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Problem with Friction dependent on velocity, mostly a math problem.

  1. Jan 28, 2012 #1
    Hello, first time here for me, I hope I posted in the right subforum.
    I have a task at hand, just started a new physics course, but sadly I am far from deft with mathematics, and my physics book is in a different language and uses different notation than I am used to. The part I am having trouble with is the following:

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


    We have a block, with the starting velocity 5m/s.
    The friction from the block is given as a = -μ|v|g
    Where μ = 0.1 and g = 9.8 m/s^2

    Find v(t)


    2. Relevant equations
    v(t) = v(0)+at

    a = dv/dt = (d/dt)(dx/dt) =(d2x)/dt2


    3. The attempt at a solution

    As it stands now, I I realize I should integrate a in order to obtain v(t), but I am horrible at math, and do not know where to start, for some reason I keep ending up with an expression without v at all, but that does not help things either. If someone could show me the first steps in this that would be great. I've written a python program to solve it numerically as well, though I can not check if it is working, because I am too inept to get my analytical solution.

    Would something like this be a step in the right direction?
    a = -0.98|v|
    v(0) = 5 m/s
    a(0) = 0

    dv/dt = -0.98*v

    dv/dt2 = -0.98*v*dt

    (dv/dt2)1/v = -0.98dt

    And then integrate from here? Could someone show me an example? Doesn't need to have any of my numbers, so long as I can learn some of what I need from it.

    If anyone could provide any help, that would be greatly appreciated!
     
  2. jcsd
  3. Jan 28, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hello Simen! Welcome to PF! :wink:
    (you left out a µ)

    Now you "separate the variables" …

    dv/v = -0.98µdt …

    carry on from there :smile:
     
  4. Jan 29, 2012 #3
    Thanks for the welcome:)

    I actually didn't forget the μ, since μ = 0.1 and it was to be multiplied with g = 9.8 I just multiplied them before I started integrating.

    Anyways, does this look right?
    dv/dt = -0.98v

    dv/v = -0.98dt

    Integrate:

    ln(v)-ln(v0)=-0.98(t-t0)

    Clean up a little:
    v/v0=e-0.98(t-t0)

    v = v0e-0.98(t-t0)

    Then putting in t0 = 0 and v0 = 5 and getting
    v(t) = 5e-0.98t

    Does that look about right?
     
  5. Jan 29, 2012 #4

    tiny-tim

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    (nice formatting, btw! :biggrin:)

    Excellent! :smile:

    (btw, always best to check by mentally putting the solution back into the original differential equation. to see if it comes out right … which it does! :wink:)
     
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