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www.iop.org/journals/physed
Investigating the conservation of
mechanical energy using video
analysis: four cases
J A Bryan
Department of Physics and Astronomy, Ball State University, 2000 West University Avenue,
Muncie, IN 47306, USA
E-mail: jbryan@bsu.edu
Abstract
Inexpensive video analysis technology now enables students to make precise
measurements of an object’s position at incremental times during its motion.
Such capability now allows users to examine, rather than simply assume,
energy conservation in a variety of situations commonly discussed in
introductory physics courses. This article describes the use of video analysis
software in studying energy conservation for (1) objects in freefall, (2) simple
pendulums, (3) objects rolling down inclines, and (4) masses oscillating on
springs.
Introduction
My first encounter with the prospect of using
motion videos to teach high school physics
mechanics concepts occurred one summer in the
early 1990s while I was teaching at a large
suburban high school in the southern USA. I
proposed to film an object’s motion, place the
recording in a video cassette player (VCR), and
place an overhead transparency over the television
screen. Then, using the pause and frame advance
features of the VCR, my students could mark the
transparency to indicate the object’s location in
each frame and obtain a data source of successive
dots similar to what they obtained when using ‘dot
timers’, carbon, and paper tape. They would then
measure changes in the object’s position with time
and calculate velocities and accelerations just like
they had done previously with other position and
time data sets. I furthermore planned to use this
method to analyse the motion of more than one
object in the same video, which would enable us to
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study projectile motion, relative velocity, circular
motion, collisions, and energy conservation of
falling objects and pendulums.
Soon after the school year began, I took
my advanced placement physics students to the
school’s gymnasium, set up a video camera that
I borrowed from the school library, and had one
student take a basketball to the top of the bleachers
and drop it while being filmed. Another student
stood on the floor below and held a metre stick in
view that we could use for scaling when analysing
the distances that the ball fell between frames.
I had also found the specifications for the video
camera so that we would know how much time
passed between successive frames.
After filming this motion and returning to the
classroom, I placed the tape in the VCR, put an
overhead transparency over the television screen,
and played the video. What we observed was
terribly disappointing. The quality of the recording
and/or playback was so poor that the basketball
was just one big blur as it fell. When using the
0031-9120/10/010050+08$30.00 © 2010 IOP Publishing Ltd
Investigating the conservation of mechanical energy using video analysis
pause and frame advance features, viewers could
not even tell that there was a basketball anywhere
in the frame. Although the prospect of using video
to study motion was promising, the technology of
the early 1990s (or the affordable technology that
we had access to) was not yet sophisticated enough
to make it possible. However, today’s inexpensive
high quality cameras—even small Web cameras
(Wyrembeck 2009)—and inexpensive (or free)
computer software now make this technology
affordable to all.
Video analysis in the 21st century
I did not think much more about using video for
studying motion for several years until I attended
a conference in the autumn of 2002 and became
aware of new developments in video capture and
analysis that once again made the prospect of performing video analysis attractive. At this meeting,
I learned that not only had developments in digital
video increased the quality of video recordings so
much that you could actually see a falling basketball during video playback, but that several computer programs could now perform calculations
and readily produce graphs of position, velocity,
and acceleration. Short video clips suitable for a
variety of motion analyses and information related
to several free and/or inexpensive video analysis
programs may be found at http://jabryan.iweb.
bsu.edu/VideoAnalysis/index.htm. Commercially
available programs linked to this site include
LoggerPro (www.vernier.com/soft/lp.html), Measurement in Motion (www.learninginmotion.com/
products/measurement/index.html), and VideoPoint (www.lsw.com/videopoint/). Free software
programs linked to this site include Tracker
(www.cabrillo.edu/∼dbrown/tracker/index.html),
Physics ToolKit (www.physicstoolkit.com/),
DataPoint (www.xannah.org/datapoint/), and
KCS Motion (http://fac-staff.seattleu.edu/mason/
web/kcs/). Additional programs are constantly
being developed and may be found through Web
searches. Which program is best suited for a
particular user may depend in part upon cost
considerations, ease of use, and the various
features unique to each program.
