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Homework Help: Uncertainties calculation

  1. Jul 23, 2006 #1
    Hi guys, i am trying to work out the uncertainty of this equation

    Y = (AC-CX)/(B+X)
    and i am needed to work out the uncertainty in Y.

    values for these are:
    A=29m Uncertainty in A denoted (Sa)=3mm
    B=710mm Uncertainty in B denoted(Sb)=3mm
    C=5.85mm Uncertainty in C denoted(Sc)=0.2mm
    D=0.150mm Uncertainty in D denoted (Sd)=0.005mm
    X=18.68m Uncertainty in X denoted (Sx)=0.005mm

    using these values i used the formula:

    Sy/Y = (Sc/C)+ S[(A-x)(B+x)]/[(A-x)(B+x)]
    Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
    Sy= 0.7182971382

    i obtained an uncertainty of 0.7 it is very large hence i think i may have done something wrong in my calculations.

    to obtain S[(A-x)(B+x)]
    i did
    [S(A-x)/(a-x)] + [S(B+x)/(B+x)]
    =[(3mm+.005)/(29-18.68)] + [(3mm+.005)/(710+18.68)]

    so can anyone please check this thanks!!!

    also another simple question
    Y= (AC-CX)/(B+X)
    how do i derive for B, keeping everything else constant?
    eg if i were to derive with respect to C, whilst keeping everything else constant i would get
    : [A-X/(B+X)] .... so how do i derive with respect to B while keeping everything else constant since it is in the denomitor...

  2. jcsd
  3. Jul 23, 2006 #2


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    Science Advisor

    First question: Looks to me like your arithmetic is just wrong!
    0.2/5.85= 0.034188... and 0.1099555934/0.3723445134= 0.29530606591642170268376325203836. Their sum is about 0.329, not 0.7.

    As for the derivative of Y= (AC-CX)/(B+X) with respect to B, use the quotient formula:
    [tex]\frac{\partial Y}{\partial B}= \frac{(0)(B+X)- (AC-CX)(1)}{(B+X)^2}= \frac{CX- AC}{(B+X)^2}[/tex].
  4. Jul 23, 2006 #3
    Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
    yes you are correct the sum is 0.329
    but i had
    Sy= 0.7182971382

    which is the sum multiplyed by Y
    which is the uncertainty in Y... but i dont know if its right or not the way i went about it all.

    so is their another way of working out uncertainty?
    Last edited: Jul 23, 2006
  5. Jul 23, 2006 #4


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    Science Advisor

    Well, one thing you could do is this: calculate each of the given number plus[\b] their "uncertainty" and minus. Use those to see what is the largest and smallest values Y could have.
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