11 March 2015: Propagated Uncertainty

Lab 4: Propagated Uncertainty

Purpose: The purpose of this lab is to understand how to mathematically solve for the propagated uncertainty of several masses. Then use this knowledge in order to calculate three masses of different densities and find the uncertainties of this density.

Part 1: We took three metal cylinders that are made of copper, aluminum, and steel.We then used a scale and found the mass of each object and used calipers which helped us to find the dimensions of each object which we would then use to solve for the density of each of the cylinders.

The picture above shows the materials we used, the three masses are steel,copper, and aluminum which are on the bottom left. The scale we used to find the masses is also at the bottom left. And the caliper is the measuring instrument also on the bottom left in the picture. All of our data was recorded and the next steps taken was determining the densities which we found by using the volume of a cylinder (pi*d^2h/4). 

This is how we solved for the densities of each of the cylinders. We can then begin to find the propagated uncertainty by then differentiating the diameter, height, and mass, we were able to add up those uncertainties to figure out the exact propagated uncertainty.

These calculated values will now replace the original uncertainties of .1g,.01cm, and .01cm.

aluminum: 2.61g/cm^3 +/- .03

copper: 8.73g/cm^3 +/- .12

steel: 7.66g/cm^3 +/- .11

Part 2: The second part of the lab was found by choosing a tension diagram made by the professor in class. Where we first found the able of measurement of tensions and then had to solve for the mass of the equation. 

This is the work above on how to solve for the hanging mass by setting up vectors directions for the tensions. I solved for the unknown ganging mass by solving for the mass in both the y and x directions of vectors. 

Final Thoughts: The main purpose of this lab was for us to practice our free body diagrams for part two and also being able to solve for an unknown mass given two tensions and a hanging mass. We learned in part one that most things have propagated uncertainty which we now know how to solve using calculus.