Calculation

Name of the innovation: Project-based Model building in Physics
(CN012)
China, Hong Kong
Population 3
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PART I: INNOVATION DESCRIPTION
A. Descriptive Background Information
CN012 is a co-educational secondary school in the New Territories of Hong Kong.
There are 27 classes with a total of 996 students and 54 teachers in this school. Most
of the students come from lower middle class families in the neighboring public
housing. Two physics teachers, one laboratory technician and 35 Secondary 6
students were involved in this innovation. This practice was mainly implemented in
Physics lessons. It addresses the importance of engaging students in designing some
experiments that verify a mathematical model in scientific phenomena which is
related to the curriculum content,
B. Summary of the Innovation
Goals and Origin
This practice was first implemented in 2000. The aims for this practice are four-fold:
1. To establish the relationship between modeling and the development of science
2. To let the students appreciate the scientific theory
3. To use technology for designing, developing and evaluating different models which strikes
for a better understanding of the characteristics of the scientific phenomena
4. To simulate different physical phenomena by the use of computer software
As the designed experiment was related to the curriculum content, it provided a
familiar environment for the students to experience the scientific investigation.
Pedagogical Innovation
In this practice, students need to carry out an experiment to verify one of the rules that
they learnt in Physics lessons. This project lasted about three months. Major activities
in this project included:
a) Students tried to identify problems and design an experiment for verification of a
physics phenomenon;
b) Teachers discussed with the students from time to time and gave advice;
c) Students carried out the actual experiment after school;
d) Students presented their findings in class and wrote a report
The experimental work usually took place after school with participation of two
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groups of students (AS Level and A Level). There were also some special
arrangements at the final stage of the project: the rearrange ment of timetable for
investigation and presentations during the normal class periods.
In this practice, teachers acted as advisors, providing suitable information and
equipment for students and allowing students to perform various kinds of experiments.
They also acted as project managers, arranging the timeline for implementing the
whole project. The students took an active part in generating questions, designing the
experiments and drawing conclusion from the results. They became active
constructors of meaning while exploring the investigation.
Regarding the assessment, students needed to hand in a project report which covered
the aims of the experiment, required equipment, experimental procedures,
experimental results, plus discussion and errors. They also had to present their
findings in front of the class.
ICT Use
10 notebook computers with Internet access, a projector, digital camera and software
such as Crocodile Physics were used. Students also used PowerPoint for presentation.
Instructional Organization
This innovation was first implemented in 2000 with the duration of three months. It
mainly took place in the laboratory after school, though students conducted their
investigations and presentations in class at the latter stage of the project.
PART II: ANALYSIS
A. MESO-LEVEL CONTEXT OF THE INNOVATION
A1. School Background
CN012 was founded in 1988. It is located in the New Territories of Hong Kong.
There are 27 classes with a total of 996 students and 54 teachers. Its six thousand
square meter campus has a range of facilities including two playgrounds, 24
classrooms, 22 special rooms, a library, a students’ activity room, a lecture hall that is
equipped with projector facilities and two elevators for the handicapped.
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A2. School Culture
Vision on teaching and learning of the school
The school is committed to helping each student discover his potential fully. As stated
in the school prospectus, the mission of the school is as follows:
l To cultivate a proper moral belief and responsible attitude among students
l To cater for individual differences in students' learning, by provid ing a happy
learning environment for the students to develop their knowledge and contribute
to the society at large.
History of innovation of the school
Being aware of individual differences, the school encourages all kind of innovations
that help students realize and develop their potentials. As pointed out by the principal,
two innovations have been implemented in the school during this academic year apart
from the project based modeling project in physics. They were: a cross-curriculum
project between the language and the humanity subjects; the arrangement for both
boys and girls to attend both the home economics and technical design courses. She
pointed out that these innovations did help students' personal development and
establish a collaborative culture. She said,
'At the beginning of last academic year, boys and girls are mixed together to
attend both home economics lessons and technical design lessons. Parents
appreciated it. For example, boys were more willing to do the housework
when they went home and girls could be more skillful in the technical
aspect.'
The leadership style of the principal
The principal proclaimed that she did not know much about the information
technology. Nevertheless, she greatly supported the development of the ICT
infrastructure and the use of ICT in teaching and learning. The principal is
open- minded who welcomes all kinds of innovations that are good for students. She
said,
'I give freedom for my teachers to try out new things. I believe that they have
the professional expertise in their subject area. I just provide the resources
for them. I would not intervene with what they are doing because I trust my
teachers' professional knowledge.'
