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European Journal of Applied Sciences – Vol. 9, No. 4
Publication Date: August 25, 2021
DOI:10.14738/aivp.94.10508. Sharma, O., & Sharma, D. (2021). How Elastic are Bands Those are Used in Everyday Life? European Journal of Applied Sciences,
9(4). 54-70.
Services for Science and Education – United Kingdom
How Elastic are Bands Those are Used in Everyday Life?
Om Sharma
Natick High school, Natick, MA 01760, USA
Dipti Sharma (PhD)
Emmanuel College, Boston, MA 02115, USA
ABSTRACT
Elastic materials are found all around us and knowing at least a general overview
on how they behave is useful and important. The purpose for this research work is
to understand what Physics is behind rubber bands and how it is connected with
the dimension of rubber bands (length, width, thickness and area) and its stiffness
(spring constant and Young’s modulus). To test this, a handmade wooden stand by
student author was used with a ruler attached to it. Then various types of rubber
bands were hung and their increase in length was measured by increasing weight
on it each time. The obtained data of dimensions of the bands and increase in length
was compared to Hooke’s Law and Young’s modulus to understand stiffness of the
bands. A higher spring constant represents that the material is stiffer and requires
more force to stretch it whereas higher Young’s modulus shows the stability of the
material. This research is a project work done by a high school student to present
in MA science fair in USA and project won an honorable award at regional level and
went to the state level in USA in 2021.
Keywords: Application of Physics, Rubber bands, Elasticity, Hooke’s Law, Stiffness,
dimensions, hands on experiments during COVID time at home!
INTRODUCTION
Rubber bands show elastic properties. When you stretch a rubber band, it stretches and as soon
as you remove external force, it comes back to its original state. If you apply more force, it
extends more and then come back to its state as soon as force applied is removed. It is called
linear deformation when an object changes its length under an external force and then comes
back to its original shape. Rubber molecules have a peculiar structure and arrangement, and
they always move around and shows property of flexibility. There is science behind rubber
band, and it can be seen in this reference [1]. Since spring also extends when a force is applied,
we can compare behavior of a rubber band with a spring. Because of its flexibility, the rubber
band can follow Hooke’s law which is an important law of spring. To learn more about Hooke’s
law, these sites can be seen [2-3]. The property of elasticity can be related to Young’s modulus
and it can be seen in these sites [4-6].
While performing research on rubber bands, following questions came to mind that: 1) How
does elasticity play a role in rubber bands those are used in everyday life? 2) How does elasticity
depend on the length, width and thickness of the rubber bands? 3) How are spring constant and
Young’s modulus related to the dimensions and flexibility of the rubber bands? Before starting
this research, following hypothesis can be decided: Flexible materials have a smaller spring
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Sharma, O., & Sharma, D. (2021). How Elastic are Bands Those are Used in Everyday Life? European Journal of Applied Sciences, 9(4). 54-70.
URL: http://dx.doi.org/10.14738/aivp.94.10508
constant whereas thicker and stronger bands have a greater spring constant. Three types of
variables used in this project work, can be defined as: Independent: types of rubber bands,
length, width, thickness, masses hang on them, Dependent: Extension in each rubber band,
Force, spring constant, cross-sectional area, Young’s modulus, Constant: gravity in
force/weight, temperature of the room, environment where experiment is performed, stand
where rubber bands hung, and Control: The first rubber band R1 which is thinnest and most
flexible, used to compare other rubber bands of different thickness. The expected Outcomes of
this project work can be mentioned as “The predicted outcomes are that flexible bands will
stretch more with less force and have a small spring constant while stiff bands will need more
force to extend and give a high spring constant. Based on the dimensions of bands, their Young’s
Modulus will change too.” The points need attention during experiment can be considered as
“Risk and Safety issues” and they can be: 1) The rubber band falling off the hook. 2) The mass
falling and causing something to break. 3) The stand might break as well.
Figure 1: Household Rubber bands used for the experiments. The numbers show the order of
rubber band as they were used in the experiment
Figure 1 shows the list and images of the rubber bands those are found easily in everyone’s
home, and they are used on daily purposes. Authors interests were to see how the concepts of
force, Hooke’s Law, and elasticity can be applied in everyday life. The same rubber bands shown
in Figure 1 were used for experiments. Knowing scientific information of bands can help people
who use them more effectively when doing things in their life. It can help them because they
can make predictions or estimates about what is going to happen and make the best choice.
Rubber bands and elastics are used everywhere, from tying things together in jewelry,
machines, games, STEM activities etc. It is a good way of doing hands on experiment at home
during COVID time to learn Physics and see how concepts of Physics are around us and being
useful in our daily life!
MATERIALS AND METHODS
All homemade material and easily available rubber bands in daily life were used for this project
work. The list of material can be given as: A wooden stand (home made by high school student);
several types of rubber bands varying in length, width, and thickness; various masses to hang
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European Journal of Applied Sciences (EJAS) Vol. 9, Issue 4, August-2021
Services for Science and Education – United Kingdom
with; a ruler or measuring tape; a string; a calculator; a notebook; a pen; tape; and a Vernier
Caliper.
Following steps were followed as procedure to perform these experiments at home during time
of COVID:
1. Take a rubber band and measure its length with a ruler and measure its width and
thickness with a Vernier Calipers.
2. Tape a ruler (or the end of the tape measure) to the top of the stand.
3. Put the rubber band on the hook end.
4. Measure the length of it.
5. Hang the weight holder (50g) on it and record the length extended and mass.
6. Put on a weight and record the length and mass again.
7. Repeat step 5 while adding masses until the band breaks, no more weights fit, or you
decide to stop.
8. Take off weights and measure to see if the length is different from the beginning.
9. Calculate the change in length of the rubber band for each mass hung and then calculate
k and Y.
