force resolution in daily life

AWARD SCHEME

ON INSTRUCTIONAL DESIGN

2015/2016

Force Resolution

In Daily Life

Entry number: C056

Subject: Physics

Education Level: Form 4

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Abstract

Force resolution is a common topic in GCE/IAL/IGCSE curriculum. However,

this topic seldom has particular attention in teaching regarding its application in daily

life and experimental approach in order to allow students "learning by doing".

Therefore, this instructional design aims to demonstrate how the daily

application of force resolution can be combined with traditional mathematical

approach and experiment such that arouse students’ interest of learning physics in

daily activities and enable students to discover the knowledge as well as develop their

motor skills in experimentation by themselves.

In addition, throughout this 4-session course, a SWF simulation software will be

introduced that the students can discover and understand the concept of force

resolution further using traditional means as well as digital techniques, without the

limit of learning place.

It is sincerely the desire of the entrants and authors to put this instructional

design as a platform to share their ideas in teaching as well as learn from all peers in

the teaching profession.

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Table of Content

Cover Page…………………………………………………………………………….1

Abstract………………………………………………………………………………..2

Table of Contents……………………………………………………………………...3

Table of Teaching Progress……………………………………………………………4

1. Introduction to Instructional Design………………………………..………………4

1.1 Teaching objectives……………………………………………...……………..4

1.2 Main Content……………………………………………………...……………4

1.3 Creativity and Characteristics of the Design………………………...…………5

1.4 Teaching Focus………………………………………………………...……….6

1.5 Difficult Points in Teaching……………………………………………..….…..7

1.6 Teaching Equipment……………………………………………………..….….8

1.7 Teaching Time……………………………………………………………..…...8

1.8 Extra Information concerning the ICT method used…………….…………......8

2. Teaching Lesson Plans……………………………………………………………...9

2.1 Teaching Lesson Plan for Session 1………….……………………………...…9

2.2 Teaching Lesson Plan for Session 2…………………………………………..20

2.3 Teaching Lesson Plan for Session 3…………………………………………..24

2.4 Teaching Lesson Plan for Session 4………………………………………......25

3. Evaluation after first teaching…………………………………………… ….……27

4. Reflections and Suggestions for improvement………………………………..…...28

5. References……………………………………………………………………....…29

Appendix……………………………………………………………………………..30

A. Supplementary teaching material for Session 1……………………………..31

B. Supplementary teaching material for Session 2………………………….…..34

C. Student Assignments for Session 2…………………………………………..36

D. Lab. material for the experiment of Session 3………...…………………..…39

E. User manual for Tracker Program……………………….…………………...42

F. Supplementary teaching material for Session 4……………………………...43

G. Sample Report for Session 3 …….………...…………………...…….…..…50

H. Photos of class instruction…………………………………………...………68

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Table of Teaching Progress

Instruction

session

Name of Topic Content Date of

Instruction

Number

of

periods

1 Relationship between

vector (force) resolution

and daily life activities.

Discover the

relationship between

vector (force) resolution

and daily life activities.

05/05/2016 1

2 Mathematical

representation and

application of vector

(force) resolution

Understand the three

major means of

mathematics related to

force resolution and be

capable of applying the

knowledge in question

solving

10/05/2016 2

3 Experiment verification

of vector (force)

resolution

Verify the nature and

solving means of force

resolution through

experiment

12/05/2016 2

4 Conclusion - Theory

and experiment of force

resolution in daily life

Summarize the major

aspects of the theories,

experiment as well as

application of force

resolution in daily life

17/05/2016 2

Note: 1 period = 40 minutes

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1. Introduction to Instructional Design

1.1 Teaching Objectives

The key teaching objectives of this instructional design are listed below.

Cognitive Domain

a. Comprehend the nature and characteristics of force in 2 dimensions.

b. Realize the relationship between vector (force) resolution and daily

life activities.

c. Capable of explaining phenomena in daily life by applying the

concepts of force resolution.

Psychomotor Domain

a. Able to describe the nature of force resolution.

b. Use mathematical means (component method, and Lami’s theorem)

as well as pictorial expression (head-to-tail method) to solve

problems related to force resolution.

c. Verify the learnt concept of force resolution by experimental mean.

Affective Domain

a. Acknowledge the importance of force resolution in solving problems

in daily life.

b. Actively participate in class discussion related to force resolution in

daily life activities.

c. Appreciate the mathematical, pictorial and experimental means to

solve problems related to force resolution.

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1.2 Main Content

This instructional design is divided into four sessions with a particular topic.

These sessions are listed as followings:

Session Topic

1 Relationship between vector (force) resolution and daily life activities

2 Mathematical representation and application of vector (force)

resolution

3 Experiment verification of vector (force) resolution

4 Conclusion - Theory and experiment of force resolution in daily life

The followings are the emphasis of each session in this instructional design.

Session 1

This session mainly aims to arouse students’ interest in discovering and

learning the relationship between force resolution and daily life activities.

Throughout continuous teacher-student as well as student-student interactions,

teacher presents some simple demonstrations and digital simulation s with a

series of well-designed questions being asked in the process in order to allow

student “discover” the learning content by themselves. A brief in-class exercise

will be carried out at the end of the session to evaluate the effectiveness of

learning.