Practice related to teacher professional development
There was a staff development day this academic year, which offered a general
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perspective on using ICT in teaching. In house training courses for staff development
on using ICT in teaching and learning were also conducted throughout the academic
year. A total of eight training courses were run this year. Usually these courses were
organized after school. Each training course lasts for 3 hours. Teachers could
participate in these courses on a voluntary basis. The IT coordinator also told us that
the same kind of courses would also be available for teachers during the summer
vacation.
Practices related to teacher collaboration
In this innovation, two teachers (Teacher A, Teacher B) worked together to implement
this project. Both teachers pointed out that insight for teaching the same kind of topics
was gained. As mentioned by the principal, other collaborations between teachers in
the same subject could be found.
A3. ICT in the School and Beyond
Vision on ICT in the school
The IT vision is to utilize information technology for enhanc ing the quality of
teaching and learning. The following is the mission statement in their IT plan in this
academic year.
l To set up an Intranet and Internet service so as to provide the basic infrastructure
for using IT in teaching and learning;
l To nourish teachers' and students' information technology culture, and enhance
their skills and competence on using information technology;
l To enhance the quality of teaching and learning by the use of Information
technology
In order to achieve the above vision, a variety of different tasks have been done. A
database, which contained the past examination papers in different subject discipline
and a collection of exercises, was established. This database would be uploaded to the
school Intranet. Apart from this, the school also encourages teachers to prepare for
electronic teaching materials in their teaching, and to upload the teaching materials
onto the web. In this way, students could review these materials when they went
home. As the IT coordinator pointed out, all these policies were aimed at providing a
pathway for students' self-learning.
Use of ICT in teaching in the school as a whole
The principal reported that most of the teachers in this school could prepare for
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students’ worksheets and examination papers students with ICT. However, the use of
ICT in teaching was still in an infant age. Science teachers used ICT in their teaching
more frequently then those who were teaching in the arts disciplines. For the students,
the word-processing was the most frequently used feature. The concept of submitting
assignments electronically is still new to most of the students in this school.
Accessibility of ICT resources in the school and at home for students
Concerning the accessibility of ICT in school, students were allowed to use
computers in the computer laboratory and the multimedia- learning center during
lunchtime and after school until 6 pm. Only 50% of students have access to a
computer with Internet access at home, and most of them are students in the upper
form.
A4. ICT support structure in the school
Infrastructure
A total of 94 multimedia computers with Internet access are available for students.
These computers are located in the computer room and the multimedia- learning
center. A room equipped with up-to-date computers, scanners and printer is allocated
to teachers for preparing for teaching materials. Apart from this, 20 laptop computers
are available for teachers to prepare for their lessons either in school or at home, and
for conducting lessons with the support of ICT. Software for science subjects and
languages were available for teachers as well.
Setting up an IT team
The IT team in this school consists of four teachers who teach Science, Mathematics
and Computer Science. Their main dut ies are: to organize training courses for teachers;
to set up the basic infrastructure in school; and to maintain the ICT infrastructure.
Besides, they also play a supportive role for teachers who use ICT in their teaching. In
order to encourage teachers to use ICT in teaching and to ensure that there is a smooth
run down during the lesson, there were some special arrangements in their timetable.
One teacher said,
'… basically our[IT team members’] free lessons are on a roster system, that
meant if teachers have problems on using IT in their teaching, they could at
least find one of us . We would give them immediate support… '
Support from the government
Under the five year plan ‘ Information Technology for Learning in a New Era Five
Year Strategy’, funding was granted to schools for ICT implementation. The principal
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pointed out that they used the funding for buying more computers for teachers and
students to use. Besides, teachers mentioned that the government also offered training
programs and seminar, which gave them some inspiration of using ICT in teaching
and learning. Furthermore, the establishment of the Quality Education Fund, which
provides funding for innovative and quality practices, also facilitated ICT
implementation in school.
B. MACRO-LEVEL CONTEXT OF THE INNOVATION
B1. National and State Policy
Teachers told us that the five-year policy ‘Information Technology for Learning in a
New Era Five Year Strategy’ boosted the ICT implementation and the use of ICT in
teaching and learning in this school. It was mentioned by the IT team that an
additional teacher was granted to the school under the ICT scheme of the Quality
Education Fund. This teacher took up part of the responsibilities for managing the
school network system and teaching teachers how to use some of the software.
