Lab 7-01 Density and Error Analysis 201D v1 (11) - Copy
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Table 1 - Densities of Selected Materials
Solid
Copper
Brass
Iron
Steel
Aluminum
Density, ρ (g/cm3)
8.9 ± 0.1
8.5 ± 0.2
7.86 ± 0.02
7.7 ± 0.3
2.8 ± 0.1
Table 2
Cylinder #
1
54.27
2
18.2
3
57.37
Table 3 - Measurements Using a Ruler
Height H (cm)
Diameter D (cm)
Cylinder #
Trial 1
Trial 2
Trial 3
Trial 1
Trial 2
Trial 3
1
5.0
5.1
5.1
1.2
1.2
1.2
2
5.1
5.1
5.0
1.2
1.3
1.2
3
5.0
5.0
5.0
1.2
1.3
1.2
Volume and density will automatically be calculated once D, H and m (Table2) are filled in.
Use a calculator to verify the answers for Cylinder 1
Table 4 - Average Values Using a Ruler
ρ = m/V
Cylinder #
H avg (cm)
D avg (cm)
1
5.1
1.2
5.7
9.5
2
5.1
1.2
6.0
3.0
3
5.0
1.2
6.0
9.6
m
best (g)
V= (π/4) D
2 H
Volume (cm
3
)
Density (g/cm
3
)
Table 5 - Measurements Using a Caliper
Height H (cm)
Diameter D (cm)
Cylinder #
Trial 1
Trial 2
Trial 3
Trial 1
Trial 2
Trial 3
1
5.085
5.089
5.096
1.265
1.264
1.265
2
5.069
5.067
5.069
1.271
1.270
1.270
3
5.079
5.089
5.093
1.266
1.266
1.266
Volume and density will automatically be calculated once D, H and m (Table2) are filled in.
Use a calculator to verify the answers for Cylinder 1.
Table 6 - Average Values Using a Caliper
ρ = m/V
Cylinder #
H avg (cm)
D avg (cm)
Volume (cm3)
Density (g/cm3)
1
5.090
1.265
6.394
8.488
2
5.068
1.270
6.424
2.833
3
5.087
1.266
6.404
8.959
Table 7 - Uncertainties of Measured Quantities using a ruler
Measured Quantity
Uncertainty
Mass
δm (g)
0.005
Height
δH (cm)
0.05
Diameter
δD (cm)
0.05
Use a calculator to verify the answers for Cylinder 1.
Table 8 - Final Result for Densities Using a Ruler
V= (π/4) D
2 H
σ
ρ will automatically be calculated once Tables 2, 4 and 7 are completed.
𝜎_𝜌
=
ρ√(
〖
(𝛿_𝑚/𝑚_𝑏𝑒𝑠𝑡 )
〗
^2+
〖
(
〖
2𝛿
〗
_𝐷/𝐷_𝑎𝑣𝑔 )
〗
^2
"+
" 〖
(𝛿_𝐻/𝐻_𝑎𝑣𝑔 )
〗
^2 )
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