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Classical Dynamics: Given v(x), find F(x), x(t), and F(t).

  1. Oct 7, 2009 #1
    1. The problem statement, all variables and given/known data
    The speed of a particle of mass m varies with the distance x as v(x) = (alpha)*x-n.
    Assume v(x=0) = 0 at t = 0.
    (a) Find the force F(x) responsible.
    (b) Determine x(t) and
    (c) F(t)


    2. Relevant equations
    Likely:
    F = ma


    3. The attempt at a solution
    I obtain
    a(x) = -n(alpha)x-(n+1)
    So
    F(x) = ma(x) = -mn(alpha)x-(n+1)

    The back of book claims:
    F(x) = -mna*x-(2n+1)

    They use 'a' for the answer, I think they mean alpha, unless a IS alpha...
     
  2. jcsd
  3. Oct 7, 2009 #2

    gabbagabbahey

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    Gold Member

    Hi BlueFalcon, welcome to PF!:smile:

    Careful, acceleration is the change in velocity with respect to time, not position; you need to use the chain rule:

    [tex]\frac{d}{dt}v(x)=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}[/tex]

    P.S. In the future, problems like this should probably be posted in the introductory physics forum instead.:wink:
     
  4. Oct 7, 2009 #3
    BAH!

    I swear I tried that method and got a bunch of warrgarrbllll.

    Thanks.

    I can't believe I messed it up that bad.
     
  5. Oct 7, 2009 #4
    Although, I can't seem to find x(t). Running into the same wargarbl.
     
  6. Oct 7, 2009 #5

    gabbagabbahey

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    Hint: You have a separable ODE for x(t):

    [tex]\frac{dx}{dt}=v(x)\implies \int \frac{dx}{v(x)}=\int dt[/tex]

    (Don't forget the constant(s) of integration!:wink:)
     
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