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Mechanics - Velocity over Time

  1. Dec 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle is moving, through a medium in which the friction is: f = bv^2 (v is the velocity).
    In t=0 the velocity is [itex]v{0}[/itex]. There is no gravity.
    Write the velocity of the particle over time.

    2. Relevant equations
    I used: F = ma.


    3. The attempt at a solution
    -f=-m*a
    Solving the differential equation - v(t)=m/(b*t-m/v0)
    The thing is, the mass is not known in the question.
    Is there a different way of solving this?
     
  2. jcsd
  3. Dec 8, 2012 #2

    mfb

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    Just keep m as parameter, similar to b. There is no way to get rid of it.
     
  4. Dec 8, 2012 #3
    Thanks!
     
  5. Dec 8, 2012 #4
    Indeed, you don't have to get rid of the mass. But the solution is not correct; it should be:

    m[itex]\dot{v}[/itex] = - b v [itex]\Rightarrow[/itex] v(t) = v0 exp(-γ t )

    where γ = b/m
     
  6. Dec 8, 2012 #5

    mfb

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    Don't forget the square in the force.
     
  7. Dec 8, 2012 #6
    Ooops... I used linear friction! Sorry, the velocity will be:

    v = m v0 / (b v0 t + m)
     
  8. Dec 8, 2012 #7
    Which is what I wrote :)
     
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