5 v

é

.a.
Vt ‘

 

 

 

 

.¢... lrflr.‘ I
.. ; 4,5

1....

 

a

4.

 

 

 

 

 

 

 

 

 

.l!‘
:2 . a;
man“.- Ila—‘5‘
II. 3"..-

31%?

a

I .1».
1: 22.. .a »
20......Inl !

at, ,

all! 1.
its ..D..I~¢fia3t
.e :1: Ir...

73%.. I: ‘58:”

1t.
«’1qu 5..."
AV: .1. L‘asif...’

thug-)3

laud, .. u»...

E: 3,
{3.1.1:
I}, A — A, . 7

fig? W... , ifiwmmw

t.

01.4

A.“

2?...
u .4.

¢

 

THESIS
’W
0‘

9 "U0

AR

lHIlull1lillllllllfilllllllllglllillHHI

31293 01834

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the

thesis entitled

COMPARATIVE STUDY USING TECHNOLOGY VS TRADITIONAL LEARNING
IN HIGH SCHOOL CONCEPTUAL PHYSICS

presented by

.David Kim McCreight

has been accepted towards fulfillment
of the requirements for

MASTERS degree in BIOLOGY

@411.“

Major professor

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

PLACE IN REFURN BOX to remove this checkout from your record.
To AVOID FINE-S return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

N 0 4 2004

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

use www.mu

COMPARATIVE STUDY USING TECHNOLOGY VS TRADITIONAL LEARNING
IN HIGH SCHOOL CONCEPTUAL PHYSICS

By

David Kim McCreight

A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of
MASTER OF SCIENCE

Division of Science and Mathematics Education
College of Natural Science

1999

Professor Merle K. Heidemann

ABSTRACT

COMPARATIVE STUDY USING TECHNOLOGY VS TRADITIONAL LEARNING
IN HIGH SCHOOL CONCEPTUAL PHYSICS

By

David Kim McCreight
This study compared high school conceptual level physics students’ progress on a pretest
and post-test using two different teaching methods for laboratories and demonstrations in
the unit on vectors and projectile motion. Using both teaching methods, the study also
evaluated how students achieved based on gender. For two weeks, students in the vector
or projectile motion control group were given traditional laboratories and demonstrations.
The experimental group for each was given laboratories and demonstrations, using
technology in the form of graphing calculators and video laserdiscs. The statistics
included finding the means and standard deviations and applying the Wilks’ Lambda test
on the separated pretest and post-test vector and projectile motion questions. When
comparing the control with the experimental group statistically, the vector experimental
group performed better than the control group. On the other hand, analysis of the
projectile motion part of the study revealed no statistical differences between the control
and the experimental groups. In addition, when comparing gender, there was no
statistically significant difference between female and male students. Moreover, there
was no statistical significance between group and gender. Overall, both group and gender
analysis showed improved scores from pretest to post-test. From this study, technology in
the form of graphing calculators and videolaser disc had an enhanced effect on student
achievement in learning only the topic of vectors. On the topic of projectile motion, the

experimental and control groups did not differ significantly from pretest to post-test.

ACKNOWLEDGEMENTS

I would like to thank my family, whom I love very much.
I would like to thank Jeff Chomy and Brian Drobert for their help on graphing calculators

programs. Also, thanks to my colleague, Glen Deslich for his expertise and support.

I would like to thank Pam Hartman at Texas Instrument for theTI3 workshops and
graphing calculators loan program. Also, thanks to the mathematics department at

Eastern High School for their loan of graphing calculators.

I would like to thank statisticians, Margarida Geraldes and Ray Bingham for expertise.

I would like to thank the Lansing School District’s Evaluation Services for assisting me

with the data formatting and demographics.

I would like to thank my advisor, Merle Heidemann for her patience, guidance, and
support and to the two committee members Dan Stump and Gerd Kortemeyer for their

willingness to improve physics education.

Finally, special thanks to Helen Waldo for her expertise, professionalism and caring.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .................................................................................................... vii—viii
INTRODUCTION
Statement of Problem and Rationale for Study ........................................................ I
Literature Review ..................................................................................................... 3
Demographics .......................................................................................................... 9
IMPLEMENTATION OF UNIT
Overview ................................................................................................................ 10
Vector Control Lab 1 ............................................................................................. 17
Vector Control Lab 2 ............................................................................................. 18
Projectile Motion Control Lab 1 ............................................................................ 18
Projectile Motion Control Lab 2 ............................................................................ 20
Vector Experimental Lab 1 .................................................................................... 20
Vector Experimental Lab 2 .................................................................................... 22
Projectile Motion Experimental Lab 1 ................................................................... 23
Projectile Motion Experimental Lab 2 ................................................................... 24
Vector and Projectile Motion Control Demos ....................................................... 26
Vector and Projectile Motion Experimental Demos .............................................. 28
EVALUATION .................................................................................................................. 30
DISCUSSION AND CONCLUSION ................................................................................ 40
APPENDIX A (Control Group Labs—Vector and Projectile Motion)
1. Control Vector Lab l—Vector Addition Lab ............................................... 43
11. Control Vector Lab 2—The Equilibrium Lab .............................................. 46
III. Control Projectile Lab l—Bulls Eye Lab ..................................................... 50
IV. Control Projectile Lab 2—Softball Throw ................................................... 56
APPENDIX B (Experimental Group Labs—Vector and Projectile Motion)
1. Experimental Vector Lab l—Find R, given the X and Y components ........ 60
II. Experimental Vector Lab 2—Find the X and Y components, given R ........ 64
[11. Experimental Projectile Lab l—Parametric Equations ................................ 68
IV. Experimental Projectile Lab 2-—‘V0 and 6 to find T, R, and H ..................... 72
APPENDIX C (Control Group Demos—Vector and Projectile Motion)
I. Cut Out Vectors ............................................................................................ 75
II. Vector Rope and Potato Bag Demo .............................................................. 76
III. 2—Dimensional Motion Demo ....................................................................... 77
IV. Shoot the Monkey Demo .............................................................................. 78
V. Hall Cart Demo ............................................................................................. 80

iv

APPENDIX D (Experimental Group Demos—Vector and Projectile Motion)

1. Vectors by Video Laserdisc Demo ............................................................... 81

II. Videolaser disc's 2-Dimensional Motion Demo ........................................... 83
APPENDIX E (Assessments)

I. Vector and Projectile Concept Map .............................................................. 85

II. Vector and Projectile Concept Map Key ...................................................... 86

III. PreTest /PostTest .......................................................................................... 87
BIBLIOGRAPHY .............................................................................................................. 9O

LIST OF TABLES

IMPLEMENTATION OF UNIT
TABLE 1: Week One Lesson Plan ........................................................................ 12
TABLE 2: Week Two Lesson Plan ....................................................................... 13
TABLE 3: Week Three Lesson Plan ..................................................................... 14
TABLE 4: Week Four Lesson Plan ....................................................................... 16
EVALUATION
TABLE 1: Vector Pretest/Posttest Statistics by Group .......................................... 32
TABLE 2: Vector Pretest/Posttest Statistics by Gender ........................................ 33
TABLE 3: Vector Pretest/Posttest Statistics by Group and Gender ..................... .34
TABLE 4: Projectile Pretesthosttest Statistics by Group .................................... 35
TABLE 5: Projectile Pretest/Posttest by Gender ................................................... 37
TABLE 6: Projectile Pretest/Posttest Group and Gender ...................................... 38

vi

LIST OF FIGURES

EVALUATION

Vector Statistical Graphs
Figure 1: (Vector Pretest and Posttest mean scores by Group) .......................... .32
Figure 2: (Vector Pretest and Posttest mean scores by Gender) ......................... .33
Figure 3: (Vector Pretest and Posttest mean scores by Group and Gender) ....... .34

Projectile Motion Statistical Graphs

Figure 4: (Projectile Motion Pretest and Posttest mean scores by Group) .......... 35

Figure 5: (Projectile Motion Pretest and Posttest mean scores by Gender) ........ .37

Figure 6: (Projectile Motion Pretest and Posttest mean scores by Group and
Gender) ............................................................................................... 38

APPENDIX A (Control Group Labs—Vector and Projectile Motion)

Vector Addition Lab 2
Figure 1: (Force Table—Kramer,l995) ................................................................. 46

Projectile Motion Graphing Calculator Check Program for Bull's eye lab (BALLCUP)
Run Sample

Figure 2: (Entering the value of g) ....................................................................... 55
Figure 3: (Entering the horizontal distance) ........................................................ 55
Figure 4: (Entering the vertical distance to floor) ................................................ 55
Figure 5: (Entering time one to compute horizontal speed) ................................ 55
Figure 6: (Entering time two to compute horizontal speed) ................................ 55
Figure 7: (Entering time three to compute horizontal speed) .............................. 55
Figure 8: (Displaying the horizontal speed and time to fall) ............................... 55
Figure 9: (Displaying how far out to place the target) ......................................... 55

Projectile Motion Graphing Calculator Check Program for Softball Throw Lab
(PROJMOT) Run Sample

Figure 10: (Entering the value of g) ..................................................................... 58
Figure 11: (Entering the total time of travel) ....................................................... 58
Figure 12: (Entering the range of distance) ......................................................... 58
Figure 13: (Displays the Total Time, Time up and horizontal velocity) ............. 59
Figure 14: (Displays the vertical velocity, initial velocity, and angle) ................ 59
Figure 15: (Displays the maximum height) ......................................................... 59

vii

APPENDIX B (Experimental Group labs—Vector and Projectile Motion)

Vector Graphing Calculator Program (VECT RES) Run Sample

 

Figure 1: (Entering the number of vectors) ......................................................... 63
Figure 2: (Entering the magnitude of 1“ vector) ................................................. 63
Figure 3: (Entering the angle for 1‘ vector) ........................................................ 63
Figure 4: (Entering the magnitude for 2"d vector) ................................................ 63
Figure 5: (Entering the angle for 2“d vector) ........................................................ 63
Figure 6: (Displaying resultant vector magnitude and angle) .............................. 63
Vector Graphing Calculator Program (VECTCOMP) Run Sample
Figure 7: (Entering the vector magnitude) ........................................................... 67
Figure 8: (Entering thevector angle)- - .......................................... 67
Figure 9: (Displaying the vector's X component) ................................................ 67
Figure 10: (Displaying the vector's Y component) ................................................ 67
Projectile Motion Graphing Calculator (Parametric Equations) Sample Problem
Figure l 1:(Entering parametric equations into Y==). .............................................. 70
Figure 12:(Resulting Graph) .................................................................................. 70 _
Figure l3:(Drawing the wall using 2"d Draw) ........................................................ 70
Figure 14:(Entering Line from Draw menu) .......................................................... 70
Figure 15:(Resulting Graph) .................................................................................. 70
Figure 162(Entering another set of equation using 25°) ......................................... 70
Figure 17:(Resulting Graph with more than one set of equations) ........................ 71

Projectile Motion Graphing Calculator Program (PROJYVST) Run Sample

Figure 18:(Entering the value of g) ........................................................................ 74
Figure 192(Entering the initial velocity) ................................................................ 74
Figure 20:(Entering the initial angle) ..................................................................... 74
Figure 21:(Displaying the projectile's graph) ........................................................ 74
Figure 22:(Displaying the graph with equation, T, X, and Y set to 0) .................. 74
Figure 23:(Displaying T = 2.03, X = 7.5.00m, Y: 19.6m) ..................................... 74
Figure 24:(Displaying T = 4.05, X = 50.01m, Y: 0.01m) ..................................... 74

APPENDIX C (Vector and Projectile Motion Demos)
Figure 1: (Shoot the Monkey) ............................................................................. 78

viii

INTRODUCTION
STATEMENT OF PROBLEM AND RATIONALE FOR STUDY
Meetings in physics education and the advertisements on the pages of The Physics
Teacher, show that the use of technology in physics education is quite evident. Many
educators have touted using graphing calculators, computer simulation programs and
laboratories via computer or calculator units with probes (Thornton, 1990; Taylor, 1995;
Stump, 1995; Squire, 1987; Phillips, 1999; Nicol, 1997; Krieger, 1990; Flynn, 1994;

Embse, 1990).

I have read how technology increases cooperative learning (Thornton, 1990), critical
thinking (Krieger, 1990; Engelhardt, 1993), and motivates students through hands-on
experiments (Squire, 1987; Phillips, 1999; Thornton, 1990). Can technology make

students more active learners and learn at a deeper level?

This technology could be in the form of microcomputers, TV, radio, video camcorders,
audio sounding, graphing calculators, MBL or CBL units (Microcomputer Based
Laboratories, MBL, or Calculator Based Laboratories, CBL), and video laser discs. For
my unit, technology was in the form of graphing calculators and a video laserdisc player.
Because microcomputers and MBL or CBL units were not available to me, the
mathematics department let me use their ten TI 83 (Texas Instrument) graphing
calculators. I also used the science department's video laserdisc player. It allowed
students to view parts of two physics Iaserdiscs: Physics At Work and Cinema Classics.
During the summer of 1997, the research for this unit was done at Michigan State

University with the intent of my unit being based on microcomputers along with MBL or

CBL units with graphing calculators. Moreover, I even had Pam Hartman at Texas
Instrument setup a workshop in the fall at another school to gain experience using CBL
units. The workshop was a success; however, the computers never showed at my school
and CBL units were not available for the study. So, the ten graphing calculators and

Videolaser disc player had to suffice.

The unit topic was on vector and projectile motion because I wanted to learn more about
them as well as learn how technology could be utilized effectively in physics education.
Moreover, I chose vectors because I wanted to determine if I should expand or reduce
teaching vectors based upon my research findings. In addition, with projectile motion, I
wanted to learn some alternative labs and demonstrations. The topic of vector and
projectile motion also requires a lot of constructing, calculating, and visualizing. I

thought technology could address all three of those concerns.

This work required a literature search on laboratories and demonstrations that utilized
technology in learning the conceptual physics, panicularly vectors and projectile motion.
I also critiqued a software program called Interactive Physics, which had some vector and
projectile motion simulations. In addition, a colleague and I, modified or developed

vector and projectile motion programs on TI-81 and TI-82 graphing calculators.

