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Finding the uncertainty

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    M = (a-b)/2 + a

    a = 15
    b=5

    What is the uncertainty in M if the uncertainty in a and b is ±0.7?


    2. Relevant equations

    for c = a + b
    Error in c =√[(error in a)^2 + (error in b)^2]

    3. The attempt at a solution

    Error in M = √[0.7^2 * 3] = 1.2124

    The problem I am having is that we learn that the above formula can only work when the errors are independent of one another. the error in a is obviously not independent of the error in a. so i think i'm wrong.

    What do you think?

    Thank you.
     
  2. jcsd
  3. Feb 5, 2012 #2

    rock.freak667

    User Avatar
    Homework Helper

    If I remember correctly, the errors work like this:

    s= a+b ⇒ Δs=Δa + Δb

    s= a-b ⇒ Δs= Δa + Δb

    s=ab ⇒ Δs/s = Δa/a + Δb/b

    So you can apply the first two as needed.
     
  4. Feb 5, 2012 #3
    yes. but that only works when the uncertainties in a and b are independent. however in my equation for M, a appears twice. since the error of a is not independent of a, how do i go about finding the uncertainty?

    thanks.
     
  5. Mar 15, 2012 #4
    Why not just simplify your problem

    (a-b)/2+a

    into

    (3a-b)/2

    and then use the rules for the error of 3a+b. You don't need to worry about the independency of error a to error a.
    This way I get

    (3 Δa + Δb)/2 = 1.4

    Or using the other rule [ √(Δa2 + Δb2) ]

    ( √(9*Δa2 + Δb2) ) / 2 ≈ 1.1068
     
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