PHYS 4A/ Fall 2014; Determining Unknown Masses

Purpose: To understand how to calculate propagated uncertainty and use that knowledge in experimental calculations. This will be done by taking the densities of different objects and calculating their density uncertainties.

This experiment was split up into two parts. For the first part, three metal cylinders were weighed and the mass was determined. Calipers were also used to measure the dimensions of each object. These values were used to determine the density of the object and to propagate the uncertainty for the density.

The metal cylinders looked similar these, ( I forgot to take pictures of the equipment)

The dimensions of each cylinder were measured and recorded along with their masses as shown below. The uncertainties of each density were also calculated using propagation. However, these uncertainty values in the pictures are incorrect as the square root was not taken. Therefore the correct density values are as follows, Aluminum: 2.689+/-0.25g/cm^3, Copper: 8.780+/-0.41g/cm^3, and Steel: 7.866+/-0.39 g/cm^3. Since the real values are not given as everything would need to be calculated for each object, the uncertainties show that the numbers should not create much deviation from what the true value is.

For part 2 of the experiment, we had to find the density of an unknown object that was hanging on Newton meters by measuring the angles and forces coming from the tension in the bands holding the object. Again, I forgot to take a picture of the equipment but here is a sketch of what it looked like. 

Below we have the Free-Body Diagram of the System with the known values.

Using Newton's Second Law, the mass of the object was determined by using the equation F=ma. Below are the calculations for the unknown mass as well as the propagation of uncertainty for the mass.

In conclusion, the mass of the unknown object was calculated to be about 638 grams. The uncertainty was calculated to be very large however which may have been due to the way the measurements were taken or an incorrect equation. Also, for reference, we had mass #10 in the lab.