Calculating Density and the Error in Density Measurement

1. Ana Leyva and Christian Valencia
3/6/17
2. For the first part of this lab we were trying to calculate the density of two metal cylinders. In my case I had to find the density of an iron and aluminum. After we found the density of both of those cylinders we calculated the propagated error in both of the density measurements.
3. The first thing that we did for this lab was to measure the diameter, height ,radius,and mass of the two cylinders. Once we had these measurements we calculated the density by dividing the mass from  the volume. Then, we still had to calculate the propagated uncertainty of these density measurement.

                                                                     Caliber

 4. This lab had a very simple procedure. First, we calculated the diameter and height of the cylinder using a caliber. We used a caliber because it allowed us to find the diameter and height to two decimal places.

 Next, we calculated the mass of the cylinder using a scale that gave us the mass to first decimal place. After that, we used the density formula to calculate the density of the two metal cylinders. Once we calculated the density we were able to calculate the uncertainty in the density measurements.

 We did this by getting the density formula and multiplying everything by the natural log. We then took the derivative of everything and got dp/p. We then squared and took the square root of the other side. When we got the answer of this we multiplied it by the density to get the uncertainty of measurements. This gives us how off our density might be off by.

8. In conclusion my results weren't too far off from the actual density. For my iron cylinder I got a density of 7.27 +- 0.12 g/cm^3 with the actual density being 7.87 g/cm^3. For the aluminum cylinder I got a calculated density of 2.64 +- 0.049 g/cm^3 with the actual density being 2.70 g/cm^3. The difference in these measurements might be due to us not having pure iron and aluminum cylinder. These cylinders also have small amounts of other measurements mixed into them. This might be one of reasons why our calculated densities are different than the actual densities. Another reason for these differences might be an error in measurement of calculations.