Download The Laws of Motion (Dynamics

Lesson Plan
Topic: Dynamics
Subtopics: Newton’s three laws of motion, linear momentum and its conservation
Content:
1. Newton’s three laws of motion
2. Conservation of Linear momentum
Level: JC1
Time: 80 minutes (Lecture)
Lesson Objectives:
At the end of the lesson, students should be able to, without any reference or notes:
1. State Newton’s First Law of Motion as: “If there is no net resultant force acting
on an object, then if it is at rest, it will remain at rest and if it is moving with
constant velocity, it will continue to do so”
2. State Newton’s Second Law of Motion as: “The net resultant force acting on an
object is proportional to the rate of momentum change”
3. State Newton’s Third Law of Motion as: “When two bodies exert mutual forces
on one another, the two forces are always equal in magnitude and opposite in
direction.”
4. State that the momentum of an object is a vector which has the same direction as
the velocity of the object.
5. Derive the impulse of a force in given problems
6. Correctly use the impulse-momentum theorem.
7. Solve problems which requires an understanding of Newton’s second and third
Laws
8. Recall that the principle of conservation of linear momentum follows from
Newton’s second and third laws of motion.
9. State the principle of conservation of linear momentum
Prior Knowledge
1. Acceleration as the rate of change of velocity.
2. Newton’s second law of motion as F=ma
3. Concept of Vectors
New Concepts:
Inertia
Force
required to
change state
of motion
Dynamics:
Newton’s Laws of
Motion
First Law
Third Law
Second Law
Momentum
Force proportional
to rate of change
of momentum
Impulse
Principle of conservation of
linear momentum
Impulse-momentum
theorem
Learning Aids and Resources:
1. Smooth tablecloth
2. Big bowl of water
3. Basketball
4. Medicine ball
5. Wooden board
6. Newton’s cradle
7. Shockwave simulation
8. Powerpoint slides
9. Office chair with well-oiled castor wheels
IT:
1. Powerpoint slides.
2. Shockwave simulation to allow students to derive the definition of the principle of
conservation of linear momentum
Lesson Presentation
Time/min
3
3
2
Activities
Lesson Opening
 Talk about the publishing of the Principia and what it is. Then say that
amongst the laws that Newton described in the Principia are the 3 laws
of motion which will be the focus of the lecture.
 Show scope of the days lesson
 Show lesson objectives
Newton’s First Law
Set induction
 Put the bowl of water on top of the smooth tablecloth and very quickly
pull the table cloth from beneath the bowl of water. The bowl of water
should not move.
 Pose the question, “Why didn’t the bowl of water move?”
 Get responses from the students
 Direct the responses towards the fact that the bowl of water didn’t move
because not enough force acted on it for it to move
Resources Rationale
Powerpoint Set induction to arouse
slides
interest of students
Give structure to the lesson.
Students know what to expect
Table
cloth, bowl
of water
Attract the attention and
interest of the students.
Prime the students to induce
for themselves the first law of
motion
Development
Powerpoint Allow students to induce for
Slides
themselves the first law.
 Ask the students “If something is moving, what must you do to make it
stop, speed up, slow down or change direction?”
 Get responses from students.
 Congratulate students on understanding Newton’s first law of motion.
Engage students
 Ask students “So now if I were to ask you to state Newton’s First law of
motion in your own words, what would you say?”
Humour to interest students
 Show slide of Calvin
 Show slide with definition of Newton’s First Law.
Link the idea of inertia with
 Talk about inertia, relating to real life examples of car breaking, trying to
Time/min
20
Activities
wake up in the morning
 Show cartoon
Resources
Newton’s Second Law (Part 1): Momentum
Set induction
 Tell students, “So Newton’s first law tells us that a net resultant force is
needed to change the state of motion of an object. But how much force is
needed? That, we will learn, is what Newton’s second law of motion will
tell us.”
Lesson development
Basketball,
Powerpoint
 Ask for a volunteer. Throw the basketball to the volunteer asking
slides
him/her to catch.
 Throw the basketball to the volunteer, only this time, throw such that the
basketball moves faster. Ask the class, “Now that the ball was moving
faster, do you think he/she needs more force to stop the ball?”
 Get response from class. Confirm with the volunteer.
 Throw the medicine ball to the volunteer at about the same speed as the
second time the basketball was thrown. Tell the class that the medicine
ball is more massive than the basketball. Ask the class, “Do you think
he/she needs more force to stop the medicine ball than to stop the
basketball, if the 2 were travelling at the same speed?”
 Get response from the class. Confirm with the volunteer.
 Explain to the class the amount of force needed is dependent on 2
quantities, the mass and the velocity.
 Relate it to what the students have learnt in O-Levels that F=ma, and a is
the rate of change of velocity with respect to time.
 Tell the students that F=ma is not a complete definition of Newton’s
second law.
 Tell the students that there can be instances when velocity does not
Rationale
the first law
Link between first law and
second law
Get students to recall
Newton’s second law as they
have learnt using an example
which they can relate to.
Time/min
5
Activities
change, but mass changes, and instances when both velocity and mass
changes and in all these instances, there is a force.
 Tell the students that in the Principia, the full version of Newton’s
second law talks about changes in a quantity that is a product of mass
and velocity, which Newton called momentum. Show the complete form
of Newton’s second law of motion
 Ask the students, “Is momentum a scalar of a vector quantity?”
 Get students’ response, acknowledging the correct one that momentum
is a vector.
 Ask the students’, “What direction is momentum in?”
 Get students response, acknowledging the correct one that momentum is
in the same direction as velocity. Ask students’, “Does the force have to
be in the same direction as the momentum? Why?”
 Get students’ response, acknowledging the correct answer that
momentum and force need not be in the same direction as force is in the
same direction as the change in momentum which need not be in the
same direction as momentum.
 Give sample problem 1: Air being pushed downwards by the blades of a
helicopter travels at a velocity of vair m/s. Assuming the cross-section of