Session 2

With the acquired knowledge from mathematics lessons learned within the

same academic year, this session stresses both mathematical as well as pictorial

representations of vector (force) resolution. Students will discover and

understand the mathematics that describes daily life activities related to multiple

applied forces and make use of these methods to explain as well as solve

various problems in daily life. This session will end with in-class exercise for

evaluating the effectiveness of learning. Homework as well as SWF simulation

software (performed in class as well) will also be assigned for consolidating

their learnt concepts from this session.

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Session 3

Students will verify the nature and solving means of force resolution

through experiment. In the process, students will strengthen their experimental

skills as well as consolidate their knowledge through “learning by doing”.

Session 4

In the last session of this instructional design, homework assigned in

Session 2 and the experimental results of Session 3 will be discussed and

evaluated via teacher-student as well as student –student interactions. After that, a

summary of all concepts discussed in this course will be recapped. A short test

will also be conducted to evaluate the effectiveness of learning.

1.3 Creativity and Characteristics of the Design

Everyone encounter lots of examples about force resolution everywhere in

daily life. This indicates understanding the physics as well as mathematics behind

those examples is not just important from an academic perspective but also

necessary from the perspective of further comprehending the environment that we

are living in.

The topic of force resolution is common in high school of both Chinese and

English section. However, students’ motivations in “learning by doing” as well as

experimental investigation are not paid enough attention in the learning process of

this topic. Prof. Sian Beilock, an internationally known expert on the mind-body

connection, emphasizes that the sensory and motor-related brain areas are known

to be important for human’s ability of making sense about forces, angles and

trajectories. Based on his recent studies, he also suggests that students who

“physically experience” difficult science concepts learn them better and perform

better in application. Therefore, this instructional design mainly focus on

combining traditional mathematics approach of learning force resolution with a

series of student-orientated interactions as well as experiments such that students

may discover and “physically experience” the knowledge by themselves. Deeper

understanding and interest in physics investigation about force resolution in daily

life would also be expected.

Various ICT resources from internet are used throughout the course and also

provided to student via the intranet system of our school (my ITschool). This is

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purposely done to show students that there is a lot of valuable information in the

internet and encourage students to have a good use of the web. Another advantage

of using internet resources in the course of instruction is to facilitate students for

self-learning and revision after classes.

1.4 Teaching Focus

There are four sessions with a total of seven periods consisted in this

instructional design. The teaching focus of each session is stated as followings.

Session 1 (1 period)

Relationship between vector (force) resolution and daily life activities

a. Relationship between force resolution and daily life activities

b. Nature of vector (force) in 2-dimension;

horizontal and vertical component of a vector

c. Pictorial expression of vector (force) resolution

Session 2 (2 periods)

Mathematical representation and application of vector (force) resolution

a. Mathematical means of force resolution (component method and Lami’s

theorem)

b. Pictorial mean of force resolution (head-to-tail method)

c. Application of mathematical and pictorial means in solving problems from

daily life


Experiment verification of vector (force) resolution

a. Important practical concerns for conducting the experiment

b. Comparison of results from experiment, component method, head-to-tail

method and Lami’s theorem


Conclusion - Theory and experiment of force resolution in daily life

a. Summary of all major theories and methods related to force resolutions

b. Evaluation of findings from experiment in Session 3

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1.5 Difficult Points in Teaching

Session 1 (1 period)

Relationship between vector (force) resolution and daily life activities

a. Understand the horizontal and vertical component of a vector

b. Use arrows to express the direction and magnitude of vector correctly


Mathematical representation and application of vector (force) resolution

a. Apply the component method in solving problems

b. Draw arrows correctly in the process of head-to-tail method

c. Mix up the equations in Lami’s Theorem


Experiment verification of vector (force) resolution

a. Complete the experiment procedure within the allowed time without

teacher’s intervention

b. Maintain discipline in the laboratory

Session 4

Conclusion - Theory and experiment of force resolution in daily life

a. Mix up the methods and equations when resolving forces

b. Various conclusions will be achieved by students due to immature

experimental skills, careless mathematical mistakes and imprecise

interpretation of their experimental findings in Session 3

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1.6 Teaching Equipment

Session 1, 2 and 4

Computer, projectors, blackboard and chalk, internet access, test paper, student

desk, toy car and newton spring

Session 3

PASCO Super Pulley Force Table, masses, threads, User Manual of Force Table,

Experiment Report

1.7 Teaching Time

Total number of periods 7 periods

Total instruction time 280 minutes

Note: 1period consists of 40 minutes

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2. Teaching Lesson Plans

The teaching lesson plans for each session are listed as followings.

2.1 Teaching Lesson Plan for Session 1

2.1.1 Students’ acquired knowledge

(1) Basic concepts of scalars and vectors

(2) International system of units (S.I. units)

(3) Concepts of balanced and unbalanced force

2.1.2 Teaching Process

Teaching Process Comments / equipment

/ key points

I. Lead-in

(1) Introduce the topic of the day

(2) Picture 1 to Picture 5 are shown to the

students

Picture 1

Picture 2

(2) Equipment:

Computer, projector

and internet access

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Picture 3

Picture 4

Picture 5

(3) Ask students to describe the direction of

applied forces in each picture

(3) Responses from students:

Responses may vary.

Possible responses are up,

down, left, right etc. Some

students with sufficient

background will give the

answer as at angle with

respect to x-axis.

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(4) Ask students to describe the direction of

motion of objects / person in each picture

(5) Conclude the lead-in by summarizing the

ideas of students in (3) and (4).

(6) The students will be informed that that the

answers in (3) and (4) can be resolved and

explained by physics concept – force

resolution - and the methods of finding the

answers will be clear at the end of this

learning unit.

