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This lab aims to gain knowledge about density and determine the density of several materials experimentally; practice measurements and calculations. The density of three metal cylinders, aluminum, brass, and iron will be measured.
Density is used in numerous calculations in physics, chemistry, and technology. It is of greatest importance for industrial processes. Density is the relative heaviness of an object; it is measured in mass units per units of volume. Density describes how compact or concentrated the substance is. It explains how massive an object is comparing to the volume.
Density is calculated by the following formula:
where M – the weight of the sample, V – the volume of the sample. The standard CI units for density are kg/m3.
Therefore, if weight and volume of a sample is known, it is possible to calculate density. In some cases, one can determine which material the sample is made of.
During the lab, the following procedures are performed: measurements of the mass, length and diameter of the cylinders. After this, the density calculations are involved.
Three solid cylinders made of different metals, namely aluminum, brass and iron were used. The cylinders were cut from the metal rod by hand on a band saw in order to introduce some uncertainty in their lengths. The laboratory balance, calibrated masses and calipers have been applied.
The measurements of cylinders mass and dimensions are presented in Table 1.
As a first step, we calculated average values of the mass, length and diameter for all three metal cylinders of three trials. The average value is calculated as:
where M1, M2, M3 – the sample weights of obtained from different measurements.
For example, for aluminum:
Following this procedure, the average values of mass, length and diameter of all samples are calculated. The results are presented in Table 2.
After the measurements, the calculation of the sample volume has to be performed. The cylinder volume is calculated as:
where S - cylinder basis square, mm2, L – length of the cylinder, mm.
Square of the cylinder basis is calculated as:
S = π∙d2/4,
where d – diameter of the cylinder.
The average values of length and diameter measurements are applied. For example, for aluminum sample:
S = 3.14∙12.62/4 = 124.63 mm2,
V = 124.63 ∙ 49.37 = 6152.98 mm3
The volume of the samples are presented in Table 3.
Finally, the density of each cylinder is calculated:
For aluminum sample: D=17.976147.83=0.0029 g/mm3.
For brass sample: D=54.876838.26=0.008 g/mm3.
For iron sample: D=49.86277.45=0.0079 g/mm3.
Table 4. Density of the aluminum, brass and iron samples
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