Lastly, research focused on physics pedagogy topics: active learning techniques, novice

vs expert, student misconceptions, and the constructivist approach in science education.

LITERATURE REVIEW
Many physics teachers want their students to be more active learners. Arnold Arons, a
past president of the Association of Advancement of Physics Teachers (AAPT), probed
students with questions during lectures and laboratories guided by what he referred to as
“insightful inquiry” or “guiding inquiry.” Another researcher, David Pinkerton used
what he refers to as “Active Mental Processing (AMP) Journal” to help students become
more active learners. Students were graded by the following: notes of the day, question of
the day and application of the day. His TEST group that covered one semester of
introductory physics at the high school level showed improved scores on a posttest
compared to those taught prior to AMP. (Pinkerton, 1996). “The Mastery Process” was
another approach to students becoming more active learners developed by Horace (Rog)
Lucido (1992). This consisted of weekly packet evaluations, along with teacher/student
interactions and the mastery conference with the student to assess their grade. I .

incorporated some of the elements of these active mental process techniques in my unit.

The merits of using technology, primarily using computers and graphing calculators, at
the university and secondary level, had been documented in introductory physics courses.
Computers, along with other forms of technology, had been used to help student
motivation, problem-solvin g, critical thinking and develop understanding of certain
physics topics. Andrea diSessa contends that computers (technology in general) will
“revolutionize the way we think about thinking and the way we deal with learning,” once
we get beyond just getting them into the schools (1987). David Squires, believes a new
way of thinking or learning could be the use of computer software that adheres to the

constructivist approach. In his paper, be reviewed the traditional or “conventional”

approach, where learning is done in three phases: “formal presentation of prescribed
information by teacher exposition; verification of the information by closed practical
work; and practice of material presented in the first two phases through written

exercises.” (Squires, 1987)

Moreover, he along with others (Hestenes, et al., 1992; Ibrahim and Hestenes, 1985;
Larkin, et al. 1980; Mestre and Touger, 1989; Van Heuvelen, 1991), feel that there is a
need to have students progress from a novice to an expert level of thinking like a
physicist. The goal of Piaget’s constructivist theory for science education is the same.
This may be done by first assessing what is some of the naive or novice thinking in
physics. Then one would try to confront these misconceptions and try to change them.
However, John Clement (1982), points out that students have a stable alternative view or
misconception of many concepts. These misconceptions are “highly resistant to

change. . .” It takes creative ways to change them. Squires (1987) seems to indicate that
technology could be our saving grace or one creative way to get students to actively learn

physics and help confront some misconceptions.

In 1993-94, North Carolina State University sent out surveys to 3000 high school
teachers in the US, which obtained information about hardware, software and teaching
styles (Beichner, 1995). It revealed that “the typical classroom had between 6 to 7
computers. Technology, in the form of computers were used an average of 1.6 times per
week, and occupied 73% of the classroom time when used.” Teachers thought computers
allowed for more depth of coverage, allowed for new topics to be introduced, and

allowed students chances for repetition. The responses were mixed as to whether time

was saved in teaching topics in mechanics. Teachers helped students in graphing
techniques which allowed the students to analyze their graph at a higher level (Beichner,
1995). Other studies using spreadsheet software (Krieger, 1990; Engelhardt, 1993)

indicate the same benefits.

Also, Ron Thornton at Tufts University, adds that laboratories using computers
(microcomputer based laboratories or MBL) “. . .allow students to take an active role in
their learning and encourage them to construct physical knowledge from observation of
the physical world.” His study, based upon pretest and posttest observations, showed that
MBL format classes improved scores when compared with college lecture style format in

learning basic kinematics.

However, besides the obvious issue of cost, the need for professional development, and
curricular adjustment, “William J. Leonard points out that an unacceptable error can arise
because the programmer did not understand the mathematics or physics involved or the
calculations. For instance, having a timer collect data with a lot of significant digits
doesn't mean that the results are more accurate. Students believe this to be true. Finally,
students should be able to manually run the experiment and not “blindly” trust the
software. We should avoid the “black box” scenario, where no one understands how the
numbers were generated and/or calculated (Leonard, 1997). During the summer of 1996
Physics for Teachers course, we encountered difficulty in understanding how a photogate
timer that was controlled by a software program kept time in the determining the value of
“g” (g is the symbol for the acceleration due to gravity). My lab partner and I could have

accepted the values, but we didn't. We tried to analyze how the software program was

determining times it generated. Ultimately, my lab partner and I, along with the lab
instructor, determined there was a software problem in determining the times, which

affected the “g” value.

What happens if your school budget does not allow for microcomputer based
laboratories? The alternative is to obtain graphing calculators and connect them to sensor

probes. These are referred to as calculator based laboratory (CBL) units.

These units allow students to extend the physics lab beyond the classroom’s four walls.
Some educators have used these units in amusement parks (Escobar, 1990; Taylor, 1994)
and on playgrounds (Taylor, et al. 1995). These probes can make “... 10,000
measurements per second. . .500 points can be stored” for five channels simultaneously.
They are cheaper than the probes and unit used with a microcomputer. The programs for
various labs can now be downloaded from the Texas Instrument web-site for CBLs
(http://wwwti.com/calc/docs/cbl.htm). Moreover, if you have access to microcomputers,
then you can link them to the CBL and analyze the data in a spreadsheet program or
create reports in a word-processing program (Taylor, et al. 1995). Most articles
published regarding CBLs have been anecdotal and have not been researched as
extensively as Microcomputer Based Laboratories. For example, Richard Taylor points
out that he used them to collect data in the playground. He did not compare it to a
traditional lab. Likewise, Barbara Pecori (1998), Thomas Moses (1998), and Dan Stump
(1995) just mention how they use CBLs or just the graphing calculators alone in learning
topics like electricity, waves, and mechanics. None of them did a statistical comparison

of teaching methods using CBLs or graphing calculators vs traditional teaching methods.

Moreover, I have not seen any studies comparing the effectiveness of using technology
(i.e., graphing calculators) in conceptual level high school physics. To do a rigorous

comparison, I chose teaching with technology vs traditional teaching.

What happens if you still cannot afford the graphing calculators and the CBL units with
probes? Then graphing calculators alone can be utilized along with existing labs or can be

used to generate labs and activities to learn physics concepts.

Many articles describe, some mentioned above, the use of graphing calculators in physics
education. These calculators have been used to represent two-dimensional motion plots
either using parametric equations or programming the calculator (Brueningsen and
Bower, 1995; Stump, 1995; Vonder Embse, 1990). Moreover, parametric equations have
been used to calculate the planetary motion around the sun and to understand circular
functions in trigonometry (Cieply, 1993; Franklin and Waits, 1989). In addition, graphing
calculators were central to teachers learning physics of collisions, oscillations, and two-
dir'nensional analysis at Michigan State University in a summer program for teachers
wanting to learn more about physics. (Stump, 1995). Finally, Dennis Phillips (1999)
provided two additional examples of using only the graphing calculator in understanding
blackbody radiation and Rutherford scattering without making comparisons to other

teaching methods.

Unlike the articles describing Calculator Based Physics Laboratories articles, the use of
only graphing calculator effectiveness has been well documented in mathematics
education (Dunham, 1994; http://www.ti.com/calc/docs/research-b.htm). However, Carol

Williams from Pepperdine University, pointed out their ineffectiveness when many

students with graphing calculators failed to show work, lack the confidence to use them
for multi-line problems or did not know how to use parentheses correctly, and did not

know how to scale graphs (window and range). (1993)

Finally, another component of this research involved the use of a video laserdisc. Many
articles report their use in elementary and middle school level classes. Mary Ellen
Fitzhenry, a history teacher says, “Laserdisc technology has greatly improved my
students’ interest level.” While Glenn Gurley, a science teacher indicates “... students
listening to [video laserdisc] presentations have also become more attentive and ask
relevant questions.” Certainly, lots of teachers use the video laserdisc for reinforcement

of lectures and/or to introduce a topic (Carole Beckwith

,ht_tp;//www.pioneerusa.com/txt/teachg&a,html , 1999).

Therefore, a rigorous comparison of technology vs traditional teaching methods, which

included Videolaser disc technology was sorely needed at the high school level.

DEMOGRAPHICS
School Demographics
The high school population where the study took place in 1998—99 was 1,487 and had the
following ethnic breakdown: 1.2% Native American; 23.9% African American; 7.1%
Asian American; 16.6% Hispanic American; 51.2% European American. The gender
population for the school was 51.0% males and 49.0% females. The demographics were

for an urban school.

Study Demographics

The study was based upon on 65 students, consisting of primarily 11‘” and 12‘” graders
and two 10”1 graders. The following was the ethnic breakdown: 1.5% Native American;-
6.1% African American; 10.8% Asian American; 12.3% Hispanic American; 69.3%
European American. The study was also evaluated in part on gender, the percentages
were 51% males and 49% females. The study’s ethnic demographics did not reflect the
school’s ethnic demographics. However, the gender demographics were the same. Three

classes were used for the study.

Hour Time Student Number

1‘ 7:45 a.m. to 8:50 a.m. 19 (9 females; 10 males)

3“1 1&05 a.m. to 11:00 a.m. 18 (11 females; 7 males)

5"“ 12:05 pm. to 1:00 pm. 28 (12 females; 16 males)
Total 65 (32 females; 33 males)

IMPLEMENTATION OF UNIT
Overview
This unit was taught in the first semester towards the beginning of the second marking
period, which is nine weeks. Prior to this unit on vectors and projectile motion, we

discussed Newton's three laws of motion; the next unit of study would be on momentum.

The unit was four weeks long, with two weeks on vectors and two weeks on projectile
motion. For the vector part of the unit, 1“ and 3rd hour served as the control (38 students)
and 5‘“ hour (27 students) was the experimental group. For the projectile motions part of
the unit, 1'”t and 3'“ hour served as the experimental group and 5“I hour served as the
control. This switching was to establish a control for the unit and to allow all students to

be exposed to the technology teaching methods.

Both the control and the experimental groups were asked to take notes and answer
conceptual questions from the classroom text, Paul Hewitt’s Conceptual Physics, along
with question and answer problems and supplemental activity assignments. Finally, both
groups were given the same pretest, posttest and concept map test. The difference
between the control and experimental groups were the labs and the demonstrations. Both

groups were given two labs and had three demos, but varied in format.

The control group labs for vectors pertained to understanding vector resultant and
components using conventional classroom techniques. This consisted of using half and
full meter sticks for one lab and using force tables for the other one (Appendix A-1 and

A-II). The experimental group utilized technology in the form of graphing calculator

IO

programs designed to understand vector components and resultant. (Appendix B-1 and B—
11)

The control group labs for projectile motion learned projectile motion by going outside
and using a softball to determine projectile range, time, height, and angle. They also
conducted a lab where a bearing was allowed to roll down an incline plane to land into a
container, fast-food ketchup container (see Appendix A-III and A-lV). Both control labs
were a hands—on approach. The experimental group used graphing calculators to
understand projectile motion utilizing parametric equations for the first lab. Using
graphing calculators, the second lab consisted of finding the time, range, and height of a

projectile when the initial velocity and angle are known (see Appendix B-III and B-IV).

Tables 1—4 provide an overview of the four weeks on instruction for both the control

and the experimental group.

11

TABLE 1

 

 

 

 

 

 

 

(Week One Lesson Plan)
Date Topic Experimental Control
11-9-98 Vectors/Projectile 0 Pretest 0 Pretest
(Week 1) Motion 0 Started Notes 0 Started Notes
11-10-98 Vectors 0 Worked on Notes 0 Worked on Notes
from Conceptual from Conceptual
Physics Physics
0 Small groups to view 0 Vector Cut Out
Videolaser disc demo Activity (Introduce
(Introduce vectors vectors and define,
and define, adding adding vectors) Write
vectors) Answer up activity in lab
questions in lab notebook
notebook
11-11-98 Vectors - Worked on vector 0 Worked on vector
questions from questions from
Conceptual Physics Conceptual Physics
0 Work on Videolaser - Work on vector cut
disc activities out activity
11—12-98 Vectors - Go over selected 0 Go over selected
assigned questions assigned questions
0 Introduce graphing - Start Vector Addition
calculators. Lab (lab focuses on
0 Start Vector Lab 1 two ways to add
using VECT RES vectors using meter
(program finds and half meter sticks
resultant vector when and scaling
two component techniques)
vectors are entered)
11-13-98 Vectors - Collect Notes and 0 Collect Notes and
Questions Questions

 

Finish Vector [ab 1
and collect lab
notebooks

 

 

0 Finish Addition Lab
and collect lab
notebooks

 

 

TABLE 2

 

 

 

 

 

 

 

(Week Two Lesson Plan)
Date Tepic Experimental Control
11-16-98 Vectors 0 Return notes and - Return notes and
(Week 2) questions and lab questions and lab
reports reports
0 Vector Lab 2 using 0 Potatoes and Rope
VECT COMP (allows Demo (shows
students to enter two resultant and
or more vectors find components vectors)
the resultant vector) 0 Addition of Force
Vectors Lab
11-17-98 Vectors - Finish Vector Lab 2 0 Finish Addition of
0 Compare the two labs Force Vector Lab
- Compare the two labs
11-18-98 Vectors 0 Q & A 1 (Problems 0 Q & A 1 (Problems
using a protractor and using a protractor and
a ruler to find a a ruler to find a
resultant by resultant by
parallelogram and parallelogram and
head-to-tail methods) head—to—tail methods)
and collect and collect
0 Small groups and 0 Review vector
review Videolaser disc terminology and
from week 1 check concepts
answers
11-19—98 Vectors - Pass back Q & A 1 0 Same as experimental
and discuss
0 Concept Development
6-1 (CD 6—1 is a
review of vectors)
11-20-98 Vectors - Quiz on vectors 0 Quiz on vectors

 

 

0 Worked on projectile
questions from
Conceptual Physics

 

0 Worked on projectile
questions from
Conceptual Physics

 

l3

 

TABLE 3

 

 

 

 

 

 

(Week Three Lesson Plan)
Date Topic Experimental Control
11-23-98 Projectile Motion ' Pass back quizzes 0 Pass back quizzes
(Week 3) 0 Go over selected 0 Go over selected
assigned problems assigned problems
0 Small groups using 0 2-Dimensional
Videolaser disc demo Motion (predict
(2—Dimensional which object will hit
Motion: predict which the ground first,
object will hit the horizontal or vertical)
ground first, 0 Projectile Motion
horizontal or vertical) overview
- Projectile Motion
overview
11-24-98 Projectile Motion - Projectile Motion Lab - Projectile Motion Lab
1 (Baseball Problem 1 (Bulls eye, helps
using parametric students introduce
equations, helps what equations are
students introduce involved for projectile
what equations are motion, and looks at
involved in projectile variables)
motion, and looks at
variables)
0 Finish 2-Demo on
video laserdisc
11:25—98 Projectile Motion 0 Finish up Projectile 0 same as experimental
Motion Lab 1
0 Go over parts of
Concept
Development 6—2
(looks at objects
thrown off a cliff)
11-26-98 Projectile Motion - Collect CD 6-2 0 Collect CD 6—2

 

 

- Videolaser demo
(Monkey shoot, looks
at when objects fall
together, they hit
together)

 

0 Monkey shoot demo
(hand out paper to
follow along)

 

l4

 

TABLE 3 cont.

