Proceedings of the Conference on the Introductory Physics Course, J Wilson,
editor. Published by John Wiley, 1997.
From Concrete to Abstract: How Video Can Help.
Dean Zollman
Department of Physics
Kansas State University
Manhattan, KS 66506
In selecting the title for this talk I made the assumptions that concrete experiences are a good way to start
the study of any topic in physics and that our job is to help students move from the concrete to the
abstract. The value of that idea has been discussed in some detail in other presentations. Thus, I
assume that the most appropriate way to teach physics is the strategy based on the work described by
McDermott and Redish. In this presentation I will describe how interactive video can provide one
component in the process of helping students move from concrete experiences to the abstract theories of
physics.
Interactive Video
By interactive video I mean a type of video in which the teacher and/or the
students have control over the visual images which appear on the screen. For
a video system to be interactive the learners must be able to have random
access to a wide variety of video images or sequences, be able to stop the
image on any of the individual frames, play those images at a variety of
speeds backward and forward. This student control can be achieved through
several devices -- a keypad that allows entry of commands, a bar code reader
which sends commands based on printed bar codes, or a computer which is
connected to the video player via a serial port.
Interactive video can be recorded in a variety of formats. For a long time truly
interactive video was possible only with laser-read videodisc. Recent
improvements in the quality and types of videotape players now make it
possible to use these tape players in a much more interactive environment.
While random access is not as convenient as on a videodisc, many of the
variable speed playing and stopping options are now available with rather high
quality pictures. Finally, digital video systems in which the video is stored on a
hard disk or on a CD-ROM provides another way to create interactive video.
This digital format also offers the opportunity to go beyond the present
concepts of interactive video and start considering image processing
techniques for the study of physics.
Modeling and Visualization
Several of the speakers during this conference have already mentioned the
importance of modeling to the physicist and the importance of teaching
students how we use modeling to understand nature. Students need to
understand how one might create a model and why we believe abstract
models are valuable in describing nature. Thus, in this paper I will concentrate
on modeling as an example of abstractions and used by physicists and
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demonstrate how interactive video can help students understand the process
and use of modeling.
I will divide modeling into three broad categories -- mathematical modeling,
visual modeling, and visualization. Mathematical modeling is the most
standard form which appears in introductory textbooks such as Resnick and
Halliday. When physicists or students create a mathematical model, they
prepare an equation which describes some event as accurately as possible.
Visual models are also used extensively by physicists but are not often
introduced explicitly in the introductory physics course. However, we do rely
on them frequently in discussing items such as the Bohr model of the atom or
an ideal gas model for the behavior of a collection of molecules. Finally, a
form of modeling which has become popular with the increased availability of
computational power is visualization. With visualization one tries to create a
representation of a rather complex event. Visualization techniques, which
sometimes can be quite abstract in themselves, can help students move from
a concrete event to a more abstract model or representation of that event.
Mathematical Modeling
As physicists we know that mathematical models can be quite effective in
describing very complex events. To demonstrate this idea to students we
have used a laboratory activity based on a video scene which shows a
collision of an automobile with a solid wall (Figure 1). This collision was filmed
by General Motors as part of its research on automobile safety and has been
included on the videodisc, Physics and Automobile Collisions1.
The goal of this activity is to determine equations which govern the motion of a
car as it collides with the wall at a normal city driving speed. Students reach
this goal by collecting distance and time data from the video. To set the scale
the students use the markers which are separated by 0.5 meters on the
automobile. Thus, we have a distance scale built into each frame of the video.
From documentation provided with the video we know that the frame rate of
the camera which recorded the event was 500 frames per second. With this
information we can collect distance and time data from the video sequence.
Several methods are available for collecting such data. Here we will consider
the method which is least expensive in terms of technology and equipment
requirements. (Other methods will be discussed in other section below. They
could be applied to this scene.) To collect the data the students place a clear
sheet of acetate on the video screen. Using an overhead transparency pen
they mark the location of a point of interest on the car. Then, they step the
video forward and mark the same point on the car again. Continuing through
the entire collision of the automobile with the wall, they collect distance-time
data for this collision.
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Figure 1: A picture from the videodisc Physics and Automobile Collisions.
The scene from which this picture was taken is used to create a mathematical
model of the motion of this car as it strikes a solid wall.
Students may step the video forward by using a key pad. However, a
convenient way to control the videodisc player is with a series of bar codes.
The bar code shown in Figure 2 plays the videodisc forward by 20 frames (.04
seconds of the automobile collision). With a series of these types of bar codes
the students can be given control over the video and can collect the data quite
easily without the worry of accidentally pressing a wrong button on the keypad
and becoming "lost" on the videodisc.
