In this lab we show how to calculate propagated error for each of our measurements. We will then use these measurements to calculate the density of these cylinders.
Here we have a set of calipers we used to take measurements of height and diameter in order to calculate or volume and then our density using the mass of the cylinders and the
density formula where density = mass/ volume
Above is recorded measurements of the cylinders and the calculated density of each cylinder.
In the lower portion of the picture you can see we used partial derivatives
to calculate the error in each of our measurements
After we derived a formula for calculating the uncertainty of each measurement, we plugged in our recorded values and got an uncertainty for the density of each of the cylinders
Conclusion:
The propagated error for our results were well within an acceptable range considering that our scale and calipers had an error of ± 0.1. For this experiment, it was well within the accepted values.
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