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Advanced Mechanics Problem

  1. Sep 8, 2015 #1

    mch

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    I'm new to this site, so please bear with me.

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

    A particle of mass m has speed v(x) = α/√x. Calculate the force F(x) responsible. Then, calculate the displacement x(t) of the particle.

    2. Relevant equations

    The equations that I believe we are supposed to use are f=ma and f=m*dv/dt

    3. The attempt at a solution

    Since F= m*dv/dt, i tried this:

    F = m*dv/dx*dx/dt = mv*dv/dx = -mvα/(2(x)^(3/2))

    And that's as far as I could get for the first problem. However, this seems off because the force is in terms of two variables, right? V and x?
     
  2. jcsd
  3. Sep 8, 2015 #2

    Orodruin

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    You already know v as a function of x so it is really only one variable ...
     
  4. Sep 8, 2015 #3

    vela

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    You're given an expression for v in terms of x...
     
  5. Sep 8, 2015 #4

    mch

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    Oh okay great! So F(x) = -mα^2/(2x^2). Thank you! How silly of me.

    So now I need to find x(t). Do i say that F = -mα^2/(2x^2) = mx'' and solve the second order differential equation? My initial conditions are that v(x=0) = 0 and x(t = 0)=0.
     
  6. Sep 8, 2015 #5

    Orodruin

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    Those initial conditions are incompatible with v(x) = α/√x.
     
  7. Sep 8, 2015 #6

    Orodruin

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    Also, you do not need to use the force equation, you already know that dx/dt = v(x) so you can just integrate this.
     
  8. Sep 8, 2015 #7

    mch

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    Thank you. I figured this out and I believe I got all the right answers.

    Thanks a lot for your help!
     
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