Furthermore, teachers also told us that the equipment for this project was also granted
by the Quality Education fund.
C. THEMATIC ANALYSIS OF THE INNOVATION
C1. Curriculum Content, Goals and Assessment
Subject matter and topic (s) addressed in the Innovation
This practice was implemented in secondary six Physics classes. The aim of this
project is to provide students with an experience in conducting an experiment with the
help of technology. In the process, students need to explain their objective and try to
solve the problems that they might encounter. This project addressed the importance
of engaging students in designing experiments that verify a mathematical model in
scientific phenomena. Students were required to design an experiment to verify one of
the rules that they have learnt in the physics lesson. It was hoped that through this
practice the following goals would be achieved.
l To establish the relationship between modeling and the development of science
l To appreciate the scientific theory
l To use technology for design, development and evaluation of different models
which strikes for a better understanding of the characteristics of the scientific
phenomena
l To simulate different physical phenomena with the use of computer software
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Organization of the Innovation
35 S6 students, two teachers and one technician participated in this project. These
students came from two different classes. Some of them were studying AS level
physics and some were studying A- level physics. Teachers who took part in this
project are the physics teachers. One of them taught the AS Level class while the
other taught the A Level class. The timetables of these two classes were not the same.
Therefore, most of the preparation work was carried out after school. Special
arrangements were made in order to allow the final trials and the presentation of the
findings to be conducted in the normal class period.
Assessment Goals and Organization
By the end of this project, students were required to hand in the project report which
covered the aims of the experiment, the equipment needed in this investigation, the
procedure followed, results, and discussion and errors. Apart from this, they also had
to present their findings in front of the class. Students also commented that the
assessment of this project was not only confined to the product but also the process.
They explained,
'It is not sufficient to measure what we have learnt if only the pencil and
paper test was used. It is because the pencil and paper test only measure the
end product. But in this project teachers also consider our preparation work
and what we have done during the investigation. In other words, the process
is also important… '
C2. Teacher Practices and Outcomes
Teachers’ background
There were two teachers involved in this practice. Teacher A, who was the
vice-principal in this school, was in charge of this project. He had 13 years of
teaching experience. He taught the AS level class. He learnt most of the computer
skills by self- learning. He also actively participated in the Physics working group of
the Education Department. He believed that the use of IT in teaching Physics
provided more varieties in learning, and that IT did help students in learning some
abstract concepts. However, he strongly supported that IT just acted as a method for
enhancing the quality of teaching and learning. It was simply a method of
implementation, not the be-all and end-all matters. He also pointed out that the use of
PowerPoint did not make a big difference from traditional pedagogical approaches.
He would like to use IT for enhancing the level of thinking. When using computers in
teaching, he preferred the collaborative approach in such a way that students could
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help and learn from each other, and had more interactions.
Teacher B taught A Level class. He had 10 years teaching experience. His main role in
this project was in assisting Teacher A and acted as a consultant that gave advice to
the students.
Required Key Teacher Competencies for carrying out the practice
There are no special requirements for the teachers to carry out this project. Teachers
only need to know how to use the software and try it out beforehand.
Role of the Teacher
Both teachers pointed out that the role of the teacher has changed. They acted as a
facilitator rather than as an instructor. They gave students more time in discussion
rather than just giving them instructions. Apart from this, teachers also acted as a
project manager who planned the development of the project and organized the
rearrangement of the timetable for the students and kept track of students' work. In
addition, students also mentioned that teachers acted as a co-learner. They explained,
'In the traditional classroom, teachers seem to know everything and they
were experts. But with the use of technology we would sometimes know more
than the teachers and they learnt with us.'
Impact of the Innovation on Teachers
l Fostered collaboration between teachers
The classroom observations showed that Teacher A and Teacher B worked together in
conducting the lesson. Each of them walked around the classroom and gave
suggestions and comments to each group. Both Teacher A and B mentioned that this
project increased the collaboration between them. Teacher B said,
‘There are nine groups of students. We shared the workload. We work together
closely in examining students’work’
l Trial of a different approach in teaching
Teachers said that this practice would provide them with new teaching approaches.