 

 

l I-27-98

 

Projectile Motion

 

0 Return CD 6-2 and
lab reports

0 Videolaser demo
(Snowmobile and
flare to show
parabolic)

0 Go over parts of
Concept
Development 6—3

 

0 Return CD 62 and
lab reports

0 Hall cart demo

0 Go over parts of
Concept
Development 6-3

 

15

 

TABLE 4

 

 

 

 

 

 

 

(Week Four Lesson Plan)
Date Topic Experimental Control
11—30-98 Projectile Motion 0 Collect CD 6—3 . Collect CD 6-3
(Week 4) ' Projectile Motion Lab 0 Projectile Motion Lab
2 (using graphing 2 (Softball toss
calculator to outside to determine
determine the range, the angle, initial
time, and height when velocity, and height
the initial velocity when range and time
and angle are entered) are measured)
12-1-98 Projectile Motion 0 Return CD 6-3 - Same as experimental
- Finish up Projectile
Motion Lab 2 and
collect
12-2-98 Projectile Motion - Return Projectile - Same as experimental
Motion Lab 2
0 Gooverparts on&
A 2 (Problems in
calculations)
12—3-98 Projectile Motion 0 Go over concerns on 0 Go over concerns on
Q & A 2 Q & A 2
0 Concept Map Review 0 Concept Map Review
12498 Vectors/Projectile - Collect Q & A 2 and 0 Collect Q & A 2 and
Motion Concept Map Review Concept Map Review
- Posttest 0 Posttest

 

 

 

16

 

 

Below are overviews of each of the labs for both the control and experimental group, an
overview of the demos for both groups, and an overview of the pro/posttest format and

design.

Vector Control Lab 1

For the first control group lab, the Vector Addition Lab (Appendix A-I) had three parts.
The first part was designed for students to find the resultant vector from two component
vectors with either two one meter sticks; one meter and one half meter stick; or two half
meter sticks. Once students constructed their resultant and components on the lab table,
they then had to scale it down to draw in their lab notebook for their lab report. For
direction, students were told North would be zero degree. This is what is used in

experimental vector algebra.

The second part of the lab was the reverse, where a resultant vector, either one-meter
stick or one half-meter stick, was placed at some angle. Then the component vectors were
determined by using the parallelogram method described in the textbook. 1 gave a short
discussion on scale factor: what is it, and why is it used. Most students that had chemistry
or understood their algebra had no problems with scale factors, since they were just

ratios.

The third part consisted of creating zigzag patterns, where one-meter and two half-meter
sticks were used, and finding their sum. This could be done either by head-to—tail or
geometric and analytic method. Most students had no difficulty with the head-to—tail or
geometric method of just measuring out the resultant or sum of the vectors. However, I

had to work out a problem on the board for the analytical method (adding all the x-

17

components and y-components and using the Pythagorean theorem was difficult at the
conceptual level physics) for solving the resultant vectors when more than two vectors

are involved.

Question number 5 from the lab, explaining errors, was left blank by some even though
we went over it prior to turning in lab notebooks. All students were done collecting data
the first day, but some students needed the next day for help on calculations and

answering questions. Overall, I thought the lab went well.

Vector Control Lab 2

Another control lab was the Equilibrium Lab, which was based upon the Addition of
Force Vectors Lab from the laboratory book for Merrill Physics (see Appendix A-II for
copy of lab and teacher's notes). We used method 1, which involved using force tables
and spring scales. 1 had students make sure the ring was centered. This lab utilized some
old force tables that used chain links that measured in grams. 1 had students convert the
grams to dynes. We should have converted to Newton’s, but didn’t. Some of the scales

were not at zero and had to be adjusted.

The direct measurement part of the lab did not take long. For the angle, 0°was north or

top of the round table. They were told to measure to the nearest degree.

Some students had difficulty with the calculations, because they were unfamiliar with
cosine and sine. All of them have seen the Pythagorean Theorem that allows them to find
the resultant force. Some students were amazed at how close their calculations were to

their measurement of forces.

18

Projectile Motion Control Lab 1

This lab is a classic. Most introductory physics lab manuals include this or some variation
of it. April Fowler had her class use dart guns taped to tables to hit a target on a wall
(1996). Another physics teacher created his own ball launcher made of 2 x 4 lumber and

three 12-inch rulers that was clamped onto a rolling cart (Beach, 1996).

For this lab, I modified the “Bulls Eye Laboratory” by Robinson (1992) (see Appendix
A-III) using “hotwheel” tracks and PSSC 2-Dimensional apparatus that had a ruler
attached to a metal ramp. The 2—D apparatus was clamped down and attached to the
hotwheel track. Students took three timings, instead of one. They were instructed on
using a plum bob to make sure the target was straight under. The majority of the students
hit the mark the first time. After the lab, we talked about what would be some of the
variables involved, i.e., height of ramp, height of table, distance of roll on table, etc.

Students found this lab fun and exciting, especially those that hit the mark the first time.

To check a student‘s calculations, Brian Drobert, a Michigan State University intern, and
I developed a program using the graphing calculator. Students were not given access to
this program from either the control or experimental group. Appendix A—III has an
example of student data and result of this program. This program was really nice for
checking lab results. In the future, I probably will use the graphing calculator to show
students what happens if we change certain data values or variables (i.e., changing “g”

value, horizontal distance, ramp height, fall distance, and times).

19

Projectile Motion Control Lab 2

Appendix A-IV has a copy of the lab as well as teacher's notes. This was a fun lab for
everyone. As Brancazio puts it, “one surefire way to make physics come alive in the
classroom is to illustrate physical principles with examples from sports.” ( 1985) After
reading an article on People demos in The Physics Teacher that involved students
participation inside and outside, I decided this lab would involve students going outside
for a softball toss (1983). A worksheet from Merrill Physics (1995) was modified for
class use. Both female and male students volunteered to throw a softball out on a football
field for the lab. I had students timing total time in the air, students spotted and recorded
the range. Then I had one student throw at different angles, where the time and range as
well as angle were recorded. Once the data was obtained outside, we went into classroom
to analyze them. Sample calculations were gone over in front of the class with an
overhead. The only problem with this lab was the part of having one student throw at
predetermined angles, which were not easy to control as revealed when we did the

calculations.

Brian and I wrote a program to check student calculations (see Appendix A-IV for a
sample run). In future labs, I will use this program to show students how the data was

calculated and what the results would be if the variables or data changed.

Vector Experimental Lab 1
For this lab, students had to find the resultant vector from two component vectors by
using a protractor and a graphing calculator program (see Appendix B-I for a sample

run). Then students were asked to compare the accuracy of their diagrams. I thought it

20

was interesting using the graphing calculator to check the results with the traditional labs,
even though in reality it’s the other way around. Also, students were asked to construct

vectors based upon the graphing calculator's output.

Michael Harmon, from Texas Instruments had developed a vector program for T1 81
graphing calculator and posted it on the TI's web—site( 1994). The program was nice but
was limited to vectors from 0° to 90°. During the 1997 summer, Jeff Chomy, a fellow
summer teacher researcher, and I modified the program to work for 0° to 360°. Also, the
program did not allow a student to enter a negative number of vectors or just one vector,
It would just repeat the first screen to ask for the number of vectors. This was to prevent
students from being confused or frustrated. Most vector problems use positive magnitude

and account for negative in the directional part of the vector.

Because there were only ten graphing calculators, I had students work in small groups of
two to three. This also limited the program access to only the experimental group
students. Also, it avoided the possible problem of the program not running on T1 85, 92,
or other graphing calculators that some students had for their math classes. Also, down
loading the programs allowed the students to not have to learn programming the T1
calculator. This allowed students to get to the labs. However, if a student happened to
erase the program or parts of the program, I was able to download it from my calculator
or one of the other ten calculators with graph link cable. This did happen during the
study, especially when students had to see the source code for the program though the

edit program menu. Some did not know how to exit program properly and erased one or

21

more line of code. In addition, I chose not to have students key in the program because of

the time involved and the potential student and teacher frustration that would ensue.

Students thought this lab was easy and interesting. Many students' measurements were
close to the calculated values. If students had difficulties, it was usually drawing the right

direction from the program output and creating a data table that reflected the data.

Because the program had relatively few equations and students worked in small groups,
the lab questions were not difficult to answer. Some students seemed to skip them
altogether. This happens in the traditional labs as well. For a sample program run and

additional teacher's notes (see Appendix B-l). Most students finished the lab in one day.

Vector Experimental Lab 2

This lab required students to work back from the resultant vector, to determine the
component vectors that created it. This was done in a similar fashion as the experimental
vector lab 1, where students recorded their vectors in a data table and diagramed the
vectors in their lab notebooks.

This program was also developed in collaboration with Jeff Chomy, since there was no
modifiable program from the TI web-site. Microcomputers were unavailable, the
Interactive Physics software program that has vector demonstrations and simulations

could have been used.

Generally, students did not have a problem with the program or lab. Some students
needed help interpreting the output screen. They were not used to seeing the horizontal

vector component labeled Vx and vertical component Vy. Also, if a student entered in a

22

negative resultant vector, it would repeat the first screen to vector magnitude, since

negative resultant vectors were not allowed for this program.

Also, this program was a check on the first program or method of finding a vector's
resultant and components. There is a sample problem that shows the check of the first

experimental vector lab 1 in Appendix B-II. Most students finished the lab in one day.

Projectile Motion Experimental Lab 1
This was quite an involved lab and challenging at the conceptual level. This lab used the
parametric features of the graphing calculator. It required students to enter equations, and

use the graphing features i.e., window, trace, and draw feature.

Before students broke up into their lab groups, we worked through a sample problem.
This problem was based upon Chuck Vonder Ernbse’s baseball problem of whether or
not a hit ball will clear the wall of a baseball field. (Appendix B-III). Conversions from
miles per hour to feet per second (Mr. Embse’s problem used English units), keeping
track of equations, window settings, and accounting for new variables, i.e., initial height

the ball was thrown were concerns for the students.

First we talked about parametric equations, where a person can see three variables on the
same graph. In our case, it was range (X), height (Y), and time (T). More importantly,
parametric equations solved using graphing calculators allowed students to separate the

horizontal component from the vertical component vector.

Parametric equations used to be very time consuming to learn in mathematics because of
the paper and pencil graphing involved. The graphing calculators made parametric
equations a lot easier to solve in mathematics because paper and pencil graphs were not
required, although some teachers required paper and pencil graph for the first problem
only (Cieply, 1982). In physics, the graphing calculator also helped solve projectile
motion problems that can be solved with parametric equations (Embse, 1990; Flynn and

Sumerix, 1994; Stump, 1995) and polar equations (Demana, 1990).

Then we went through a sample problem together on the overhead. (Appendix B-III)

Projectile Motion Experimental Lab 2

Students worked in groups found that the range, height, and time of flight of an object
when g value, initial velocity and angle of flight were entered into the graphing calculator

program. (Appendix B-IV has the lab, teacher’s notes that includes a sample run)

The groups also answered questions from projectile motion program PROJYVST. The
name is an abbreviation for a program that can find the path of a projectile (PROJ). The
Y represents the height of a projectile and the T represents the projectile flight time. We
wanted to add R for range; however, TI graphing calculator programming only allows for

eight characters for a name.

Students were asked to graph and find the relationship between the initial angle and the
range. Also, a graph to find relationship the maximum height and the angle was done by

the students. This required the students to run the PROJYVST program several times and

record their results in a data table. For this relationship between angle and range, the
students had to keep the initial velocity constant and change the angle. Some students
were surprised to find out that 45" was not the angle for maximum range even though
their textbook said 45° was the angle for maximum range. Two articles in The Physics
Teacher point out that 45° is the angle for maximum range when firing an object on a flat
horizontal surface in the absence of friction (Brown, 1992; Inouye and Chang, 1992).
Moreover, they point out that most projectiles are fired from some height, h, above the
surface. Ron Brown then points out that “In this case, the angle launch for maximum
horizontal travel will then become dependent on the height, h, and is in general less than
45°.”

They were to graph and find the relationship between the maximum height and the angle
and the relationship between maximum height and initial velocity. Students had to vary
the initial angle and keep the initial velocity constant. This was opposite of what was

asked of them before.

Finally, students graphed and determined the relationship between the angle and the time

and the relationship between maximum height and time.

On the second day, I discussed the similarities of this lab with the previous lab that used

parametric equations. Both labs found the same information through different means.

Overall, the lab was easy. However, one detraction was that all of the graphs were the
same size on the screen, so that when a student entered an initial velocity of 20 m/s with
varying anng (i.e., 20° graph looked like a 60° graph). In comparison, the 20° graph

should have looked smaller than a 60° graph.

25

Vector and Projectile Motion Control Demos

The vector demo was based on one from The Physics Teacher, where students out out and
laminated vector arrows of all shapes and sizes to demonstrate vector addition and
subtraction (Snyder and Faulstick, 1991). These authors indicated; “We’d draw pictures
[of vectors] on the board and use all sorts of examples, . . .students still seemed unable to
grasp the vectors.” Also, James Helrnick had difficulty having students visualize vectors,
so he created a mobile frame of reference made out of wood and paper arrow tips (1993).
The students cutout various size vectors, and asked some questions to guide their activity
(see Appendix 01). The majority of the students found it beneficial to visualize and

manipulate the vectors.

