Lab 3 Propogated Uncertainty in Measurements

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 7 September 2016 

Propagated Uncertainty in Measurements

Mission Statement:To determine the propagated error of our measured density of two different cylinders.

Theory: Every kind of calculation is in truth an approximation, and the tolerance of uncertainty depends on the application the calculation will be for. When multiple calculations are involved, then the uncertainty ripples, or propagates, through to the final result. Learning the method by which this kind of propagated uncertainty is determined is the essence of this lab.
Experimental Procedure:

 In order to determine the propagated uncertainty of our measurements, we first needed to familiarize ourselves with the calipers provided to us. Before beginning the experiment ourselves, the professor showed us a clever technique for accurately reading measurements up to the hundredths place. Then we proceeded to measure the height and diameter of two different cylinders with the aforementioned calipers, together with weighing the cylinders on a digital scale. Now equipped with these measurements, we proceeded to carry out the computations, shown below, to obtain the propagated uncertainty of the calculated density of the aluminum and tin cylinders, respectively.

Lists/Tables/Graphs of Collected Data with Explanation:

From the calculations above, I determined that the density of aluminum is 2.87 plus/minus 0.058 g/cm^3 and the density of tin to be 11.73 plus/minus 0.058 g/cm^3. The density I determined for aluminum is roughly close to the scientific value of 2.70 g/cm^3, but the density I determined for tin is considerably off of the accepted value of 7.26 g/cm^3.

Conclusion- The difference between our calculated values and the accepted value, particularly for the tin cylinder, is most likely due to errors in weighing the cylinders, since our calipers were mechanical in nature. I suspect the oddly higher-than-expected density of tin is more than anything else due to human error in calculations, although reviewing my written work above, I honestly do not know where I went off.