Teacher A shared that,
‘There are lots of benefits. We can try different pedagogical approaches. For
example, what will the students response be when using this kind of method
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and what kinds of pedagogical approaches would suit the students’needs?
l Learning more about the software
Both teachers told us that after this practice they were more familiar with the use of
software. Teacher A said,
‘Through this practice, I am more familiar with the instrument. For example, I
will force myself to use the data-logger system more often’
l Understanding of the source of students' misconceptions
Teacher A pointed out that through this project, he knew more about students’
misconceptions which was helpful in his teaching. He stated,
‘… during the discussion with the students, I knew what were their problems and the
misconceptions. This helps me in planning how to teach the same topic next time,’
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C3. Students Practices and Outcomes
Role of the Student
In this project, two classes of students divided themselves into groups of four or five.
They identified one of the content related problems and designed an experiment in
order to verify one of the rules that they have learnt in the secondary six physics
curriculum. During the process, students were required to design the experimental set
up, use different kinds of software and equipment to collect and analyze the data, and
finally present their findings to the whole class. Students reported that they were more
devoted to learning, for they had the right to choose wha t kinds of topic they were
going to investigate. The learning atmosphere changed. They took an active role in
their learning and had the ownership of what they had learnt. One students pointed out
that,
'In the past we were just injecting the knowledge by the teacher but now we
are going to discover what we need to learn. We have more freedom in
deciding what we should learn and I think it is self-learning'
Besides, students also acted as tutors, teaching their classmates more in-depth
knowledge of the topic during the presentation and the collaborative group work.
Students even said that in some aspects they knew more then the teachers. It was an
interesting experience that they could teach the teachers.
Impact of the innovation on the student outcomes
l Enhancement of computer knowledge and skills
According to the students' interviews, students told us that they learnt more
computing skills from working on this project.
'I learnt how to use PowerPoint for the presentation. For example, (we learnt
how to) add some animation into it. We have a sense of satisfaction'
''… I learnt different techniques - for example how to edit videos and capture
data.'
l
Fostered collaboration between students
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Students mentioned that they learnt from one another with different talents by
working in groups, One students explained,
'We learnt how to collaborate. For example, we went to one of our team
members' home and worked out the procedure together. Some of us plotted the
graph and some of us used Excel to analyze the data. It was collaborative
work.'
' It was project work - we learnt how to work as a team. This is an important
skill for us to learn. This is because teamwork is essential in the society. You
cannot do everything by yourself. It needs collaboration.'
As this project involved two classes of students working together, Teacher A pointed
out those students could also benefit from this arrangement. He said,
'The reason for this arrangement was that the more capable students could
offer their help to the less capable students. For example, the AS level
students had less computer knowledge then the A level students. Some of the
AS level students do not have computers at home. Most of the A level
students are studying Computer Science and they could help the AS level
students. It is collaboration. I hope that through this collaboration students
could co-construct their knowledge.'
l Enhance the problem solving skills
According to the students’ interview and the lesson observations we found that
students considered various aspects while conducting experiment and encountering
problems. Students also expressed that it enhanced their problem solving skills. One
of the students said,
'Through this project I learnt how to think independently, handle data and
analyze data. In traditional learning we do not need to handle lots of data
and solve different kinds of problems in order to achieve one goal. We lack
this sort of learning experience. However, through this learning practice it
enhanced our problem solving skills.'
l Enhanced presentation skills and worked more patiently
Students also mentioned that they learnt presentation skills in this project. Students
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said,
'I also learnt how to present in front of the class. Instead of shivering in front
of the class now I am braver and can stand calmly during the presentation.'
As students needed to try out the experiments many times and to work with the same
sort of data for hours, they expressed that one of the gain is to learn to work patiently.
l Foster the interactions between teacher and students
Students pointed out that a better relationship between teachers and students is
achieved with increase in interactions between students and teachers.
'We have a better relationship with teachers. Both teachers are very friendly
and approachable. We would ask teachers more questions and they gave us
guidance from time to time.'
l Better understanding of the topic
According to the student interview, students mentioned that the use of ICT provided
immediate feedback and allowed them to use different methods in displaying the
results. Therefore, more comprehensive understanding of scientific phenomena was
achieved. They said,
'When you use graphs to present the data, it seems more readable and
accurate. '
'If there is no computer the experiment would have become very difficult and
intangible. It is because it is impossible for us to find out about those
areas… Now that the graph is available to us, and the computer helps us to
find out about those areas. We can therefore have a better understanding of
the relationship.'
C4.
