Lab#6 (Propagated uncertainty in measurements) Daniel Guzman

Daniel Guzman

Lab#6 propagated uncertainty in measurements

Physics 4A.


The purpose of this particular experiment was to measure the density of two different cylinders made out of different materials, to then calculate the propagated uncertainty of the measurements made, to then compare the propagated uncertainty of the densities of the cylinders to the accepted value.

Apparatus (description)
The apparatus for this experiment was very simple due that it only consisted of a caliber and a analytical balanced. The caliber in this experiment was used to make very specif measurements of the diameter and the height of the cylinders, and the analytical balance was used to measure the mass of the cylinders. These very specific measurements were used to find what was the density of the two different cylinders.

Experimental procedure

In this particular experiment the procedure was quite simple due that it consisted of making simple measurements. The first part of this experiment was to obtain two different cylinders, one made out of aluminum and the other made out of zinc. After having obtained the two different cylinders we had to use a caliber to make specific measurements on the cylinders. one of them was the height of the cylinders and the other one was the diameter. After having obtained these measurements on the cylinders, one had to record them in a data table, and at the same time write the uncertainty that the caliber gives when one uses it measure, in this case the uncertainty was +- 0.01. After having the measurements for the diameter and height we also had to measure the mass of the cylinders; therefore, we used an analytical balance where we put each cylinder separately and obtained a measurement for the mass, which had an uncertainty of +- 0.1. Once these measurements were collected we proceeded and calculate it the total partial differential of the density for the cylinders separately, due that the cylinders are made out of different materials, so is important to find the propagated uncertainty for the cylinders separately.

Data Table Cylinders(Aluminum and Zinc)

List of calculated results

For the first set of calculation I used the values of the measurements to calculate what would be the density of the cylinder. After having calculated the density of the cylinder I took the partial derivative of the equation of density by taking the ln of both sides of the equation and then I took the derivative of it, which gave me the expression that is boxed in the calculations above.

 Once the for the total partial differential was found I proceeded and used the values that I measured, for the cylinder made out of aluminum and the cylinder made out of zinc, to solve for dp, which represents the uncertainty that exists in the density found experimentally for the cylinders

These final calculations are the calculations for the conclusion part which are the relative error between the accepted values and the experimental values, and the relative uncertainty, which represents the precision of the measurements.

Conclusions
For the aluminum cylinder the calculated value for density and the propagated uncertainty was 2.74 +- 0.04.g/cm^3, The accepted value for the density of aluminum is 2.7 g/cm^3, which lets one infer that the measurements done for the aluminum cylinder were very precise due that we obtain a value relatively close to the accepted value for the density of aluminum. On the other hand when comparing the density for the zinc cylinder I found out that the measurements made for this cylinder were not precise because the value obtained for the density of it is far from the accepted density of the zinc.

The source of error in this experiment might come from the cylinders themselves because they are probably alloids, which is a mixture of different metals and this would definitely affect the results, another source of error in this experiment specially in the final results might come from a miss calculation, which would affect the desired results.