Activity 5.3 Determining Density
Introduction
Nicholas Lacy and Logan Hagans
How full is the bag that you take to each of your classes? Can you put any more
stuff into it? What happens to the size of the bag? What happens to the mass of the
bag? The size of the bag likely stayed the same, though the bag itself is probably
about to burst open. When the volume of something stays the same while the mass
increases, then the density increases.
In this activity you will measure volume and mass to determine the density of several
objects.
Equipment
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Engineering notebook
Triple beam balance or scale
Graduated cylinder
Dial calipers
Automoblox people and
wheels
Wooden puzzle cube blocks
Steel spheres
Delrin spheres
Paper clips
(Optional) Aluminum ruler
Density and Uses of Common
Materials Chart
Procedure
Part I. Determining Density of a Material
1. Measure the mass or weight of the Delrin, steel, and wood samples as directed
by your instructor. For improved accuracy, measure ten samples of each material
and calculate the average mass or average weight. Record values including units
to the appropriate precision based on the precision of the scale. Note that you
need only measure either mass in SI units or weight in US units, not both.
Delrin
Steel
Wood
Mass/weight of 10
samples
(include units)
Mass (SI)
Weight
(US)
Mass (SI)
Weight
(US)
Mass (SI)
Weight
(US)
See
paper
See
paper
See
paper
See
paper
See
paper
See
paper
Average
mass/weight of a
single sample
(include units)
Mass (SI)
Weight
(US)
Mass (SI)
Weight
(US)
Mass (SI)
Weight
(US)
1.55g
.00354lbs
8.65g
.01852lbs
1.405g
.00276lbs
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Introduction to Engineering Design Activity 5.3 Determining Density – Page 1
2. Calculate the volume of the Delrin, steel, and wood samples. For improved
accuracy, measure three samples of each material and calculate the average
volume. Record and calculate values to the appropriate precision including units.
When adding or multiplying measurements, record the sum or product to the
precision of the least precise number involved in the calculation.
Delrin (diameter)
Volume formula
Steel (diameter)
4/3 pi r3
4/3 pi r3
.5in
.5in
(sphere or rectangular
prism, as appropriate)
Measurement #1
Wood (wdh)
Width x Height x
Depth
W
D
H
.489
.51
.489
Calculate volume
4/3 * 3.14 *.253
4/3 * 3.14 * .253
.489 * .51 * .489
(Show all steps
including units)
.0654
.0654
.122
Measurement #2
.5in
.5in
Calculate volume
(Show all steps
including units)
Measurement #3
W
D
H
.509
.51
.502
4/3 * 3.14 *.253
4/3 * 3.14 *.253
.509 * .51 * .502
.0654
.48in
.0654
.5in
.130
W
D
H
.504
.485
.505
Calculate volume
4/3 * 3.14 *.243
4/3 * 3.14 *.253
.504 * .485 * .505
(Show all steps
including units)
.0579
.0654
.123
.0629
.0654
.125
Calculate average
of three volume
measurements
(Show all steps
including units)
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 2
3. Calculate the density of the Delrin, steel, and wood samples. Show units for each
measurement or quantity.
Delrin
Steel
Wood
Average of a
single sample
.00322
.1854
.0012
Average of three
volume
measurements
.0629
.0654
.125
Formula for
density
D=W/V
D=W/V
D=W/V
Calculate density
0.04892966360856269 0.28318042813455657 0.02262295081967213
113149847094801
492354740061162
114754098360656
(Show all steps
including units)
Formula to convert
from SI to US
system or from US
to SI system
Convert density
from SI to US
system or from US
to SI System
(Show all steps
including units)
4. Do your results correspond to published values for the density of steel, Derlin
and wood? If not, why do you think your density value(s) vary from the published
values? Yes
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 3
5. (Optional) Create an Excel Spreadsheet to perform calculations and present the
data calculated in number three above. Format the information in a table similar
to that shown below. Print your table and attach to this activity.
Delrin
Units
Steel
Wood
Units
Units
Mass of 3 samples
Mass Average
Volume of sample
Density (SI)
Density (US)
6. Consider how you might determine the material from which an object is made. If
you are given a sample of a metal (which you know is either steel or aluminum),
a graduated cylinder and a balance or scale, how could you determine from
which metal the object is made? Calculate weight density and look online for
properties of aluminum or steel to see which measurement is closest
Part II. Determining the Plastic Materials used in Automoblox Vehicles
Obtain an Automoblox vehicle from your teacher. Study the Automoblox people and
the wheels.
1. Are the Automoblox people made of the same material as the Automoblox
wheels? Why do you think so? How might you test your hypothesis?
2. You will determine the density of the plastic used to manufacture the Automoblox
people and the Automoblox wheels. Measure the mass of the four Automoblox
people and wheels. For improved accuracy, measure the four Automoblox
people together and then measure the four wheels together. Record values
including units to the appropriate number of significant digits.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 4
Automoblox People
Automoblox Wheels
Total
mass/weight
of all
sample(s)
(include units)
3. Measure the volume of the four Automoblox figures and then measure the
volume of the four wheels. Because of the irregular form of each object, the
volume is more easily measured using a graduated cylinder.
a. Add water to the graduated cylinder until it is approximately 2/3 full.
b. Record the water level.
c. Carefully add samples.
d. Record the new water level.
Automoblox People
Automoblox Wheels
Water level without
samples
(Include units)
Water level with
samples
(Include units)
Water volume
displaced = volume
of sample(s)
(Show calculations)
4. Calculate the density (by hand or using Excel) of the four Automoblox figures and
four wheel samples. Complete the table below or attach a print of your Excel
worksheet. Be sure to include units with all measurements and quantities.
Automoblox People
Automoblox Wheels
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 5
Total mass/weight
of sample(s)
Volume of
sample(s)
Formula for density
Density (SI)
Density (US)
5. Does your data support or refute you hypothesis (from number 1 above)?
Explain.
6. Refer to the Common Materials Density and Uses Chart. Use your results to
make an educated guess as to the material used in the manufacture of the
Automoblox people and wheels. What other tests might further substantiate your
guess?
Extend Your Learning
1. Measure the mass of the aluminum ruler and paper clip samples. Choose the
appropriate number of samples of each if an average is needed for improved
accuracy. Record values including units.
Aluminum Ruler
Paper Clips
Total mass of
sample(s)
2. Measure or calculate the volume of the aluminum ruler and paper clip samples.
[Note that you can calculate the volume of the ruler without submerging it in
water.] Show all measurements if using the indirect measurement. Sketch the
object if using the calculation method.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 6
3. Calculate the density of the aluminum ruler and paper clip samples by hand or
using Excel. Complete the table below or include a print of your Excel worksheet.
Be sure to use the mass and volume based on the same number of objects.
Show units for all measurements and calculated quantities.
Aluminum Ruler
Paper Clips
Mass of sample(s)
Volume of
sample(s)
Formula for density
Density (SI units)
Density (US units)
4. Do your results support the manufacturer’s claim that the ruler is made of
aluminum? Justify your answer. (Refer to the Common Materials Density and
Uses chart.)
5. Are the paper clips made from the same material as the ruler? How do you
know?
Conclusion
1. How can you use density to identify a material?
2. What are limitations of the calculated and indirect volume measurement?
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 7
3. Explain the difference between weight and mass.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 5.3 Determining Density – Page 8