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Finding Uncertainties

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Calculate the density p and its uncertainty [tex]\Delta[/tex]p showing all working

    Mass M (kg)
    0.0163

    [tex]\Delta{M}[/tex] (kg)
    ?

    Diameter D (m)
    0.014

    [tex]\Delta{D}[/tex] (m)
    ?

    2. Relevant equations
    [tex]\rho=MV[/tex]
    [tex]p= \frac{6M}{\Pi{D}^3}[/tex]
    [tex]Z=\frac{A^2B}{3C^{0.5}}[/tex]
    [tex]\frac{\Delta{Z}}{Z}=\frac{2\Delta{A}}{A}+\frac{\Delta{B}}{B}+(1/2)\frac{\Delta{C}}{C}[/tex]


    3. The attempt at a solution
    I have tried to use [tex]p= \frac{6M}{\Pi{D}^3}[/tex] but i don't think this is the equation to get the answer.
    To find [tex]\Delta{p}[/tex], I don't understand how i can find [tex]\Delta{p}[/tex] if i do not have [tex]\Delta{m}[/tex] and [tex]\Delta{D}[/tex](which i don't understand how to get) from the equation:

    [tex]\frac{\Delta{p}}{p}=\frac{\Delta{m}}{m}+\frac{\Delta{D}}{D}[/tex]

    Hope someone can help me
    P.S Paymemoney
     
  2. jcsd
  3. Mar 2, 2010 #2
    You are indeed in a pickle. I've never seen an uncertainty analysis like this.

    Do you know the resolution of the measuring devices? The resolution is the "smallest marking
    " on your measuring device. For example: Most rulers have 1/16th of an inch as the smallest mark, therefore the resolution would be 1/16th of an inch.

    Once you know that, you should be able to preform a uncertainty analysis using the Kline and McClintock method.

    An example can be found http://lyle.smu.edu/me/2142/uncert/uncert.htm"

    I feel like this will not answer your question because I've never seen a uncertainty method like this.

    Taking a compete stab in the dark, and making quite a few assumptions.

    I assume that since kg is measured to .0103, that these are all significant digits and that the resolution is .0001 kg. Therefore, the zeroth-order uncertainty is .0001/2 kg = .00005kg.

    Similarly for the diameter. .014, all significant. The uncertainty1 is .001 m. The Zeroth-Order uncertainty is .001m/2=.0005m

    See Attachment
    Uncert.jpg
     
    Last edited by a moderator: Apr 24, 2017
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