Lab 6: March 3, 2017: Propagated Uncertainty

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Lab 6: Measuring the Density of Metal Cylinders 
Amy, Chris, and John 
March 3,2017

Today's lab purpose was to measure the density of two metal cylinders and calculate the propagated error in each one of our density measurements by using a Vernier caliper and a scale. 

Theory: In this lab we had to figure out the density of two unknown metal cylinders and calculate the propagated uncertainty for each. For this particular lab there are factors where our calculations may have been slightly incorrect propagating a further error in our data. When measuring the density of each metal we used a Vernier caliper that outputs measurement readings in centimeters and is more precise up to two decimal places. 

In order to calculate propagated uncertainty in our lab we used the propagated uncertainty of density we took partial derivatives and generated this formula: 


Apparatus and Procedure: For this lab we used the Vernier caliper and a scale. The Vernier caliper has two decimal points and so does our scale. We calculated our density by dividing mass by volume. We had to measure the mass, height, and diameter for both cylinders and plugged them into the formula 4m/(pi*d^2*h). 
Disclaimer: Both masses were not weighed at the
same time
Measuring the diameter of the cylinder





                   
                       





















Measured Data: 

Cylinder 1: mass= 84.48 g      height= 4.89 cm     diameter= 1.59 cm
Cylinder 2: mass= 28.93 g      height= 3.28 cm     diameter= 1.29 cm

Uncertainty;    dm= 0.01 g      dD= 0.01 cm          dh= 0.01 cm

Calculations for the density: 
Cylinder#1 Calculations

Cylinder#2 Calculations
Conclusion:
We were able to calculate the propagated error of the density of the two metals using the uncertainty of each measurement. Our ratio of delta however was a small percent, roughly 1.58% for metal 1 and 1.27% for metal 2. We go back to our calculation and determine where the greatest source of error is. Within our uncertainty calculation, we see for each squared term within the square root the one for diameter is different. There is a coefficient of two within and when squared produces a factor 4 times greater than the other measurements. Should our measurements be more exact and used pure material cylinders then maybe we would have come to a much better uncertainty. 
    

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