The potato and rope demo, illustrated and reinforced vector addition and subtraction and
vector components and resultant vector. This demo was a modification of a problem from
Hewitt and Merrill. In this problem, a person with a rope or chain tries to pull the rope or
chain straight horizontally when a weight is suspended in middle. Students with heart or
other physical problems did not participate. In one class ten students on each side could
not pull the rope horizontally taught to lift the bag of potatoes. After the demo, students
were asked questions about the force vectors involved and about the types of applications

that related to the demonstration (see Appendix 011).

The 2-Dimensional demonstration used a number of variations of showing the
independence of horizontal and vertical motion. An example of a question related to this
demo is: “At the instant a horizontally-held rifle is fired over a level range, a bullet held

at the side of the rifle is released and drops to the ground. Which bullet—the one fired

26

down-range or the one dropped from rest-strikes the ground first?” (Hewitt, 1992)
Another variation of this demonstration is to use either washers or coins on a ruler that
spin freely on a piece of wood nailed down; however, I chose to use the traditional 2-D
launcher, which propels one bearing horizontally and drops another vertically (see
Appendix C-III). Students had to listen very carefully for one or two hits on the floor. I
do this demo on a ladder to allow students to hear and see both bearings hit at the same
time. Students have a hard time with this. One or two will always think they heard two

separate hits.

The monkey shoot illustrated the independence of horizontal and vertical motion. The
setup had an electromagnet which held up a tin can with a painted monkey, hence, the
name the monkey shoot. The electromagnet was turned off when a bearing broke a circuit
coming out of the barrel. Because the bearing is going horizontally and the can is going
vertically at the same time, they hit each other in mid-air. The question that is always
asked is, “Where does one aim the gun to hit the monkey: above, at, or below?” A lot of

students focus on the setup and demonstration more than the concept. (Appendix CW)

27

Vector and Projectile Motion Experimental Demos

Using the Videolaser disc for demonstrations in small groups was a challenge. In the past,
the Videolaser disc was used to introduce to the whole class concepts, show video clips
(i.e., bungee jumping, ripple tank demos, Tacoma Narrows Bridge Collapse, etc.), and

review. (Appendix D-l has detailed teacher’s notes)

This unit, I wanted students to be active in finding the topics and demonstrations. Since
there was only one laserdisc player, I had students work in small groups of two to three.
All groups were given a quick lesson on “how to use” the scanner and/or remote control,
Videolaser discs and TV monitor. Most students liked the big remote. However the

scanner frustrated a lot of groups.

For this unit, we used two Videolaser discs, Physics At Work and Cinema Classics.
Groups cycled through using the Videolaser disc, which was in front of the class; students
were able to work on another assignment (see Table 1-4) in back in the lab area. All
groups were given questions to answer before using the Videolaser disc. Students were to
go through the Videolaser disc material without taking notes. The second time through
they were to take notes after viewing the disc and answer questions. I got a lot of blank
answers for the questions before the students used the Videolaser disc, especially if they
did not take notes and answer questions from the text prior to this activity. Students were
hesitant at first in using the Videolaser disc player. I had to remind groups to go and use

the Videolaser disc player when it was not in use.

The Videolaser disc material should have simply reinforced their notes on vectors from
the classroom text. Using the disc was also to help students who did not take notes from

their textbook.

For the 2-Dimensional Motion Demos (Projectile Motion), students answered three
questions prior to viewing the Videolaser disc (see Appendix D-II for questions). Just like
the vector section, students also were given questions after viewing the laserdisc.
Moreover, they took notes describing how the demonstration was done and documented
the purpose of the demonstration. Of the three demonstrations, the most misunderstood
one was the snowmobile and flare. There were several shots of the snowmobile moving

with the flare being launched at different positions of the snowmobile moving.

Students were prepared for the posttest by answering questions on constructing vectors
with a ruler and protractor. We went over projectile motion calculations. Finally, to help
students with concepts and terminology, a concept map was given the day before the
posttest and gone over the day of the posttest (see Appendix E] and EU). The review

was the same for both experimental and control groups.

29

EVALUATION
Overview

The pretest and posttest were the same and designed to have conceptual level,
construction, and calculation questions (see Appendix E-III for pre/posttest). Open-
ended or free response questions were not used to reduce the subjectivity in grading.
There were a total of twenty questions, where twelve questions were vector related and
eight questions were projectile type questions. The analysis was based upon separating
the questions that relate to vectors from the questions on projectiles and finding their
pretest and posttest means, respectively. Furthermore, the means and standard deviations
were separated by group (control vs experimental), gender (all female students vs all
male students; included both control and experimental group students), and then by group
and gender. From the means, the variances were determined and utilized in repeated
measures analysis of variance, the Wilks’ Lambda test, the F test and the P value. The
means and standard deviations are not directly involved in calculating the Wilks’ Lambda
test, the F test and the P value. Generally, the higher the F-value and a p-value of less
than 0.05, the more confident the investigator is in rejecting the null hypothesis. The null
hypothesis in this study was that all students should be able to learn at the same level
regardless of teaching method used. Conversely, students learning via technology will

perform better than those learning via traditional methods or worse.

The investigator focused on the pwalue. Therefore, if the p-value was greater than 0.05,
the null hypothesis was not rejected, regardless of the F-value. The F—value is just an

indicator of the ratio of variance.

3O

Table 1 and subsequent tables represent the statistical analysis for the unit. First the
means and the standard deviations are provided for pretest and posttest for group, gender,
and group and gender combined. The Wilks’ Lambda test is one of the many standard
multivariate tests done with statistical computer software programs (i.e., SPSS or SAS;
SAS was used for this unit) that analyze the variances or eigenvalues. It is beyond the
scope of this study to discuss the details of the formula for the Wilks’ Lambda test (see
Rao, 1952 for formula and meaning). The F value part of the Wilks’ lambda test is a
ratio of the variance, where Num DF is the degrees of freedom for the numerator and Den
DF is the degrees of freedom for the denominator. The F value is an estimation test and is
not heavily weighted as compared to the next part. The Pr > F part of the Wilks’ Lambda
test is the last part and is known as the p value that is a proportionality test for the
variances. If the p value is less than 0.05, the test or experimental value is significant. The
F value may or may not be a large value (F > 1.00), which is also a good indicator of
significance. All of the tests used in the study are widely accepted statistical analysis for

life science and social science research studies involving multivariate analysis.

31

TABLE 1: VECTOR PRETEST/POSTTEST STATISTICS BY GROUP

C = CONTROL; E 2 EXPERIMENTAL; N = NUMBER OF STUDENTS;

SD = STANDARD DEVIATION

 

 

 

 

 

 

 

 

 

-----PRET EST ---------- POSTTEST—m
GROUP N Mean SD Mean SD
C 37 3.76 1.57 8.76 2.12
E 28 2.57 1.51 8.96 2.18
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.92739998 4.7753 1 61 0.0327
FIGURE 1

Pretest and Posttest mean scores by Group

 

Mean Test Score
( points)

O-‘Nw-bU‘ImVCDQDO

PRETEST
Test Type

Vector Pre/Posttest—Group

 

POSTT EST

 

 

[—0—— Control - -I— - Experimental I

 

 

 

Based upon the p value being 0.0327 (less than 0.05 is significant), the null hypothesis

can be rejected. Hence, the experimental group out performed the control group in the

vector part of the unit. Moreover, having a large F value also indicated significance. In

Figure l, a greater slope for the experimental than for the control supports the Wilks’

Lambda test. Finally, Figure 1 shows a positive slope for both the experimental and

cone-cl indicated improvement from pretest to posttest.

32

 

TABLE 2: VECTOR PRETEST/POSTTEST STATISTICS BY GENDER

N = NUMBER OF STUDENTS; SD = STANDARD DEVIATION;
M = MALE; F = FEMALE

 

 

 

 

 

 

 

 

 

 

------PRETEST----- ---POSTTEST -----
GENDER N Mean SD Mean SD
F 32 3.34 1.84 8.90 2.13
M 33 3.14 1.54 8.79 2.17
Statistic Value F Num DF Den DF Pr > F
Wilks' lambda 0.99914093 0.0524 1 61 0.8196
FIGURE 2

Vector Pretest and Posttest mean scores by Gender

 

Vector Pre/Posttest—Gender

 

Mean Test Score (points)
0 —- N w a m as \I on to o

PRETEST POSTTEST
Test Type

 

 

 

[—0— Female — 4 - - Male

 

 

Based upon the p value being 0.8196, the null hypothesis cannot be rejected. Hence, the
female students performed about the same as the male students in the vector part of the

unit. Figure 2 shows about the same slope for the female students and the male students,

33

which supports the Wilks’ lambda test. Finally, a positive slope in Figure 2 for both

genders indicated improvement from pretest to posttest.

TABLE 3: VECTOR PRETEST/POS'I'TEST STATISTICS BY GROUP AND GENDER

C = CONTROL; E = EXPERIMENTAL; N = NUMBER OF STUDENTS;
SD = STANDARD DEVIATION; M = MALE; F = FEMALE

 

 

 

 

 

 

 

 

 

 

 

Vector Pretest and Posttest mean scores by Group and Gender

--—--PRETEST ----- ----POS'I'TEST----
GROUP GENDER N Mean SD Mean SD
C F 20 3.80 1.82 8.55 2.13
C M 17 3 .70 1.25 8.88 2.17
E F 12 2.58 1 .57 9.33 2. 14
E M 16 2.55 1.63 8.59 2.24
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.991341 51 0.5328 1 61 0.4682

FIGURE 3

 

 

Vector Pre/Posttest—Group & Gender

 

 

 

 

 

 

 

 

 

 

 

 

g 10

a .. 8

u 3 6

n .5

.2 a 4

5 v 2

f o *

PRETEST POST—T EST
Test Type
T—o— Control Female + Control ”3'95

- i- - Experimental Female - -x- - Experimental Male

 

 

 

 

34

 

Based upon the p value of 0.4682, there

was no significance between group and gender.

The null hypothesis cannot be rejected. This indicates that both the group and the gender

effect did not agree on significance. Figure 3 shows the experimental female students

having a different slope than the experimental male students, which shows the non-

significance between gender and group.

TABLE 4: PROJECTILE MOTION PRETEST/POSTTEST STATISTICS BY GROUP

C = CONTROL; E = EXPERIMENTAL; N = NUMBER OF STUDENTS;

SD = STANDARD DEVIATION

 

 

 

 

 

 

 

 

 

 

 

-----PRETEST----— --—--POS'I'TEST----~
GROUP N Mean SD Mean SD
C 37 3.08 1.59 6.00 1.49
E 28 2.32 1.35 5.86 1.67
Statistic Value F Num DF Den DF Pr > F
Wilks' lambda 097648732 1.4688 1 61 0.2302
FIGURE 4
Projectile Pretest and Posttest mean scores by Group
Projectile Motion Pre/Posttest—Group
7
9 6
(g d; 5
I- 3 3
S V 2
i 1
O
PRETEST POSTTEST
Test Type
—O— Control — -I- - Experimental

 

 

 

 

 

 

35

 

Based upon the p value being 0.2302, the null hypothesis cannot be rejected. Hence, the
experimental group performed about same as the control group in the projectile motion
part of the unit even though the F value is greater than 1.00 (1.4688). In Figure 4, the
slopes for the experimental and for the control, are the about the same as opposed to the
slopes in Figure 1. Finally, Figure 4 shows a positive slope for both the experimental and

control indicated improvement from pretest to posttest

36

TABLE 5: PROJECTILE MOTION PRETEST/POSTTEST—GENDER

N = NUMBER OF STUDENTS; SD = STANDARD DEVIATION:
M = MALE; F = FEMALE

 

 

 

 

 

 

 

 

 

 

----PRETEST--- ---POS'ITEST----
GENDER N Mean SD ‘ Mean SD
F 32 2.53 1.22 5.62 1.60
M 33 2.97 1.78 6.24 1.48
Statistic Value F Num DF Den DF Pr > F
Wilks’ lambda 0.99818235 0.1 11 1 1 61 0.7401
FIGURE 5

Projectile Pretest and Posttest mean scores by Gender

 

Projectile Motion Pre/Posttest—Gender

Cameo-bureau

 

Mean Score (points)

PRET EST POSI'T EST
Test Type

 

—o—— Female - -I- - Male

 

 

 

 

 

 

Based upon the p value being 0.7401, the null hypothesis cannot be rejected. Hence, the
female students performed about the same as the male students in the projectile motion
part of the unit. Figure 5 shows about the same slope for the female students as the male
students, which supports the Wilks’ Lambda test. Finally, a positive slope in Figure 5 for

both genders indicated improvement from pretest to posttest.

37

TABLE 6: PROJECTILE MOTION PRETEST/POSTTEST STATISTICS BY

GROUP & GENDER

C = CONTROL; E 2 EXPERIMENTAL; N = NUMBER OF ST UDENTS;
SD 2 STANDARD DEV IATION; M 2 MALE; F = FEMALE

 

 

 

 

 

 

 

 

 

 

 

 

--«-—PRETEST----- ----- POSTTEST-—--
GROUP GENDER N Mean SD Mean SD
C F 20 2.90 1.29 5.90 1.58
C M 17 3.29 1.89 6.12 1.41
E F 12 1.92 0.79 5.17 1.59
E M 16 2.62 1.63 6.37 1.58
Statistic Value F Num DF Den DF Pr > F
Wilks' lambda 0.992 10181 0.4856 1 61 0.4885

FIGURE 6

Projectile Motion Pretest and Posttest mean scores by Group and Gender

 

Mean Test
Score (points)
Oanammw

PRETEST

Test Type

Projectile Motion Pre/Posttest—Group
& Gender

 

POST EST

 

—o—-Control 8: Female

 

 

—I—— Control & Male

—-a--Experimental & Female +-x—-Experimental & Male

 

 

 

 

Based upon the p value of 0.4885, there was no significance between group and gender.

The null hypothesis cannot be rejected. This indicates that both the group and the gender

38

effect did not agree on significance. Figure 6 shows the experimental female students
having a different slope than the experimental male students, which shows the non-

significance between gender and group.

