This Exercise Set has been submitted for peer review, but it has not yet been accepted for publication in the PICUP collection.

Density measurement and Propagation of Error

Developed by Hai Nguyen

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.
Subject Area Experimental Labs First Year **Students will** 1) do the experiments to determine the density of a metallic solids (cylinder and ball) and use this result to identify the materials. **(Exercise 1, 2, and 3)** 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, and 4)** 120 min
**Exercise 1** Record data measuring cylindrical solid given in the lab including Mass, Length, Diameter, and appropriate uncertainties. **Exercise 2** a) Enter into Exel b) Import into Python c) calculate averages and standard deviations **Exercise 3** 1) Propagate the errors to find the resulting $\rho$ for the cylinder and associated error $\Delta \rho$ for it. 2) Compare the accepted value to the experimental value. **Exercise 4** Students repeat the previous exercises for a spherical ball.