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Finding the maximum/absolute error in calculating the density of a metal sample.

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    "You are measuring the density of a metal sample. You have determined that the mass of the sample is 63.8 grams, and your error in this result is plus or minus 0.1 g. The volume of the sample is 8.8 +/- 0.1 cm^3. What is the maximum error (in g/cm^3) in your measurement of the sample density? "

    2. Relevant equations
    density=mass/volume
    For z = x/y:
    δz/z = δx/x + δy/y


    3. The attempt at a solution
    Well, filling into the equation for δz/z and substituting this for δρ/ρ and solving for δρ:
    δρ=ρ(δm/m + δv/v)
    =(63.8g/8.8cm^3)(0.1g/63.8g + 0.1cm^3/8.8cm^3)
    =(7.25g/cm^3)(0.01293)
    =0.0937g/cm^3


    However, it says this answer is incorrect.
    Any hints on where I am going wrong?
     
  2. jcsd
  3. Sep 27, 2012 #2
    Maybe it should be done in this way:
    [tex]\rho_{max}=\frac{m+\Delta m}{V-\Delta V}\\
    \rho_{min}=\frac{m-\Delta m}{V+\Delta V}\\
    \Delta\rho=max\left(\rho-\rho_{min},\rho_{max}-\rho\right)
    [/tex]
     
    Last edited: Sep 27, 2012
  4. Sep 27, 2012 #3
    I'm not quite sure I understand that last equation..
     
  5. Sep 27, 2012 #4
    You choose larger of these two differences.
     
  6. Sep 27, 2012 #5
    ok thanks for the clarification but that still doesn't produce the correct answer. Thanks for your help though.
     
  7. Sep 29, 2012 #6
    What is the correct answer?
     
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