Figure 2: An example of a bar code for playing video from a videodisc. This
bar code will play Frames 14810 - 14830 of Car-Wall Collision
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Once the students have collected the data, they may enter them into a
computer, graphical calculator or plot them directly on paper. In general, we
prefer a spreadsheet or a program such as MathCAD for data analysis. Using
rudimentary curve fitting routines available in many different programs the
students can see how well a simple mathematical model fits the data which
they have collected.
In this example, the simplest approximations work. Before the collision, the
car is moving at a constant velocity. A straight line fit of the data gives that
velocity. This result is not a surprise because the car was being pulled at a
constant velocity before the collision occurred. However, the students can use
this curve fitting as a test of their data collecting and analysis ability.
Using the velocity calculated above one can fit with a parabola the data for the
time during which the car is in contact with the wall. This parabola is a very
good fit to the data. This result is, perhaps, a little surprising to the students.
In spite of all of the complex motions and changes which are happening to the
car during the time that it is in contact with the wall, a point on the car can be
treated as if it undergoes a constant acceleration. This exercise shows the
students how a simple mathematical model can be used to describe an
extremely complex event. (A model of a constant velocity after the car leaves
contact with the wall seems to work for the remaining video that we have.)
Students frequently complain that the standard approach to teaching physics
with its frictionless planes have little connection with reality. Here, we have
students work with a very real event and one which many students find rather
interesting. By completing this experiment before the students are introduced
to constant acceleration situations we can show the value of motion under
constant acceleration as a good approximation to real-world events.
Visual Modeling
We define a visual model as one in which a sketch, diagram or picture rather
than an equation provides the model. Thus, the picture of gas molecules
bouncing around as hard spheres would be a visual model of an ideal gas.
We use athletic events to help students understand how physicists can use
simplified visual models of an object, in this case a person, to understand an
event involving that object. Here, we borrow from the research techniques of
kinesiologists --people who study the motion of humans, particularly athletes.
They frequently use stick figures of those athletes to try to understand why one
technique results in a superior athletic performance than another. Using this
concept we introduce three models of the human being for consideration. The
first model is that we treat the human being as a point mass which is located
at the center of mass when the athlete is standing erect. This point is
approximately at most people's hips. Two other models involve stick figures of
three and five segments as shown in Figure 3. Using these figures students
can take data on the different models and see how the motion of the center of
mass of the athlete varies with each of the models.
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Figure 3: Three models of a high jumper. (a) The high jumper is treated as if
she were a point mass with her mass concentrated at her hip. (b) The jumper
is treated a three segments. Each segments has the percentage of body
mass indicated and has a uniform mass distribution. (c) This five segment
model is similar to the three segment one.
A very interesting event to study in this manner is the high jump. Using a
sequence from the Physics of Sports2 we can play the video frame by frame.
Students can draw the model on each individual frame of the athlete (Figure
4), and then collect the coordinates for the end points of each segment of the
model. Entering these points into a spreadsheet allows the student to
compare the motion of the center of mass for each of the models. To most
students' surprise they find that the center of mass using a three segment or
five segment model will sometimes go under the bar while for the point mass
model it must always go over the bar.
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Figure 4: A frame from the high jump scene. In this frame the three segment
model with bending at the hip is a very good model.
For this exercise students can use the same technological system as
described for the car collisions data collection. They may place acetates on
the screen, draw the models of the athletes for each of the video frames and
place the acetates on graph paper to read coordinates. Alternately, we can
also use a computer graphics which is placed on top of the video image. Here
the students can either draw, using the mouse, the stick figure and thus show
the model or click on the location of the athlete which represent the end points
of each segment. The computer can draw straight lines connecting them.
The computer overlay method, using a video tool such as the CUPLE video
tool described by Wilson during this conference, is a way to collect data
quickly and easily.
Independently of which of the models or data collection techniques that a
student chooses to use, he or she will always finds times when the athlete's
configuration does not match that of the model. For example, in the three
segment model which we have presented we assume that the athlete does not
bend her knees. High jumpers, of course, bend their knees significantly during
parts of their jump. However, if we are going to limit ourselves to a three
segment model and use one of those segments for the arms and hands, we
must limit ourselves either to a bend at the knees or at the hips but not both.
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When students have chosen a model, they must keep it throughout the entire
motion. Thus, by analyzing a real event they quickly see both the value of
simplified models and their limitations (Figure 5).
Figure 5: Another frame of the high jump. Here the jumper has bent her
knees, so the three-segment model which bends only at the hips does not fit
well. Pictures such as this one help students understand the limitations of
models.
