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Homework Help: Error Propagation Formulas

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    What are the uncertainty propagation formulas for:
    Area of a rectangle
    Density of a sphere
    Height of an opposite side wall calculated by tan(θ)=o/a
    Resistance


    2. Relevant equations

    Area of rectangle= side A *side B
    Density of a sphere= mass/(4/3piR^3)
    tan(θ)=opp/adj
    Resistance= R=V/I


    3. The attempt at a solution

    Rectangle I have: A=LW
    dA=dlW+dwL
    dl and dw are the relative uncertainty of L and W by instrument.

    Sphere: I have dp=(3 dm/4piR^3)+(3m/12piR^2dr)
    dm and dr are uncertaintities of mass and radius

    For heigh: do= tan(θ)da+sec2(θ)a*dtan(θ)
    da and dtan(θ) are the relative uncertainties

    For resistance: dR= 1dV/I+ VdI/1

    If these are correct would I use a sum formula like u(c)= sum of all squares? or would I separate the partial derivatives from the uncertainties and then square and sum like (dl2)W2+(dw2)L2? I'm kinda confused which formula is the general formula for uncertainty propagation.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 26, 2010
  2. jcsd
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