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Uncertainty power rule

  1. Sep 23, 2012 #1
    1. The problem statement, all variables and given/known data

    D= A +/-ΔA
    D= 5.160 +/- 0.01 cm

    D^2= 26.6 +/- 0.1 cm^2

    2. Relevant equations

    for the power rule uncertainty
    :
    A ((ΔA/A) + (ΔA/A) )
    So then its (5.160)( (0.01/5.16)(2)) = 0.004

    3. The attempt at a solution
    im getting 0.004 as the absolute uncertainty but the uncertainty calculator i found online gives me 0.1 .
    is my formula wrong?
     
  2. jcsd
  3. Sep 23, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    For the uncertainty as a result of a power in general, let Q = xn and δx be the uncertainty in x. Then
    $$\frac{\delta Q}{|Q|} = |n| \frac{\delta x}{|x|}$$
    In your case the power is n = 2 and x is a positive value, so that δQ becomes:
    $$\delta Q = 2 x^2 \frac{\delta x}{x} = 2 x \delta x$$
    Your formula A ((ΔA/A) + (ΔA/A) ) should have been A2 ((ΔA/A) + (ΔA/A) ).
     
  4. Sep 23, 2012 #3
    oh ok. so that is what i did wrong. I got it now. THANK YOU SO MUCH.!!
     
  5. Sep 23, 2012 #4
    To make this problem simple, see D² as D * D.

    Well, the rule for finding the uncertainty in multiplication is Δw = √((yΔx)² + (xΔy)²), coming from w = xy. It's the simpler similar version of the formula other user uses.

    Now, you try to use that formula.
     
  6. Sep 23, 2012 #5
    using this equation, gives me 0.0729, whereas the previous one i used gives me 0.1032.
    so, i can conclude that Δw = √((yΔx)² + (xΔy)²) formula gives me more precise uncertainty?
     
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