the air being pushed away by the blades is A m2, what is the average
force that the blades are exerting on air? State any other assumptions
made.
 Solve sample problem, highlighting that the problem is one of variable
mass rather than variable velocity.
Newton’s Second Law (part 2): Impulse
Set Induction
 Stand on wooden board and tell students, tell the students, “I am weigh
700N. And the board is supporting my weight, meaning that in order to
break the board, I have to exert a force of greater than 700N.”
Resources
Rationale
Introduce the term
momentum.
Highlight to students that
momentum is a vector which
is in the same direction as
velocity
Highlight to students that
change in momentum need
not be in the same direction as
force.
Demonstrate that there are
situations where it is mass
which changes and not
velocity and hence Newton’s
definition of force as rate of
change of momentum is more
useful than just F=ma.
Pine wood
board
Keep students’ interest in the
lesson.
Create cognitive conflict to
Time/min
20
Activities
Resources
 Get off the board, proceed to break the board with right hand, making
sure to break along the grain.
 Ask students, “Is my right arm really able to exert more than 700N of
force? But I know that I cannot lift 700N with my right arm. So how was
I able to break the board?”
Lesson Development
Powerpoint
slides
 Ask for volunteer.
 Get volunteer to stand on chair and jump down.
 Ask the volunteer to do it again. But before volunteer does so, ask the
class to focus on the knees of the volunteer.
 Ask the volunteer whether he/she would jump and land without bending
his/her knees (but do not actually get the volunteer to do so).
 Thank the volunteer. Ask the class “why isn’t it a good idea to land
without bending your knees?”
 Get response from students, reminding students that force is proportional
to rate of change of momentum with respect to time.
 Explain that bending of knees increase time over which momentum
changes.
 Explain that breaking of board is possible because the board is unable to
‘absorb’ the impact, so change of momentum takes place over a very
brief period of time, hence force the board experiences is very high.
 Tell students that there is a special name for change of momentum and
that it is called impulse.
 State the impulse-momentum theorem: F t  p
 Show Force vs Time graph. Explain how the area under the graph gives
the impulse using a simple case of a uniform force over a period of time,
where it is straightforward to conclude that area under the graph is the
impulse. Extend to a general Force-Time graph but caution that the
students would need to know how to solve first order Differential
Rationale
engage students’ thinking.
Engage students
Use of everyday example to
introduce concept of impulse.
Engage students in thinking.
Introduce the term “impulse”
Time/min
2
5
Activities
Equations for a more rigorous mathematical analysis of why the area
under the Force-Time graph gives impulse.
 Caution that with the Force vs Time graph, we can only find the
momentum change, but we are absolutely clueless about the initial and
final momentums.
 Give sample problem 2: A baseball is moving horizontally at a velocity
of v m/s when it is struck by a baseball bat. It leaves the bat horizontally
at a velocity of v m/s in the opposite direction. (a) Find the impulse of
the force exerted on the ball. (b) Assuming the collision lasts for x ms,
what is the average force?
 Work out sample problem, demonstrating how the impulse-momentum
theorem can be useful.
 Caution the students to be careful of conversion of units. In this
example, time was given in milliseconds which need to be converted to
seconds so that everything is in SI units.
Newton’s Third Law
Set Induction
 Show comic strip of Garfield, telling students that Odie is framed
because of Newton’s Third Law of motion
 Tell students, “Now I shall show you another effect of Newton’s Third
Law of motion.”
 Sit on the office chair, throw the medicine ball. Should see the office
chair and me moving in the opposite direction of the direction of travel
of the ball.
 Tell students that what they just saw was an example of Newton’s third
law in action
Lesson Development
 State Newton’s third law.
Resources
Rationale
Highlight the limitations of a
Force vs Time graph.
Consolidate the concept of
impulse and the impulsemomentum theorem
Medicine
Inject humour
ball, chair,
Powerpoint
slides.
Demonstrate the effect of
Newton’s third law of motion
Prime the students that we are
going to be discussing the
third law
Make explicit that the action-
Time/min
5
10
5
Activities
Resources
 Use demonstration to further explain Newton’s third law.
 Show free body diagrams of other examples of Newton’s third law in
action
 Highlight that the 2 forces in the action-reaction pair acts on different
objects.
 Give sample problem 3: From sample question 1, what is the force
acting on the blades of the helicopter?
Principle of Conservation of Momentum
Set Induction
 Show Newton’s cradle.
 Ask students to explain why it behaves as such
 Get response from students
Lesson Development
 Show shockwave simulation of girl jumping off cart (See Annex 1)
 Repeat the simulation with different values of masses of girl and cart and
velocity. Direct students to note that momentum is always the same
before and after the girl jumps off the trolley.
 Show students the derivation of the principle of conservation of
momentum using the second and third laws of motion.
Closure
 Summarise the lesson
 Show key terms and key concepts
Rationale
reaction pair of forces act on
different bodies.
Reinforce that pair of forces
act on different bodies.
Let students begin to derive
the principle of conservation
of linear momentum.
Show the students that the
principle of conservation of
momentum is not something
new but is built upon
Newton’s laws of motion.
Recap and make connections
between new concepts learnt
Appendix 1: Shockwave simulation – Girl jumping off a trolley
Appendix 2: Solution to Road Block
Solution to Road Block 1
Say if the cross sectional area is in the shape of a circle, and assuming that the volume of
air being pushed out by the rotor blades takes the shape of a cylinder:
Cross-sectional area, A m2
Length of cylinder, l m
We know that the air being pushed from the rotor blades move at a velocity of vair m/s.
So in 1s, the length of the ‘air cylinder’ formed is vair m. In other words, the volume of air
V
being pushed away by the rotor blades in a second, air , can be written as:
t
Vair
  A  vair m 3 s 1
t
mair
Therefore the mass of air being pushed away by the rotor blades per second,
, can
t
be written as:
mair  air Vair