Kinds of Technology and Ways They were Used
In this project the hardware used included: data- logger systems with different kinds of
interfaces and sensors, digital video cameras and 10 notebook computers. Different
kinds of software such as Modullus, I-Film Edit, Video Point, and Quick Time Player
were used for data collection and data analysis. Software like MS Word, Excel and
PowerPoint and a projector were used for presentation. The followings illustrate how
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ICT was used in this practice.
l Tool for performing experiments that the traditional method cannot
Teacher A pointed out that students could carry out experiments which could not be
done by the traditional method. with the use of ICT. He said,
'With the use of ICT most of the experiments are doable. For example, it is
difficult for students to measure the amount of force in the experiments of
momentum or centripetal force. Now with the use of data timer and sensor,
they can do these experiments.'
l Tool for collecting data and analyzing data
In this practice, students used ICT for data collection and analysis. One student
asserted,
'I have not thought before that there is software like this; it helps us in
conducting the experiment and analyzing the data. The software can help
you to capture data, and simulate a model for you.'
l Tool for motivating students
Teachers pointed out that the use of ICT did motivate students' learning with vivid
animation and graphical display. Students became more attentive in class and be more
willing to try this new mode of learning.
l Tool for communication
Students told us that they also used ICT for the communication purpose in this project.
They sent messages and discussed the progress of the project via e-mail and ICQ.
Students pointed out that it was more convenient for them to carry out their
investigations with ICT. One student said,
' As we are very busy we do not have much time after school; therefore, we
usually discussed our project in the evening. We used ICQ to communicate and
discuss the progress. We also used e-mail to send the PowerPoint file and to
give comments to each other and see how we should improve it.'
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l Tool for presentation
ICT also acts as a presentation tool for students. Students used PowerPoint for their
presentations. Most of them included graphs and text in their presentation. Some of
them also captured video clips and pictures for illustrative purposes.
C5.
Problems and Solutions Related to the innovation
Teacher B pointed out that at the beginning there was a problem in gathering these
two classes of students together as they have different timetables. However, Teacher A,
the vice-principal in this school, had rearranged the timetable during the project
implementation. As a result, this problem was solved.
Teacher A also pointed out that there were not enough resources like the lack of
computers and not enough manpower. He explained that, as teachers had a hard time
in managing 35 students, for they needed to give advice to students and discuss with
them from time to time they. It would be much better if more teachers participated in
this practice and increased the teacher: student ratio.
In order to increase the resources available, teachers suggested that they would apply
for more funding, so that they could buy more computers. Regarding the problem of
manpower, teachers pointed out that it was still an unsolved problem.
Apart from this, students also claimed that there was not enough time for their
investigation, and they hoped that more time could be spent on conducting the project.
Another problem that we have observed was that there were a significant number of
students who did not pay attention to the other students' presentation.
C6.
Sustainability
Regarding the sustainability of this project, teachers and principal summarized that
this was a value-added project both on the curriculum content and for the students'
development. As mentioned by the principal,
' I really hope that this project would be continued. As you know, our society
is changing and there should be a change in teaching methods. This practice
is a good try. I would encourage teachers to continue this project'
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Apart from the support of the principal, both teachers and students also welcomed this
practice and perceived that the same kind of practice should be conducted next year.
Furthermore, as Teachers A and B have conducted some sharing sessions for teachers
in other schools, the practice was recognized by the teachers in the local district area.
Finally, with the existing resources which included the data logger system and
10-notebook computer, teachers thought that there was no problem for the practice to
be carried on next year. In addition teacher A mentioned that they would apply for
more funding, so that they could have more computers in the coming years.
Besides, every school would be granted with 5 data- logging system by the
government too. To conclude, it is highly probable that the project would continue
next year.
C7.
Transferability
Concerning the transferability of this practice within the school, we observe that
similar practice of using ICT in the lower form science lesson was found. Teachers
and principal asserted that this practice could be transferable within the school.
'Basically there are no problems; we have regularly use the software in the
lower form. However the actual implementation depends on time.'
In order to transfer this practice to other schools, principal mentioned that the most
important thing is the teachers' willingness. She said,
'I think the most important thing [for the practice to be transferable] is
whether teachers are willing to use this new pedagogical approach or not. If
they accept it, they can do it.'
