September 7, 2016: Propagated Uncertainty in Measurements

Anthony Betancourt
Lab Partner: N/A
Professor Wolf

Lab #6: Density and Propagated Uncertainty

Purpose: 

The Purpose of this experiment is to review the concept of significant figures and introduce the use of vernier calipers.  Also, determining the density of metal cylinders by taking measurements in order to identify the specific metal.

Procedure:

1. Grab two different sized metal cylinders. Make sure to choose two cylinders that are of different metals.  
2. Grab a set of Vernier Calipers. If unsure on how to use calipers be sure to watch the following video on how to use and read the vernier calipers: https://www.youtube.com/watch?v=Wo3iVrSUKPE&feature=plcp
3. Measure each cylinder's length and width.  Keep in mind that the width will also be the diameter for the cross sectional area of the cylinder.  
4. Measure both cylinders on electronic scales in the back of the classroom and record the masses.
5. Once both cylinders are measured and the volume is calculated, use formula to calculate the uncertainty for your cylinders.  

Theory:  

The accuracy of your final measurement depends on the accuracy your measurement tools.  The more accurate a tool is the less amount of uncertainty there is in your final calculations.  To an extent, uncertainty will allow anyone who is verifying your calculations to determine how much a value can deviate ± for a taken measurement.  Depending on how many significant figures the readout on a measurement device is, this will determine the amount of uncertainty on a measurement.  Below is an example of a vernier caliper with a given measurement:

(Example of how to read a vernier caliper measurement)

Measured Data:

(Measurements of each cylinder)

(Formula for calculating uncertainty)

(Calculated uncertainty in iron density)

(Calculated uncertainty in Aluminum density)

Conclusion: 

The accepted masses for iron and aluminum (according to google) are 7.87 g/cm^3 and 2.70 g/cm^3.  My experimental value of iron falls within the range of uncertainty of the accepted value for the density of iron.  Also, the experimental value for aluminum is within the experimental uncertainty for the density of aluminum.  Overall, the accuracy of the measurements taken have shown to be reliable in calculating the density of metals with a low level of uncertainty.