22_mamolo


97

Teaching Physics Modeling

Science Diliman (January-June 2003) 15:1, 97-99

Teaching Physics Modeling Using Computer Interfaced Video:
The Case of Paper Baskets

C. Mamolo1*, N. Capistrano, and E. van den Berg2
Science and Math Education Institute

University of San Carlos
Cebu City, Philippines

E-mail: 1cbmamolo@yahoo.com; 2edberg@cnms.net

MODELING IN PHYSICS

In typical high school and BS Physics courses, students
study the results of physics rather than the process of
doing physics. Even most laboratory work are
verification of known results of physics, rather than
doing physics with yet unknown results. Students are
rarely exposed to a core activity of physicists:
modeling. The availability of computer-video
interfacing and analysis software, such as Videopoint
and Coach, has greatly expanded the possibilities of
doing real modeling in physics education at the high
school and college levels. In this paper, we present and
work out a simple modeling problem on the free fall
of paper baskets. Our purpose is to illustrate the
possibilities of modeling in the classroom.

THE PROBLEM

When leaves of trees or sheets of paper fall, they fall
in a very irregular way. The paper zigzags slowly to
the ground in an unpredictable way. However, if we
fold the edges of the paper and make it into a little
“basket”, the fall is much more regular. The paper
basket moves slowly, but nearly straight to the ground.
This is not free fall; air resistance plays a big role. How
can we describe this motion mathematically? Is it
possible to make a model so that we will be able to
predict what influence different factors have, such as
the mass of the paper, the area of the bottom of the
basket, etc.?

When observing the basket falling, we notice that
almost immediately a constant velocity is reached: the
terminal velocity (v). Different baskets have different
terminal velocities. Factors which influence the
terminal velocity might be the mass (m) of the basket
(greater m, greater v) or the area (A) of the basket
(greater A, smaller v). In high school level physics
courses, we may use aerodynamics to get a proper
model. In lower level courses, we can do some smart
trial and error. Let us try this:

(1)

* Corresponding author

This is a simple formula that mathematizes our idea
that a greater mass should result in a greater terminal
velocity and that a greater area should result in a smaller
terminal velocity. The k is just a constant that we can
try to find experimentally. Also, perhaps it should not
be m, but m2 or m1/2. Similarly, we might have to take a
function of A rather than A straight, or if we know
something about aerodynamics, we might already want
to write v2 rather than v.

Our next task is to try to test the model in an experiment.
Then we can use the results to improve our formula
and get a better fit with data.

Please note that so far we have not used any physics
beyond high school level. At this stage we could still
introduce a force equation:

Our task is now to design an experiment to test the
model represented by Eq. (1).

m
k

A
ν = ⋅

dragF mg F= −∑



98

Mamolo, Capistrano, and van den Berg

THE COMPUTER-VIDEO INTERFACE

We can capture our own video of a falling paper basket
or we can right away analyze a video which had been
captured and edited earlier.

Videos are recorded by way of a video capturing device
like the VIDCAP. The videos are processed using a
video editing software such as Corel Draw. The
essential series of frames are saved. The edited videos
are then converted to a position-time graph by marking
the center of mass of the paper basket at every frame.
Fig. 1 shows an example of a graph recorded with the
Coach software.

With the same software, a velocity-time graph is
derived from the position-time graph as shown in Fig.
2. The slope at any point of each of these graphs can be
determined, and therefore, the terminal velocity.

THE VARIABLES

From the graphs, we determine the terminal velocity
of the falling paper basket (varying bottom area and
mass). Then, we can commence the investigation of
the correctness of the model (Center for Microcomputer
Applications, 1999).

With the mass of the paper basket held constant while
varying the cross sectional area of the paper basket, we
obtain a graph of v versus 1/A as shown in Fig. 3. The
curve formed by the data points seems parabolic.

Taking the square root of A (Fig. 4), the result looks
linear. From this we can then revise Eq. (1) to:

(2)

To investigate the influence of mass on terminal
velocity, we keep the cross sectional area constant and
vary the mass by adding whole pieces of paper of the
same kind into the basket. The result looks linear
(Fig. 5).

Based on these experiments, our best model is
represented by Eq. (2).

We could experiment further and try some other
variations of the basic formula. We could be more
sophisticated in deciding which graphs provide the best

P
o

s
it

io
n

Time (s)

0.0

-0.4

-0.8

-1.2

-1.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Fig. 1. Position-time graph recorded with the Coach software.

m
k

A
ν =

Data points

Linear (Data points)

5

4

3

2

1

0

0 0.1 0.2 0.3

T
e

rm
in

a
l 
v

e
lo

c
it

y

1/A

Fig. 3. Graph of v versus 1/A.

Fig. 2. Velocity-time graph derived by the Coach software
from the position-time graph shown in Fig. 1.

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.5

-0.1

-1.5

-2.0

-2.5

Time (s)

V
e

lo
c

it
y

 (
m

/s
)



99

Teaching Physics Modeling

fit, for example, we could use least squares techniques.
But remember that this modeling exercise is intended
for students in introductory physics courses. We think
this semi-quantitative way of working with data
provides an attractive experience in modeling.

Sources of error in this modeling exercise are the
following: (1) some inherent instability in the motion
of the paper basket; even in basket shape, it still wobbles
a bit; (2) the clicking on the marked point could be off
by a few millimeters, and in addition, there could be a
slight parallax error; (3) within the series, no frame
should be dropped in order to have a reliable time base;
and (4) differentiation of the position-time graph in
order to obtain a velocity-time graph introduces some
instability.

In spite of these inaccuracies, it is possible to obtain
and verify a reasonable model for students in
introductory physics courses.

CONCLUSION

In physics, we try to describe phenomena. Once we
have a good description, we can use that to predict or
even control phenomena. We try to describe phenomena
as precisely as possible using mathematics to create
our models. With a creative use of theory we try to
make a model and then we conduct experiments to test
the model and to improve it. That is what we did in this
experiment. The purpose of doing it was to illustrate
the way we work in physics. This experiment shows
that modeling in physics can also be done with the

simple physics available to high school and lower level
college physics.

REFERENCE

CMA Centre of Microcomputer Applications, 1999. Coach
system workbook. AMSTEL Institute, Universiteit van
Amsterdam.

Fig. 4. Graph of v versus A .

5

4

3

2

1

0

Data points
Linear (Data
points)

0 0.1 0.2 0.3 0.4 0.5 0.6

T
e

rm
in

a
l 
v

e
lo

c
it

y

A

Fig. 5. Graph of v versus m.

Data points
Linear (Data
points)

0

-1

-2

-3

-4

0 2 4 6 8

Mass

T
e

rm
in

a
l 
v

e
lo

c
it

y