VIRTUAL LEARNING ENVIROMENT FOR PHYSICS

INSTRUCTION

Pilar Martinez Jimenez, Gerardo Pedros Perez, Marta Varo Martinez

Department of Applied Physics, Cordoba University,Cordoba, Spain

Mª Carmen Garcia Martinez, Rosario Posadillo, Elena Varo Martinez

Department of Applied Physics, Cordoba University,Cordoba, Spain

Keywords: Simulation, Virtual Laboratory, Web portal, Physics Instruction.

Abstract: In this work the characteristics and educational applications of a virtual computer-assisted environment

teaching related with the motion of projectiles subjected to the force of the air

(http://rabfis15.uco.es/lvct/descargas/fisica/17/) is presented . This web portal has been designed as an

interactive tutorial system including several modules (simulations, problem resolution, knowledge

evaluation, etc.), it has been applied as a complementary teaching aid for the subject Physics in the first year

of Engineering and it is aimed to improve the understanding of the influence of the friction forces which

vary with the speed of the two-dimensional motions. The software presented has all the following features:

integrative character, self-evaluation tests, personalized and active learning process, adaptability to teacher’s

aims, versatility as a teaching tool, multimedia resources and simplicity. This study has been carried out

with students of the Higher Technical College (in Spanish: Escuela Politécnica Superior, EPS) Cordoba

(Spain), with highly favourable results when compared with students who did not use the software.

1 INTRODUCTION

Many researchers (Andaloro, G, et al., 1991, Fernando

Espinoza 2005, Dahlmann N., 2007, Sharma, S. V.

et al 2007, Murphy T.D., 2008, Anastasiades P.S., et

al. 2008) have shown the usefulness of computers

as an interactive communication means permitting

an access to all kinds of information (texts, images,

different types of data, graphics, etc.), as an

instrument for problem resolution and exercises, as a

tool for carrying out simulations of physical

phenomena and experiments, or to measure and

monitor laboratory experiments.

The computer applications in education have

been greatly extended adopting (

Baker, D.R., 1991,

Bacon, R.A., 1992)

, in most cases, a technological

educational model in which it was assumed that the

learning process can be improved as the means and

procedures for presenting the information go on

improving (Sharma, S. V. et al 2007). To sum up,

computers can also be a tool to help students to be

the protagonists in the progress of their own learning

process (Hicks and Laue, 1989; Li, 1998, Murphy T,

et al. 2002).

From this perspective, our work line has been

focused on the development and evaluation of

tutorial systems including the development of

interactive simulation laboratories (Martinez

Jimenez, P. et al., 2004, 2006).

Students´ learning difficulties related to

projectile motion have already been dealt with in

many research studies for many years (Borghi L. et

al 2005; Sharma S.V. , 2007). Furthermore, although

many computer programs have been developed in

Mechanics (Gillet D., et al. 2005), using simulations

of force and motion, but the motion of bodies

subjected to variable friction forces in resistive media

has not received much attention up till now, either in

the didactic research field or in education training. In

spite of this, the analysis of the characteristics of this

phenomena is an activity of great educational value in

university physics since it makes students study speed-

dependent forces and the influence of the different

variables affecting the motion (Marion, 1992).

For all these reasons we have conducted an

educational investigation process related with the

Martinez Jimenez P., Pedros Perez G., Varo Martinez M., Garcia Martinez M., Posadillo R. and Varo Martinez E. (2009).

VIRTUAL LEARNING ENVIROMENT FOR PHYSICS INSTRUCTION.

In Proceedings of the First International Conference on Computer Supported Education, pages 73-77

DOI: 10.5220/0001975300730077

 SciTePress

development, application and evaluation of a web

system devoted to the study of projectile motion in

resistive media.

2 OBJECTIVES

The general aims intended in this process were:

• To provide free access, via Internet, to

upgraded teaching tools related to engineering and

its teaching.

• To create a single environment in the web

joining together all the simulation computer

programs in the field of Science and Technology, as

well as the virtual laboratories.

• To incorporate a single evaluation system

(evaluation manager), and an examination executor.

• To relate the theoretical and practical aspects of

teaching.

• To upgrade engineering curricula looking for

more logical links among their subjects and

promoting the methodological change towards an

education system based on self-learning.