Regardless of the specific program used,
video analysis is performed using the same basic
principles. The video camera is used to ‘collect’
position and time data, which can then be used
to mathematically and graphically model anything
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related to the position and/or motion of the
object. By using digital video’s frame advance
features and ‘marking’ the position of a moving
object in each frame, students are able to more
precisely determine the position of an object
at much smaller time increments than would
be possible with common timing devices such
as photo-gates, stopwatches, and the mechanical
‘dot timers’. Once the student collects data
consisting of positions and times, these values
may be manipulated to determine velocity and
acceleration, and, if mass is known, other values
such as kinetic and potential energies, force,
momentum, etc. Students may then graphically
display their collected and calculated data and
insert these graphs and information into other
documents.
Using digital video analysis to investigate
energy conservation
Nothing is more fundamental to studies in
physics than energy and its conservation. Four
of the most common situations in which the
conservation of mechanical energy is studied and
applied include (1) objects in freefall, (2) simple
pendulums, (3) objects rolling down inclines, and
(4) masses oscillating on springs. Each of these
situations typically requires students to assume
that mechanical energy is conserved in order
to determine velocities, positions, and energy
levels of objects at various locations along the
path of movement. Seldom do the students
or instructor perform actual measurement-based
calculations of the energies involved, or collect
any data to support the assumption that mechanical
energy is in fact conserved. Video analysis now
provides a cost-effective, yet sophisticated method
in which energy conservation may be examined
and verified. When using this technology, students
not only generate actual data supporting claims
of energy conservation in these situations, they
may also investigate the loss of mechanical energy
due to friction. The use of video analysis in
these four energy conservation situations that
are appropriate for use in introductory physics
courses are described in the following cases. All
figures are displayed from analyses using Vernier’s
LoggerPro software, although other programs
previously mentioned and linked to my video
analysis website will produce similar results.
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J A Bryan
Case 1: a bouncing ball
Introductory level physics courses typically present
rising and/or falling objects as the foremost
example of the conservation of mechanical energy.
Instructors and textbooks typically inform students
that after a ball is tossed upward, it loses kinetic
energy (KE = 0.5 mv 2 , where m = mass and
v = velocity of the object) and gains gravitational
potential energy (PEg = mgh , where m =
mass, g = the gravitational acceleration value of
9.8 m s−2 , and h = the height above the arbitrarily
chosen zero position) as it rises; and then loses
gravitational potential energy and gains kinetic
energy as it falls, such that the total mechanical
energy (TE = KE + PEg ) remains constant at
every location during the trip. Since the stationary
ball’s kinetic energy at this maximum height is
known by direct observation to be zero, the total
mechanical energy of the ball at any location
is therefore equal to its maximum gravitational
potential energy. Although students must use
the mechanical energy conservation relationship
(TE = KE+PEg ) to specify the amounts of kinetic
and gravitational potential energies at any location
of the ball’s path, they rarely collect any actual
data to support these calculations.
In my experience, few students have had any
difficulty remembering this energy conservation
and transformation relationship, and are able to use
the energy conservation assumption in working on
many problems. Despite this ability, they have
demonstrated great difficulty in sketching those
energy relationships in graphical form (Bryan
2004). This inability to relate actual motion to
its graphical representations, despite being able to
correctly articulate the description of the motion,
has been studied and described in numerous
reports (Beichner 1994, 1996, 1999, McDermott
et al 1987).
Figure 1 displays the movie window screen
capture in which the location of a ball has been
marked while falling and bouncing three times.
The origin was chosen to be located at the lowest
position marked so that potential energy values
would be greater than or equal to zero at all
instances. This position and time data were then
manipulated to determine the velocity, kinetic
energy, and gravitational potential energy of the
ball each one-thirtieth of a second along its path.