Teacher A also pointed out that manpower was another crucial element for the
transferability of practice. He explained,
'It would be manpower. If there were only one teacher teaching the whole
class, it would be impossible for them to carry out this practice. The
situation in this school was a little bit better because we have two teachers
in a class. The ideal case would be 3 teachers for a class of 30 students. The
resources was not a great problem… .'
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Appendices
Appendix A: Glossary
A level: Advanced Level
Students sit for the Hong Kong Advanced Level Examination (HKALE) at the end of
Secondary Seven. Three subjects, plus the AS-Level Use of English and Chinese
Language and Culture examinations, are usually taken. Science track students usually
take physics, mathematics, and chemistry; humanities track students take economics,
geography, and history. Grading for the Hong Kong Advanced Level Examinations
match with grades on United Kingdom A-Level exams. The HKALE is used as the
basis for admission to Hong Kong's seven tertiary institutions, whose undergraduate
courses last three years.
AS levels: Advanced Supplementary Levels
Students who began Secondary Six in 1992 were the first group of students to have
the opportunity to sit for the Advanced Supplementary Level Exams (AS Levels).
AS-Level courses, which are designed to broaden students' curriculum, take half the
teaching and study time of a regular A-Level course. A student in an AS-Level course
usually attends four or five periods of 40 minutes each, every week over a period of
two academic years. The syllabi of the exams are designed to be as demanding as an
A-Level course, and the grades from two AS Levels will be equivalent to one A Level
grade. It is expected that students will substitute one A Level exam with two AS
Levels.
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Appendix B Classroom layout
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Appendix C Lessons clips 1
Students conducting their experiments
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Appendix D Lesson Clips 2
Students presenting their work
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Appendix E Sample of Students' PowerPoint Presentation
By studying the elastic collision
between
between marbles
marbles and
and circularcircularshaped magnet,
magnet, to
to verify
verify the
the
conservation of momentum
momentum and
and
energy.
Law of conservation of momentum
m1u1 = m1v1 + m2 v2
Law of conservation of momentum
momentum
When bodies in a
a system
system
interact the total momentum
remains constant provided no
external force acts on the
the
system.
Law
Law of conservation
conservation of energy
1
1
1
mu 2 = mv 2+ m v 2
2 1 1 2 1 1 2 2 2
M1:mass
:mass of
of blue
blue ball
ball
M2:mass
:mass of
of red
red ball
ball
V
V22
M
M11
U
U11
M22
90°
90°
V1
U1: velocity of blue ball
ball before
before
collision.
V11:velocity
:velocity of
of blue
blue ball
ball after
after collision.
collision.
V22:velocity
:velocity of
of red ball after collision.
V2
M
M1
U
U11
M
M2
90°
90°
V
V22
V11
90°
90° V
V
V11
U
U11
Several big and small
marble ball ,
Assume the mass of the balls are the same,
Circular-shaped magnet,
DV, tripod,
i.e. MM11 = M 2
Proof:
u 2 = v1 + v2
2
A box with small
particles.
2
Capture the data:
magnet
magnet
1. Prepare a box with small particles inside.
2. Place the DV on top of
of the
the box
box with
with tripod
tripod and
andstart
start
recording.
DV
DV
tripod
tripod
3. Put a magnet(A) at the center of the box and another
magnet(B) aside.
4. Apply a force to B with direction toward A.
5. B hits A and they move in different path.
6. Repeat the steps(3-5) for several times to get
enough data.
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After capture the data:
After capture the data:
7. Import the video by Firewire to the computer and save
as * .avi file.
8. Cut the useful video into small parts from the original
11. Mark positions and the path of the magnet by using
VideoPoint.
12. Find the angle between two magnets after collision,
and the velocity of the two magnets before and after
video by using ‘iFilmEdit’.
9. Convert * .avi to *.mpg file by using ‘PowerVCR ’.
10. Convert *.mpg to *.mov file by using QuickTime Player.
the collision by using Modellus
13. Calculate the momentum before and after the collision
to see if the momentum is conserved or not.
