Punctuality

1. Class Rules • Punctuality • The last person to come into the class later than me will teach the class for 10 minutes • Homework to be returned during the first Theory lesson of the week. • Cleanliness • Courtesy • If you need to speak, raise your hands. • Consistency • You must always have your notes with you.

2. Dynamics Part 1 Interactions & Forces

3. Learning Objectives • By the end of the lesson, you should be able to: • State Newton’s 3rd law of motion. • Identify forces acting on an object and draw free body diagram(s) representing the forces acting on the object (for cases involving forces acting in at most two dimensions).

4. Topic Overview CLASSICAL MECHANICS Kinematics Motion without looking at its cause HOW? Dynamics Motion and its causes WHY & WHAT? Statics Lack of Motion and its causes WHY & WHAT? N F Ff Ignore Forces W

5. m Fundamental Interactions When two bodies meet, we often find that they may interact with one another. For instance, when two like charges come in proximity with one another, they repel. When two unlike charges meet, they attract. When two masses meet, they gravitate towards one another. All these motion, attraction or repulsion, are all the effects or outcomes of underlying INTERACTIONS between 2 bodies. + + m m - m

6. Fundamental Interactions Love Gravity Bodies may only interact if there are more than 1 of them involved (ie. 2 or more). In the earlier example, we have already seen two types of interactions: Electrostatic Gravitational Can you think of other kinds of interactions? Magnetic Interaction! Electrostatic m m - +

7. Force and Motion • Physicists describe the effect of these interaction (whether it is an attraction or a repulsion) on ONE of the two interacting bodies as the result of a FORCE. • In any interaction, both objects are influenced equally. • Hence, in any one interaction, there will always be a pair of FORCES, with each of the two bodies bearing one of the pair of forces. Magnetic Interaction Magnetic Force acting on Magnet B by Magnet A Magnetic Force acting on Magnet A by Magnet B

8. Force • A force is a vector. • Like all vectors, it is represented by an arrow, whose • Length proportional to magnitude of the vector (ie. Strength of the force) • and the direction is that which the arrowhead points. • The unit for measuring Force is the newton (N). • One Newton is defined as the force required to cause 1 kg of mass to accelerate at 1ms-2. Gravitational Force

9. Newton’s Third Law of Motion • Also known a the Law of Reciprocal Actions. • States that • Whenever a body A applies a force (known as the “action”) on a body B, body B will exert another force (known as the “reaction”) that is equal in magnitude, but opposite in direction to the force applied by A. The two forces hence act on two different bodies that are interacting with one another. Magnetic Interaction Magnetic Force acting on Magnet A by Magnet B Magnetic Force acting on Magnet B by Magnet A

10. Learning Objectives • Are you able to: • State Newton’s 3rd law of motion. • Identify forces acting on an object and draw free body diagram(s) representing the forces acting on the object (for cases involving forces acting in at most two dimensions).

11. Review of Newton’s Third Law Gravitational Gravitational • Let’s go back to the Earth-Moon example: • What is the interaction that exist between them? • Is the gravitational force of the Moon on the Earth stronger, weaker or the same compared to that of the Earth on the Moon? • Can you show some characteristics of action-reaction pairs in this example?

12. Learning Objectives • By the end of the lesson, you should be able to: • Identify forces acting on an object, • Describe and use the concept of weight as the effect of a gravitational field on a mass. • Draw free body diagram(s) representing the forces acting on the object (for cases involving forces acting in at most two dimensions). • Describe the effect of balanced and unbalanced forces on a body

13. Multiple Forces at Work Magnetic • An object may experience more than one form of interaction simultaneously • Eg. a magnet experiences gravitational influences and magnetic influences all at once. • Hence, there may be several forces acting on the same body at any one time. • This also suggest that the body is interacting with several different partners at the same time. Magnetic Gravitational Gravitational

14. Characteristics of Action-Reaction Pairs • Action-reaction pairs of forces MUST ALWAYS BE TRUE for the below characteristics: • They are equal in magnitude • They are opposite in direction • They act on DIFFERENT bodies • They act along the same line of action. • They arise from the same type of interaction. • If any of these characteristics are not satisfied, then the two forces under examination are NOT action-reaction pairs.