Kinetic and gravitational potential energies
were then summed in order to determine the
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Figure 1. Screen shot of marked video.
total mechanical energy. Plots of these energies
with time are displayed in figure 2. Note that
the total mechanical energy does indeed remain
constant while the ball is in the air. However,
mechanical energy is lost during each bounce,
the amount of which may be determined by the
students. Interesting discussion can result by
having students speculate about where the ‘lost’
mechanical energy ended up. Not displayed, but
also informative, are time dependent graphs of
velocity, net force, and acceleration that may be
used to reinforce other essential physics concepts
related to objects in free fall.
Case 2: a simple pendulum
An assumption of energy conservation in a
simple pendulum (a mass suspended by a string)
allows one to determine the ideal velocity of
the pendulum bob at any location and/or time
after its release. In reality, the amplitude of a
simple pendulum will noticeably diminish as it
loses energy during its motion, so all velocity
calculations are in error.
Figure 3 displays
the marked video screen shot of a 305 g ball
that swings through three complete cycles while
suspended from a light string. The origin was
chosen to be the equilibrium position directly
below the suspension point where the ball would
reside if not displaced, therefore making all
gravitational potential energy values greater than
or equal to zero.
The energy graph of this simple pendulum
is shown in figure 4. An analysis of the graphs
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Investigating the conservation of mechanical energy using video analysis
energy vs time
7
video analysis: total mechanical energy
video analysis: kinetic energy
video analysis: gravitational potential energy
6
energy (J)
5
4
3
2
1
0
–1
0
1
2
time (s)
Figure 2. Energy graph of the bouncing ball.
Figure 3. Screen shot of marked video.
gives proof that the ball’s maximum kinetic energy
occurs when the ball is at its lowest position,
and that its minimum kinetic energy occurs
when the ball is at its highest positions during
each cycle. The graph also clearly shows that
mechanical energy is not conserved in this case—
as the pendulum ‘lost’ approximately one-fourth
of its total mechanical energy after only passing
through three complete cycles. Not displayed
are time dependent graphs of horizontal and
vertical positions, velocities, and accelerations,
also indicating damped motion, which may be
used to reinforce other essential physics concepts
related to simple pendulums and other objects in
periodic motion.
January 2010
Case 3: an object rolling down an incline
In addition to linear kinetic energy and gravitational potential energy, one must also consider
rotational kinetic energy when analysing energy
conservation of objects rolling down inclines.
If we consider the object’s lowest position on
the incline to be the zero reference point for
gravitational potential energy, then the total energy
available in the system is equal to the gravitational potential energy at the top of the incline.
Students regularly use the relationship that the
sum of the gravitational potential energy, linear
kinetic energy, and rotational kinetic energy at
any position on the incline will be equal to
the gravitational potential energy at the top of
the incline to calculate velocities at any position
along the path. Regardless of how beneficial
this problem-solving approach may be to students’
understandings of energy conservation and their
abilities to solve for unknown velocities and/or
positions, students must once again assume that
energy is conserved without having performed
any data collection experiments to validate that
assumption.
Figure 5 displays a screen capture of the
marked movie window in which a 5.44 kg solid
rubber sphere starts from rest and rolls down
an incline. The origin has been moved to the
lowest marked position of the ball. The increasing
separation of the marks clearly indicates that the
ball increased its speed as it rolled down the
incline.
Figure 6 displays the graph obtained when
plotting the energy forms relevant to this situation.
PHYSICS EDUCATION
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J A Bryan
energy vs time
0.8
video analysis: kinetic energy
video analysis: potential energy
video analysis: total energy
energy (J)
0.6
0.4
0.2
0
0
1
2
3
time (s)
4
5
6
encountered in any of the other three cases—
elastic potential energy. As a mass suspended
on a spring rises and falls, its mechanical energy
consists of elastic potential energy, gravitational
potential energy, and kinetic energy. Figure 7
displays a screen shot of a 500 g mass suspended
by a large metal elastic spring in which the top
of the mass in each frame of the video has been
marked. The origin has been chosen as the lowest
point marked on the movie.