 Avair m 3 s 1
t
t
Now Newton’s Second Law of motion states:
mv
F
t
where F is the average force that the rotor blades exert on the air.
In this case, v remains constant but m changes. Therefore:
 mair 
2
N
Faverage  
v air  Avair v air  Avair

t


Solution to Road Block 2
Let the initial direction that baseball is travelling in be positive. Therefore, initial
momentum, pinitial, is:
pinitial  mvkgms1
The final momentum, pfinal, is
p fnial  mvkgms1
because the ball is now moving horizontally in the opposite direction.
(a) Therefore impulse is:
p  p final  pinitial   mv  mvkgms 1  2mvkgms 1
(b) By the impulse-momentum theorem:
Ft  p
t =x ms =
x
s
1000
Therefore the average force, Fave, is:
F ave 
p
t

 2mv  1000
x
N 
 2000mv
x
N
Solution to Road Block 3
By Newton’s Third Law of Motion, the force acting on the rotor blades is equal and
opposite in direction as the force that the rotor blades exert on the air.
Appendix 3: Reflections on Microteaching
1. Slow down My pace was too fast, which would be alright if the students are of a
higher ability. However, considering that the lesson is conducted in a lecture, it is
most probably going to be quite a large class, hence highly likely that the abilities
of the students would be mixed. As such, it would be much better to slow down so
that even the slower students would not find it a struggle to keep up.
2. Board Breaking The board did not break during my microteaching. As such, the
effect was not there. To remedy this, I should use pine wood boards, which have
bigger grains and hence easier to break, instead of jelutong boards.
3. Aggressive I realised that I did not smile and came across as too ‘aggressive’ in
the way I taught. I should tone down and smile more. Slowing down will also
help me come across as less aggressive.