The educational objectives that this tutorial system

aims to develop are the following:

• To understand the influence of the friction

coefficient, the initial speed and the flight angle of a

projectile subjected to a resistive force of the air

proportional to the speed.

• To understand the influence of these factors for

the case of a projectile subjected to a linearly

dependent force of resistance of the air and also

proportional to its square.

• To find out and assess the advantages of

different mathematical methods (analytical, graphic

and numerical) which permit the resolution of the

problem of projectile motion in resistive media for

high and low velocities.

3 ANALYSIS OF PHYSICAL

PROBLEMS AND STRUCTURE

OF THE PROGRAM

The software for the simulation of the motion of

projectiles with a speed-dependent force is included

in the web portal

http://rabfis15.uco.es/lvct/index.php?q=node/22 .

This software offers the main Windows

facilities: interactivity and versatility. It comprises

four different parts that can be reached from the

program’s main menu: Previous Knowledge (In

Spanish “Preconceptos”), Tutorial (In Spanish

“Tutorial”), Simulation (In Spanish “Simulación”)

and Evaluation (In Spanish “Evaluación”), i.e. all

the tasks carried out in the educational process. As

they are intended for students, the programs are

highly user-friendly.

In addition, the program opens with an

animation representing the phenomena studied with

the aim of attracting the students´ attention from the

outset and obtaining a high degree of interaction

between the user and the physical simulation

implemented. In the second screen (Figure 1)

students can select the type of approximation to

perform: a) linear dependence or b) quadratic.

Figure 1: Main menu of the program.

Simulation has two sections; a study of the

motion of projectiles for resistance forces whose

dependence with respect to the velocity is linear, and

the second in which the correlation is quadratic. We

have thus applied and compared different numerical

methods as a function of the value of the velocity

exponent. Help on program functioning is always

available, animated icons illustrate the uses of

different buttons and the window calculator and the

text processor Word are accessible from the

program. With these last features, the student has

direct access to a list of exercises, hints,

complementary explanations, etc., which can be

written by teachers in order to fit the software to

their own pedagogical aims. The setup of the physics

problem to be simulated is also carried out in a

completely interactive way since users can choose

and design the work conditions.

In this application, the problem of projectile

motion in resistive and non-resistive media has been

used to make an approximation to Computational

Physics. The solution has been found with the

implementation of different numerical methods such

as the Newton-Raphson, the Iterative Fixed-Point,

the Euler and the Runge-Kutta methods.

The air resistance force over a projectile is a

linear dependence function of the velocity when

this is under 24 m/s. Furthermore, when the velocity

CSEDU 2009 - International Conference on Computer Supported Education

is over this limit, the force of the air friction is

proportional to the square of speed. Firstly, the

motion of a projectile was studied in the atmosphere

in which it was supposed that the force of resistance

was linearly speed-dependent. It is aimed to

determine the decrease in the range as well as the

influence exercised by the velocity on that decrease

both on the module and on the direction. The

equations defining the motion are:

´´´ Kmxmx −= and mgyKmmy −−=

´´´ (1)

Where m represents the mass, x´´ and y´´ the

components of the acceleration, x´ and y´ the

components of the velocity, K is the constant of the

air resistance and the g is gravity acceleration. The

solutions to these equations are

()

−

−= 1

(2)

()

gKv

−

+−= 1

(3)

The range of the projectile R is determined by

calculating, first, the time T (flight time) necessary

for the object to complete the whole trajectory and

substituting this in equation 1 corresponding to the

displacement.

()

gKv

−

= 1 (4)

The complexity of the procedure is presented in

the solution to equation 4, which is transcendental.

The mathematical methods used for obtaining the

analytic expression of the projectile’s flight time are

the following:

a) Graphic: in which the flight time is obtained as a

graphical solution of the system of equations, as

observed in Figure 2.

Ty =

()

gKv

−

= 1

(5)

Figure 2: Graphic method for solution of flight time.

b) Approximate: in which by a sequential evolution

and taking limit when k tends to zero, the following

linear approximations are obtained.