Figure 5. Screen shot of marked video.
Rotational kinetic energy was calculated using
the relationship KEr = 0.5 I ω2 , where I =
the rotational inertia of a solid sphere = 0.4 mr 2 ,
and ω = the rotational velocity of the ball =
v/r . This leads to a rotational kinetic energy of
0.2 mv 2 , where v is the linear velocity of the
ball. Gravitational potential energy and linear
kinetic energy were calculated as usual. Note that
the sum total mechanical energy did not in fact
remain constant, but decreased by approximately
20% during its brief trip. This loss of mechanical
energy is most probably attributable to friction
between the soft rubber exterior of the ball and the
metal channel through which it rolled.
Case 4: a mass oscillating on a spring
The investigation of a mass oscillating on a
spring involves an additional form of energy not
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PHYSICS EDUCATION
Graphs of the energies involved in this
situation are displayed in figure 8. Gravitational
potential energy has been calculated with respect
to the lowest marked position and is therefore
always greater than or equal to zero. The relatively
low amounts of kinetic energy are also greater
than or equal to zero at every instance. In
order to make elastic potential energy values also
always greater than or equal to zero, the elastic
potential energy has been calculated as PEe =
0.5kx 2 = (0.5)(7.9 N m−1 )(0.84 m − Y )2 ,
where Y = the height above the origin (the y coordinate of the marked point), 7.9 N m−1 is
the spring’s elastic constant, and 0.84 m is the
maximum displacement of the stretched spring.
Note that mechanical energy was very nearly
conserved through three complete oscillations of
this system. Not displayed are time-dependent
graphs of vertical position, velocity, acceleration,
and net force, which may be used to reinforce other
essential physics concepts related to the mass on a
spring and objects in periodic motion.
January 2010
Investigating the conservation of mechanical energy using video analysis
energy vs time
20
energy (J)
15
10
video analysis: total energy
video analysis: rotational kinetic energy
video analysis: translational kinetic energy
video analysis: gravitational potential energy
5
0
0
0.5
1.0
time (s)
1.5
2.0
Figure 6. Energy graph of a solid sphere rolling down an incline.
software, however, cannot be classified as the
typical delay-time graphing because once these
programs have initially produced the graphs in
delay time, users then have the capability of
viewing the action multiple times while following
the graph in real time.
While it is possible that some investigations
may be made just as easily, accurately and
precisely using probe-ware and/or sensors, I see
several important advantages of video analysis
over probes and sensors.
Figure 7. Screen shot of marked video.
Comparison of video analysis to motion
rangers
Technology savvy physics teachers may readily
call attention to the fact that similar results can
be obtained in ‘real time’ using a microcomputer
based laboratory (MBL) motion sensor probe.
Beichner (1990) and others have described the
benefits of real-time graphing, although the
benefits of real-time graphing versus ‘delay-time’
graphing are debatable. Brasell (1987) did find
that real-time graphing with MBLs improved
students’ graphing skills more than ‘delay-time’
graphing of the same events, and a later study
in which students analysed motion contained
on videotape showed no significant differences
(Brungardt and Zollman 1995).
Graphing
using today’s more sophisticated video analysis
January 2010
(1) Video analysis allows for study of
two-dimensional motion, such as revolving
objects or projectiles.
(2) More than one object can be analysed in any
video, which can lead to detailed
comparisons of multiple objects that are in
the same system.
(3) Video analysis can be performed without all
of the cumbersome wires and sensors
associated with MBLs.
(4) Video analysis can be performed on objects
that are located well beyond the range of
most motion sensors.
(5) Video analysis software is much less costly
than MBL motion sensors.
(6) Anything that ever has been, or can be
videotaped, may be analysed (see Laws and
Pfister 1998).
