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

  • #1
nerdy_hottie
19
0

Homework Statement



"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? "

Homework Equations


density=mass/volume
For z = x/y:
δz/z = δx/x + δy/y


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?
 

Answers and Replies

  • #2
szynkasz
115
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:
  • #3
nerdy_hottie
19
0
I'm not quite sure I understand that last equation..
 
  • #4
szynkasz
115
2
You choose larger of these two differences.
 
  • #5
nerdy_hottie
19
0
ok thanks for the clarification but that still doesn't produce the correct answer. Thanks for your help though.
 
  • #6
szynkasz
115
2
What is the correct answer?
 

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