⎟

⎠

⎞

⎜

⎝

⎛

−≅

oyoy

(6)

oyox

(7)

⎟

⎠

⎞

⎜

⎝

⎛

−≅

(8)

This program can make a representation of factor

ΔR/R versus the friction constant for the linear

approximation and for the real values (ΔR=R’-R),

this approximation is only valid for constant values

equal to or under 0.01; above this value the

deviation of the real range with respect to that

calculated rapidly increases and, thus, the linear

approximation becomes unfeasible.

The linear projectile motion screen presents five

superimposed files, which permit the introduction of

the data of five different projectiles. For each of these

are obtained the numerical results corresponding to the

flight time, range, etc., by the analytic method

(approximation) graphic method, the Iterative Fixed-

Point and Newton-Raphson methods. Also, the errors

in each method are studied and all of them are

compared with the Newton-Raphson method, which is

the most accurate one, and the computation of each

algorithm is timed.

For this physical approximation, two numerical

methods have been implemented: the Iterative Fixed-

Point method and the Newton-Raphson method

(Curtis F. Gerald and Patrick O. Wheatley, 2003).

The function solving the first numerical method is

based on the Graphic Method. Its way of working is

to drag the two functions looking for the cross

section which indicates the flight time value, and

then replace this, T, in the equations 3 and 4 to

determine the maximum height and range. Likewise,

we make the calculation of the flight time and range

by the Newton-Raphson method.

Figure 3: The projectile Trajectories.

VIRTUAL LEARNING ENVIROMENT FOR PHYSICS INSTRUCTION

The graphic results permit users to visualize the

trajectories of all the projectiles studied for each of

the methods implemented (Figure 3). It is necessary

to point out that with this program the user is able to

understand the significance of the mathematical

model in the design of the physical model and,

therefore, in the understanding of the reality.

For velocities of over 24 m/s the force of

resistance of the medium, the air, is proportional to

the square of the speed:

FKv=− (9)

Using simple algebra and trigonometry, we find

that:

vKva ⋅−= and

vKvga ⋅−−= (10)

The solution methods of these equations are the

numerical methods: the improved Euler or Heun and

the Runge-Kutta method, the 2

, and 3

orders.

When the force of resistance of the air is

proportional to the square of the speed (section 2)

the operation is the same as in the first part of the

simulation. In this second section the improved

Euler and the Runge-Kutta methods, 2

, and 3

, are

implemented.

4 EDUCATIONAL

APPLICATIONS OF THE

PROGRAM AND PROPOSED

WORK METHODOLOGY

This virtual laboratory has been designed as a

support tool for the subject of Physics in the first

year of sciences or engineering.

Before doing the practical, the student

downloads the department’s web page

(http://rabfis15.uco.es/deptfisica/eps/ ) the program

guide for the practical, it is an open document

(included in the portfolio of the system) which can

be modified by any teacher.

In general, it is recommended to begin by the

problem of low-speed projectile motion, in which

the friction force of the air is proportional to the

velocity. Students can find out the analytical

solution offered by the program and analyze the

results obtained by the Iterative Fixed-Point and

Newton-Raphson methods, attempting to interpret

the errors predicted in each method. It is interesting

to analyze the results obtained in the graphic method

(Figure 2) and to explore how the graph obtained

changes as the resistance of the air is modified. It is

also desirable to analyze the errors obtained in each

resolution method. Finally, it is necessary to access

to the graph of the trajectories of the different

projectiles (Figure 3) with the aim of analyzing their

physical significance and draw the pertinent

conclusions.

In second time, the students can go on to study

the behavior of moving objects with an initial high

speed which are subjected to a friction force

proportional to the square of the speed. This problem

can be resolved by the numerical methods of Euler

and Runge-Kutta.

In order to assess the educational value, a

comparative analysis was made (2006-2007, 2007-

2008) of the learning results achieved by students

who had worked with this tool (experimental groups

GE1 and GE2) and other students at the same level

who followed a traditional teaching method (control

groups GC1 and GC2) based on a theoretical

exposition. The two experimental group students

worked in small groups with the simulation

program, following the instructions in an activity

program guide.

The evaluation of the learning program was

made through an analysis of the individual reports of

each student on finishing the experiment and a

complementary questionnaire on the understanding

of the phenomenon studied. The same evaluation

process was followed with the control group

students.