In addition, computer simulations and other
technologies, such as MBL probes and sensors,
often take away the possibility for ‘experimental
error’ and raise concerns according to Chinn and
PHYSICS EDUCATION
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J A Bryan
energy vs time
video analysis: total mechanical energy
video analysis: elastic potential energy
energy (J)
3
video analysis: kinetic energy
video analysis: gravitational potential energy
2
1
0
0
1
2
3
4
5
time (s)
Figure 8. Energy graph of a mass oscillating on a spring.
Malhotra (2002) that the ‘messiness of the natural
world is artificially cleaned up’ (p 208) with the
result that ‘students may not learn to control
variables in situations where they are not presented
with a priori lists of variables’ (p 209), students
may introduce and encounter error using video
analysis via the ‘marking’ process. Collected data
can only be as accurate as students are in marking
the exact same location on the moving object(s)
in each frame. Although each frame is precisely
timed by the digital recording, the exact positions
of the object(s) at those times are dependent upon
the marking skill of the student. The quality of
the video is also a factor that influences marking
errors. The faster the object is moving, the more
blurred it may appear in each frame. The accuracy
in which the distance scale for the motion is
marked is also a possible source of error. If the
known distance is marked too long or too short,
then all values calculated by the program will be
in error. While these error sources do not usually
lead to as much error as is normally found in
other timing and position measuring techniques,
the introduction of error does make this form of
analysis more realistic as a scientific process than
do many simulations and/or MBL probes.
Because it is a relatively recent technological
development, few studies have been conducted
in order to examine the effectiveness of implementing video analysis as an instruction tool in
either mathematics or science. Like Escalada and
Zollman (1997) and Rodrigues et al (2001), I
have also found that most of my students found
the video analysis software relatively simple to
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learn to use and recognized its benefits in helping
them to learn physics. A more recent study by
Pappas et al (2002) did find that the VideoPoint
video analysis program was successful in helping
pre-service teachers better understand the links
between multiple representations of motion presented in graphical, tabular, and formula formats.
In addition to this, because video analysis software
may be used for many of the same purposes as
are currently served by MBL motion sensors and
photo-gates, one can cautiously make assumptions
that some of the same features that make MBL
laboratories effective, such as quickly generating
graphs so that students may spend more of their
time studying physics concepts instead of in
burdensome point plotting (Barton 1998), should
also lead to success using video analysis.
Conclusion
Video analysis technology has improved immensely since the seemingly ancient 20th century
method of placing an overhead transparency on
a television screen and marking the locations
of some object during pause and advance with
a videocassette player/recorder (VCR). Today’s
higher quality digital video, which increases the
number of coordinate points and allows for more
precise study, causes many past studies on the effectiveness of video analysis instructional methodologies to be outdated and/or obsolete. Many
of the studies on the effectiveness of real-time
and delayed-time graphing from the past 20 years
will need to be replicated in order to see whether
January 2010
Investigating the conservation of mechanical energy using video analysis
and/or how recent technological advances have
influenced the value of this instructional method.
Furthermore, neither the use of video analysis
software and other forms of technology, nor any
innovative practices can guarantee that learning
will be enhanced for the user (Coleman et al 1998).
The effectiveness of computer technology depends
not only on how the computer and software are
used, but also on the interactions of the students
as they use the technology (Otero et al 1999).
Regardless of the type of computer technology or
any other educational innovation used in physics
instruction, student learning will be maximized
only when the instructional practices ‘are designed
according to different educational and psychological theories and principles’ (Schacter and Fagano
1999, p 339) in relation to individual students’
needs and abilities. Research on the effectiveness
of video analysis should occur in a variety of
instructional methodologies, including, but not
limited to constructivism, guided and unguided
enquiry, and direct instruction.
Received 16 September 2009, in final form 17 September 2009
doi:10.1088/0031-9120/45/1/005
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J A Bryan is a former high school
physics teacher and is currently an
assistant professor of physics education at
Ball State University, Muncie, IN, USA.
His research interests include the use of
physical and technological resources for
teaching and learning physics, and
pre-service and in-service teacher
preparation and professional
development.
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