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Finding the overall uncertainty

  1. Jan 4, 2016 #1
    1. The problem statement, all variables and given/known data
    How do I find the overall uncertainty of R when R = (h2+l2)/2h

    2. Relevant equations
    uncertainty in h = ±0.57%
    uncertainty in h2=±1.14%
    uncertainty in l2=±7%

    3. The attempt at a solution
    √1.142+72+0.572
     
    Last edited: Jan 4, 2016
  2. jcsd
  3. Jan 4, 2016 #2

    HallsofIvy

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    Use the "differential"- R = (h2+l2)/2h [itex]dR= [(1- 2(h^2+ l^2))/h^2]dh+ (l/h)dl. Set dh and dl equal to the uncertainties in h and l respectively. You will need "current" values for h and l as well as for dh and dl. I do not understand you last values. Where you have "h = ±0.57%" do you mean the uncertainty in h (my "dh") rather than h itself? Also you have "h2=±1.14%" which is 2 times your h, not h squared.
     
  4. Jan 4, 2016 #3
    Yeah those are the actual uncertainties in the values
    h = ±0.57% is the % uncertainty, where h is a measurement of length in m
    To get the uncertainty in h2 you multiply the %uncertainty of h by 2 yeah?
     
  5. Jan 4, 2016 #4

    HallsofIvy

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    You are confusing me by saying "actual uncertainty" at one point and "% uncertainty" at another- those are NOT the same thing. If h= 10, say, and the "actual uncertainty" (I would say "relative error") is 0.5 then the "percentage uncertainty" is (0.5)/(10)= 0.05= 5%. If f(x)= x2 then df= 2x(dx) The "actual uncertainty in f is 2 times the value of f time the "actual uncertainty" in x. The "percent uncertainty" in f is df/f. Dividing both sides of the previous equation by f, df/f= 2x(dx)/f= 2x(dx)/x2= 2(dx/x) so the percent uncertainty in x2 is 2 times the percent uncertainty in x.

    There is an engineer's "rule of thumb" that "when quantities are added their errors add and when quantities multiply their relative errors add".
     
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