---------------------------------------------------------------

II. Development

(1) Recall the basic concepts of scalars and

vectors with a demonstration of the teacher.

The teacher will pull a toy car by using

newton spring, with 2 N for 2 s.

(2) Ask students what are similarities and

differences, in nature, between the quantities

“time” and “force” in the demonstration.

Picture 6

(3) Pull and push the toy car again for

reminding students to pay attention to the

motion of the car, and ask students how to

present a vector quantity, i.e. force.


Responses may vary.

Possible responses are

stationary, up, down, left,

right etc.

(5) Equipment:

Chalk and blackboard

(6) Teacher-student interaction;

Teacher will not provide the

correct answers until the end

of session 2.

----------------------------------------

(1) Equipment:

A toy car and a newton

spring


Most of them will be able to

answer “similarly have

magnitude and unit and only

force has direction in nature”

Equipment:

Computer and projector



answer “by numbers”. Some


background will answer “by

drawing arrows”

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(4) Conclude students’ answers in (3) and

extend their ideas that the direction of the

arrow head pointing at represents the

direction of force while the length of the

arrow represents the magnitude of force.

Picture 7

(5) Ask students if vector AB and vector c in

picture 7 are the same, given that the lengths

of arrows as well as the angle θ are the

same.

(6) Conclude the students’ answer in (5) and

emphasize that forces are identical when

their length and direction, other that

location, are the same.

(7) Continue the discussion on pictorial

expression of vector by inviting 3 students

(student X, Y and Z) for a set of guided

demonstrations. Firstly, student X and Y are

placed in one end of rope while student Z is

place in another end of rope. When the

teacher says “start”, student X and Y pull

the rope away from student Z while student

Z only needs holding the rope and moving

without addition of opposing force on the

rope.

(4) Equipment:


(5) Responds from students:

Most of them will answer

“the same”.

Equipment:


(6) Equipment:


(7) Teacher-student and

student-student interaction;

Equipment:

A long rope

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(8) Ask student Z to describe the applied force

he felt during the demonstration

(9) Ask the rest of the class to describe the

motion of student X, Y and Z respectively

and their possible relationship.

(10) Students X, Y and Z are placed at three

different locations as shown in Picture 8,

where student X and student Y are holding

the rope. Once the teacher says “Start”,

student X pulls the rope along x-direction

away from student Z with similar

magnitude of force as before while

student Y pulls the rope along y-direction

away from student Z with similar

magnitude of force as before altogether;

student Z remains standing at the place

and allow to move along with the

resultant force from the rope at his back.

Picture 8


Respond from student Z:

He will describe that the

direction of his motion is

along with the direction of

the applied forces from

student X and Y.


Responds from students:

Most of them likely discover

that the motion of student Z

is resulted by the direction

of resultant force from

student X and Y; the

magnitude of resultant force

that student Z feels would

be same as the applied force

of student X and Y.



Equipment:

A long rope

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(11) Ask student Z to describe the applied

force he felt during the demonstration

(12) Ask the rest of the class to describe the

motion of student X, Y and Z respectively

and their possible relationship.

(13) Summarize students’ ideas from the set of

demonstrations and conclude students’

findings that the magnitude of the

resultant force, in term of numeral value,

is not equivalent to the addition of applied

forces if they are acting in different

directions; the direction of the resultant

force would not be same as either one of

these applied forces as well.

(14) Re-emphasize that the resultant force is

resulted by the forces going to x-direction

and y-direction.

(15) Continue the discussion by illustrating a

resolution of a force into force

components to the students. After

recalling their acquired knowledge about

trigonometry from mathematics class, ask


Respond from student Z:

He will likely describe that

the direction of applied

force is not neither along

x-direction nor y-direction;

the resultant force he would

felt is smaller than that in

previous demonstration.


Responds from students:

Most of them likely discover

that the motion of student Z

is resulted by the direction

of resultant force from

student X and Y; student Z

moves less under the similar

magnitudes of forces from

student X and Y, compared

with those in previous

demonstration.

(13) Two demonstrations

between step (7) to (12) are

designed to lead students to

discover the differences, in

nature, of resultant force in

two dimensions from that in

one dimension instead of

being informed by the

teacher.

(14) Activity of students:

Note the key points in their

notebooks

(15) Equipment:


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students how we can find out the

magnitude of force x and force y, as

shown in Picture 9.

Picture 9

(16) Three voluntary students will be invited to

show their solutions onto blackboard.

(17) Summarize students’ ideas and conclude

that what they have done is called

resolving vector; teacher reminds that a

force which is not on an axis can be

broken down into horizontal and vertical

components.

Picture 10

(18) The key points of Picture 10 are pointed

out and emphasized.



Equipment:

Blackboard and chalk

(17) This is done to consolidate

the concept of forces acting

in x- and y-direction results

a resultant force at an angle

with respect to x- or y-axis;

Equipment:


(18) Key concepts to be

emphasized:

a. The horizontal and

vertical force are called

x- and y-component of

the resultant force

b. The sum of x- and

y-component results the

magnitude and direction

of resultant. (which will

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(19) SWF Simulation software is then played

to show how the magnitude and direction

of a resultant force are varied with its x-

and y-components.