Visualization
In each of the examples described above, we are creating and collecting
digital data from an analog video signal. That digitalization occurs by having
the student pick points of interest and collect the coordinates and time for
those points. This process is required, in part, because videotape and
videodisc provide analog signals. Recent advances in the storage of video as
digital information on computer disks offer a new way to use video in teaching.
Because video can now be stored digitally, we are able to bring to motion
video much of the image processing that has been available for still pictures.
These digital video images provide a new way for us to help students to learn
about some aspects of physics and to visualize physical events.
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As an example of this new visualization technique we have begun the testing
of a procedure to help students understand space-time diagrams and graphing
by visualizing a collision. Unlike the videodisc, the students collect data from
an experiment which they have completed. Thus, the students have more
flexibility in determining the scene than with the videodisc because they
operate the camera.
The first step in the procedure is for the students to capture onto their hard
disk digital video images of a collision. Once they have recorded these
images, they can select a section of the video which they consider most
interesting. From this selection consecutive pictures of the video can be
placed on top of each other to create a still image which contains images of
the cart at different times. The students see clear images of the cart but the
consecutive images start forming an overall image which looks something like
a graph of distance versus time for each of the two carts. By making the size
of the image from each of the consecutive frames smaller we lose the
recognizable image of the cart but are able to put additional pictures on the
screen at one time. Such images are shown in Figure 6 and are, in fact,
space-time diagrams of the motion of these two carts. By using this procedure
the students are better able to see how a graph or space-time diagram builds
up from looking at the motion of an object during consecutive time intervals.
(a)
(b)
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Figure 6: A visual space-time diagram of the collision of two carts. (a) The
space-time diagram created by placing 240 consecutive images on the screen
and viewing it from the lab reference frame. (b) The same collision and same
number of frames as viewed from a center of mass reference frame.
We can take this a step further and ask the students how the space-time
diagram would look if we were to view it from a different reference frame.
Figure 6(b) is an example of the space-time diagram for the collision in Figure
6(a) from the center of mass when one cart is much more massive than the
other. Using the data from these visual diagrams we can manipulate the video
frames without taking any new video to see what the view would be from the
reference frame of either cart or from the reference frame from the center of
mass. Going beyond this we can return to the video and ask: how would it
look if the collision were viewed from each of the different reference frames?
Because the video is digital we can in fact manipulate its location on the
screen and modify it so that the students can view the image from these
different reference frames. We now have a way to allow the students to
visualize how this collision would look in each of a collection of reference
frames. This visualization of motion, which was never actually recorded but
created from digital effects, provides a new way for students to look at
information in a variety of different reference frames.
This process of using digital video is now in its first steps of development3. As
we explore this new medium further we will find other ways to exploit the
advantages of digital video in the teaching of physics. Certainly the ability to
capture images onto a hard disk and then give the students control over those
images to collect data from their own video is a major step forward over the
prepared videotape or videodisc in which the students had to rely on someone
else for the images.
Conclusions
Video in a variety of formats - videotape, videodisc, and digital video - offer a
way to begin with familiar concrete events. Then, by analyzing these events
through modeling and digitalization students can explore real-world events
through hands-on experiences and see how physicists use abstract
mathematical and visual models to understand nature better. Because the
students see that simplified models are effective in understanding complex
events, they can be better motivated to work with these simplified models.
We would hope that a further outcome of this type of activity would be for
students to begin seeing how physics is applicable in the real world and in
other videos that they observe. For example, many special effects in films,
television, and music videos are created through an unusual shift in reference
frame. By studying reference frames through processes such as capturing
digital video onto a hard disk and manipulating the reference frame through
the video camera, they can begin to understand these effects and to unravel
the puzzle of how special effects are created. By applying models to scenes
such as the car collision or the athlete's motion, students may extend the idea
to other scenes or events which they see outside the classroom. Thus, video
can be a way to create an important bridge between concrete, everyday
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experiences and the more abstract models which are used by physicists to
describe those events.
Acknowledgments
Much of the videodisc work described in this paper was completed in
collaboration with Robert Fuller. The digital video work was completed with S.
Raj Chaudhury. The study of the use of digital video as a means to teach
physics is supported by the National Science Foundation under grant number
MDR 915022.
References
1.
2.
3.
Dean Zollman, Physics and Automobile Collisions videodisc (John
Wiley & Sons, New York, 1983).
M. Larry Noble and Dean Zollman, Physics of Sports videodisc
(Videodiscovery, Seattle, 1988).
For more details on the use of digital video in physics teaching, see S.
Raj Chaudhury and Dean Zollman, submitted to Computers in
Physics.
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