39

DISCUSSION and CONCLUSION
Teaching a unit on vectors and projectiles was informative, challenging and fun at times.
I learned a lot about physics education, and new labs and demonstrations and working
with technology, in the form of graphing calculators and videolaser disc. The goal of this
unit was to quantitatively compare student performance using two different teaching
methods for labs and demonstrations: using technology, the graphing calculators (T 183)

and the video laserdisc, or using traditional conceptual physics format.

The analysis showed that the experimental group did improve over the control group
from pretest to posttest on the vector part of the unit. All other tests proved to be not
significant. Finally, both group and gender test revealed improvements from pretest to
posttest. This means that the students in the projectile motion experimental group were

not disadvantaged nor were the students in the vector control group.

Based upon the findings, the graphing calculator programs on vectors may have been
easier to learn and understand or the control labs were not as easily understood. Using the
videolaser disc may have been more effective for demonstrating or reinforcing vector
concepts than the traditional demonstrations. Finally, the actual pretest/posttest may have
not been reliable or designed effectively to test for the unit. Maybe I could have designed
a test to utilize the Mechanics Baseline Test developed by David Hestenes and Malcolm
Wells, which tested Newtonian concepts (1992). Another assessment test was the F orce
Concept Inventory, which tested on the same topics as the Mechanics Baseline Test
(1992). Both are excellent tests and were used by some researchers to improve active

learning and deeper understanding of physics concepts (Pinkerton, 1996; Novodvorsky,

1997), but most covered one semester of college level physics. My unit was only four
weeks. Because of the time differences and how I usually design my test, I chose not to
use the above mentioned tests. However, some of the concepts pertaining to my unit were

covered on the pre/posttest.

This unit may have been improved many ways. One such way would be a student survey.
This would be a way of finding out if students felt they learned more from the labs or
demonstrations or both. Such a survey would have determined their likes and dislikes
regarding the labs and demonstrations. This would help me improve for next year.
Finally, I would like to find out what they thought about the TI graphing calculators and

the video laserdisc likes and dislikes.

Using the programmable calculators had some limitations. The TI graphing calculator
graphs for physics should show units both on their x and y-axis. Also, the graphs looked
the same for the projectile experimental lab 2 regardless of angle used (see appendix B—

11). That is, a small angle did not show a small curve relative to a larger angle.

The videolaser disc should have been designed so one would not have to take the disc out
to view material on the other side. Also, the video audio part should not start out with
multiple languages. A lot of the groups fumbled around to get only English audio,

although some liked the Spanish option.

Future studies could include a student survey as well as use a different form of
technology . CBLs (Calculator Based Laboratories) or MBLs (Microcomputer Based

Laboratories), to compare with traditional labs and demonstrations at the conceptual

41

physics level. Moreover, future studies could just focus on laboratories and not include
videolaser disc demonstrations. Future studies could also use DVD or CD-ROM
laboratories and/or demonstrations, instead of using a videolaser disc player. Finally,
other future studies could evaluate the effectiveness of using the Internet in physics

education for on-line labs and/or demos or long distance learning.

Technology is just a tool for learning physics. There is no doubt that different forms of
technology will continue to appear in physics meetings and journals. Along with the new
technologies will be the need for comparative studies like this one and others to
determine their effectiveness in getting students more active in learning and

understanding physics at a deeper level.

42

APPENDIX A-I

Vector Control lab l—Vector Addition Lab

Purpose: To learn how to construct resultant and components vectors using the
parallelogram method and vector addition using the graphical or the analytical
method.

Background: Write a paragraph or two about the concepts learned in this lab. Use your

text or other resources for this section.

Materials: 2 one-meter sticks, 3 half-meter sticks, protractor, and metric ruler

Diagram: Make a sketch of one of your vector setup and label the materials used.

Procedure:

Part 1: Use combinations of two-meter sticks; one-meter and half-meter sticks; or two

half—meter sticks to construct two components. Record your direct measurement vector

magnitude and directions in the data and calculations section of lab (em = 0.25 m).

Determine the resultant vector by the head-to-tail method in your notebook. Record the

resultant vector using the two methods.

Part 2:

Next use a one-meter stick as a resultant vector and find its associated components (0° is

north). Record the direct measurement vector components and resultant in data and

calculations section. Diagram the vectors in your lab notebook (use scale factor of 1 cm =

0.25 m).

43

Part 3:

Finally, use one meter and two half-meter sticks to form a zigzag pattern (not a right
triangle or one straight-line pattern). Use both the head-to—tail or geometric method and
the analytic method. Make a diagram of your vectors in your lab notebook (use scale

factor of 1 em = 0.25 m) and show work for any calculations and use correct units

Data and Calculations: (Displacement vectors measure to 0.001 m and 0.5“)

 

 

 

 

 

 

 

 

 

 

 

 

 

Part 1

Dx = m at Dy = m at

D A = m at (Method 1: )

DB 2 m at (Method 2: )
Difference: D A — DB 2 m at (Note: subtract the angles as well)
Part 2

Dx ..—_ m at Dy = m at

D: mm
Part 3 Show Work (include units)
' D1 = m at
D2 = m at DR 2 m at
(DR is the resultant vector)
D3 : m at

 

Analysis: Write the following questions in laboratory notebook and write response in

complete sentences.

Q1) Why is a scale factor important; provide three examples where scale factors are used
in today’s society; finally, what was your scale factor? Ans. Diagramming physical

events; maps, carpentry, architectural designing.

Q2) Component vectors can only be what directions? Ans. Components must be 0’, 90",
I 80", or 270”.

Q3) When adding two or more vectors, describe two different ways to find the sum of
these vectors? Ans. Students should describe the head-to-tail method or graphical
method or analytic method.

Q4) In part one of the lab, which method did you think was more accurate? Explain. Ans.
Student answers will vary.

Q 5) Explain what were some of your sources of error. Ans. Some sources of error could
be accuracy of reading measurements and angles, movement of meter stick during

measurement, calculation error, chipped or warped meter stick, etc.

Teacher’s Notes:

This was an easy lab to setup. I was fortunate to have both meter sticks and half meter
sticks. It's important that student are familiar with vector terminology. I had them take
notes and answer some questions prior to lab day; other teachers may just want to have a
prelab discussion on terms and vector addition methods. I did talk about scale factors in

my prelab discussion and quickly reviewed terminology and methods.

Some students had difficulties with directions or vector angles. Some of the protractors
were circular and some semi-circular. I also encouraged students to be creative for the
three vector addition problem. For question 4, most students thought the method that they
used was the most accurate way to add vectors. Some students had a hard time with
question 5, I got some blank answers when you ask students to account for error. Overall,

I thought the lab was effective.

45

APPENDIX A-II

Vector Control Lab 2—Equilibrium Lab

(Based upon Addition of F orce Vectors by Kramer, 1995)
Purpose: Apply the laws of vector addition to resolve forces in equilibrium.

Background: Write a paragraph or two about the concepts learned in this lab. Use your

text or other resources for this section.

Materials: Force table and 3 spring scales, protractor, metric ruler

Diagram:
Figure 1

Force Table—Kramer, 1995

 

Procedure:

1) Setup the apparatus so that the spring scales are in equilibrium (make sure the ring is
centered with the post). (Figure 1 has Force Table setup) Check to see that each scale
needle or bar is zero before attaching to table. If the scale reading is not zero, then
you will need to add the needle value to the final reading. Attach spring scales to the

force table so that each scale registers a force at approximately mid-range.

2) Place a piece of paper beneath the spring scales. Using a sharp pencil, mark several

points along the line (the string) of action of each force. Trace the ring.

46

3) Remove the paper and, using the points that you marked, construct lines all the way to
the edge of the paper and label A, B, and C, each representing the direction of force

action for scales A, B, and C. Mark a point in the center of the traced ring.

4) Record the lengths, angles, and readings of each spring scale next to its corresponding

line into your data table. Measure lengths to 0.1 cm and angles to the nearest degree.

Data and Calculations:

Vector Resultant cm

Horizontal
cm) 0

 

Calculate the following vectors:

Bx-Bcose- - CI-Ccosfl- -

By -Bsin0 - - Cy -Csin6- -
fi_‘,fi;3+§yz- _ C-Jsz+erz-_____-__

 

 

1‘. - (Amwsocm/s2 - .-
Fi -(Bm)x980cm/sz - -
Fe -(Cm )x980cm/ s2 - ..

 

47

Note: Am, B”, and CW are read directly off the spring scale. The 980 cm/s2 is the

value of g for the cgs system.

Analysis: Write the answer to these questions in your lab notebook in complete

1)

2)

3)

4)

6)

sentences.

Write the algebraic notation for A, B, and C vector addition. Ans.

1+fi-E

Compare the magnitude and direction of the computed resultant force of A + B with
the measured or known magnitude of force C. Explain your findings. Calculate the
relative error in the magnitudes using force C as the reference value. Ans. The

resultant of A + B should be nearly equal to and opposite of C.

Suppose that you had added B to C. What result would you expect?

Ans. If B is added to C, the resultant should be the negative of the value of A.

What result would you expect if you added C to A?

Draw a vector representing the vector sum of A + B, the resultant. Ans. The addition
of C + B should give the same result as the addition of B + C + A. The resultant is
zero.

Explain some sources of error. Ans. If the circle is not centered, an error in
calculations will result; calculating incorrectly is a source of error; reading the scale

wrong; if the measuring needle did not start at zero, etc.

Teacher’s Notes:

This lab was also an easy lab to setup. Some students will experience difficulties in the
calculations. There may be error in reading the scale, zeroing the scale, or drawing the
correct lines with the links in place. Students should be familiar with the trigonometric
functions cosine and sine to understand how get the components. Otherwise the lab
becomes a lesson in pushing buttons. Many of the students did not answer the questions
correctly, even question 1 was missed a lot. A lot of the questions were simply just

applying the commutative property of addition.

There were students with calculations close to their measurement. The direct
measurements were easier for most students. Overall, this lab was harder to implement
than the first control lab and harder to understand its meaning. The number of student

questions and lab report scores reflected this.

49

APPENDIX A-III

Control Projectile Motion Lab l—Bulls Eye laboratory (Robinson, 1992)

 

 

 

Name Date Hour
Chapter 6 Vectors Projectile Motion
Purpose

To investigate the independence of horizontal and vertical components of motion. To

predict the landing point of a projectile.

Required Equipment/Supplies

Ramp or Hot Wheels track

0.5 inch (or larger) steel ball

empty ketchup container from fast food restaurant

meter stick

plumb line

stopwatch

Discussion

Imagine a universe without gravity. In this universe, if you tossed a rock in outer space, it
would just keep going—forever. Because the rock was going at a constant speed, it would

cover the same amount of distance in each second. The equation for distance traveled

when motion is uniform is

The speed is

Coming back to earth, what happens when you drop a rock? It falls to the ground and the
distance it covers in each second increases. Gravity is constantly increasing its speed.

The equation of the vertical distance d fallen after any time t is

d = 0.5 gt2
where g is the acceleration of gravity. The falling speed v after time t is
V = gt
What happens when you toss the rock sideways? The curved motion that results can be
described as the combination of two straight-line motions: one vertical and the other
horizontal. The vertical motion undergoes the acceleration due to gravity, while the
horizontal motion does not. The secret to analyzing projectile motion is to keep two

separate sets of “boo ”: one that treats the horizontal motion according to

d = vt

and the other that treats the vertical motion according to

a z 0.5 ge
Horizontal motion
0 When thinking about how far, think about (1 = vt.
0 When thinking about how fast, think about v = d/t.
Vertical motion
0 When thinking about how far, think about d = 0.5 gt’.
0 When thinking about how fast, think about v = gt.
Your goal in this experiment is to predict where a steel ball will land when released from
a certain height on an incline. The final test of your measurements and computations will

be to position an empty ketchup container can so that the ball lands in the container the

first time!

Step 1: Assemble your ramp. Make it as sturdy as possible so the steel balls roll smoothly

and reproducibly. The ramp should not sway or bend. The ball must leave the table

51

horizontally. Make the horizontal part of the ramp at least 20 cm long. The vertical height

of the ramp should be at least 30 cm.

Step 2: Use a stopwatch to measure the time it takes the ball to travel from the first
moment it reaches the level of the table top to the time it leaves the table top. Divide this
time interval into the horizontal distance on the ramp to find the horizontal speed.
Release the ball from the same point (mark with tape) on the ramp for each of three runs.
Do not permit the ball to strike the floor! Record the average horizontal speed of the three
runs.

Horizontal speed =

 

Step 3: Using a plumb line and a string, measure the vertical distance h the ball must drop

from the bottom end of the ramp in order to land in an empty ketchup container on the

floor.

1. Should the height of the container be taken into account when measuring the vertical
distance h? If so, make your measurements accordingly.

[1:

 

Step 4: Using the appropriate equation from the discussion, find the time t it takes the ball
to fall from the bottom end of the ramp and land in the container. Write the equation that
relates to h and t.

equation for vertical distance: =

 

Show your work in the following space.

I:

 

Predict the range. Step 5: The range is the horizontal distance of travel for a projectile.

52

Analysis

2. Compare the actual range of the ball with your predicted range. Compute the
percentage error.

3. What may cause the ball to miss the target?

4. You probably noticed that the range of the ball increased in direct proportion to the _
speed at which it left the ramn The speed depends on the release point of the ball on

the ramp. What role do you think air resistance had in this experiment?

Teacher’s Notes:

Students found this lab fun and exciting, especially those that hit the mark the first time.
In order to obtain a reasonable value for horizontal speed, students took three timings and
average. Also, students used a plum bob to make certain of target. Most students never
heard of such a tool as a “plum bob.” After the lab, we talked about what would be some
of the variables involved, i.e., height of ramp, height of table, distance of roll on table,

etc.

