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Metal block sliding horizontally

  1. Oct 1, 2013 #1
    1. The problem statement, all variables and given/known data
    A metal block of mass m slides on a horizontal surface that has been lubricated
    with a heavy oil so that the block suffers a viscous resistance that varies as the 3/2
    power of the speed: F(v) = -cv3/2

    If the initial speed of the block is vo at x = 0, show that the block cannot travel farther than 2mvo1/2/c


    2. Relevant equations
    F = ma = m[itex]\frac{dv}{dt}[/itex]



    3. The attempt at a solution
    So, I took

    m[itex]\frac{dv}{dt}[/itex] = -cv3/2
    I rearranged it and got

    dv/v3/2= [itex]\frac{-c}{m}[/itex]dt

    I've tried integrating this and I can't seem to end up with the right answer. I'm totally lost. Anyone have any ideas?

    EDIT: No help at all?
     
    Last edited: Oct 1, 2013
  2. jcsd
  3. Oct 1, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    You are not integrating wrt the correct variables; you need dx, not dt.

    Use the chain rule to write dv/dt = dv/dx dx/dt = dv/dx v.

    Then when you rearrange the terms you will be integrating dv/sqrt(v) = -c/m dx
    The integrals run (v0, v_final) and (0, d); if we carry the integral to v_final = 0 then the distance covered will be d_final.

    When I do this I get 2m/c sqrt(v0) = d_final, which supports the expected conclusion.
     
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