Picture 11

Picture 12

Picture 13

(20) In order to consolidate students’

understanding in what have been

discussed, an in-class worksheet

(Appendix A) with 2 questions is

conducted.

be further discussed in

session 2)

(19) The web link for

downloading this

simulation software is

provided to students for

self-study at home

(20) The discussion of solutions

will be done through T-S

(teacher-student) and S-S

(student-student) interaction

and expected to last for 5

minutes.

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III. Conclusion

(1) Force, as a vector, has both magnitude and direction and can be represented

by pictorial expression (arrow).

(2) A horizontal and a vertical force applying on the same object results a

resultant force in a direction at an angle with respect with x-axis

(3) A force vector can be broken down into horizontal and vertical components

(4) The (2) and (3) are very useful in solving daily problems such as picture 1 to

picture 5.

(5) Give a prelude to students about what will be discussed in the upcoming

sessions

IV. Feedback/ Assigned Homework

No homework is assigned for Session 1

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(1) Knowledge from Sessions 1

(2) Concept of equilibrium

(3) Sine rule and quadrant (from mathematics lesson)



/ key points

I. Lead-in

(1) Briefly introduce the objective of todays’

session

(2) Show the following photos that were used

in Session 1

Picture 1

Picture 2

(1) Equipment:

Computer, projector

and internet access

(2) Equipment:

Computer, projector

and internet access

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Picture 3

Picture 4

Picture 5

(3) Ask students to describe the characteristics

of applied forces and the motion of the

objects/ persons.

(3) T-S and S-S interaction;

Key concepts of Session 1

will be revised;

Equipment:

Computer, projector

and internet access

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(4) Conclude the Lead-in by summarizing

students’ ideas in (3) and introducing the

topic of discussion in this session will

consist of several methods solving

problems related to:

a. Objects in motion (picture 1, 2 and 5)

b. Objects in equilibrium (picture 3 and 4)

--------------------------------------------------------------

II. Development

Part A – Component Method

(1) Ask students what the x and y component

of the man’s pull (Fp) in Picture 1-1 are;

Picture 1-1

(2) Ask students what the force is leading the

suitcase in Picture 1-1 to move forward.

(3) Continue the discussion by asking what the

force is leading the child to slide downward

in picture 2, even though she sits still

without push or pull (neglect friction).

Picture 2-1

(4) The continuous use of picture

1 to 5 from Session 1 to 2

serves as a link for smooth

transition between sessions.

----------------------------------------


Responses from students:

With acquired knowledge

from Session 1, most of the

students will be able to write:

x-component = Fp cos 30∘

y-component = Fp sin 30∘

Equipment:

Computer, projector,

blackboard and chalk




answer “x-component” or

“Fp cos 30º”



Responses may vary.

Possible responses are

“weight”, “(weight)(sin

(unknown angle))”. Some


background will give the

answer as “(weight)(sin 30º);

Equipment:



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(4) Invite two students to demonstrate their

ideas about (7) on blackboard.

(5) Conclude students’ findings and extend

their findings by demonstrating a similar

example (Picture 16) and emphasizing the

following points:

a. As discussed in Session 1, weight W of

the object can also be resolved into x-

and y-component, where the direction

of x-component along with the surface

while that of y-component

perpendicular to the surface.

b. As found by students, it is the

x-component of object’s weight to lead

itself moving downwards

Picture 16

(6) Continue the discussion by asking students

what is/ are the condition(s) that allow the

car in Picture 16 to remain at rest on

inclined road. (For recalling students’

acquired knowledge, teacher puts a toy car

on top of an inclined desk and stops it at

times while it is sliding downwards)

(7) Conclude students’ findings and recall that

an object become equilibrium when all the

forces acting on it are balanced (sum of

horizontal components of forces as well as

sum of vertical components of force equal

zero)

(4) Equipment:

Blackboard and chalk.


Equipment:



(6) Responds from students:


“friction = x-component of

weight” or “net force in x-

or in y-direction equal 0”.

Equipment:

Computer and projector,

a toy car and a desk

(7) Via T-S and S-S interaction,

students will “discover” the

phenomenon instead of being

informed by the teacher.

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(8) For consolidating what students have

learnt from discussion sessions, an

in-class worksheet (Appendix B) with 3

short questions is conducted. Students are

asked to solve Question 1 in the

worksheet.

(9) Taking +y-axis as positive, teacher asks

what the sign of the boy’s weight should

be and with what the condition the boy

remains at rest while holding the hangers.

(10) Invite a student to show his solution on

blackboard and ask students to evaluate

the solution.

Picture 14

Picture 15

(8) Through T-S and S-S

interaction, the learning

effectiveness of steps (5) to

(11) will be evaluated.

Equipment:

Computer, projector, papers

of in-class exercise,

blackboard and chalk.


Respond from students:

Students will be capable of

answering the sign of

weight is “negative”; they

will also be able to state the

condition is “sum of

vertical and horizontal

components of forces equal

zero”.


most of students will

“discover” the method of

solving the problem instead

of being informed by the

teacher.

Equipment:


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(11) Ask students to solve Question 2 in the

in-class worksheet.

(12) Taking +x- and +y-axis as positive,

teacher asks with what the condition the

sign board will remain at rest.



the solution.

(14) Ask students to solve Question 3 in the

in-class worksheet.



the solution.

(16) Derives Question 3 that is needed to deal

with the case in which provided that only

the coefficient of friction μ for the two

surfaces is given.



effectiveness of steps (5) to



Respond from students:

Students will be capable of

answering “sum of vertical

and horizontal components

of forces equal zero”.






teacher.

Equipment:




effectiveness will be further

evaluated by Question 3.






teacher.

Equipment:


(16) Chalk-and-talk

demonstration; students will

learn the friction equation,

which will make a good use

of y-components (same

magnitude but opposite

direction of normal reaction

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Part B – Head-to-Tail Method

(17) Referring to Question 2 in worksheet,

invite a student to draw three arrows

corresponding to the weight of sign board,

tension by the steel rod (given in

question) and the resultant force (found,

with opposite direction, by student just

now) on blackboard.

(18) Ask students what they can discover if the

three arrows can be relocated as they

wish.

(19) SWF Simulation software is then played

to show whether students’ ideas about step

(17) is correct.

Picture 16

force, N) of object’s weight:

Friction =μ N


recall students of what they

have learnt about pictorial

expression in Session 1.

Equipment:




discover that the resultant

force can be found from the

tail of the tension’s arrow to

coincide with the head of

weight’s arrow after moving

the arrow of weight until its

tail touches the head of

tension’s arrow, instead of

being informed by the

teacher.

Equipment:


(19) Simulation software is used

to assist, especially

less-able, students to

visualize their ideas about

step (17) from their mind

into visible image; the web

link for downloading this

simulation software is

provided to students for

self-study at home.

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(20) Referring to Question 1 in worksheet,

students are asked to check their solutions

using head-to-tail method.

(21) Recall that if something is scientifically

true, it can be repeated tested with

different scientific methods and the results

remain the same.

(22) Continue the discussion by asking

students to use pictorial expression to

show the result if three forces acting on

the same object are balanced

(23) Summarize students’ ideas and emphasize

that there will be no arrow of resultant

force formed between head and tail of

applied forces

Part C – Lami’s Theorem

(24) Using SWF simulation software, teacher

draws Picture 17 and Picture 18 with the

same set of data from Question 2 in

in-class worksheet. Given in Question 2

that all forces are balanced, students are

asked to find the angles, in terms of a, b

and c, inside the triangle in Picture 19.

Picture 17



effectiveness of step (17) to

(19) will be evaluated; most

of the students will have an

answer that approximately

equals to 400N downwards.

(21) Learning by doing;

Recalling for a smooth

transition to next session

(experiment)

(22) Response from students:

Some students may be

capable of drawing a ring

shape made of three arrows

only.

(23) T-S and S-S interactions in

this case allow students to

learn from their own

discovery or other students’

ideas.


Students’ ideas may vary.

Only some students with

sufficient mathematics

training may provide the

correct answer as “180-a”,

“180-b” and “180-c”.

Equipment:


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Picture 18

(25) Ask students what the possible

relationship is between angle (180-a),

(180-b), (180-c) and the force A, B and C.

(26) Summarize students’ ideas and conclude

that the equation (stated by students) is

the well-known Lami’s Theorem.

(27) Derive a case of a stationary ball affected

by three forces acting upon at the same

time, as shown in Picture 19. With the use

of Lami’s Theorem, students are asked to

find out the direction of the 27N force

acting on the ball in a true bearing.

Picture 19


Many students will be

capable of stating:

𝐴

sin 𝑎=

𝐵

sin 𝑏=

𝐶

sin 𝑐

(26) Step (26) to (29) are

designed to guide students

to find the Lami’s theorem

with their acquired

knowledge in Session 1 as

well as sine rule and

quadrant learnt recently in

mathematics class ;



effectiveness of step (24) to


Response of students:


correctly; chalk-and-talk

guided demonstration will

be conducted if the majority

of students unable to find

out the correct answer

Equipment:



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(28) Ask students whether Lami’s Theorem

can be used to find the resultant force of

multiple forces.

(29) Summarize students’ ideas



Most of them are capable of

stating “Yes, but in opposite

direction”.

(29) T-S and S-S interaction in

this case help to consolidate

what have been discussed

and leant by the students in

this session; Chalk-and-talk

demonstration of students’

ideas will be used for

providing clearer concept to

the less-able students in

class.

III. Conclusion

(1) Problems related to multiple forces can be solved by three methods:

Component Method (Force Resolution), Head-to-Tail Method and Lami’s

Theorem.

(2) Results of a certain problem found with different methods should be identical.

IV. Feedback / Assigned Homework

(1) Homework (Appendix C) is assigned to students. (Due on the coming Friday)

(2) Before the commencement of Session 3, Experiment Guideline (Appendix D)

and User Manual (Appendix E) will be posted onto “my ITschool” website for

students to prepare upcoming experiment in Session 3.

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(1) Knowledge discussed in Session 1 and 2

(2) Familiarization with the usage of PASCO Super Pulley Force Table.

2.3.2 Aim of Experimentation

The aim of this experiment is for the

students to investigate the influence of the

direction and magnitude of forces (i.e. the

masses subjected to the gravitational pull) on an

equilibrium object, thereby verifying the

findings with results found from another three

methods of force additions.

2.3.3 Flow of Experimentation

Students are firstly divided into groups of

four to five and each student will be given an

Experiment Report to complete. The

Experiment Guideline (Appendix D) that have

been posted on “my ITschool” a couple of days

before this Session describes vividly what they

have to do in the laboratory session and helps

students to complete their Experiment

Guideline.

Essentially, students in the same group will set up a PASCO pulley force

table according to the User Manual (Appendix E). Three threads with masses are

tied onto the table. Two of the threads with masses will be set according to the

given condition of Case Study in the Experiment Report. Photos of the test

set-up used and class instruction are shown in Picture 20 and in Appendix G.

By varying the angle of the third thread with respect to another threads and

the corresponding mass(es), the clear disk in the middle of the force table will be

moved from side to side over a short distance. When the clear disk is pulled at

center of the force table exactly, sum of forces from three threads at angles

equals zero. Students will measure and record the angles of the threads,

especially the third thread, and the masses involved.

Picture 20

Picture 21

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2.3.4 Feedback/ Assigned Homework

(1) Students are recommended to record their findings from experiment and

verify them using the simulation software used in Session 1 and 2 of this

instructional design.

(2) A sample of students’ worked report is included in Appendix F.

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(1) Knowledge from Sessions 1 and 2

(2) Results and findings from reports of Session 3



/ key points

I. Lead-in

(1) Motivate students to discuss their worked

solutions in Homework (Appendix C)

(1) Equipment:



II. Development

(1) Reveal the teacher’s worked solutions of

Homework on the screen and discuss the

solutions with students

(2) Discuss students’ findings in the submitted

reports of Session 3

(3) Re-emphasize the major concepts that have

been discussed in Session 1 – 3 by

projecting the outline of the entire course on

the screen

(1) Marking of Homework are

completed before Session 4

begins;

Equipment:


homework books, blackboard

and chalk

(2) A summary of students’

findings will be projected on

the screen. Any flaws in

students’ reports will be

discussed. Nevertheless, the

key design of this session is

to allow students “discover”,

by themselves, that the

concepts as discussed in

Session 1 and 2 are in

coherence to the results

found in Session 3.


Equipment:

Computer, project,


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(4) Conduct a test (Appendix H) as a summary

of the whole series of the instructional

design

(4) Equipment:

Test paper

III. Conclusion

Re-emphasize all the key concepts that students have learnt, with the display of

course outline on the screen

IV. Feedback/ Assigned Homework

(1) The marked test will be distributed back to students for corrections and

revision.

3. Evaluation after first teaching

Class observations of the authors and interviews with some students after first

teaching have been conducted. Comments from the class observers as well as students

are summarized as follows:

Comments from class observers

a. In general, most of the students who participated in the instruction are

highly motivated in class discussion and interactions.

b. A minority of students seemed being difficult to keep up with others during

Session 2, especially when working on in-class exercises.

Comments from interviewed students who participated in this instruction

a. They enjoyed the entire series of instructional design.

b. They found the in-class exercises and homework helpful in consolidating

their knowledge acquired during student-student interaction in class

c. They think the instructional content are interesting and useful in their daily

lives

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Comments and conclusions from the authors of this instructional design

a. The passing rate of homework from Session 2 is around 65%. This indicates

that almost two-thirds of the students are capable of applying acquired

knowledge in solving problems. Nevertheless, after conducting experiments

and evaluation of homework and experimental findings in Session 3 and 4,

the passing rate of the test is more than 80%. This implies that an number of

students deepen their understanding and ability of application about the

major concepts from this instruction through experiment in Sessions 3 as

well as student-orientated evaluation in Sessions 4. The test result also

suggests that the majority of students have already mastered the key

concepts as presented in this instructional design.

b. Although all the students actively participated in the in-class activities in

Session 1, 2 and 4, there are several students found with little preparation

for the Session 3. Additional instruction was therefore needed from the

authors for these students in order to complete the experiment effectively

and correctly.

c. Generally, the qualities of the Experiment Reports are better than authors’

expectation and some of them extremely well written with valuable insights

and creative methods of problem solving. However, the content of some

reports are weak. These students fail to use their acquired knowledge to

analyze and solve the problem set in the Experiment Report.

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4. Reflections and Suggestions for improvement

The followings are the authors’ reflections and suggestions for improvement

about their instructional design after first teaching.

a. For Session 2, one more period of 40 minutes should be included in order to

allow sufficient time for the less-able students to keep up with others and

further understand the content.

b. For a smoother run-down of Session 3, a brief introduction of experiment in

Session 3 should be conducted in Session 2. This would help the less-able

students have a better understanding about the purpose of the experiment and

how to conduct the experiment with the given apparatus. A quiz about the

experiment conducted between Session 2 and 3 could also be an alternative

way for encouraging students to have a better preparation about the related

content before the experiment.

c. For Session 3, demonstrating the key procedural steps of the experiment via

video recording in laboratory would be a good idea to guide those students

with insufficient experimental skills. This would likely spend less time of

additional instruction for individuals, enhance students’ working efficiency

in conducing experiment and improve overall experiment safety as well.

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5. Reference

Reference for the characteristic of the Design

https://news.uchicago.edu/article/2015/04/29/learning-doing-helps-students-perform-b

etter-science - 2016/03/18

Pictures of session 1

http://static1.squarespace.com/static/52d56225e4b0e9203b2a6579/t/54aa0d18e4b032

a504c14735/1420430617536/ - 2016/04/30

http://download.mobile01.com/topic/375-2934756-f58b8fdb06d9f6e29c0f23083ac9ba

e5.jpg - 2016/04/30

http://tbl.tec.fukuoka-u.ac.jp/bridge/39okumonobe/39okumonobe-01-0309s.jpg -

2016/04/30

http://static.apple.appledaily.com.hk/images/e-paper/vdo/20150807/392pix/14389515

38_784a.jpg - 2016/04/30

http://img.epaper.com.tw/img/lion/20111122/6.jpg - 2016/04/30

Web links for downloading simulation software in session (player and simulation file)

http://swf-player.en.softonic.com/download#downloading

https://phet.colorado.edu/en/simulation/vector-addition

Pictures of Session 2

http://www.hk-phy.org/contextual/mechanics/for/add_force/3-04.gif - 2016/04/30

Picture of laboratory material used in Session 3

User manual – PASCO super pulley force table

https://news.uchicago.edu/article/2015/04/29/learning-doing-helps-students-perform-better-science

https://news.uchicago.edu/article/2015/04/29/learning-doing-helps-students-perform-better-science

http://static1.squarespace.com/static/52d56225e4b0e9203b2a6579/t/54aa0d18e4b032a504c14735/1420430617536/

http://static1.squarespace.com/static/52d56225e4b0e9203b2a6579/t/54aa0d18e4b032a504c14735/1420430617536/

http://download.mobile01.com/topic/375-2934756-f58b8fdb06d9f6e29c0f23083ac9bae5.jpg

http://download.mobile01.com/topic/375-2934756-f58b8fdb06d9f6e29c0f23083ac9bae5.jpg

http://tbl.tec.fukuoka-u.ac.jp/bridge/39okumonobe/39okumonobe-01-0309s.jpg%20-%202016/04/30

http://tbl.tec.fukuoka-u.ac.jp/bridge/39okumonobe/39okumonobe-01-0309s.jpg%20-%202016/04/30

http://static.apple.appledaily.com.hk/images/e-paper/vdo/20150807/392pix/1438951538_784a.jpg%20-%202016/04/30

http://static.apple.appledaily.com.hk/images/e-paper/vdo/20150807/392pix/1438951538_784a.jpg%20-%202016/04/30

http://img.epaper.com.tw/img/lion/20111122/6.jpg

http://swf-player.en.softonic.com/download#downloading

https://phet.colorado.edu/en/simulation/vector-addition

http://www.hk-phy.org/contextual/mechanics/for/add_force/3-04.gif

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6. Appendix

Appendix A – In-class worksheet in Session 1

Appendix B – In-class worksheet in Session 2

Appendix C – Homework 1 in Session 2

Appendix D – Experiment Guideline

Appendix E – User Manual of Super Pulley Force Table

Appendix F – Sample of Student’s Experiment Report in Session 3

Appendix G – Photos of class instruction

Appendix H – Test Paper in Session 4

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Appendix A – In-class worksheet in Session 1

F4 Physics In-class Worksheet – Vector (Force) Resolution I

Please write down all the solutions into your notebook

Question 1

Draw the components of the following vectors

Question 2

Find the magnitudes of the components of the following forces

Question 3

Find the magnitude and direction of the following forces

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Appendix B – In-class worksheet in Session 2

F4 Physics In-class Worksheet – Vector (Force) Resolution II

Please write down all the solutions into your notebook

Question 1

With the help of his friend, a naughty boy of mass

40 kg holds two hangers and lifts up himself in an

MTR train, as shown in Fig. 1. What is the tension

in each hanger if the train is at rest?

(Take g = 10m𝑠−2)

Fig. 1

Question 2

A sign board of weight 500 N is supported by a

steel rod and a wire (Fig. 2). The tension in the

wire is 300 N and it makes an angle of 30° with the

horizon.

Find the force exerted by the steel rod on the

board.

Fig. 2

Question 3

Santa Claus (Fig. 3) is riding on a sledge to

distribute Christmas presents to children as shown.

The deers apply a force of 5000N to pull the

sledge up a slope at a constant speed. The slope is

at an angle of 10 degree to the horizontal. Suppose

the friction acting on the sledge is 4250N and the

total weight of Santa Claus and the sledge is

3000N. Find the weight of the presents. Fig. 3

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Appendix C – Homework 1 in Session 2

F4 Physics Homework – Vector (Force) Resolution

Please write down all the solutions into your physics homework book.

1. The two diagrams below depict the free-body diagram for a 1000-kg roller coaster

on the first drop of two different roller coaster rides. Determine the net force and

acceleration of the roller coaster cars. Assume a negligible effect of friction and

air resistance.

2. In the following questions, three forces are in equilibrium. Two forces are

provided and you are to find the 3rd

one.

(a) i. 20N, 50° , ii 30N, 75° (using component method)

(b) i. 50N, 75° , ii. 50N 105° (using head-to-tail method)

(c) i. 15N, 135° , 25N, 315° (using Lami’s theorem)

3. A strong man holds a 500 N weight at a constant height as shown. The ends of the

chain make angles of 30˚ and 60˚ to the horizontal respectively.

a. Draw ALL the components of the tensions

b. Under what condition will the weight be held at a

constant height?

c. Find the tensions T1 and T2 in the chain, and the

tension T3 in the wire. Neglect the weight of the

chain and wire in your calculation.

d. Do you think he can make the chain completely

straight by horizontally pulling it hard?

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Appendix D – Experiment Guideline

Experiment Guideline - Forces Resolution

1. Objective

This experiment is, by using a PASCO pulley force table, to investigate the

influence of the direction and magnitude of forces (i.e. the masses subjected to the

gravitational pull) on an equilibrium object, thereby verifying the findings with results

found from another three methods of force additions.

2. Set-up

The set-up of a PASCO pulley force table

(Fig. a) for this experiment is shown on the right.

(Please refer to the User Manual).

3. Description of the Experiment

Three threads with masses are tied, as shown in Fig. b,

onto the table. Two of the threads with masses will be set

according to the given condition of Case Study in the

Experiment Report (which will be given in laboratory).

By varying the angle of the third thread with respect to another threads and the

corresponding mass(es), the clear disk in the middle of the force table will be moved

from side to side over a short distance. When the clear disk is pulled at center of the

force table exactly, sum of forces from three threads at angles equals zero. Students

will measure and record the angles of the threads, especially the third thread, and the

masses involved.

Fig. b

Fig. a

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4. Procedure

Students add a mass and then try to alter the angle of the third thread in order to

enable the clear disk in the middle of force table back to its original position (at center

of the table). If the clear disk cannot go back to the center of the force table after

placing the third thread at different angles, add or unload masses will be needed and

alter the angle of the third thread again.

Repeat the process(es) until the clear disk is at the center of the force table, i.e.

all forces on the three threads in equilibrium.

5. Experiment Report Requirements

i. Complete ALL the questions in the Experiment Report.

ii. Write all the solutions in black ink

iii. Other requirements in report format and contents are identical to what we

discussed in the beginning of the academic year

iv. The deadline of Report submissions : 5 p.m., 17/05/2016

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Appendix E – User Manual of Super Pulley Force Table

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Appendix F – Sample of Student’s Experiment Report

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Appendix G – Photos of class instruction

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Appendix H – Test

F4 Physics Test – Force Resolution

40 points is equivalent to 100% of the test

Instruction: Answer in black ink only. No correction fluid is allowed.

Session A: Multiple Choice – Circle the letter of the best possible answer.

1. An object is acted on by a vertical force of 25 N and a horizontal force of 34 N.

The angle to the horizontal of the resultant force is given by

A cos–1 (25/34) B sin–1 (34/25) C tan–1 (25/34) D tan–1 (34/25)

2. A block of weight 20N is suspended by a light string from the ceiling. A force F is

applied such that the block is displaced to one side with the string making an

angle of 25˚ with the vertical as shown. Find the magnitude of F.

A 8.5 N B 9.3 N C 18.1 N D 47.1 N

3. A student lets block X slide down an inclined plane. The friction acting on X is

0.2 times its weight. Then she uses another block Y with a larger mass and the

friction acting on it is also 0.2 times its weight when it slides down the plane.

Which of the following statements about the two blocks when they slide down the

plane is/are correct?

(1) If the blocks accelerate, the net force acting on Y will be larger than that on X.

(2) If the blocks accelerate, the acceleration of Y will be larger than that of X.

(3) If X slides down the plane at a constant velocity, Y will also slide down at a

constant velocity.

A (1) only B (1) and (3) only

C (2) and (3) only D (1), (2) and (3)

(Total 6 points)

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Session B: Structured Questions

Question 1

A girl is sliding down a slide. Her mass is 45 kg. The slide is inclined at 50˚ to the

horizontal.

a. Draw the free-body diagram for the girl. (2)

b. What is the direction of the nect force acting on her if she

(i) comes down the slide faster and faster? (1)

____________________________________________________________

____________________________________________________________

(ii) comes down slowly at a constant speed? (1)

____________________________________________________________

____________________________________________________________

(iii) sits on the slide and does not move? (1)

____________________________________________________________

____________________________________________________________

c. What is her acceleration if the friction between her and the slide is 300N? (2)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

(Total 7 points)

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Question 2

The figure below shows a crane lifting an object. Assume that the mass of the object

is 225 kg. Each of the four ropes connected to the object are at an angle of 40˚ to the

vertical and have the same tension.

a. The object is held stationary.

(i) What is the net force acting on the object? (1)

_____________________________________

_____________________________________

_____________________________________

(ii) What is the tension in each rope? (2)

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

b. If the object is raised upwards with an acceleration of 0.4 m/sIf the object is raised

upwards with an acceleration of 0.4 m/sIf the object is raised upwards with an

acceleration of 0.4 m/s2, what is the tension in each rope? (2)

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

c. A rope may break if the tension in it is too large. Is it safer to hang the object with

longer or shorter ropes? Explain briefly. (3)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

(Total 8 points)

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Question 3

Four horizontal forces act on an object placed on a smooth horizontal surface as

shown. The object remains stationary. The mass of the object is 20kg.

a. By using the head-to-tail method,

(i) construct a head-to-tail diagram of all the

applied forces with appropriate scale. (3)

(ii) find the magnitude of F. (1)

____________________________________________________________

____________________________________________________________

(iii) find the direction of F. (1)

____________________________________________________________

____________________________________________________________

b. If the 70-N force disappears suddenly, what is the magnitude and direction of the

acceleration of the object at that instant? Assume that the three other forces remain

unchanged. (3)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

(Total 8 points)

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Question 4

A man is standing on a cable.

The tension in the cable is 1280N.

a. Sketch a vector diagram of all the forces

acting on the man. (2)

b. By using Lami’s theorem, find the weight of the man. (3)

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

(Total 5 points)

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Question 5

A man pushes a trolley up a slope. He applies a

forceof200Nparalleltotheslope.Theslope is at an

angle of 10˚ to the horizontal. The total mass of

the trolley including its contents is 50 kg. The

friction acting on the trolley by the slope is 80N.

a. By using the component method, find the

magnitude of the normal force acting on the

trolley by the slope. (2)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

b. Find the acceleration of the trolley. (4)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

(Total 6 points)

- End of the Test -

force resolution in daily life

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