To check student calculations, Brian Drobert, a Michigan State University intern, and I
developed a program using the graphing calculator. Students were not given access to this
program from either the control or experimental group.
Below is an example of a student's data and screen shots:

value of g = 9.8 m/s’;

horizontal distance (distance the ball rolled on lab bench) = 1.00 m

vertical distance (distance from the ramp to the floor) = 0.75 m

Time (Used to calculate the horizontal speed)

1.525 1.565 1.555

Below are the screens for a sample student’s data.

lggrsg value or e §¥§$§HEERIZ°"THL ggT;§.HEIGHT
.1.aol

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2 Figure 3 Figure 4
(g value) (Travel distance on table) (Distance to the floor)

 

 

 

TIME 1 THE 2 TIME 3
FIEEE STEE- SEE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5 Figure 6 Figure 7
(1" Horizontal Time) (2" Horizontal Time) (3"1 Horizontal Time)
stems.
. 65 PLACE CUP 25 3
TIHE TO FELL =39 eggnognehs) '
U I
Figure 8 Figure 9

(Horizontal Speed and Fall Time) (Distance to Hit Target)

This allowed me to check their precision on timing and to check calculations and

rounding errors. Most of the students had collected sound data.

55

APPENDIX A~IV

Projectile Control Motion Lab 2—Softball Throw Laboratory
(Merrill, Lab Worksheet, p.11)

 

 

 

Name Date Hour

Chapter 6 Vectors Projectile Motion
The Softball Throw

Calculations

1. Determine the initial values of v, for each throw.

2. Determine the initial value of vy.

3. Draw a triangle as shown in your text. Record your value of v" and v,.

4. Use the Pythagorean Theorem to find the value of v,.

Observation and Data

Trial Range (m) Time (s) Vx (mls) Vy (mls)

1

Vi (mls)

Analysis

1. Did each person throw at about the same range?

2. Did each person throw about the same speed?

Teacher’s Notes:

I took the students out to the football field next to the school to throw a softball for this
lab. We had several volunteers to throw the ball; both genders were represented. We had
about eight to ten throwers. Several students were markers for ten feet intervals. One
student timed the flight of the ball from release to initial hit on the ground. Two more
students were the spotters to help determine the range. Finally, one student was the
recorder. Our data table also included the angle and height the ball traveled.

In addition to the lab, I had students make two graphs: Total time vs Initial Angle; Initial
Angle vs Range. The former graph was to determine if the total time and angle were
directly related or inversely related. One student was asked to throw at 90°, 60°, and 45 °,
respectively. This data was recorded along with the time and range.

To check a student’s calculations, Brian Drobert and I developed a program using the
graphing calculator. Students from either the control or experimental group were not
given access to this program.

Below is an example of a student’s data and screen shots.

Example:

value of g = 9.8 mls’;

Total time of flight: 2.50 seconds

Range == 85 m

 

 

 

53% 'JHLUE OF 6 w TOTE. TIME 5155!? Tl-E RINSE

 

 

 

 

 

 

 

 

 

Figure 10 Figure 11 Figure 12
(g value) (Travel time in air) (Travel distance)

 

 

 

 

 

 

 

 

TOTFI. TIME s W s
' 2.5 ' 12.25
TIHE UP 8 VI B
W1 .3 1.25 ENGLE : 36.14
34 19.81
Figure 13 Figure 14

(Time, Time up and horizontal velocity) (Vertical and initial velocity and 0)

 

"BX. l-EIGHTBEagg

 

 

 

Figure 15

(Maximum height in meters)

Students graphed the initial angle vs the range to determine what angle resulted in the
maximum range. We talked about how we did not account for the initial height of the ball

being thrown (1 to 1.5 m). Everyone enjoyed this lab.

APPENDIX B-I

Vector Experimental Lab l-Finding the resultant vector from the component vectors

Purpose: To determine the resultant vector by two different methods when provided the
horizontal and vertical components.

Materials: protractor, graphing calculator, and VECTRES program. (Short for VECTor

RESultant program)

Procedures:

Construct four sets of components of varying lengths within each quadrant (i.e., 0° to 90°

is quadrant 1; 90° to 180° is quadrant 2; etc.) in your lab book. Measure the

corresponding resultant vectors. Then use the 11$ Graphing Calculator program

VECTRES to determine the same four resultants using the same set of components.

Record your results in a data table. Finally, reverse the process and use the calculator

program first, then draw them out in your lab notebook. Record all component and

resultant vectors in data table. Also, use different lengths than what was used in the first

part. Write down the source code for VECTRES.

Analysis:

What equation in the program actually determined the magnitude of the resultant?
Indicate in the source code what section determined the direction for the components?
What was percent error? %Error 2 (measured — calculated)/calculated * 100

What benefit(s) does using the VECTRES program provide(s)?

What problem(s) do/does using the VECTRES program pose?

Teacher’s Notes:

Before beginning the calculator based lab, the class reviewed the four quadrants and how
they relate to vectors. Lab groups were given a review or taught on vector drawing and
how to run the program. 1 emphasized that all students, not just one student, should 11111
the program. Below is the source code for the T183 graphing calculator VECTRES
program. This could be used for TI-81, 82, and 85. I did not try to down load it into a TI-
92. For 11.81, the program must be keyed in manually since it does not have graph link
on the bottom. The program was downloaded to the ten student calculators used for the
study only. Having the program on ten calculators avoided incompatibility problems of
the program with the TI 85, 92, or other graphing calculators that some students have for
their math classes. This also limited the program access to only the experimental group
students. This program was developed and tested in the summer of 1997 with the help of
Mr. Chomy, fellow teacher researcher, and was based on a program down loaded from

Texas Instrument's web site on graphing calculator programs (Harmon, 1994).

This program will determine the resultant vector when provided with the magnitudes and
directions of two or more different vectors.

VECTRES - Source Code

:Degree

:Func

:Lbl 3

:Cerome

:Disp “INTER VECTOR NO.”
:Input N

:If N<= 1

Goto 3
:0

:0

61

:0__Y

:1__Z

:Cerome

:Disp “VECTOR NUMBER”
:Disp__Z

:Disp “MAGNITUDE =”
:Input M

:Disp_ “ANGIE =”
:Input D

:X + (Mcos(D)__X

:Y + (Msin(D)_Y

:Z+ 1_Z

:N - 1_N

:If N_ 0

:Goto 0

:Sqrt((X2 + Y2)__R (This is equation determines the magnitude.)
:HX=0

:Goto 5

:HY=0

ibmé

:If R = 0

:Goto 1

:tan" (Y/X)_ 0

:HY<0

:360 - abs(tan“(Y/X)) (This section and below is where direction is
:If X< 0 determined.)
:180 + (tan"(Y/X))___
:Lbl 1

:Cerome

:Disp “MAGNTTUDEz”
:round(R, 1)_Y

:Disp R

:Disp “ANGLE=”
:round(__, 1)_

:DiSP ..

:Stop

:Lbl 5

:HY>0

:90___

:HY<O

:270___

:Lbl 6

:HX<0

:180__

:End

62

Below is a sample run with corresponding screens. In between each screen, the student

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

would push the enter key.
EEITER VECTOR NO. VECTOR NUMBER 1 VECTOR NUMBER 1
' naeurrune= marinara:
?100I ?IBB
RNBLE=
?OI
Figure 1 Figure 2 Figure 3
(Enter number of vectors) (Enteringl‘ vector size) (Enteringl‘ vector angle)
VECTOR NUMBER ULTBNT VECTOR
:Egkiiugsmefi naeurrune= 2 %ENITUDB r41 4
?100I ' ?1 a RNBLE= '
Fl LE= 45
1790' Done
Figure 4 Figure 5 Figure 6
(Enter 2"“ vector size) (Entering 2"“ vector angle) (Resultant vector screen)

Most vector problems have two vectors and students determine the resultant of these two.
However, most software programs only address vectors between 0° and 90°, which limits
the variety of problems. My program will work with vectors from 0° to 360°. Moreover, it
can handle many more than two vectors. I gave an extra credit program to draw and find
the resultant vector magnitude and direction for 15 vectors. If done correctly, it traced out

an outline of a shape of a duck.

If you should make a mistake (i.e., entering too many vectors), then just press 2"“ Quit to
exit the program. You can check your answer with the next program, VECTCOMP,

which does the reverse.

APPENDIX B-II

Vector Experimental Lab 2—Finding the components from a known resultant vector

Purpose: To determine the horizontal and vertical components from a resultant vector.

Materials: protractor, graphing calculator, and VECTCOMP program. (VECTCOMP is

short for VECTor COMPonent)

Procedures:

Construct a resultant vector within each quadrant (i.e., 0° to 90° is quadrant 1; 90° to 180°
is quadrant 2; etc.) in your lab book. Measure the corresponding component vectors,
using the parallelogram method. Use the TI-$ Graphing Calculator program

VECT COMP to determine the corresponding sets of components. Record your results in
a data table. Then use the program to test four different resultant vectors. Find their
corresponding component vectors and record in data table and diagram in lab notebook.

Write down the source code for VECT COMP.

Analysis:

What equation(s) in the program actually determined the magnitude of the components?
Indicate in the source code, what section detemrined the direction for the components?
What benefit(s) does using the VECTCOMP program provides?

What problem(s) does using the VECTCOMP program pose?

Teacher’s Notes:

Below is the source code for the TI-83 graphing calculator for the VECTCOMP program.
This could be used for TI-81, 82, and 85. I did not try to down load it into a TI-92. This
program must be keyed in manually for the TI—81 since it does not have graph link on the
bottom. For this lab, I down loaded the program to the student calculators. This program
was developed and tested in the summer of 1997 with the help of Mr. Chomy, fellow
teacher researcher, and was based upon program down loaded from Texas Instrument's
web site on graphing calculator programs (Harmon, 1994).

This program will determine the horizontal and vertical components' magnitude

and direction when a resultant vector’s magnitude and angle is provided. It should be
noted the program will not resolve any vectors with (_) :2 0°, 90°, 180°, 270°, and 360°,

respectively.

VECTCOMP— Source Code

:Degree

:Func

:Lbl 1

:Cerome

:Disp “ENTER VECTOR”
:Disp "MAGNITUDE”
:Input V

:If V<= 0

:Goto 1

:Lbl 2

:Cerome

:Disp “ENTER VECTOR”
:Disp “ANGLE”

:Input __

:If _ <= 0

:Goto 2

:0__X

:0_Y

:0_A

65

:0 B

:Vcos(_)__X (This section determines direction for the X component.)
:IfX >0and (_>0 and__<90)

:0_Q

:IfX >0 and (_ >270 and __ <360)

:360_

:If X <0

:180_

:Vsin(_)_Y (This section determines direction for the Y component.)
:HY>0

:90.R

:HY<0

:270_R

Lbl 3

:Cerome

:Disp “VX MAGNITU DE 2” (This equation is used to determine the horizontal
:(round(X,1))_X component vector.)

:Disp X

:Disp “VX ANGLE =”

:Disp Q

:Pause

:Disp “VY MAGNTTUDE _—.-” (This equation is used to determine the vertical
:(round(Y,1))_Y component vector.)

:Disp Y

:Disp “VY ANGLE =”

:Disp R

:Stop

Below is a sample run with corresponding screens. In between each screen, the student

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

would push the enter key.
ENTER VECTOR ENTER VECTOR
MBGNITUDE ENGLE
o 41, 4 ?45I
Figure 7 Figure 8
(Resultant vector length) (Resultant vector angle)
VX I'IFIGNITUOE TOO: VX BNGLE =
VX FlNGLE = 8 W l‘lFlGNITUDEs
W fiNGLE=
9%
Done
I
Figure 9 Figure 10
(Horizontal component vector) (Vertical component vector)

67

APPENDIX B-III

Experimental Projectile Motion lab l—Baseball lab
(Parametric Equations to find T, R, and H) (Modified from Vonder Embse, 1990)

Purpose: To simulate the flight of a baseball and determine if the ball can be caught.
Materials: TI—81 to TI-89 graphing calculator and PROJMOT program.
Procedures: Set the graphing calculator's mode to Par (Parametric Equation) and window

settings to the below values.

Tmin = 0 Xmin = 0 anin = -25
Tmax = 5 Xmax = 430 Ymax= 100
Tstep= 0.05 Xscl = 50 Yscl = 10

Then type in or down load the program PROJMOT. Make sure any conversions are done
so the units will cancel. Write down in your lab book your X 1T, Y1T and other X: and Y:
expressions. Diagram your results in your lab book as well. Answer the questions in the
analysis section in lab book.

Problem:

[A baseball player] is at the plate, in the bottom of the ninth inning of the last game of the
season, for the Detroit Tigers. This is his last chance to hit his 50'” home run of the
season. The pitcher serves up a fastball at the waist (3 feet above the ground) and [the
batter] hits the ball at a velocity of 150 feet per second at a vertical angle of 20° toward
straight away center field. The center field fence is 20 feet high and 400 feet from home
plate. At the moment he hits the ball there is a 6 mph wind blowing straight in from
center field. 15 this hit a home run? Is the ball able to be caught? Use the Line function to
draw the wall. (Deamana and & Waits, 1990)

Analysis:

Q1) What would happen to the ball if the wind suddenly died? Or increased to 12 mph?
Graph three possibilities at the same time.

Q2) What would happen if the ball were hit at an angle of 25°? Compare this hit with the
original hit of 20° with a 6 mph wind.

Q3) A line drive is known as a “rope” in baseball lingo. Consider a line drive to be hit at
a 10° angle. What velocity would it take to hit a line drive home run?

Q4) Compare the time of flight of a high fly ball to a line drive using the Trace function.
Graph both simulations at the same time.

Q5) What is the best angle to hit the ball?

Q6) What factor is more important in the problem, the angle of the hit or the initial
velocity? Why?

Q7) Change the problem situation to a punter on the football field. What should the
punter do to produce the best “hang-time” for his punt?

Q8) Change the problem situation to a golfer hitting a golf ball with different types of
clubs. For example, a driver has a head angle of 95° to 11°. Simulate several

different iron shots at the same time.

69

Teacher’s Notes:

The students should have entered the following parametric equations: T = Time in sec.
X1T = (150c0320°)T - 8.8T

Note: 150st was the initial velocity; and 8.8 was 6 mph converted to ft/s)

Y1T = -16T2 + (1505in20°)T + 3

Note: -16 Ms2 is half of g value (32 ft/sz) and 3 ft was the height the ball was thrown.
Below are some of the screens that the TI graphing calculator will show in solving the
above problems. If you have access to a view screen that shows your graphing
calculator’s screen on the overhead, then most of students can follow along. I found a lot
of students had difficulties with entering the mathematical formulas for this lab.