15. Characteristics of Action-Reaction Pairs • In the magnet example, are the following 5 characteristics satisfied? • They are equal in magnitude • They are opposite in direction • They act on DIFFERENT bodies • They act along the same line of action. • They arise from the same type of interaction. • WHAT DOES “SAME TYPE” MEAN? Magnetic Interaction Magnetic Force acting on Magnet A by Magnet B Magnetic Force acting on Magnet B by Magnet A

16. Types of Forces • What types of forces are there? • Gravitational Force • Magnetic Force • Electrostatic Force • Friction (Demo) • Air/Water Resistance • Normal Contact Force • Tension • Nuclear Forces in the nucleus of an atom m m - +

17. Normal Contact Force • Normal Contact Force is a force that acts perpendicular to the surface of contact between two bodies that are being pushed together. EXTERNAL FORCE Normal Contact Force appears between the surface of contact when the two bodies are subjected to external force pushing them together. CONTACT FORCE CONTACT FORCE No Normal Contact Force when the two bodies are just placed next to each other, touching but NOT pushed together. EXTERNAL FORCE

18. Book on Table Example Normal BOOK Are you able to identify the forces acting on the book? Normal Contact force of the Table acting on the Book Are you trying to read what is written here? Are you trying to read what is written here? Weight Weight = gravitational force of the Earth acting on the Book Are the Weight and the Normal Contact force an action-reaction pair?

19. Book on Table Example BOOK • The reaction pair of the weight of the book, which is in fact, the gravitational force acting on the book by the Earth, is the gravitational force acting on the Earth by the book! • If the book is only 0.5kg of mass, which translate to 5N of weight, then, the force of the book on the Earth is also 5N. • The Earth is as light as the book!

20. Book on Table Example • If the yellow arrow, the weight of the book, is NOT the reaction pair of the red arrow, or the Normal Contact force acting on the book, then… where is the reaction pair of the normal contact force acting on the book? • Discuss with your partner. BOOK Yes! The reaction is the Force of the Book on the Table!

21. Book on Table Example Putting everything into perspective… There is an action-reaction pair between the Book and the Table. These are a pair of Normal Contact Forces. With the book pushing against the table downwards. There is yet another action-reaction pair, between the Earth and the book. These are a pair of Gravitational Forces. With the Earth pulling on the book and vice versa. If we look at the book only, it so happens that the Normal Contact Force caused by the Table on the book, balances the Gravitational Force (or Weight) caused by the Earth on the Book. Can you analyze the forces acting on the table? BOOK

22. Learning Objectives • By the end of the lesson, you should be able to: • Identify forces acting on an object, • Describe the effect of balanced and unbalanced forces on a body • State each of Newton's 1st and 2nd laws of motion. • Show an understanding that mass is the property of a body which resists change in motion. • Recall and solve problems using the relationship F = ma, appreciating that acceleration and force are always in the same direction.

23. Types of Forces • RECALL: What types of forces are there? • Gravitational Force • Magnetic Force • Electrostatic Force • Friction (Demo) • Air/Water Resistance • Normal Contact Force • Tension (Practical) • Nuclear Forces in the nucleus of an atom    m   m  - +

24. Friction Normal External Pulling Force There are two types of Friction: Static Friction - Increases up to a max value given by: Fstatic ≤μsN Dynamic /Kinetic Friction Fdynamic =μdN Frictional forces are only dependent on: The material of the two bodies in contact (μ). The Normal acting on the body of interest (N). Static Friction COMMON MISCONCEPTION! Friction is NEVER dependent on the Surface Area of Contact! Unlike Fluid Resistance, Dynamic Friction is also NEVER dependent on the velocity of the moving object. Weight Velocity = 0ms-1 Normal External Pulling Force Dynamic Friction Weight Acceleration = a ms-2

25. Slope Example What are the forces acting on the box on the slope? There is an action-reaction pair between the Box and the Slope. These are a pair of Normal Contact Forces. Thus, the box experience a NORMAL CONTACT FORCE caused by the slope. There is yet another action-reaction pair, between the Earth and the box. These are a pair of Gravitational Forces. With the Earth pulling on the box and vice versa. The gravitational force of the Earth on the box is known as WEIGHT. STATIC FRICTION also arises as the box experience the component of the weight that is parallel to the slope. If we look at the book only, then there are just three forces acting on the body: WEIGHT, NORMAL and FRICTION. Net/Resultant Force = 0 Friction Normal Weight

26. Tarzan Example What are the forces acting on Tarzan? Tension There is a force caused by the Earth acting on Tarzan known as “Weight”. There is also a force caused by the Tree Branches acting on Tarzan (through the vine) known as “Tension”. Weight

