Measuring Potential and Kinetic Energy using a Pendulum
Thomas Ehret
Adam Cooke, Marc Hnatyshin
B.C. Boivin
SPH3U, Grade 11 University Physics, Rockland District High School
Wednesday, November 14th, 2012.
Introduction:
The goal of this experiment is to accurately measure and calculate the potential and
kinetic energy of a pendulum.
Potential energy describes the energy that is
stored when an object is within a gravitational field
(Anonymous). For example, if a soccer ball is kicked into
the air, at its maximum height, it will have a lot more
potential energy than when it is on the ground, where it
has very little or none. Kinetic energy describes the
energy that is present during the motion of an object. If
an object is not in motion, it will have no kinetic energy.
Going back to the soccer ball example, while the ball
rests stationary on the ground, it has no kinetic energy,
but as soon as it is kicked, the ball has a lot of kinetic
energy (See Figure 1.).
A pendulum is
Figure 1. The potential and
kinetic energy of a baseball
shown based on its height
and motion (Anonymous,
Derivation of Kinetic Energy
Formula and Worked
Examples, 2012).
the system of a weight
of some sort suspended by a string that is attached to
something allowing it to swing (See Figure 2.). It was
discovered in 1602 by Galileo Galilei and was once used to tell
time in pendulum clocks. The total energy, represented by the
equation: 𝐸𝑇 = 𝐸𝑔 + 𝐸𝑘 , in a pendulum is always the same
Figure 2. A drawing of a
pendulum showing the
motion on either side of the
equilibrium (Colwell).
because the potential energy and the kinetic energy work with
each other. When one starts decreasing, the other increases
and it works for both types of energy.
The Law of Conservation of Energy is a law of physics that states that energy cannot be
created or destroyed (Anonymous, Law of Conservation of Energy). This means that the sum of
the potential, kinetic and other various types of energy in a system is always the same, just like
in a pendulum. When the ball of the pendulum reaches its maximum height, there is no kinetic
energy but plenty of potential energy. At the very middle/bottom of the swing, the potential
energy will be nothing and the kinetic energy will be plenty. When the math is done, it is proved
that the total energy will always be the same when adding the potential and kinetic energy.
The purpose of this experiment is to prove that the amount of energy in a closed system
obeys the equation: 𝐸𝑇 = 𝐸𝑔 + 𝐸𝑘 .
Theory:
𝐸𝑔 = 𝑚𝑔ℎ
𝐸𝑔 - gravitational energy/ potential energy
m – mass of the object
g – gravitational constant/ acceleration of gravity
h – height
𝐸𝑘 =
1
𝑚𝑣 2
2
𝑬𝒌 – Kinetic energy
m – mass of the object
v – speed
Materials and Methods:
Were those of Measuring Potential and Kinetic Energy using a Pendulum lab sheet on
Wednesday, November 7th,
2012 (Boivin, 2012).
Figure 2. Measuring Potential and Kinetic Energy using a Pendulum
lab setup (Ehret).
Results and Observations:
Table 1. Determining potential energy of the pendulum.
Mass in kg
Drop Height in m
0.05
0.2
0.5
0.98
0.995
1.00
Potential Energy, 𝑬𝒈 in J using
𝑬𝒈 = 𝒎𝒈𝒉
0.481
1.952
4.905
Table 2. Determining kinetic energy if the pendulum.
