1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the uncertainty in this result?

  1. Jun 10, 2008 #1
    1. The problem statement, all variables and given/known data
    The density of the material of a rectangular block is determined by measuring the mass and linear dimensions of the block. The table shows the results obtained, together with their uncertainties.

    Mass [tex]= (25.0 \pm 0.1)g[/tex]
    Lenght [tex]= (5.00 \pm 0.01)cm[/tex]
    Breath [tex]= (2.00 \pm 0.01)cm[/tex]
    Height [tex]= (1.00 \pm 0.01)cm[/tex]

    The density is calculated to be [tex]2.50gcm^-3[/tex]
    What is the uncertainty in this result?

    2. Relevant equations
    Density = Mass / Volume
    Percentage Uncertainty = Acutal Uncertainty / True Value * 100

    3. The attempt at a solution

    Mass % Uncertainty [tex]= \frac{0.1}{25.0} \times 100 = 0.4\%[/tex]
    Lenght % Uncertainty [tex]= \frac{0.01}{5.00} \times 100 = 0.2\%[/tex]

    Breath % Uncertainty [tex]= \frac{0.01}{2.00} \times 100 = 0.5\%[/tex]

    Height % Uncertainty [tex]= \frac{0.01}{1.00} \times 100 = 1\%[/tex]

    Density % Uncertainty = [tex]\frac{Mass \% Uncertainty}{Volume \% Uncertainty} = \frac{0.4}{0.2+0.5+1} = 0.5\%[/tex]

    Absoulte Value = [tex]\frac{0.5 \times 2.50}{100} = 0.0125gcm^-3[/tex]

    Density = [tex]2.50 \pm 0.0125 gcm^-3[/tex]

    Is this right?
     
    Last edited: Jun 10, 2008
  2. jcsd
  3. Jun 11, 2008 #2

    dynamicsolo

    User Avatar
    Homework Helper

    You are fine up to here.

    Sadly, perhaps, percentages of uncertainty don't divide in this way. In products and quotients, the percentages of uncertainty always add. (This can be shown from differentiation of products or quotients to solve for what are called "relative errors".)

    The percentage of uncertainty in the density will be

    0.4% (for the mass) + [0.2% + 0.5% + 1.0%] (for the volume product) = 2.1% .

    So the density would be reported as

    2.50 gm/(cm^3) +/- 2.1% or 2.50 +/- 0.053 gm/(cm^3) .

    You can check this by looking at the density value obtained by using the highest mass in the uncertainty range divided by the smallest volume in its uncertainty range, and then the lowest mass divided by the largest volume. The agreement won't be exact because the "rules of thumb" for handling percentages of uncertainty are only approximate (the agreement is ideal only for infinitesimal changes).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is the uncertainty in this result?
Loading...