Finding Uncertainty in Calculating Density p

In summary, the conversation discusses how to calculate the density and its uncertainty, given the mass and diameter of an object. The equations \rho=MV and p= \frac{6M}{\Pi{D}^3} are mentioned, as well as the Kline and McClintock method for uncertainty analysis. The conversation also includes a discussion on measuring device resolution and how it relates to uncertainty calculations.
  • #1
Paymemoney
175
0

Homework Statement


Calculate the density p and its uncertainty [tex]\Delta[/tex]p showing all working

Mass M (kg)
0.0163

[tex]\Delta{M}[/tex] (kg)
?

Diameter D (m)
0.014

[tex]\Delta{D}[/tex] (m)
?

Homework Equations


[tex]\rho=MV[/tex]
[tex]p= \frac{6M}{\Pi{D}^3}[/tex]
[tex]Z=\frac{A^2B}{3C^{0.5}}[/tex]
[tex]\frac{\Delta{Z}}{Z}=\frac{2\Delta{A}}{A}+\frac{\Delta{B}}{B}+(1/2)\frac{\Delta{C}}{C}[/tex]


The Attempt at a Solution


I have tried to use [tex]p= \frac{6M}{\Pi{D}^3}[/tex] but i don't think this is the equation to get the answer.
To find [tex]\Delta{p}[/tex], I don't understand how i can find [tex]\Delta{p}[/tex] if i do not have [tex]\Delta{m}[/tex] and [tex]\Delta{D}[/tex](which i don't understand how to get) from the equation:

[tex]\frac{\Delta{p}}{p}=\frac{\Delta{m}}{m}+\frac{\Delta{D}}{D}[/tex]

Hope someone can help me
P.S Paymemoney
 
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  • #2
You are indeed in a pickle. I've never seen an uncertainty analysis like this.

Do you know the resolution of the measuring devices? The resolution is the "smallest marking
" on your measuring device. For example: Most rulers have 1/16th of an inch as the smallest mark, therefore the resolution would be 1/16th of an inch.

Once you know that, you should be able to preform a uncertainty analysis using the Kline and McClintock method.

An example can be found http://lyle.smu.edu/me/2142/uncert/uncert.htm"

I feel like this will not answer your question because I've never seen a uncertainty method like this.

Taking a compete stab in the dark, and making quite a few assumptions.

I assume that since kg is measured to .0103, that these are all significant digits and that the resolution is .0001 kg. Therefore, the zeroth-order uncertainty is .0001/2 kg = .00005kg.

Similarly for the diameter. .014, all significant. The uncertainty1 is .001 m. The Zeroth-Order uncertainty is .001m/2=.0005m

See Attachment
Uncert.jpg
 
Last edited by a moderator:

1. How is density calculated?

Density is calculated by dividing the mass of an object by its volume. The formula for density is: Density = Mass/Volume.

2. What are the units for density?

The units for density can vary depending on the units used for mass and volume. However, the standard unit for density is grams per cubic centimeter (g/cm^3) for solids and liquids, and grams per liter (g/L) for gases.

3. How do you find uncertainty in calculating density?

To find uncertainty in calculating density, you need to consider the uncertainties in both the mass and volume measurements. The uncertainty in mass can be determined by the precision of the measuring instrument used, while the uncertainty in volume can be determined by the precision of the length, width, and height measurements. These uncertainties can then be used to calculate the overall uncertainty in density using the formula for propagation of uncertainties.

4. Why is it important to consider uncertainty in density calculations?

Considering uncertainty in density calculations is important because all measurements have some level of uncertainty, and this uncertainty can affect the accuracy and reliability of the calculated density. By accounting for uncertainty, you can have a better understanding of the precision and accuracy of your results.

5. Can uncertainty affect the results of an experiment involving density?

Yes, uncertainty can affect the results of an experiment involving density. The calculated density value may be within the expected range, but the uncertainty can indicate that the results are not precise enough to be considered accurate. In some cases, uncertainty can also reveal errors in the experimental setup or procedures, leading to inaccurate results.

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