This document summarizes a student laboratory experiment to measure the density of unknown materials using two methods - volume displacement in water and caliper measurements. Five cylinders and one implant of unknown composition were examined. Mass was measured with a scale and volume via either calipers or water displacement in a graduated cylinder. Densities were calculated and compared to literature values to identify the materials. Results found the cylinders were made of glass, PMMA, UHMWPE, brass, and stainless steel while the implant was titanium. The caliper method yielded more accurate densities than displacement. The goal of identifying unknown materials and comparing measurement techniques was achieved.

1. Kevin Midlash 9/14/2014
Patrick Deck
David Donovan BME Density Measurements
BME:2500
1
I. Introduction
When selecting potential biomaterials, the density is among the first things to be considered.
Furthermore, with density being unique to any given compound, the density can be key to identifying an
unknown compound. As such, being able to obtain a correct value for density is crucial. In this lab, our
goal is to practice using two common density measuring methods. The first of which is to measure the
volume of water the object displaces and its mass for use in Equation (1). The second is to use caliper
measurements to calculate a volume by using Equation (2) and then plugging this value once again into
Equation (1). Upon completion of this lab, we should be able to determine the identities of five cylinders of
unknown material and a fabricated implant whose composition is unknown as well.
Equations
Density(ρ), Mass(m), Volume(V), Height(h), Radius(r)
𝜌 = 𝑚/𝑉 (1)
𝑉( 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟) = 𝜋 ∗ 𝑟2
∗ ℎ (2)
| 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒−𝑇𝑒𝑥𝑡 𝑉𝑎𝑙𝑢𝑒|
𝑇𝑒𝑥𝑡
𝑉𝑎𝑙𝑢𝑒 (3)
II. Methodology
Five cylindrical unknown materials were examined during this lab. Quantitative measurements of
both mass and volume were obtained for each unknown objects. The measurements for each sample
were carried out independently by each group member, the data was then shared amongst the group.
To start, the mass of each object was obtained. The mass was found by placing each unknown
material on a digital scale. Second, the volume of the samples were assessed. This was carried out using
two techniques.The first involved diagnostic measurements of both length and diameter for each
unknown using a digital caliper. This length and diameter of each unknown was used to calculate volume
of the object by Equation (2). The second used water as a form of liquid displacement. A graduated
cylinder was filled with water and the initial volume was recorded. Each unknown was then placed in the
water one at a time, once again the volume was recorded. The change in volume from initial
measurement to final measurement is the displacement of the individual unknown. Since water has a
density of 1g/𝑐𝑚3
= 1ml of water, the mass of the object can be divided by the volume of displaced water
to yield density of the unknown. This is represented in Equation (1), where density is equal to
mass/volume. These methods of obtaining volume were used to calculate two sets of density values.
These values were then compared to textbook values for accuracy.
III. Results
Table 1: Results f rom scale massing, caliper measuring, and graduated cy linder v olume displacement are shown below. Also included are the mean
densities calculated f rom the caliper and cy linder experiments with their respectiv e standard dev iations. The spinal cage was not measured using the
calipers.
Scale
Digital
Caliper
Graduated
Cylinder
Sample Mass
Mean
Length(mm)
Mean
Diameter(mm)
Mean
Density(g/cm^3)
Density
Stdev
ΔVolume(mL)
Volume
Stdev
Mean
Density(g/cm^3)
Density
Stdev
1 6.31 54.48 8.01 2.30 0.02 2.77 0.32 2.28 0.29
2 8.61 55.30 12.73 1.22 0.01 7.17 0.29 1.20 0.05
3 7.74 55.65 13.56 0.96 0.01 7.83 0.06 0.99 0.01
4 34.29 56.43 9.52 8.53 0.12 4.20 0.35 8.16 0.64
5 31.61 56.38 9.51 7.89 0.01 4.10 0.17 7.71 0.32
6 11.11 56.47 9.57 2.74 0.02 3.97 0.06 2.80 0.04
Spine
Cage
8.31 x x x x 1.93 0.12 4.30 0.26

2. Kevin Midlash 9/14/2014
Patrick Deck
David Donovan BME Density Measurements
BME:2500
2
Table 2: Samples’ suspected identities listed with text v alues obtained f rom v arious online resources. Also included are perc ent error calculations
comparing text v alues against the experimentally obtained densities. Percent errors were calculated using Equation (3). In the case of text v alue
ranges, median v alues were used.
Material Suspected Identity
Text Density of
Suspected Identity (g/mL)
Experiment 1 Percent
Error (%)
Experiment 2 Percent Error (%)
1 Glass 2.21 4.04 3.15
2 PMMA 1.18 3.67 1.81
3 UHMWPE 0.94 2.47 5.07
4 Brass 8.4-8.73 0.41 4.69
5 Stainless Steel 7.75-8.05 0.16 2.42
6 Aluminum 2.7 1.41 3.77
Spine Cage Titanium 4.34 NA 1
IV. Discussion
Two methods were used in obtaining our volume of the unknown materials. The first
involved using digital calipers to obtain length and diameters of the samples, the second was
displacement using water as the fluid. The displacement method is simple, fast, and accounts for irregular
surfaces and shapes of objects when measuring volume. The mathematical calculation of volume
assumes that the surface is free of defects and perfectly symmetrical. This assumption is one which can
account for a small amount of error, but overall is irrelevant. Due to the difference in accuracy between
the human eye and technology, the calipers provided more accurate results than our own observation.
This can be seen in Table 2, where the caliper measurements had lower percentage errors than the
displacement method values for a greater number of the samples. Thus, our measurements from Table 1
show that sample 1 exhibits glass-like density parameters, sample 2 PMMA-like, sample 3 UHMWPE-like,
sample 4 brass-like, sample 5 stainless steel-like, and sample 6 aluminum-like. Further examination of
Table 1 reveals relatively low standard deviations in measurements of all trials. This suggests that
variability between different observers is relatively low when using either method. Granted, these were all
done under identical conditions, but due to the samples’ solid nature, it is highly unlikely that any
environmental factors would have a noticeable effect on the results. Measuring the implant however, was
more of a challenge. Due to the irregular shape of the implant, we choose to use the displacement
method in measuring its volume. This method was more practical due to the complexity that
measurement with the calipers would have presented.
V. Conclusion
The first objective of this exercise was to calculate the density of each unknown using
specific methods of measuring volume. The second, to compare the results of the two methods of
measuring volume. And finally, to identify the materials of which the unknowns were comprised. This was
done by careful comparison of experimental densities with textbook values. In conclusion, the unknowns
were identified in Table 2. The error percentage for each method of obtaining density of the object is also
listed in Table 2.
Though the methods utilized are very lab friendly due to their ease of use and speed, they aren’t
the only options. There are a variety of ways to determine density, such as synthesizing/melting an
unknown material into a sample of known volume and then taking its mass.
Acknowledgments
Thank you to Joseph Hammond for assisting us during the lab and to the College of Engineering
for providing labs and materials.
References
Dow Chemical Company, http://www.dow.com (accessed Sept 2014)
ClearWater Composits, http://www.clearwatercomposits.com (accessed Sept 2014)
Sigma Aldrich, http://www.simgaaldrich.com (accessed Sept 2014)

3. Kevin Midlash 9/14/2014
Patrick Deck
David Donovan BME Density Measurements
BME:2500
3
The Engineering Toolbox, http://www.engineeringtoolbox.com (accessed Sept 2014)