27. Balances and Unbalanced Forces • Who is the ugliest character from the Star Wars? • Perhaps it’ll be JarJarBinks… (or maybe Jabba the Hutt) • If Yoda and Darth Vader were each attempting to use the Force to repel JarJarBinks away from themselves, who will be the more unfortunate soul? Force caused by Yoda on JJB Force caused by Darth Vader on JJB

28. Balances and Unbalanced Forces • Well Yes! Darth Vader will have to bear with all the irritation from JarJarBinks. • This is because of unbalanced forces. The repulsive force that Yoda exerts on JJB is far greater than that of Darth Vader on JJB. • Let’s revise Vector Addition. • As in Vector Addition, the RESULTANT FORCE points to the right. Ending Point Starting Point Force caused by Yoda on JJB Force caused by Darth Vader on JJB RESULTANT FORCE

29. Balances and Unbalanced Forces • If Yoda and Darth Vader are equally strong however, the two forces are said to be BALANCED. • BALANCED FORCES cancel each other out, and the RESULTANT FORCE or NET FORCE is ZERO. Force caused by Yoda on JJB Force caused by Darth Vader on JJB

30. Newton’s 1st Law of Motion • What happens when the Net/Resultant Force is zero (Forces are balanced)? • Newton’s First Law of Motion states that, a body will remain in • its state of rest or uniform motion, unless acted upon by a NET force. • 静者恒静，动者恒动 • Also known as the Law of Inertia.

31. Newton’s 1st Law of Motion • Inertia is the reluctance for an object to change its state of rest or uniform motion. Or put in another way, it is the tendency to stay at rest or in uniform motion. • Mass is a measure of inertia. • Hence the larger the mass, the greater the inertia an object has. • Demonstration of classic cup of water and table cloth. • Moon Hoax

32. Newton’s 2nd Law of Motion • What happens when the Net/Resultant Force is Non-zero? • Newton’s Second Law of Motion states that: The net force acting on a body is directly proportional to its rate of change of momentum. • OR • The net force acting on a body is directly proportional to its acceleration, given that its mass remains constant. The resulting acceleration is in the same direction as the net force applied. • F ∝ ma • F = kma (k being a constant of proportionality) • F = ma (when Force is measured in Newtons) • The Newton is adjusted so that the acceleration produced by 1N of Force on 1 kg of mass is 1 ms-2.

33. Learning Objectives • By the end of the lesson, you should be able to: • Recall and solve problems using the relationship F = ma, appreciating that acceleration and force are always in the same direction. • Apply the relationship between resultant force, mass and acceleration to new situations or to solve related problems

34. Simple Example 1 m = 5.0 kg F = 10.0 N By Newton’s Second Law of Motion,

35. Simple Example 2 m = 5.0 kg F1= 10.0 N By Newton’s Second Law of Motion, F2= 5.0 N

36. Two-bodies System 3M 2M M EXTERNAL FORCE CONTACT FORCE CONTACT FORCE By Newton’s Second Law of Motion, Analyzing the smaller block only,

37. Learning Objectives • By the end of the lesson, you should be able to: • Define linear momentum as the product of mass and velocity. • Define force as rate of change of momentum. • Describe the motion of bodies with constant weight falling with or without air resistance, including reference to terminal velocity.

38. Two-bodies System T T 0.20 kg 0.04 kg W = mg = 0.40 N Tension Action-Reaction Pairs between the two blocks. If we consider the entire system as a single body, then these forces will cancel each other out. Acceleration of the whole system, F = ma 0.40N = (0.24kg) a a = 1.7 ms-2 On the 0.20kg trolley, FR = T = ma T = (0.20kg)(1.7ms-2) T = 3.4 N 0.24 kg 0.04 kg a = 1.7 ms-2 W = mg = 0.40 N

39. The (Famous) Horse and Cart Can you explain to the horse what’s wrong with his argument? Since Action and Reaction are equal in magnitude and opposite in direction, there is no point pulling the cart, as the two forces are balanced and will cancel each other out. Tension of Cart on Horse Tension of Horse on Cart

40. The (Famous) Horse and Cart Indeed, if we consider the whole system, the Tensions of the Cart on the Horse, and the Horse on the Cart will cancel out. But if we consider the Cart alone, the Tension provided by the horse is the only force that can drive it forward. Tension of Cart on Horse Tension of Horse on Cart Driving Force from Horse’s Muscles The forces do NOT cancel out when you consider them as Separate bodies!