Conceptually, most students understood. Be prepared to walk around and help trouble-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

shoot this lab.
mu Hot: "or: POINTS 5T0
\XirE(150cos(28) rDrau
T- 8. 8T ine<
Vita 6T2+(1585 =Horizontal
in(2B) +3 :Vertical
\ers 2: Tangsnt(
YZr= Draw
\X31= 715hade<
Figure 11 Figure 12 Figure 13
(Entering parametric equations) (Graph) (Drawing the wall)
Lim<4801 20.400. mu Not: Hot:
0)I -8. 8T
Ytra 16T2+(1585
in(20)T+
\Xérg§158605(25)
Vzva %6T2+(1585
in(25)+
Figure 14 Figure 15 Figure 16

(Entering Line from Draw menu) (Graph) (Entering another set of equation at 25°)

70

 

 

 

 

 

 

 

Figure 17

Graph with more than one set of equations

Give your class about two to three days to work on this lab. The questions are a little

advanced for conceptual level physics but still worth while.

71

APPENDIX B-IV

Experimental Projectile Motion Lab 2-—Vo and B to find T, R, and H

Purpose: To determine the angle to obtain the maximum range and the relationship

between time vs angle and how initial velocity affect range at a constant angle.

Materials: TI-8l to TI-89 graphing calculator and PROJYVST program. (PROJYVST is

short for PROJectile motion YVST program, it also graphs the range)

Procedures:

Make sure your calculator is in parametric (Par) mode. Then use the program

PROJYV ST to determine the angle that allows for the maximum range or X value. Also,
determine the relationship between time vs angle. Finally, find out if the initial velocity
affects range at a constant angle. Record all your results in your lab notebook. Include

any graphs to help support your findings.

Analysis:
Q1) What was the angle that allowed for the maximum range?
Q2) What relationship existed between time and angle? Were they dependent or
independent of one another?
Q3) When the angle is kept constant, what was the relationship between initial velocity
and range? Use graphs to support your answer.

Q4) What angle allows for maximum height?

72

Teacher’s Notes:

PROJYVST Lab—Source Code

This program was created with the help of Brian Drobert, an MS U intern. The program
will create a parametric graph, where the time, height and range can be determined
graphically. A person only needs to enter the value of g, initial velocity, and the angle.
Note: g can be 9.8 m/s2 or 32 ft/s2 or other values if you're on another planet or in an

elevator while it is accelerating.

PROJYVST — Source Code
:Param
:0_V

0'68:
w>|

:0_G
:”0”_X1T

:”O”_Y 1T

:Lbl 1

:Cerome

:Degree

:Disp “ENTER VALUE OF G”
:Input G

:If G <= 0

:Goto l

:Lbl 2

:Cerome

:Disp “ENTER INITIAL”
:Disp “VELOCITY”

:Lbl 3

:Cerome

:Disp “ENTER ANGLE”
Input 0

:H0<=0

:Goto 3

:If 9 >= 90

:Goto 3

:V*(cos(6))-'A
:V*(sin(6))-’B

:”A*T”-*X1T

:”B*T- O.5*G*T2”-*Yn

( 1 .20)B/(O.5*G) *Tmax

”Note: The 1.20 is to increase the graphing time." -
:(A*Tmax)-’Xmax

:( 1.05)(B*(Tmax/2)—O.5*G(Tmax/2)2)*Ymax

"Note: The 1.05 is to increase the graphing time.**
:Draw F Y1T

:Stop

Below is a sample run of the program.

 

 

 

 

 

 

 

 

 

 

 

 

ENT R UFILUE OF G ENTER INITIHL gNTER FINBLE
?9. VEg C W .57.4?I
Figure 18 Figure 19 Figure 20

(Entering the value of g) (Entering the initial velocity) (Entering the initial angle)

 

 

“itWT/‘WfiMT-OS-

LLL

Figure 21 Figure 22

 

 

 

 

 

 

 

 

(Displaying the projectile's graph) (Displaying the graph, T, X, and Y set to 0)

[7Nhflflt‘l-O5- 87fl1t=3*T-05-

'-
3825412511 -?=1!.77323? s 88 323022 n78.3'liw0? s

 

 

 

 

 

 

 

 

Figure 23 Figure 24

74

(Displaying T=2.0s,X= 25.00m,Y= 19.6m) (Displaying T=4.0s,X = 50.01m,Y= 0.01m)
APPENDIX C-I
Vector Control Demo—Cut Out Vectors

Concept Demonstrated: Vector's have additive and subtractive properties.

Materials: Poster board or card boxes, markers, scissors, meter sticks. Cutting out paper
arrows, which then can be laminated, can easily represent vectors. Various
sizes can be made to represent different size components or resultant vectors. I

had cut out several size vectors.

Teacher’s Notes:

I asked how could I determine the magnitude of one vector. I also asked what direction
could I give the vector. Once the students understood what a vector is, I asked them what
if one of my vectors represented a plane flying with a certain velocity, having magnitude
and direction. Then I added an element of tail wind. How could the velocity vector be
represented? Then I added an element of a head wind, where the velocity vector would be
smaller. Finally, I added a crosswind. This allowed me to show students what

the new plane velocity was. Most students found this to be intuitive, while others seemed
to be unsure of components. I found it helpful to have students provide the plane’s
components and resultant velocities. Moreover, I used 90° for the crosswind so that the

Pythagorean theorem could be used.

75

APPENDIX C-II
Vector Control Demo—Vector Rope and Potato Bag Demo
Concept Demonstrated: A vector can be resolved into its horizontal and vertical
component.
Materials: A 5 or 10 lbs. bag of potatoes, 50 to 75 feet rope, and a cheese cloth bag in
which to place the plastic potato bag during pulling.
Teacher’s Notes:
This demonstration allows students to see vector components and resultants when two or
more students try to straighten out a rope with the bag of potatoes in between them. First
have two students pull the rope in a tug-of-war fashion. Students should have no
problems seeing vectors, where the vectors are equal and not equal in magnitude and
opposite in direction. Then place bag of potatoes in a cheesecloth sack and tie with rope.
Have the same two students try to pull the bag horizontally. Most likely they cannot.
Even if they can, have them allow the bag to sag. This would allow the instructor to ask
where are the resultants and components for both sides. If the students were not able to
bring the bag to the horizontal, then allow more students to join in to see if the bag of
potatoes can be brought to a horizontal position. After the demo, I asked questions to see

if students understood terminology and concepts.

Then we go back into the class and have them draw a vector representation of the potato
bag and rope labeling the horizontal, vertical, and resultant vector. They were, also, asked
to write down in their physics notebook the deseription of how vectors are involved in

clothes on a line, tight rope walking, and hanging pictures.

76

APPENDIX C-III

Projectile Motion Control Demo—2—Dimensional Motion Demo

Concept Demonstrated: Any projectile motion's horizontal and vertical motion will be

independent of one another.

Materials: Projectile Motion Demo launcher, 2 bearings, where one is solid and another
has a core section taken out of it. This is a unique device that allows two

bearings to be launched at the same time, one horizontally and one vertically.

Teacher’s Notes:

I usually place the launcher on a ladder so that both bearings can hit the floor. The
objective is to demonstrate the independence of horizontal and vertical motion. This will
result in both the horizontally shot bearing and vertically dropped bearing to land at the
same time. One could modify this demonstration by using washers or pennies on a ruler

that is anchored with a nail in the center and allowed to spin freely.(Edge, 1981)

APPENDIX C—IV

Projectile Motion Control Demo—Shoot the Monkey Demo
Concept Demonstrated: Objects under the influence of gravity will fall together and hit in
mid-air together, independently of horizontal and vertical

motion.

Materials: An electromagnet connected to a blow gun, where a bearing would break the
connection at the end of the barrel, thereby, releasing the object to fall freely at

the same time.

Teacher’s Notes:

The monkey shoot is a classic physics demonstration. (see Figure l)

 

' ’ l
a,
._ § .
,w‘“ +- 5‘~-... 31°
{‘1
Light k fig Q1

Source ‘
Compressed
Nifi . g 20. r . gp

 

 

 

Figure 1

(Shoot the Monkey Setup: Freier, G.D. and Anderson, F.J., 1981)

Rogowski says, “It is a study in mechanics of projectile motion. . .[containing] elements

of geometry, trigonometry, ballistics, projectile mechanics, vector analysis. . .[within its

78

 

I.“

gnu-4:

.urv

.u.

.o .no

‘

solution].” (1982) However, if you're for animal rights, then Yoav Ben-Dov addresses the
same problem using apples in his article, Why the Dart Always Hits (1993). Rogowski
used computer animation on an Atari 800 and another physics teacher used a raised up
table along with one meter length corner molding with a V groove as the gun (Brown,
1977). I used an electromagnet, tin can (monkey is painted on it), blow gun apparatus,
and bearing. Students are asked where the gun should be aimed: above, at, or below the
monkey, if the monkey releases the second the bullet clears the barrel. Most will pick
above the monkey due to gravity; however, this is wrong, as is aiming below the target.
This demonstration was cumbersome to setup. Moreover, I felt the students were more

focused on the apparatus and setup than the concept to be learned.

79

APPENDIX C-V

Projectile Motion Control Demo—Hall Cart Demo

Concept Demonstrated: Projectiles follow a parabolic pathway.

Materials: The Hall Cart has an upright cylinder to hold a bearing, paper clip, and string.
The center part of the Hall Cart is spring loaded and allows the teacher to

attach a straightened out paper clip tied to string.

Teacher’s Notes:

Once the cart is moving, a quick pull on the string that is attached to the paper clip will
release the bearing into the air. This will follow a parabolic pathway and the bearing will
land in the cup. If the cart is stopped after the bearing is in the air, the bearing will
continue in a parabolic pathway; however, it will not land in the cylinder. The Hall Cart
demonstration is good for the topic of inertia (seatbelt safety). This demonstration seems
to ring true the saying “If it doesn’t work, it has to be physics.” This demo worked

correctly one in four times.

APPENDIX D-I
Experimental Vector Demo-Vectors by Video Laserdisc Demo
The Physics at Work video laserdisc has some very good images of how vectors are
utilized in everyday contexts (i.e., bridge and building design, tossing a ball and cannon
firing, etc.). I have students work in small groups and go through these images as well as
through the animated vector and projectile frames using the video laserdisc. Students are
encouraged to take notes from the disc as well as answer the questions in their lab

notebook.

Questions asked to write in physics journal prior to viewing the video laserdisc:

Q1) How would you define a vector?
Q2) What are some real life applications that utilize vectors?

Q3) Identify and show two different ways of solving vector problems?

(Use one of your vector addition problems.)

Questions after viewing the video laserdisc:

Q1) How did Physics at Work define a vector?

Q2) Describe some real life applications that utilize vectors from the video laserdisc?

Q3) Identify and show two different ways of solving vector problems?

81

Teacher’s Notes:

The video laserdisc allowed students to view the images several times if they were
uncertain of the concept(s). The questions given prior to viewing the video laserdisc
served as a check to see if students were taking notes and answering questions from their

textbook. The questions after viewing served as a review or mode of learning.

APPENDIX D-II
2-Dimensional Motion Demo
The Cinema Classic video laserdisc was used to help understand projectile or 2-
Dimensional motion. Small group discussions allowed students to make some predictions
prior to viewing the video laserdisc.
Predictions:
Ql) If one bullet was fired horizontally and one dropped at the very same time, which

one would hit the ground first? (Hewitt, 1992) Explain your answer.

Q2) If a monkey in a tree could release its grip and free fall the instant a bullet cleared
the barrel of a hunter, where would the hunter need to aim: above the monkey, at the

monkey, below the monkey? Explain your answer. (Rogowski, 1982)

Q3) If you were driving down the road slowly (neglect wind resistance) in a convertible
and the instant someone in the back seat tossed a ball straight up, would the ball
travel in a parabola even if the car suddenly slowed down or speeded up? Explain

your answer.

Analysis

Based upon viewing the Cinema Classic video laserdisc, would you change any of your
answers from questions above? If so, how would they vary? In your physics lab
notebook, describe the setup for each demonstration. Finally, provide what you thought

was the purpose of the demonstration.

Teacher’s Notes:

The video laserdisc did not show any bullets, monkey, or cars. I wanted them to transfer
the concept of the pool balls being fired horizontally and vertically at the same time to the
bullet problem. Also, a crossbow arrow dart hitting a pool ball that was suspended by an
electromagnet represented the monkey shoot problem. Finally, the ball toss from a
convertible was demonstrated by a snowmobile with a flare being fired at the same time

the snowmobile moved with varying speeds.

APPENDIX E~I

The concept map below was given the day before the posttest, and any questions were

answered the day of the posttest.

Ch.” 5 Name
Vector and Projectile Motion Concept Map H‘

a...“
.isaunitfor

inaunitfor-::
. isnnnitfa' .splacement
H. .l in)

 

   
 

 

 

m/sz .
and mm fmrn directr'
parallelogram O— are"ling a on :0
00

in having both a
direction
scale factor

force l
min/1:11:11: W run-in constant became of

W

 

 

prejectrles
horizontal and . .

gravity

2-D

inertia do: to
9. 8 m/s2

vertical

force W umpnsmmor becauseofthe .

APPENDIX E—II

Students are not given the answer key concept map test.

 

 

Chapteri H
Vector and Projectile Motion Concept Map
Answer Key Date H

   
 
   
 

®isauit for acceleration h."
additioncanbedmebythe

isa

©isamtrm -i"

is a

is a unit for
is a
subdivide into scale factor

 

 

"W -
pron-actor
Usevamfi move i“ and maria; from
Ill/82 and mare from a W
cm“ ......... .. o
00

m tnvingbotha

force hortzorml
magnitude I rennin because of 0
W3 velocity vecto
jectiles
'zontal
gravity "d ' 0

 

 

 

APPENDIX E-III
The test questions came from Conceptual Physics, 2’“ Edition, Chapter Test, and from
Merrill Physics: Principles and Problems, as well as from the labs and supplemental
activities. This is the way I usually design my tests for a unit.
VECTOR AND PROJECTILE PRETEST/POST TEST
Name Date ’ Hour

Introductory Physics— Pretest/Post Vector and Projectiles

(r —.——
58pts
True or False Questions (lOpts) 270° 90°
Circle the correct answer.
180°

T F 1. Car speed can be represented as a vector quantity.