The analysis of the evaluation data was made

from a classification of the results obtained by the

different students. Four learning categories were

established: I (deficient), II (acceptable), III (good)

and IV (very good) (figure 4). On analyzing the first

results it was observed that the students in the

experiment groups generally achieved better results

than those of the control groups.

From these results, the greatest differences were

seen in level I (deficient) this being much greater in

the control groups, and in level III (good), notably

deficient acceptable good very good

GE1

GE2

GC1

GC2

Figure 4: Results of educational experience.

CSEDU 2009 - International Conference on Computer Supported Education

higher in the experiment groups.

From these facts, it is deduced that the

instruction process followed in the experiment

groups enabled students to achieve a higher progress

level than in the control groups and that the program

used constitutes a useful instrument for improving

the learning process.

The results show that the program is a useful tool

for improving the learning process in this subject.

5 CONCLUSIONS

This paper has described the creation process of a

tutorial system, carried out in several stages and

based on the computer simulation of projectile

motion in resistive media. The software has been

applied in a real teaching context, as a

complementary aid to the teaching of Physics in

first-year Engineering.

In this article we have shown the structure of the

tutorial system and described the characteristics of

the user’s interface and the physics problems

simulated. We have also shown its possible didactic

applications, establishing a methodological

proposition for using the system.

REFERENCES

Anastasiades, P.S., Vitalaki, E., Gertzakis, N., 2008

Collaborative learning activities at a distance via

interactive videoconferencing in elementary schools:

Parents' attitudes Computers & Education 50, 4,

1527-1539

Andaloro, G, et al.,1991. Modeling in Physics Teaching:

The Role of Computer Simulation, International

Journal of Science Education, 13, 243-254.

Bacon, R.A., 1992, The use of computers in the teaching

of Physics, Computers Education, 19, 57-66.

Baker, D.R., 1991, A summary of research in science

education during 1989: Computer in education, 75,

288-296.

Borghi, L., et al, 2005, A teaching–learning sequence on

free fall motion, Physics Education. 40, 266-273

Curtis F. Gerald, and Wheatley, P. O., 2003, Applied

Numerical Analysis, Addison-Wesley, London, 7

Edition.

Dahlmann N, Jeschke S, Pfeiffer O, et al., 2007, The

TEUTATES-Project: Tablet-PCs in modem physics

education, Conference Information: International

Conference on Engineering Education, Instructional

Technology, Assessment, and E-Learning, DEC 04-14.

Fernando Espinoza, 2005, An analysis of the historical

development of ideas about motion and its

implications for teaching, Physics Education, 40, 139-

146

Gillet D., Ngoc A.V.N., Rekik Y., 2005, Collaborative

web-based experimentation in flexible engineering

education, IEEE Transactions on Education, 48, 4,

696-704

Hicks, R.B., and Laue, H., 1989, A computer-assisted

approach to learning physics concepts. American

Journal of Physics, 57, 807-811.

Li, H., 1998, Information-Technology-Based Tools for

Reengineering Construction Engineering Education,

Computer Applications in Engineering Education, 6,

15-21.

Martinez-Jimenez, P., Casado, E., 2004 Electros:

Development of an educational software for

simulations in electrostatic, Computer Applications in

Engineering Education 12 , 1, 65-73

Martinez-Jimenez, P., Varo-Martinez M, Perez GP, et al.

2006, Tutorial and simulation electrooptic and

acoustooptic software as innovative methodology to

improve the quality of electronic and computer

engineering formation IEEE Transactions on

Education, 49 , 2, 302-308

Marion, J.B., 1992, Classical Dynamics of Particles and

System, Academic Press, New York and London, 2

edition

Murphy, T., Gomes, V.G., Romagnoli, J.A., 2002,

Facilitating process control teaching and learning in a

virtual laboratory environment, Computer

Applications in Engineering Education, 10, 2, 79-87

Murphy, T.D., 2008, Teaching rigid body mechanics using

student-created virtual environments IEEE

Transactions on Education, 51, 1, 45-52

Sharma, S. V., et al, 2007, Concepts of force and frictional

force: the influence of preconceptions on learning

across different levels, Physics Education, 42, 516-

521

VIRTUAL LEARNING ENVIROMENT FOR PHYSICS INSTRUCTION