Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Propagaton of errors

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data

    the mass of a particular sample of rock retrived from Mars is m=772.2+or-0.2g. The sample is in the shape of cylinder of height h=10+or-0.1 cm and base radius r=2.5 +or-0.1cm. calculate the density of the rock sample in units of kg/m^3. You must state your result in the correct units with its associated uncertainty. The volume of a cylinder is V=pir^2h.

    2. Relevant equations

    3. The attempt at a solution

    I can get the density but I cannot get the correct uncertainty.

    The density I get is

    (772.2g/196.35cm^3)((1 kg/m^3)/10^-3g/cm^3)=3932.77 kg/m^3

    I believe the uncertainty is supposed to be +or-400 but I end up with four.

    (delta p)/(3.9g/cm^3) = .2/772.2 + .14/196.35

    delta p = .004 g/cm^3

    .004 g/cm^3 ((1kg/m^3)/(10^-3 g/cm^3) = 4 kg/m^3

    Im new to this propagation of errors stuff. Using sig figs other people in my class got either 4000 +or- 400(or +or- 100) I cant remember.
  2. jcsd
  3. Sep 8, 2007 #2


    User Avatar
    Homework Helper

    The uncertainty for your volume seems off... can you show how you got it?
  4. Sep 8, 2007 #3

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    Start with the formula for the density......Take the derivatives with respect to the variables etc.... try it and we will hepl along.
  5. Sep 9, 2007 #4
    I tried to find the uncertainty for volume again. I am probably calculating the error wrong.

    (delta v/196.35) = 2pi(.1/2.5)+(.1/10)

    delta v = 51 cm^3

    (delta p)/(3.9g/cm^3) = .2/772.2 + 51/196.35 = 1.014 g/cm^3

    1.014 g/cm^3 ((1kg/m^3)/(10^-3 g/cm^3) = 1014 kg/m^3

    this seems way to high. I was given an online manuel on how to calculate propagation of error but my calculations always seem off.

    To Dr Transport I do not believe have never seen of been taught that method.
  6. Sep 9, 2007 #5


    User Avatar
    Homework Helper

    I think this is the mistake:

    looking at the quantity without pi, call it x = r^2*h:

    (delta x/62.25) = 2(.1/2.5)+(.1/10) = 0.09

    delta x = 0.09*62.5 = 5.625

    So the error in pi*r^2*h is 3.14*deltax = 17.67

    so delta v = 17.67
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook