Lesson Plan - SingaporeTeachersLearningCentre



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:

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 |Activities |Resources |Rationale |

|3 |Lesson Opening |Powerpoint slides |Set induction to arouse interest of students |

| |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 | |Give structure to the lesson. |

| |Show lesson objectives | |Students know what to expect |

| |Newton’s First Law | | |

|3 |Set induction |Table cloth, bowl |Attract the attention and interest of the |

| |Put the bowl of water on top of the smooth tablecloth and very quickly pull the table cloth from beneath the |of water |students. |

| |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 | |Prime the students to induce for themselves |

| |Direct the responses towards the fact that the bowl of water didn’t move because not enough force acted on it | |the first law of motion |

| |for it to move | | |

|2 |Development |Powerpoint Slides |Allow students to induce for themselves the |

| |Ask the students “If something is moving, what must you do to make it stop, speed up, slow down or change | |first law. |

| |direction?” | | |

| |Get responses from students. | | |

| |Congratulate students on understanding Newton’s first law of motion. | | |

| |Ask students “So now if I were to ask you to state Newton’s First law of motion in your own words, what would | |Engage students |

| |you say?” | | |

| |Show slide of Calvin | |Humour to interest students |

| |Show slide with definition of Newton’s First Law. | | |

| |Talk about inertia, relating to real life examples of car breaking, trying to wake up in the morning | |Link the idea of inertia with the first law |

| |Show cartoon | | |

| |Newton’s Second Law (Part 1): Momentum | | |

| |Set induction | |Link between first law and second law |

| |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.” | | |

|20 |Lesson development |Basketball, |Get students to recall Newton’s second law as |

| |Ask for a volunteer. Throw the basketball to the volunteer asking him/her to catch. |Powerpoint slides |they have learnt using an example which they |

| |Throw the basketball to the volunteer, only this time, throw such that the basketball moves faster. Ask the | |can relate to. |

| |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 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?” | |Introduce the term momentum. |

| |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. | |Highlight to students that momentum is a |

| |Give sample problem 1: Air being pushed downwards by the blades of a helicopter travels at a velocity of vair | |vector which is in the same direction as |

| |m/s. Assuming the cross-section of the air being pushed away by the blades is A m2, what is the average force | |velocity |

| |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. | |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. |

| |Newton’s Second Law (part 2): Impulse | | |

|5 |Set Induction |Pine wood board |Keep students’ interest in the lesson. |

| |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.” | |Create cognitive conflict to engage students’ |

| |Get off the board, proceed to break the board with right hand, making sure to break along the grain. | |thinking. |

| |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?” | | |

|20 |Lesson Development |Powerpoint slides |Engage students |

| |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 | |Use of everyday example to introduce concept |

| |volunteer. | |of impulse. |

| |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. | |Engage students in thinking. |

| |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: [pic] | | |

| |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 | |Introduce the term “impulse” |

| |impulse. Extend to a general Force-Time graph but caution that the students would need to know how to solve | | |

| |first order Differential 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 | |Highlight the limitations of a Force vs Time |

| |which need to be converted to seconds so that everything is in SI units. | |graph. |

| | | | |

| | | |Consolidate the concept of impulse and the |

| | | |impulse-momentum theorem |

| |Newton’s Third Law | | |

|2 |Set Induction |Medicine ball, |Inject humour |

| |Show comic strip of Garfield, telling students that Odie is framed because of Newton’s Third Law of motion |chair, Powerpoint | |

| |Tell students, “Now I shall show you another effect of Newton’s Third Law of motion.” |slides. | |

| |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 | |Demonstrate the effect of Newton’s third law |

| | | |of motion |

| | | | |

| | | |Prime the students that we are going to be |

| | | |discussing the third law |

|5 |Lesson Development | | |

| |State Newton’s third law. | |Make explicit that the action-reaction pair of|

| |Use demonstration to further explain Newton’s third law. | |forces act on different bodies. |

| |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? | |Reinforce that pair of forces act on different|

| | | |bodies. |

| |Principle of Conservation of Momentum | | |

|5 |Set Induction | | |

| |Show Newton’s cradle. | | |

| |Ask students to explain why it behaves as such | | |

| |Get response from students | | |

|10 |Lesson Development | | |

| |Show shockwave simulation of girl jumping off cart (See Annex 1) | |Let students begin to derive the principle of |

| |Repeat the simulation with different values of masses of girl and cart and velocity. Direct students to note | |conservation of linear momentum. |

| |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 | |Show the students that the principle of |

| |motion. | |conservation of momentum is not something new |

| | | |but is built upon Newton’s laws of motion. |

| |Closure | | |

|5 |Summarise the lesson | |Recap and make connections between new |

| |Show key terms and key concepts | |concepts learnt |

Appendix 1: Shockwave simulation – Girl jumping off a trolley

[pic]

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:

[pic]

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 being pushed away by the rotor blades in a second,[pic], can be written as:

[pic]

Therefore the mass of air being pushed away by the rotor blades per second, [pic], can be written as:

[pic]

Now Newton’s Second Law of motion states:

[pic]

where F is the average force that the rotor blades exert on the air.

In this case, v remains constant but m changes. Therefore:

[pic]

Solution to Road Block 2

Let the initial direction that baseball is travelling in be positive. Therefore, initial momentum, pinitial, is:

[pic]

The final momentum, pfinal, is

[pic]

because the ball is now moving horizontally in the opposite direction.

(a) Therefore impulse is:

[pic]

(b) By the impulse-momentum theorem:

[pic]=x ms = [pic]

Therefore the average force, Fave, is:

[pic]

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.

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Dynamics:

Newton’s Laws of Motion

First Law

Inertia

Force required to change state of motion

Second Law

Force proportional to rate of change of momentum

Momentum

Impulse

Third Law

Principle of conservation of linear momentum

Impulse-momentum theorem

Cross-sectional area, A m2

Length of cylinder, l m

[pic]

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