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Formula to calculate the uncertainty in the density

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data
    A radius of a sphere is measured to be (6.45 ± 0.27) cm, and the mass is measured to be (1.78 ± 0.09) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.


    2. Relevant equations
    Use the following formula to calculate the uncertainty in the density:
    Δρ/ρ = Δm/m + 3Δr/r.)


    3. The attempt at a solution
    I already found the density: 1583.62 kg/m3
    I just want to know how to get the uncertainty. I don't know how to use the formula given. i always get a really low number with it.
     
    Last edited by a moderator: Mar 7, 2013
  2. jcsd
  3. Feb 14, 2010 #2

    cepheid

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    Re: Uncertainty

    Welcome to PF!

    The uncertainties are the ranges by which the measured quantities can vary, and these ranges are indicated using the symbol 'Delta.' Hence:

    Δr = 0.27 cm

    Δm = 0.09 kg

    and of course, the measured values are:

    r = 6.45 cm

    m = 1.78 kg
     
  4. Feb 14, 2010 #3
    Re: Uncertainty

    This is what i did after converting to meters:
    (0.09/1.78)+(3*.0027/.0645)
     
    Last edited: Feb 14, 2010
  5. Feb 14, 2010 #4
    Re: Uncertainty

    0.17614 = Δρ/ρ so you don't need to divide by anything.
    To find the actual uncertainty in p you multiply 0.17614 by the density you have calculated.
    .
     
  6. Feb 14, 2010 #5
    Re: Uncertainty

    ok, thank you.
     
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