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Uncertainty Question

  1. Jul 8, 2010 #1

    Ush

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

    this isn't really a word problem, it's part of a series of calculations from a physics lab
    in this lab,
    Ug = energy at initial position
    Ug -> Ekrot + Ek at final position

    I need to calculate
    1. Ekrot
    2. Moment of Inertia
    3. angular velocity


    2. Relevant equations

    Ug = mgh
    Ekrot = ½Iѡ²
    Ek = ½mv²

    ѡ = v/r

    v = 2h/t (in this case)

    m = 0.100m ± 0.0005
    g = 9.8m/s²
    h = 0.800m ± 0.0005
    v = 0.21m/s ±0.01
    r = 0.004m ± 0.002
    t = 7.66s ± 0.08

    3. The attempt at a solution

    mgh = Ekrot + ½mv²
    Ekrot = mgh - ½mv²

    Δmgh = |dy/dm mgh| + |dy/dh mgh|
    = |dy/dm gh| + |dy/dh mg|
    = |dy = ghΔm| + |dy = mgΔh|

    relative error = Δmgh / mgh

    = |ghΔm / mgh| + |mgΔh / mgh|
    = |Δm/m| + |Δm/h|

    similarly, the relative uncertainty of ½mv² is..

    Δ½mv²/½mv² = |Δm/m| + |2Δv/v|


    so.... now what?
    We're not allowed to add relative uncertainties, i really don't know what to do here
    We can add absolute uncertainty but I have no knowledge on how to calculate absolute uncertainty.

    also, the angular velocity, ѡ, = v/r. There is an uncertainty on v and an uncertainty on r. so how do I calculate moment of inertia (I) after I have the uncertainty of Ekrot?? The uncertainties of ѡ and r weren't used when when calculating uncertainty of Ekrot (unless my steps above are way off.. which i doubt)

    I'm very confused, any help would be appreciated
    thank you
    ~Ush
     
    Last edited: Jul 8, 2010
  2. jcsd
  3. Jul 8, 2010 #2
    As far as I know, relative uncertainties can't be added. I normally calculate using absolute ones, in a way so that I calculate the min and max values, and use the average.

    For example, say t = 10+-0.1 secs and s = 50+-1meters, simple linear motion.

    v(min) = 49m / 10.1 secs = 4.85
    v(max) = 51m / 9.9secs = 5.15

    So then I would say that v = 5m/s +- 0.15m/s.
    Then follow the same routine to calculate other things, perhaps I=mv, according to this.
     
  4. Jul 8, 2010 #3

    Ush

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    1) You cannot calculate max / min in this because some of the measurements were taken only once and some were taken as an average.
    2) moment of inertia ≠ inertia

    someone please help =[ I need to send the lab measurements in soon
     
  5. Jul 8, 2010 #4

    Ush

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    anyone, please? =[
     
  6. Jul 8, 2010 #5

    Ush

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    NVM FOLKS, I found out how to do this! =]
    goodday
     
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