Lab 4: Propagated Uncertainty in Measurements

                                        Propagated Uncertainty in Measurements
                                                  Ian Lin 
                                              March 6, 2017

           To measure the density of metal cylinders taking into account propagated uncertainty


The density of any object can be calculated through its simple formula of mass divided by volume. In the case of a metal cylinder, the mass is determined through the use of a balance, and the volume is calculated through the formula of v=  πr2h due to it being a right cylinder. However, inherent in these measurements of the mass, radius, and height are uncertainties that are transmitted into the density value through propagated uncertainty.

The first step in measuring the density is to mass the metal cylinder on an electronic balance. Then the volume formula for a right cylinder is applied in order to find the volume. Finally, the density value is calculated through mass divided by volume.
       ( electronic balance)


                                          Data Table

Type	Values
Mass	70.58 g
Height	8.4 cm
Diameter	1.8 cm
Density	3.3 g /cm^3

This was a simple and straightforward lab. All I had to do was measure the mass of the metal cylinder and calculate the volume of that cylinder through the formula. Then the density of the cylinder could be determined by its formula. The uncertainty values for each of the measurement types were in the last digit to the right of the decimal point. The total propagated error in the density value is +/- 0.332 g/cm^3. That is within 10% of the density value calculations.