The purpose of this lab was to practice finding the uncertainty that that measuring equipment could cause us during an experiment. This done with a simple experiment in finding the density of three cylinders for the first part, and then with finding the mass of an unknown mass for the second part.
Experiment
For the first part of we have to find the density of each cylinder by measuring the height and diameter of each cylinder, then measuring the mass with an electronic balance.
After the measurements for each cylinder was recorded we then found the density for each of the cylinder with the equation d = (4 m) / (π h d^2).
Once we have found the density of each cylinder we then take the partial derivative of density function in respect to each variable that had an uncertainty, which in this case was the height, mass, and diameter.
We the plug values into the equations with the dh and dd being the uncertainty for the calipers (being 0.01) and dm being the uncertainty of the electronic scale (being 0.1)
For second part of this lab for calculating uncertainty was by find in the the mass of an unknown mass. This was done by using knowledge of force and tension to figure out the mass of different unknown mass in different set ups. The one used for this experiment was the set up seen below where a mass is hanging between two strings one at 46 degrees and the other at 33 degrees.
From the set up the tensions of each sting is read from the spring scales they are attached to, and then the mass is calculated below with the information gathered from the set up. After the mass of the unknown was calculated the equation for the uncertainty was derived in the same way as was done in part one, by partial derivatives in respect to each variable which had an uncertainty.
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