41. The Case of the Lift Tension = 40000 N Tension = 5000 N 1000 kg What is the acceleration when: Cable is intact and has a tension of 40000 N? Cable has a tension of 5000 N? Cable suddenly breaks? Weight = 10000 N

42. Revisiting Air Resistance t1 Velocity/ ms-1 t2 > t3 With air resistance however, falling objects will decelerate and reach terminal velocity. Time/s

43. Revisiting Air Resistance Air Resistance increases as velocity of object increases t1 Velocity/ ms-1 t2 > t3 Terminal velocity is the velocity at which an object in free-fall ceases to accelerate because the total resistive forces are balanced by the downward pull of gravity. The force of air resistance increases to a point where it will balance the weight! But Weight remains constant Time/s

44. Momentum By Newton’s Second Law of Motion, Substituting with the definition of uniform acceleration, Thus, Newton’s Second Law may be restated as: The NET force acting on an object is directly proportional to the rate of change of momentum. The resulting acceleration is in the same direction as the force applied. The quantity 𝑚𝑣 is known as (linear) momentum, 𝑝. It is a vector quantity. Momentumis the product of the mass and velocity of a body.

45. End of Dynamics May the Force be with you… Especially for Next Week’s Test…

46. The (Famous) Horse and Cart Some answers from the class: “In Newton's third law, it is stated that: whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. The strong form of the law further postulates that these two forces act along the same line. This law is often simplified into the sentence, "To every action there is an equal and opposite reaction." I believe the horse is wrong because the horse and the cart are considered as one unit as long as there is tension on the reins that hold the horse back. This would mean that Newton's third law would not be applicable to the horse plus cart experiment as there is only one "particle" (A) since the cart cannot and should not be counted as another particle (B). Hence when the horse exerts energy to move forward, it must merely use more energy to overcome the weight of the cart in order to get moving...not too sure though...seems like the law is too vague by stating "interaction between the two bodies" to me. Not too sure if there is a difference if it is on a vertical or horizontal plane when this rule is applied. Basically I understand that the horse's argument is wrong as the cart and itself should not be counted as two particles but one. “ - JooErn

47. The (Famous) Horse and Cart Some answers from the class: “My concept: For the movement of a cetain object, we can only consider the forces acting on the object, and in this case its the cart. assuming that the cart moves on a flat surface and the horse is pulling it, the forces acting on the cart will be the weight, the frictional force, the normal reaction force and the force of the horse pulling the cart. since the cart did not move upwards or downwards,we can say the gravitational force(weight) and the normal reaction force cancels each other out, so we dont have to consider them anymore.Therefore we are left with the frictional force and the force that the horse exerts on the cart. If the force of the horse exerted on the cart is bigger than the frictional force of the cart against the ground, the cart moves foward, otherwise it will remain stationary. basically it has nothing to do with the cart pulling him back. hope i got it right!” - LiBo

48. The (Famous) Horse and Cart Some answers from the class: “In my opinion, i feel that firstly, there are a few forces present in this case. They are the gravitational force from the earth on the cart and the horse, there is frictional force and also of course the reaction force. Since the pulling force is equal to the reaction force, I feel that as long as he uses a force greater than the frictional force of the ground, he should be able to move the cart. And the reaction force does not actually cancel out the initial pulling force, hence his argument is false... Erm, hope i got my concepts right, i am also not very sure... “ – Andrew “The argument is flawed as although the cart will indeed pull him back with a reaction that is equal in magnitude but opposite in direction, the action and reaction force acts on the two objects differently and do not cancel each other out. There is also frictional force between the horse and the ground, and also between the rope which ties the horse and the cart (assuming there is) as such, these forces are able to overcome the force by the cart and thus the horse has now no more excuses for not being able to pull the cart. “ - Benjamin

49. The (Famous) Horse and Cart Some answers from the class: “im not very sure but what i am thinking is that the cart can only exert X amount of force while the horse can increase the amount of force exerted on the cart to be larger and therefore pull the cart along?” – Nicholas Teng “Because right.. The horse will be exerting a forward motion and the tension force in the "connector" between the cart and the horse will be equal to the force of the horse pulling the cart. As the horse exerts more force to move forward, the cart will follow him. hence the horse's argument is flawwed (dk why he can talk..)” – YangXi “the pulling force exerted by the horse will be converted to kinetic energy in the wheels of the cart, overcoming the reaction force exerted by the cart onto the horse to pull it at opposite directions. ??not sure lol” - KaiYuen