Calculations
Calculations::
Calculations:
Calculations:
m1
Useful Formula:
Formula:
Momentum:
V 2 sinθ
V 1 sinφ
m 1v=m11v1cosθ+m22v2cosφ
m1
m 1v11sinθ=m22v2sinφ
1/ m v 2=11/ m v 22+1/ m v 22
2 11
22 11 1
2 22 2
Velocity before collision:
C03
(136 − 84) + ( 420 − 478) / 0.04 = 1947.43
2
2
Velocity
Velocity after
after collision
collision for
for m
m11:
::
( 268− 276) + (184 − 234) / 0. 04 = 1265. 89
2
2
Velocity
Velocity after
after collision
collision for
for m
m22:
( 420 − 364)2 + ( 232 − 240)2 / 0 .04 = 1414.2
Calculations
Calculations::
Velocity before collision:
C13
( 238 − 284) 2 + (328 − 218) 2 / 0 .04 = 2980.77
Velocity
Velocity after
after collision
collision for
for m
m11:
::
( 284 − 276)2 + (218 − 120) 2 / 0 .04 = 2458. 15
Velocity
Velocity after
after collision
collision for
for m
m22:
(504 − 438) + (260 − 262) / 0 .04 = 1650.7574
2
2
m2
θ
θ
V 1 cosθ
V 2 cosφ
Because
Because we study the elastic collision
of same mass, so we can eliminate the
mass m11, m
m22.
Kinetic energy:
energy:
Calculations
Calculations::
φ
φ
Calculations
Calculations::
By v=v11cos?+v2cosf ,
C03
1947.43=1265.89*cos63.06o+1414.2*cos36o
1947.43∼1717.6
By v11sin?=v22sinF ,
1265.89sin63.06oo=1414.2sin36
=1414.2sin36oo
1128.52=831.25
By K.E. v2=v1122+v222,
1947.4322 =1265.89
=1265.8922+1414.222
3,793,000=3,602,000
Calculations
Calculations::
By v=v11cos?+v 2cosf ,
C13
2980.77=2458.15*cos52.42
2980.77=2458.15*cos52.42oo+1650.76*cos44.57oo
2980.77∼2675.14
By v11sin?=v 2sinF ,
2458.15sin52.42
2458.15sin52.42oo=1650.76sin44.57 o
1948.1 ∼ 1158.47
By K.E. v22=v112+v222,
2980.77
2980.7722 =2458.15 2+1650.7622
8,885,000~8,768,000
22
We
We use
use the
the circular-shaped
circular-shaped magnets
magnets on
on
the
the box with tiny particles because we
would
would like
like to
to eliminate
eliminate the
the resistance
resistance in
in
order
collision.
order to have the perfect collision.
The momentum before the
the collision
collision is
is
greater than the momentum after the
collision. There are energy loss due to
to
the friction.
As the time of collision is very short,
short,
change of velocity is great. So we
should use the instantaneous
instantaneous
velocity.
The tiny particles
particles are
are uneven
uneven
distributed so that the marbles will not
flow in straight line. Error occurs.
Eliminate the errors we have, the
conservation of momentum and
and kinetic
kinetic
energy are conserved in the elastic
collision in two-dimensions.
In two dimension collision, we can see
that when the mass of balls are equal,
the angle
angle between
between the
the two
two
path is 90°
23
Appendix F Sample of Students' Report
Aim:
By studying the elastic collision between marbles and circular-shaped magnet, to
verify the conservation of momentum and energy.
Law of conservation of momentum:
When bodies in a system interact the total momentum remains constant provided no
external force acts on the system.
m1u1 = m1v1 + m2v 2
V2
U1
M2
90o
M1
V1
M1 : mass of blue ball
M2 : mass of red ball
U1 : velocity of blue ball before collision.
V1 : velocity of blue ball after collision.
V2 : velocity of red ball after collision
V2
U1
M2
M1
V2
o
90
90o
V1
V1
U1
Assume the mass of the balls are the same, i.e. M1 = M2 ,
U2 = V1 2 + V2 2
Apparatus:
24
Several big and small marble balls, Circular-shaped magnets, DV, lamp, balance,
tripod, a box with small particles.
The set up are as follows:
magnet
DV
tripod
Capture the data:
1.
2.
3.
4.
5.
6.
Prepare a box with small particles inside.
Place the DV above the box with tripod and start recording.
Put a magnet (A) at the center of the box and another magnet (B) aside.
Apply a force to B with direction toward A.
B hits A and they move in different path.
Repeat the steps (3 to 5) for several times to get enough data.
After capture the data:
7. Import the video by Firewire to the computer and save as *.avi file.
8. Cut the useful video into small parts from the original video by using ‘iFilmEdit’.
9. Convert *.avi to *.mpg file by using ‘PowerVCR’.
10. Convert *.mpg to *.mov file by using QuickTime Player.
11. Mark positions and the paths of the magnets by using Videopoint.
12. Find the angle between two magnet after collision, and
25
the velocity of the two magnets before and after the collision by using ‘Modellus’.