T F 2. A single vector can be replaced by two vectors in the X and Y
directions. These X and Y vectors are called the component of the
original vector.

T F 3. A quantity that has both magnitude and direction is called a vector.

T F 4. The horizontal component of velocity for a projectile varies with time,
even with no air resistance.

T F 5. The vertical component of velocity for a projectile does not vary with
time, even with no air resistance.

Multiple Choice Questions (20pts)
Choose the best answer to each question and write the appropriate letter in the space
provided.

6. A scalar is a quantity that has

A) magnitude and time. B) magnitude and direction.
C) time and direction. D) only magnitude.

7. When velocity is represented as a vector
A) the length of the arrow represents the speed.

B) the length of the arrow is drawn to a suitable scale.

C) the direction of the arrow show the direction of motion.
D) all of the above.

8. What is the maximum resultant possible when adding a 3-unit vector to an 8-
unit vector?

A) 24 B) 11 C) 8 D) 5

9. What is the horizontal component of a vector 5 N at 30°?

A) 5/cos30" B) 5/sin30° C) Shoo" D) 5cos30°
10. What is the value of the vertical component of a force vector of 5 N at 30°?
A) 5/cos30° B) 5/sin30° C) 5sin30° D) 5cos30°
11. Which of the following would not be considered a projectile?

A) A cannonball thrown through the air.

B) A cannonball rolling off the edge of a table.
C) A cannonball thrown straight up.

D) A cannonball rolling down a slope.

12. The horizontal component of a projectile’s velocity is independent of time
of flight.
A) time of flight
B) the range of flight.
C) the vertical component of its velocity.

13. A ball is thrown into the air at some angle between 10 degrees and 90
degrees. At the very top of the ball's path, it velocity is

A) entirely horizontal.

B) entirely vertical.
C) both horizontal and vertical.

14. In the absence of air resistance, a thrown ball will travel the greatest
distance if it is thrown at an angle of about

A) 75°. B) 45 °. C) 60°. D) 30°.
15. In the famous “monkey shoot” or some similar demonstration, where must one
aim in order for the two falling objects to hit?

A) directly below
B) directly above

C) directly at
D) doesn’t matter

16. Use the graphical method to determine the displacement of a person’s trip if they go
from the start 40 km east, 20 km south, and 70 km west.
(Use a scale of 1 cm = 10 km) (6pts)

 

 

 

Start
0
17. Using the following scale: 1 em = 20 N (4pts)
A) Draw the following vector 60 N at 290° O
A
B) Measure R = at \
B

18. Draw the component vectors and determine their magnitude and direction.
(1 cm=30km/h))(5pts)

Horizontal component: at

Vertical component 2 at

4. Determine the resultant vector using the Analytical Method or Triangle Method (head
to tail) for a plane flying North or 0° at 60 km/h while the wind blows towards 90° at
80 km/h. Label each vector and find the resultant vector, R (round to 0.1). Must

include units and show work. (6pts) (Flint: a2 + b2 = c2)

at

at

at

5. If a softball is thrown a distance of 80 m in 5.00 seconds determine the following:
(Note: g = 9.8 m/sz, round to 0.01) Please show your work below. (6pts)

t“, = U2 0 = tan"(v,/v,)
Vx = Range/t Ym = Vy(tup) — 4.90”) 2
vi! = g0...)

K-JK’+K’

Work Area:

Place answers on line provided.

tup (s) V, (mls) Vy (mls) Vi (mls) 0 (degrees) Ym (m)

 

 

BIBLIOGRAPHY

Abou, Ibrahim and Hestemes, David, 1985. Common sense concepts about motion,
American Journal of Physics, November, pp. 1056—1065.

Aguirre, José M., 1988. Student Preconception about Vector Kinematics, The Physics
Teacher, April, pp. 212-216.

Arons, Arnold B... 1993. Guiding Insight and Inquiry in the Introductory Physics
Laboratory. The Physics Teacher. Volume 31, May. 278-282.

Beach, John E., 1996. A New Old Trajectory Experiment, The Physics Teacher,
November, pp. 522-523.

Beckwith, Carole, 1999. Online: ht_tp://www.pioneerusa.gom_/§t/teachg&a.html .

Beichner, Robert J ., et. el., 1995. Hardware and Software Preferences, The Physics
Teacher, Vol.33, May, pp. 270-274.

Ben-Dov, Yoav, 1993. Why the Dart Always Hits, The Physics Teacher, Vol.31,
December, pp. 526-528.

Brancazio, Peter J ., 1985. Trajectory of a fly ball, The Physics Teacher, Vol.23, January,
pp. 20-23.

Brown, Ronald A., 1992. Maximizing the Range of a Projectile, The Physics Teacher,
Vol.30, September, pp. 344—347.

Brown, William P., 1977. Monkey and Hunter in Slow Motion, The Physics Teacher,
September, pp. 368—369.

Brueningsen, Chris and Bower, William, 1995. SYMPOSIUM: “Using the Graphing

Calculator” - in Two-Dimensional Motion Plots, The Physics Teacher, Vol.33, May,
pp. 3 143 16.

Chiaverina, Chris, and Hicks, Jim, 1983. People demos, The Physics Teacher, March,
pp. 164171.

Cieply, Joseph F., 1993. Parametric Equations: Push 'Em Back, Push 'Em Back, Way
Back! The Mathematics Teacher, vol .86. No. 6. September. pp. 470-474.

Clement, John, 1982. Students ’ preconceptions in introductory mechanics, American
Journal of Physics, January, pp. 66-71.

Demana, F. and Waits, B., 1990. Precalculus Mathematics: A Graphing Approach.
Reading, MA: Addison-Wesley Publishing Company, p. 649.

91

diSessa, Andrea A., 1987. The Third Revolution in Computers and Education. Journal of
Research in Science Teaching. Vol. 24, No.4. pp. 343-367.

Dunham, P. H., & Dick, T. P.,1994. Research on graphing calculators. Mathematics
Teacher, 87, 440-445.

Englehardt, Paula V. Scott F. Schultz, John E. Gastineau, Margaret H. Gjertsen, and John
S. Risley, 1993. Teaching the Use of Spreadsheet for Physics. The Physics Teacher. Vol.
31. December. pp. 546-547.

Embse, Chuck Vonder, 1990. Parametric Equations on the TI-81, December 14,
pp. 13-15.

Escobar, Carole, 1990. Amusement park physics, The Physics Teacher. Vol. 28. p. 446.

Flower, April, 1996. A Projectile Motion Experiment, The Physics Teacher, March,
p. 155.

Flynn, Melissa and Sumerix, Kendall. 1994. Technology Unit: Graphing Calculators,
July. pp. 25 - 29.

Freier, GB. and Anderson, FJ, 1981. A Demonstration Handbook for Physics. American
Association of Physics Teachers. p. M-8.

Goodwin, Peter, and Weston, J., 1990. Practical Physics Labs: A Resource Manual,
Walch Publishing,, ISBN 0-8251-1683-X, pp. 50-63.

Graphing Calculator Research: h :llwww. ' cl - .

Hake, Richard R., 1992. Socratic Pedagogy in the Introductory Physics Laboratory. The
Physics Teacher. Vol. 30. December. pp. 546-552.

Harrnond, Michael, 1994 VECTORADD, TI-81 program down loaded from Texas
Instrument web-site, http:/lwww.ti.com.

Helnrick, James R., 1993. The Mobile Frame of Reference. The Physics Teacher, Vol. 31,
March. p. 177.

Hendrix, Laura, 1996. Labs That Are a Blast, The Physics Teacher, April, pp. 212—213.

Hestenes, David, Malcolm Wells, and Gregg Swackhamer, 1992 F orce Concept
Inventory, March, vol. 30. pp. 141-158.

Hestenes, David, and Malcolm Wells, 1992. A Mechanics Baseline Test, March, vol. 30.
pp. 159-166.

Hewitt, Paul G., 1992. Conceptual Physics, Second Edition, Addison-Wesley Publishing
Company Inc., ISBN 0—201-28652-1, pp. 66-85.

Ibrahim, Abou Halloun and David Hestenes, 1985. Common sense concepts about
motion. American Journal of Physics. Vol. 53 (11), November. pp. 1056-1065.

Inouye, Carey S. and Eric W.T. Chong, 1992. Maximum Range of a Projectile, The
Physics Teacher, Vol. 30. March, pp. 168-169.

Johnson, Larry D., 1992. The Path of a Projectile, The Physics Teacher, February,
pp. 104-105.

Krieger, Michael E. and Stith, James H., 1990. Spreadsheets in the Physics Laboratory,
The Physics Teacher, September, pp. 378-384.

Knight, Randall D., 1995. The Vector Knowledge of Beginning Physics Students, The
Physics Teacher, February, pp. 74-78.

Kramer, Criag. 1995. Merrill Physics Principle and Problems Laboratory Manual.
Glencoe Division, Macmillan/McGraw-Hill. pp. 33-36.

Larkin, Jill, McDermott, John, Simon, Dorothea R, Simon, Herbert A., 1980. Expert and
Novice Performance in Solving Physics Problems, Science, June, pp. 1335-1342.

Leonard, William J ., 1997. Dangers of Automated Data Analysis, The Physics Teacher,
April, PP. 220-222.

Lucido, Horace (Rog), 1992. Physics for Mastery. The Physics Teacher. Vol. 20,
February. pp. 96-101.

McCloskey, Michael, 1983. Intuitive Physics, Scientific American, Volume 234, pp. 122-
130.

McDermott, Lillian C., 1984. Research on conceptual understanding in mechanics.
Physics Today. July. pp. 24-32.

Mestre, Jose and Touger, Jerold, 1989. Cognitive Research— What 's in It for Physics
Teacher?, The Physics Teacher, September, pp. 447-456.

Merrill Physics: Principles and Problems, Lab Worksheets, 1995. Glencoe/McGraw-Hill.
pp. 11 and 6T .

Moses, Thomas and Natalie L. Adolphi, 1998. A New Twist for the Conical Pendulum,
The Physics Teacher, September, pp. 372—373.

Murphy, James T., 1977. Laboratory Physics, Charles E. Merrill Publishing Co., pp. 37-
41, ISBN 0-675-07601-3, pp.61-66.

Nicol, Marsha P., 1997. How One Physics Teacher Changed His Algebraic Thinking.
Mathematics Teacher; v90 n2, February, p8689.

Novodvorsky, Ingrid, 1997. Constructing a Deeper Understanding, The Physics Teacher,
Vol. 35. April, pp. 242—245.

Pecori, Barbara and Giacomo Torzo, 1998. The Maxwell Wheel Investigated with MBL,
The Physics Teacher, September, pp. 362—366.

Penglase, M., & Arnold, S., 1996. The graphics calculator in mathematics education: A
critical review of recent research. Mathematics Education Research Journal, 8,
pp. 5890.

Phillips, Dennis W., 1999. Physics on Graphing Calculators. The Physics Teacher. Vol.
37. April. pp. 230-231.

Pinkerton, K. David, 1996. Low-Tech Solutions, High-Tech Results, The Physics
Teacher, January, pp. 30-34.

Porter, William S.,1977. The range of a projectile, The Physics Teacher, September,
p. 358.

Ramirez-Ban, R., 1990. An Interesting Problem Solved by Vectors, The Physics Teacher,
December, pp. 594—595.

Rao, C. R., 1952. Advance Statistical Methods in Biometric Research, New York, Wiley,
pp. 94- 102.

Robinson, Paul, 1992. Conceptual Physics laboratory Manual, Scott Foresman Addison
Wesley. pp. 61-64.

Rogowski, Steve, 1982. The Monkey and The Hunter. Creative Computing, December.
pp. 298- 310.

Saturnelli, Annette M., 1981. Focus on Physical Science: Activity-C entered Program
Teacher ’s Guide, Charles E. Merrill Publishing Co., ISBN 0-675—02822-1, pp. 47-49.

Snyder, Wayne and Diane Faulstick, 1992. Making A Point with Arrows. The Physics
Teacher. Vol.30, January. p. 58.

Squires, David, 1987. Providing cornputer-based experience for learning physics.
Physics Education. 22 , pp. 239-243.

Stepans, Joseph, 1996. Targeting Students ’ Science Misconceptions: Physical Science
Concepts Using the Conceptual Change Model. Idea Factory Inc.. pp. 90-104.

Stump, Daniel R., 1995. SYMPOSIUM: “Using the Graphing Calculator” - in Sample
Physics Problems, The Physics Teacher, Vol.33, May, pp. 317-319.

Taylor, Richard, et. el., 1995. Computer Physics on thePlayground, The Physics
Teacher, Vol. 33, September, pp. 332-337.

Taylor, Richard L., 1995. Physics Day at Six Flags Over Texas, Science Teacher, Vol.22,
March, pp. 2426.

Texas Instrument Web-site for CBL— ht_tp://www.§,legalgdggs/cblhtm

Teachers.Net Lesson Exchange: vectors for beginners,
http:/teachers.net/lessons/posts/214.html

Thornton, Ronald K., and Sokoloff, David R., 1990. Learning motion concepts using
real-time microcomputer-based laboratory tools, American Journal of Physics,
September, pp. 858-867.

van den Berg, Daday, and van den Berg, Ed, 1990. A Launcher for Projectile Motion,
The Physics Teacher, October, pp. 477-478.

Van Heuvelen, Alan, 1991. Learning to think like a physicist: A review of research-based
instructional strategies, American Journal of Physics, October, pp. 891-897 .

Vonder Embse, Chuck, 1990. GCSC Fall Get Together Day, December 14,. Central
Michigan University. pp. 13-15.

Williams, C. G., 1993. Looking over their shoulders: Some difiiculties students have with
graphing calculators. Mathematics and Computer Education, 27 (3). pp. 198-202.

Zitzewitz, Paul W., et. el., 1995. Merrill Physics: Principles & Problems.
Glencoe/McGraw-Hill. pp.108-150.

95

CHIGAN STRTE UNIV.

312llll all 8ll llllllllLllllllllllllllB