DoM and HL LR
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University of Illinois, Urbana Champaign *
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Course
102
Subject
Mechanical Engineering
Date
Apr 3, 2024
Type
Pages
9
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Experiment one: Density of Matter
1.
Introduction:
The purpose of this experiment was to study the density of solid objects. The greater the
volume of an object, the smaller the density of an object as they have an inversely proportional
relationship. In this lab, density will be found from found masses and volumes calculated from
measurements taken during the lab.
The mathematical equation used to calculate the volume of cylindrical solids is:
V
=
(1)
Π𝑟
2
?
where V is the volume of the cylinder,
is the ratio of the circumference of a circle to its
Π radius, r is the radius of the cylinder, and l is the length of the cylinder.
The mathematical equation used to calculate the volume of a solid rectangular prism is:
(2)
𝑉 = ??ℎ
where V is the volume of the rectangular prism, l is the length of the rectangular prism, w
is the width of the rectangular prism, and h is the height of the rectangular prism.
The mathematical equation used to calculate the density of an object is:
(3)
ρ =
𝑀
𝑉
where
is the density of an object, M is the mass of the object, and V is the volume of an
ρ object.
2.
Experiment procedures:
The materials and equipment used for this lab included the following: 3 aluminum
cylinders of varied sizes, 3 cardboard rectangular prisms of varied sizes, a balance, and vernier
calipers.
Part 1:
-
Step 1: The balance was turned on and zeroed.
-
Step 2: The mass of a cylinder was measured on the balance.
-
Step 3: The radius and height of the cylinder were measured by putting the cylinder in
between the ends of the vernier calipers.
-
Step 4: The volume was found by multiplying the square of the radius by the height of
the cylinder by pi.
-
Step 5: The density was calculated by dividing the found mass of the cylinder by the
found volume of the cylinder.
-
Step 6: Steps 1-5 were repeated twice for two other cylinders.
Description: The aluminum used were smooth, opaque, silver cylinders.
Part 2:
-
Step 7: Steps 1 and 2 were repeated for the rectangular prism.
-
Step 8: The height, length, and width of the prism were measured by putting the prism in
between the ends of the vernier calipers.
-
Step 9: The volume was found by multiplying the length by the height by the width of the
cylinder.
-
Step 10: Step 5 was repeated.
-
Step 11: Steps 7-10 were repeated twice for the other rectangular prisms.
Description: The rectangular prisms used were made of cardboard. The largest was red, the
second largest was yellow, and the smallest was blue. They were hollow and opaque with a
semi-matte finish.
3.
Results, analysis, and questions:
Table 1: Table one shows the mass, length, radius, volume, and density of the aluminum
cylinders.
Column
1
mass
(grams)
length
(cm)
diameter
(cm)
radius (cm)
volume (m^3
x10^-6)
density
(kg/m^3)
cylinder
1
27.52
7.7
1.1
0.55
7.32
3760
cylinder
2
12.56
3.1
1.1
0.55
2.95
4258
cylinder
3
6.36
7.5
0.6
0.3
2.12
3000
Based on table 1, the graph illustrated the relationship between volume versus mass of the
cylinders.
Graph 1:
From graph 1, the slope of best fit was 0.000254, which demonstrates
(based on equation 3).
1
ρ
Therefore, the density of aluminum is theoretically 3,979 kilograms per meter cubed. The
average experimental density of the aluminum cylinders was found to be approximately 3,673
kilograms per meter cubed, which means that there was around a 7.69% error. The coefficient of
determination was calculated to be 0.981. This demonstrates that the data from this part of the
experiment was relatively accurate. A likely source of error was from measuring the cylinders
with the vernier calipers, where the cylinder may not have gripped tight enough for accuracy.
Table 2: Table 2 shows the mass, height, length, width, volume and density of the blocks.
Mass
(grams)
Height (cm)
Length (cm)
Width (cm)
Volume (m^3 x
10^-3)
Density
(kg/m^3)
Block 1
(red)
134.18
303
74
150
3.36
40
Block 2
(yellow)
86.6
75
152
152
1.73
50
Block 3
(blue)
50.01
146
73
73
0.78
64
Based on table 2, the graph 2 illustrates the relationship between mass and volume of the blocks.
From graph 2, the slope of best fit was 0.0308, which demonstrates
(based on equation 3).
1
ρ
Therefore, the density of cardboard was 32.47 kilograms per meter cubed. The average
experimental density was 51.3 kilograms per meter cubed, giving a 36.8% error. The coefficient
of determination was calculated to be 0.994. This demonstrates that the data from this part of the
experiment was precise, but not accurate. A source of error was likely due to the inexact
measuring of the blocks due to a tightened grip on the vernier calipers. It is possible that the
cardboard may have been compressed, making the measurements more inaccurate.
4.
Conclusion:
Through this experiment, the density of solid objects was studied. A deeper
understanding of laboratory procedures and precise measurements were also examined. The
density of solid objects was studied. One was calculated with the volume of a set of cylinders,
and the other was calculated using a set of cardboard blocks.
was used in both parts of the
ρ experiment to represent density. The errors in this lab stemmed from improper measuring. To be
repeated with greater accuracy, the lab should be redone with measurements taken on a flat
surface.
5.
Data Sheet:
Next Page under Density of Matter
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