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Density measurement and Propagation of Error

Developed by Hai Nguyen - Published July 29, 2019

Every laboratory instrument has measurement limitations, referred to as its precision. One purpose of this experiment is to determine the density of metallic solids and use these result to identify the materials. However, the main objective is to practice the art of making careful measurements and use propagation rules to find uncertainties in calculated results. The five objects to be measured are Aluminum cylinder, Steel cylinder, Zinc rectangle, Lead rectangle, and a Mystery Ball.
Subject Area Experimental Labs First Year Python **Students will** 1) do the experiments to determine the density of a metallic solids (cylinders, rectangles and a mystery ball) and use this result to identify the materials. **(Exercise 1, 2, 3,4, and 5)** 2) making careful measurements, record data, and use propagation rules to find uncertainties in calculated results. Students utilize observational techniques that minimize systematic effects in measurements, record data illustrating all the pertinent attributes, such as, low dispersion, labels and units to identify the measured quantities and relevant descriptions for future references and demonstrate a working knowledge of the application of statistical procedures in the analysis. **(Exercise 2, 3, 4 and 5)** 120 min

These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).

**Exercise 1** Record data measuring cylindrical solid (Aluminum) given in the lab including Mass, Length, Diameter, and appropriate uncertainties. Enter these values into the code and run the "Aluminum" code. **Exercise 2** Record data measuring cylindrical solid (Steel) given in the lab including Mass, Length, Diameter, and appropriate uncertainties. Enter these values into the code and modify the "Steel" code to calculate Volume, Density, and their uncertainties. **Exercise 3** Record data measuring rectangular solid (Zinc) given in the lab including Mass, Length, Width, Height, and appropriate uncertainties. Enter these values into the code and run the "Zinc" code. **Exercise 4** Record data measuring rectangular solid (Lead) given in the lab including Mass, Length, Width, Height, and appropriate uncertainties. Enter these values into the code and modify the "Lead" code to calculate Volume, Density, and their uncertainties. **Exercise 5** Record data measuring a mystery sphere solid given in the lab including Mass, diameter of the sphere, diameter of the hole, and appropriate uncertainties. Write the code to calculate Volume, Density, and their uncertainties.

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### Credits and Licensing

Hai Nguyen, "Density measurement and Propagation of Error," Published in the PICUP Collection, July 2019.

The instructor materials are ©2019 Hai Nguyen. 