Mass in kg
Distance
travelled in m
for one swing
0.05
0.2
0.5
4.4
5.2
5.4
Time for 20
complete
swings in
seconds
42.5
45.2
45.6
Period
(time/20) in
seconds
Average
speed, v, in
m/s
Kinetic Energy,
𝑬𝒌 using 𝑬𝒌 =
𝟏
𝒎𝒗𝟐
𝟐
2.125
2.26
2.28
2.071
2.301
2.368
0.107
0.53
1.402
Calculations:
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
𝐸𝑔 − 𝐸𝑘
𝑥 100%
𝐸𝑔
Mass: 0.05kg
0.481 − 0.107
𝑥 100%
0.481
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 77.7%
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
Mass: 0.2kg
1.952 − 0.53
𝑥 100%
1.952
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 72.8%
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
Mass: 0.5kg
4.905 − 1.402
𝑥 100%
4.905
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 71.4%
%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
Discussion:
In this experiment, different weights were attached to the pendulum to find the
potential and kinetic energy for each. The potential and kinetic energy for each individual
weight should be the same or very similar based on the physics of a pendulum. For the 0.05kg
weight, the potential energy found was 0.481J and the kinetic energy found was 0.107J.The
results for this specific weight were not very accurate because the numbers are not close
enough where they should be. For the 0.2kg weight, the potential energy was found to be
1.952J and the kinetic energy was found to be 0.53J. These results were still not accurate
because the numbers are far apart. For the 0.5kg weight, the potential energy was 4.905 and
the kinetic energy was 1.402. These results were slightly more accurate but like the other two,
the numbers are too far apart.
These results are inaccurate because of many reasons and possible sources of error. It is
possible that the measurements of the distance of the swing were off because of the lack of
proper measuring material. This could be fixed by setting up the pendulum in front of a
blackboard allowing for a simple sketch of the travel of the weight. Then it would be very
simple to use a measuring tape and accurately measure the line. Another possible cause for the
inaccuracy is the friction of the swing. This friction includes air resistance and the area in which
the string was tied to the holder (ring). The air resistance is not possible to fix but as for the
string, it could be tied on to a spinning object on an axle to allow for a minimal amount of
friction. Another possibility that could have skewed the results is that the weights were not
accurately weighed/measured. This could have been fixed by weighing them to make sure, and
if they were off, using different weights or tampering with them.
Conclusion:
It was experimentally determined that for the 0.05kg weight, the potential energy was
0.481J and the kinetic energy was 0.107J with a percentage of difference of 77.7%. It was also
determined that for the 0.2kg weight, the potential energy was 1.952J and the kinetic energy
was 0.53J with a percentage of difference of 72.8%. Lastly, for the 0.5kg weight, it was
experimentally determined that the potential energy was 4.905J and the kinetic energy was
1.402J with a percentage of difference of 71.4%.
Questions:
1. Calculate the percentage difference between 𝐸𝑔 𝑎𝑛𝑑 𝐸𝑘 for the mass that gave you the
most precise results (closest) using the formula: %𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
𝐸𝑔 −𝐸𝑘
𝐸𝑔
𝑥 100%
See ‘Calculations’ (Mass: 0.5kg).
2. Calculate the percentage difference between 𝐸𝑔 𝑎𝑛𝑑 𝐸𝑘 for the mass that gave you the
worst results (furthest) using the formula from the previous question. Ensure that you
comment about how precise you feel this value is.
See `Calculations` (Mass 0.05kg). This value seems precise because of the possibilities of error
that skewed the final results. Had there been no errors occurring, this value would have been
very little or simply nothing.
3. List a few sources of error that you feel could have affected your results.
See ‘Discussion’ (second paragraph).
Selected References:
Anonymous. (2012). Derivation of Kinetic Energy Formula and Worked Examples. Retrieved
November 12, 2012, from Science Universe 101:
http://scienceuniverse101.blogspot.ca/2012/01/derivation-of-kinetic-energy-formula.html
Anonymous. (n.d.). Kinetic and Potential Energy. Retrieved November 12, 2012, from Library
Think Quest: http://library.thinkquest.org/2745/data/ke.htm
Anonymous. (n.d.). Law of Conservation of Energy. Retrieved November 12, 2012, from Library
Think Quest: http://library.thinkquest.org/2745/data/lawce1.htm
Boivin, B. (2012). Measuring Potential and Kinetic Energy using a Pendulum. Rockland: Science
Department, Rockland District Highschool.
Colwell, C. H. Simple Pendulum.
Ehret, T. Lab setup. Rockland District High School, Rockland.