13. Calculate the momentum and kinetic energy before and after the collision to see if
they conserve or not.
Calculation:
Useful Formula:
Momentum: m1 v=m1 v1 cos?+m2 v2 cosf
m1 v1 sin?=m2 v2 sinf
K.E.
: 1/2m1 v2 =1/2m1 v1 2 +1/2m2 v2 2
m1
V2 sin?
V1 sinf
m1
m2
V1 cos?
V2 cosf
Because we study the elastic collision of same mass, so we can eliminate the mass m,
m1 , m2 .
Data 1 (Using magnets):
time(s) Point S2:x-pos(pixels) Point S2:y-pos(pixels) Point S1:x-pos(pixels) Point S1:y-pos(pixels)
0
338
244
76
488
0.04167
338
244
76
488
0.08167
338
244
76
488
0.1217
338
244
84
478
0.1617
338
244
136
420
0.2017
338
244
194
356
0.235
338
244
250
290
26
0.2817
0.3217
0.3617
364
420
476
Velocity before collision:
240
232
222
276
268
260
234
184
134
(136 − 84) 2 + ( 420 − 478) 2 / 0.04 = 1947.43
Velocity after collision for m1 :
( 268 − 276)2 + (184 − 234) 2 / 0.04 = 1265.89
Velocity after collision for m2 :
( 420 − 364) 2 + ( 232 − 240) 2 / 0.04 = 1414.2
By v=v1 cos?+v2 cosf ,
1947.43=1265.89*cos63.06O+1414.2*cos36o
1947.43∼1717.6
By v1 sin?=v2 sinF ,
1265.89sin63.06o =1414.2sin36o
1128.52=831.25
2
2
By K.E. v =v1 +v2 2 ,
1947.432 =1265.892 +1414.22
3,793,000=3,602,000
Data 2 (Using marble balls):
time(s)
Point S2:x-pos(pixels) Point S2:y-pos(pixels)
0
340
262
0.04167
340
262
0.08167
340
262
0.1217
368
262
0.1617
438
262
0.2017
504
260
0.2417
570
258
Velocity before collision:
Point S1:x-pos(pixels)
140
160
238
284
276
276
276
Point S1:y-pos(pixels)
458
436
328
218
120
14
4
( 238 − 284)2 + (328 − 218)2 / 0.04 = 2980.77
Velocity after collision for m1 :
( 284 − 276)2 + (218 − 120) 2 / 0.04 = 2458.15
Velocity after collision for m2 :
(504 − 438) 2 + ( 260 − 262)2 / 0.04 = 1650.7574
By v=v1 cos?+v2 cosf ,
2980.77=2458.15*cos52.42O+1650.76*cos44.57o
2980.77∼2675.14
By v1 sin?=v2 sinF ,
27
2458.15sin52.42o =1650.76sin44.57o
1948.1∼1158.47
By K.E. v2 =v1 2 +v2 2 ,
2980.772 =2458.152 +1650.762
8,885,000~8,768,000
Discussion:
Precaution:
- We use the circular-shaped magnets on the box with tiny particles because we
would like to eliminate the resistance in order to have the perfect collision.
- As the time of collision is very short, change of velocity is great. So we should use
the instantaneous velocity.
Error:
- The momentum before the collision is greater than the momentum after the
collision. There are energy losses due to the friction.
- The tiny particles are uneven distributed so that the marbles will not flow in
straight line. Error occurs.
Conclusion:
Eliminate the errors we have, the conservation of momentum and kinetic energy are
conserved in the elastic collision in two-dimensions.
All elastic collisions between equal masses, they make an angle of 90o with each other
after collision.
Difficulties:
There is a main problem of calculation. The time is very short; there is acceleration
just after applying a force. And deceleration is just before the collision in the case of
collision of magnets due to the magnetic field. If we use the average velocity, the
kinetic energy after collision become much larger than before the collision and it is
wrong.
We find that when we perform the collision with marbles on the bench, we hardly find
the marbles producing an angle of 90o to each other.
28
Group member: Cheung Chi Wai
Lee Tak Hiem
Ng Wing Wai
Sin Man Wai
(16)
(23)
(28)
(30)
powerpoint
create movie
edit movie
report
29