raphile,

    This is indeed the right place. I'll give you a hint: You have correctly determined the acceleration, however what you actually have is a differential equation,

    [tex]a = \frac{du}{dt} = -\frac{ku^2}{m}[/tex]
    Last edited: May 11, 2008
  4. May 11, 2008 #3
    Thanks, I've got it now!
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