THEORY
Following theories were used in this project work of rubber bands.
(1)Hooke’s Law
F = - k*ʌL --- 1
M*g = - k*ʌL --- 2
(where F = M*g)
M*g = k* ʌL --- 3
ʌL = L’ – L --- 4
k = (M*g)/ ʌL --- 5
Negative sign in equation # 1 and # 2 represent the opposite nature of F and ʌL.
Where L (m) is the initial length of the rubber band, L’ is the extended length of the rubber band,
ʌL is the change in length of the rubber band, F(N) is the force applied to the rubber band, M
(kg) mass hanged on the rubber band, g (m/s^2) is the gravity of the Earth which 9.81 m/s^2,
k (N/m) is the spring constant.
(2)Young’s Modulus (Linear Deformation)
Cross sectional Area (A) = w*t -- 6
Stress = F/A -- 7
Strain = ʌL/L -- 8
Following Hooke’s Elasticity Law:
Stress α Strain
Stress = Y* Strain -- 9
Where Y is Young’s Modulus.
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Sharma, O., & Sharma, D. (2021). How Elastic are Bands Those are Used in Everyday Life? European Journal of Applied Sciences, 9(4). 54-70.
URL: http://dx.doi.org/10.14738/aivp.94.10508
F/A = Y * (ʌL/L) --- 10
F = M*g --- 11
Y = (F*L)/(A* ʌL) --- 12
Y = (M*g*L)/( ʌL*A) --- 13
Y = (M*g/ ʌL) *(L/A) --- 14
Plugging equation # 5 to equation # 14
Y = k *(L/A) ---- 15
Percent error between slope values of k_slope and calculated average value of k_avg
% error = (k_avg – k_slope)*100/k_avg --- 16
DATA COLLECTION
Table 1: Data for dimensions of six rubber bands
Six different sized rubber bands were picked for this project and their length (L), width (W),
thickness (t) and cross- sectional area (A) are shown below in the Table # 1 in SI units.
R1 R2 R3 R4 R5 R6
L (m) 0.071 0.083 0.083 0.083 0.178 0.056
W (m) 0.0018 0.0032 0.0068 0.0068 0.0035 0.0038
t (m) 0.0011 0.0012 0.0018 0.0026 0.0014 0.0019
A (m^2) 1.98E-06 3.84E-06 1.22E-05 1.77E-05 4.90E-06 4.54E-05
Table 2: Data for mass versus length extension for six rubber bands
Mass blocks of anywhere from 20 g to 100 grams were used to hand with the support of a
hanger on each rubber band and then the length of the rubber band was recorded and shown
in the Table # 2 below.
Mass (g) R1 (cm) R2 (cm) R3 (cm) R4 (cm) R5 (cm) R6 (cm)
0 7.10 8.30 8.30 8.30 17.80 5.60
50 7.60 8.70 8.35 8.45 18.30 6.50
100 9.60 9.20 8.90 8.75 19.10 6.80
120 11.30 9.40 9.00 9.00 19.40 6.90
150 12.60 9.80 9.20 9.40 19.70 6.95
170 13.70 10.20 9.20 9.60 20.25 7.00
190 15.30 10.60 9.30 9.60 20.50 7.20
210 16.25 10.85 9.32 9.70 20.70 7.40
230 17.65 11.30 9.40 9.70 21.80 7.55
250 12.20 9.60 9.80 22.60 7.60
300 13.40 9.90 9.90 24.10 7.80
350 15.10 10.00 10.00 25.90 8.00
400 16.65 10.20 10.30 28.20 8.30
500 19.60 11.10 10.60 9.10
600 12.00 11.40 9.65
800 13.60 13.40 11.30
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European Journal of Applied Sciences (EJAS) Vol. 9, Issue 4, August-2021
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DATA ANALYSIS AND CALCULATIONS
Table 3: Calculation for change in length for 6 rubber bands
The change in length of each rubber band was calculated using equation # 4 and their units are
converted to SI units, Force applied by masses hung was converted to the weight of the mass or
force applied to the rubber band using equation # 11 and shown below in Table # 3.
Force (N) R1, ΔL
(m)
R2, ΔL
(m)
R3, ΔL
(m)
R4, ΔL
(m)
R5, ΔL
(m)
R6, ΔL
(m)
0 0 0 0 0 0 0
0.4905 0.005 0.004 0.0005 0.0015 0.005 0.009
0.981 0.025 0.009 0.006 0.0045 0.013 0.012
1.1772 0.042 0.011 0.007 0.007 0.016 0.013
1.4715 0.055 0.015 0.009 0.011 0.019 0.0135
1.6677 0.066 0.019 0.0092 0.013 0.0245 0.014
1.8639 0.082 0.023 0.01 0.013 0.027 0.016
2.0601 0.0915 0.0255 0.0102 0.014 0.029 0.018
2.2563 0.1055 0.03 0.011 0.014 0.04 0.0195
2.4525 0.039 0.013 0.015 0.048 0.02
2.943 0.051 0.016 0.016 0.063 0.022
3.4335 0.068 0.017 0.017 0.081 0.024
3.924 0.0835 0.019 0.02 0.104 0.027
4.905 0.113 0.028 0.023 0.035
5.886 0.037 0.031 0.0405
7.848 0.053 0.051 0.057
RESULTS
(a)Graphs for F vs ʌL for six rubber bands
A graph is plotted between the change in length and the force for all rubber bands to find out
the slope of the linear graph. The slope of the line found is the spring constant of the rubber
band as it follows Hooke’s law and shows linearity if F is on the Y axis and dL (change in length)
is on the X axis. The first rubber band R1 shows the spring constant of 19.4 N/m. It is shown in
Figure 2.