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Physics lab on calculation of copper density using different equipment

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In this experiment I calculated the density of copper, using my knowledge of the propagation of errors I was able to arrive on a fairly accurate answer. The primary objective of this experiment was to use our prior knowledge of uncertainties to come to the most accurate conclusion to the density of the metal in the given wire.

My research question was to estimate the density of the metal in the particular wire.

I was given a small piece of copper wire, string, a micrometer screw gauge, a ruler, a weighing balance. The theory behind this was that, using the given instruments we could calculate the diameter, weight and length of the wire. This in turn would give me the density.

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Next I calculated the mass of the wire with the help of a digital weighing balance. Firstly I “reset” the balance, then I placed the wire inside and shut the glass protector. This helps to give us more accurate readings because it curbs the influence of air on the balance. I then took note of the reading and repeated this four times. Then I took the average of the readings to get the true value of the weight (in grams). The error in this case is equal to the least count of the instrument (as it is electronic). Thus the error in this case is equal to +/- 0.001 grams.

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Assuming that the wire was a cylinder, I calculated the volume using the formulae πr2h. The height here is the length. Substituting the respective values I got the volume as 0.00577 cm3. Next I used the formula Density = Mass/Volume. Again by substituting the values I got the density as 9.61 g/cm3.

Now for the uncertainties. To get the uncertainties of density, I first calculated the percentage error of the diameter, height and mass. The percent error of diameter is the uncertainty of d by the diameter, multiplied by 100. Similarly I calculated the percentage errors the height and mass as 0.66% and 0.18%, respectively. The percent error of diameter is 5.05%.

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