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Measurements for calculating density
Name: Mariyam Shaahynaa
SI:000073671
Introduction
Density is a quantity which is distinct to a specific materials. It is largely used to check if the substance is
pure and to identify the materials in which a substance is made of. This report highlights on the
measurements needed to calculate density of 5 different objects. i.e. Glass marble, Paper sheet, wood
block, a piece of wire and cylindrical glass beaker. A simple formula density = mass/volume (p=m/v) is
used to find out their density and error of each densities are estimated. Mass can be measured directly
using a balance, but to calculate volume we need to measure different dimensions using a micrometer
screw gauge Vernier caliper and a ruler. This experiment gives a good practice on using these instruments
and calculating errors in density.
procedure
Appropriate measurements are required to calculate densities of 5 different objects. The instruments that
are being used in this experiment are digital balance Vernier caliper, micrometer screw gauge and a meter
rule and a ruler.
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First of all check for zero errors in all the instruments before taking the measurements.
As the formula states (density =mass/volume) these two quantities are required for calculating
density.
To measure the mass of lighter objects i.e. for paper sheet and piece of wire a high precision
balance is used
For cylindrical beaker, wooden block and glass marble another digital balance with slightly less
precision is used.
In order to calculate volumes different quantities are needed for 5 different objects. And
appropriate formulas can be used to calculate volumes.
For 1. wooden block ; - a ruler nearest to 0.1cm is used to measure its lengths from all sides.
- 𝑉 = 𝑙 × 𝑙 × 𝑙 can be used to measure volume.
2. sheet of paper ; -length and width is measured using a meter rule and height(thickness) is
measured using micrometer screw gauge.
-The paper is first folded into 8 times to reduce error.
-Its center is then fit into gaps of micrometer and the readings are taken
-Then divide the value by 8 to get the thickness of paper
-𝑉 = 𝑙 × 𝑏 × ℎ is used to measure the volume.
MNU/FEST/physics lab report/week1/2020
2
3. Glass marble ; - the diameter is measured using Vernier caliper.
- It is fit into lower jaws of Vernier caliper the readings are taken.
4
3
𝑑 3
2
-𝑉 = 𝜋 ( ) is used to find the volume
4. Piece of wire ; - length is measured using a ruler
-And diameter measured by fitting the wire between the gaps of
micrometer and it is tightened using the ratchet. The diameter reading is then taken.
𝑑 2
2
-= 𝜋 × ( ) × ℎ
5. Small cylindrical glass beaker ; - The lower jaw of Vernier caliper is used to measure the
outer diameter of beaker The upper jaw is used to measure the internal diameter and the tail of Vernier
caliper to measure the inner depth of the cylinder.
- A ruler is then used o measure the outer height of the cylinder.
𝑑 2
- using the formula 𝜋 × ( 2 ) × ℎ Inner and outer cylindrical volumes are
calculated and inner can be subtracted from outer volume to get the volume of cylindrical glass.
-
.
Using the same formula The volume of circular bottom of the glass is
calculated and is added with the volume of cylindrical glass.
The masses and volumes can then be substituted into the formula 𝜌 =
of each object. Error of densities are then estimated.
MNU/FEST/physics lab report/week1/2020
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
to calculate density
3
Density and error calculations
Objects
Mass / g
Dimensions / cm
Volume /
cm3
Density g /
cm3
Diameter
5.0 ± 0.1
1.57 ± 0.01
2.03
2.46 ±0.04
0.337 ± 0.001
0.061 ± 0.001
0.033
10.1±0.04
4.21
2.19±0.04
64.0
0.752±0.08
25.5
0.20 ±0.04
Glass Marble
Wire
Glass Cylinder
Internal diameter External diameter
2.36 ± 0.01
2.53 ± 0.01
Inner depth
Outer Height
4.89 ± 0.01
5.09 ± 0.01
Length
width
Height
9.2 ± 0.1
wooden Block
4.0 ± 0.1
48.1 ± 0.1
4.0 ± 0.1
4.0 ± 0.1
Paper Sheet
5.076 ± 0.001
29.6 ± 0.1
mass = 5.0 ± 0.1
1. Glass marble
𝜌=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
4
𝑉𝑜𝑙𝑢𝑚𝑒 = 3 𝜋𝑟 3
𝑟=
𝑑
2
1.57 3
)
2
4
=3×𝜋×(
= 2.03 cm3
𝜌=
5.0
2.03
=2.46 ± 0.04 g/cm3
%Error in mass =
21.0 ± 0.1
0.1
×
5
100 =2%
0.01
%E in d=1.57 × 100 =0.64%
%E in volume= 3×0.64% = 1.91%
E in density =( 1.91% + 2%)/100 = 0.04
MNU/FEST/physics lab report/week1/2020
0.041 ±
0.001
diameter = 1.57 ± 0.01
4
mass = 0.337 ± 0.001
2. Piece of wire
diameter = 0.061 ± 0.001 height =11.3±0.1
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
𝜌=
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝑟 2 ℎ
𝑟=
0.061 2
)
2
=𝜋×(
𝑑
2
× 11.3
= 0.0333 cm3
𝜌=
0.337
0.0333
= 10.1 ±0.04g/cm3
%Error in mass =
0.001
×
0.337
100 =0.3%
0.001
%E in d=0.061 × 100 =1.6%
0.1
%E in h= 11.3 × 100
=0.9%
%E in volume= (2×1.6%)+0.9% = 4.1%
Error in density is =(4.1% + 0.3%) /100 = 0.04
3. Glass Cylinder
𝑚𝑎𝑠𝑠
𝜌=
𝑣𝑜𝑙𝑢𝑚𝑒
mass = 9.2 ± 0.1
outer diameter = 2.53 ± 0.01
inner diameter = 2.36 ± 0.01
inner depth = 4.89 ± 0.01
outer height = 5.09 ± 0.01
height difference = 0.2
Inner volume
Outer volume
𝑉 = 𝜋𝑟 2 ℎ
𝑉 = 𝜋𝑟 2 ℎ
𝑉 = 𝜋𝑟 2 ℎ
2.36 2
𝑉 =𝜋×(
) × 4.89
2
2.53 2
𝑉 =𝜋×(
) × 4.89
2
𝑉 = 𝜋×(
V = 21.4 cm3
V = 24.6 cm3
V = 1.01 cm3
MNU/FEST/physics lab report/week1/2020
circular bottom
2.53 2
) × 0.2
2
5
V= volume of circular part of glass
=Outer volume – Inner volume
=24.6 – 21.4
= 3.2 cm3
Total volume of cylindrical object = 3.2 + 1.01
= 4.21 cm3
𝜌=
9.2
4.21
= 2.19 g/cm3
0.1
%Error in mass = 9.2 × 100 =1.1%
0.02+0.1
×
4.21
%E in cylindrical glass volume =
100 =2.9%
Error in density is =(2.9% +1.1%) /100 = 0.04
mass =48.1g ± 0.1
length = 4.0cm ± 0.1
4. Wooden block
𝜌=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
Width= 4.0cm ± 0.1
Height= 4.0cm ± 0.1
𝑉 =𝑙×𝑙×𝑙
= 43
= 64 cm3
𝑚𝑎𝑠𝑠
𝜌 = 𝑣𝑜𝑙𝑢𝑚𝑒
=
48.1
64
= 0.752 ±0.08g/cm3
0.1
%Error in mass = 48.1 × 100 =0.21%
0.1
%E in l= 4 × 100 =2.5%
%E in volume= 3×2.5% = 7.5%
E in density =( 7.5% + 0.21%)/100 = 0.08
MNU/FEST/physics lab report/week1/2020
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5. Sheet of paper
𝜌=
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
mass = 5.076 ± 0.001 length = 29.6 ± 0.1
Width= 21.0 ± 0.1
Height= 0.041 ± 0.001
𝑉 = 𝑙×𝑏×ℎ
= 29.6 × 21.0 × 0.041
=25.5 ±0.04 g/cm3
𝑚𝑎𝑠𝑠
𝜌 = 𝑣𝑜𝑙𝑢𝑚𝑒
5.08
= 25.5
= 0.2 ± 0.04 g/cm3
0.001
%Error in mass = 5.076 × 100 =0.02%
%E in volume=
0.1
×
29.6
0.1
×
21.0
100 +
0.001
×
0.041
100 +
100 =3.3%
E in density =( 0.2% + 3.3%)/100 = 0.04
discussion
when comparing densities the copper wire has the highest density and the paper sheet has the lowest
density. This indicates that the density is independent to the size of object. The density error of wooden
block is highest because we used only a meter rule to measure its dimensions while we used much more
precise instruments for other objects. The error in density is almost same. This maybe because we used
the same measuring instruments in all of these objects. Some possible source of errors can be random
errors such as parallax error while reading micrometer and Vernier caliper readings. This error can be
reduced by taking repeated readings and taking the mean. Another possible source of error can be due
to faulty instruments. To reduce this kind of error we need to make sure we use the instrument that are
using in good condition and always check for zero errors.
MNU/FEST/physics lab report/week1/2020
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Conclusion
This report not only gave a clear understanding of how to use measuring instruments like micrometer
and Vernier caliper but also on density and error calculations. We evaluated densities of a glass marble,
a piece of wire, cylindrical glass beaker, a sheet of paper and a wood block.
Reference; The formulas for d=m/v and for volumes was taken from Cambridge IGCSE o level physics
text book published in (2010). The methods used in this experiments and writings by mariyam
shaahynaa student ID .000073671.
MNU/FEST/physics lab report/week1/2020