P11 Dynamics 1 Forces and Laws of Motion Bundle.notebook October 14, 2013

Transcription

1 Dynamics 1

2 Definition of Dynamics Dynamics is the study of why an object moves. In order to understand why objects move, we must first study forces. Forces A force is defined as a push or a pull. Forces are vector quantities they have magnitude and direction. In the last unit, the sum of all the forces acting on an object was referred to as the resultant force. Net force, f net, is another term used for the vector sum of forces. 2

3 Net Force Net Force overall (total) force 10 N 10 N Net Force is zero 10 N 6 N Net Force is 4 N to the right 3

4 Types of Forces An object can experience many different forces simultaneously. Some of the more common forces are listed below. F g : the force of gravity the downwards pull of the Earth NOTE: Weight is the gravitational force on an object. F a : an applied force a push or pull you exert on an object F f : the force of friction a force that opposes an object's motion F N : the normal force a force that acts perpendicular to the surface on which an object rests NOTE: "normal" means perpendicular F T : tension the force that acts along a rope, wire, string, etc. 4

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6 g n NOTE: 6

7 Free Body Diagrams (Note: Sound is not great...) (3.23 min) 7

8 Free Body Diagrams An apple rests on a desk. A flower pot falls in the absence of air resistance. A turkey is hung from the ceiling of a classroom. 8

9 An alligator free falls from a cliff. A snail pushes a pumpkin across the floor at constant speed. 9

10 P11 Dynamics 1 Forces and Laws of Motion Bundle.notebook 10

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12 Do Not Confuse Mass with Weight! The amount of material in a particular stone is the same whether the stone is located on Earth, on the moon, or in outer space. The mass of the stone is the same in all of these locations. The weight of the stone would be very different on Earth and on the moon, and still different in outer space. The mass of an object does not change depending on where the object is Mass can also be considered to be a measure of the inertial of an object ( the more mass an object has, the more force that is required to change its motion) 12

13 Mass vs Weight Mass Variable: m Unit: kg quantity of matter constant Weight Variable: F g Unit: N the downward pull of the Earth on an object varies depending on location 13

14 (3:13 min) 14

15 We can define mass and weight as follows: Mass is the quantity of matter in an object. More specifically, mass is a measure of the inertia, or laziness, that an object exhibits in response to any effort made to start it, stop it, or otherwise change its state of motion. Weight is the force of gravity on an object. Note Mass and weight are proportional to each other. In the same location, twice the mass weighs twice as much. F g = mg 15

16 It s just as difficult to shake a stone in its weightless state in space as it is in its weighted state on Earth. Why are Astronauts Weightless in Space? Weightless In Space 16

17 Values of g 17

18 Check Your Understanding 1. A person has a weight of 639 N at the North Pole a. What is the person's mass? b.what is the person's mass at the equator? c. What is the person's weight at the equator? d.what is the person's mass on the moon? e. What is the person's weight on the moon? 18

19 Check Your Understanding 1. A person has a weight of 639 N at the North Pole a. What is the person's mass? b.what is the person's mass at the equator? c. What is the person's weight at the equator? d.what is the person's mass on the moon? e. What is the person's weight on the moon? 19

20 Lesson Summary In this lesson you have learned that Forces are vector quantities have both magnitude and direction. Some common forces experienced by an object include: F g : the force of gravity F a : an applied force F f : the force of friction F N : the normal force F T : tension Free body diagrams can be used to identify and analyze the forces in a problem The force of gravity can be found using the equation and that the weight of an object is the force of gravity acting on that object. 20

21 The First Law of Motion Things tend to keep on doing what they re already doing. 21

22 Inertia Inertia is the tendency of an object to resist changes in its state of motion. Examples a) Which of the following animals would be the easiest to move? Justify your answer. b) Which of the following objects would be the most difficult to stop? Justify your answer. A dancing monkey. A snail moving along the sidewalk. A bus travelling along the highway. 22

23 Inertia Historically Aristotle thought that forces provide speed and that rest was a natural state. Galileo proposed that friction caused objects to come to rest and that being at rest was not necessarily and objects natural state. Inertia the natural tendency of an object to remain in its current state of motion (either moving or at rest) 23

24 Most people have experienced inertia while driving in a car that is braking. The force of the road on the locked wheels provides an unbalanced force that changes the car's velocity (it slows down). If you are not wearing a seatbelt, there is no unbalanced force to change your velocity. You will continue continue to move forward with the same speed. Hello dashboard! 24

25 Note The tendency of an object to resist changes in its state of motion varies with mass. The more mass an object has, the greater its inertia and the more force it takes to change its state of motion. Example You can tell how much matter is in a can when you kick it. Kick an empty can and it moves. Kick a can filled with sand and it doesn t move as much. 25

26 Newton s Law of Inertia (The First law of Motion) Part 1 Objects at Rest Objects in a state of rest tend to remain at rest. Only an unbalanced force will change that state. 26

27 Check your Understanding 1. Why does a package on the seat of a bus slide backwards when the bus accelerates quickly form rest? 2. Why does it slide forward when the driver applies the brakes? 27

28 Check your Understanding 3. A marble is fired into a horizontal circular tube that is anchored onto a frictionless tabletop, as shown in the diagram below (as viewed from above). Which of the 3 paths will the ball takes as it exits the tube? 28

29 Part Two Objects in Motion In the absence of forces, a moving object tends to travel in a straight line at the same speed indefinitely. Example The ball rolling down the incline rolls up the opposite incline and reaches its initial height. The ball rolls a greater distance to reach its initial height. If there is no friction, the ball will never stop. 29

30 The force of gravity acting upon the moon provides the force required to keep the moon orbiting around the Earth. If the force of gravity suddenly disappeared, in what kind of path would the moon move? The moon would move in a straight line at constant speed. Note We don t know the reason why objects persist in their motion when no force acts on them, but we know that they do, and we call this property inertia. 30

31 Newton's First Law of Motion Newtons First Law of Motion 31

32 Check Your Understanding 1. A physics book is motionless on the top of a table. If you give it a hard push, it slides across the table and slowly comes to a stop. Use Newton's first law of motion to answer the following questions. a. Why does the book remain motionless before the force is applied? b. Why does the book move when the hand pushes on it? c. Why does the book eventually come to a stop? d. Under what conditions would the book remain in motion at a constant speed? 32

33 Demonstration: Pass the Water Students will participate in a relay race carrying a plastic container of water around a "race track." At which locations around the track will the water spill from the container? In general, the water will spill when: 33

34 Lesson Summary In this lesson you have learned that Inertia is the tendency of an object to maintain its motion and that a net force is required to change to motion of an object. Newton's First Law An object in uniform motion (or at rest) will remain in uniform motion (or at rest) unless acted on by an outside net force. 34

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36 The Second Law of Motion An object accelerates when a net force acts on it. 36

37 Review Recall the definition of acceleration: Force Causes Acceleration When the net force (the sum of gravity and the normal force) acting on a hockey puck is zero, it is at rest. Hit the puck (that is, apply an unbalanced force to it) and the puck experiences a change in motion it accelerates. Kick a football and it neither remains at rest nor moves in a straight line. 37

38 Acceleration depends on the net force. To increase the acceleration of an object, you must increase the net force acting on it. An object s acceleration is directly proportional to the net force acting on it: acceleration α net force (The symbol α stands for is directly proportional to.) 38

39 Mass Resists Acceleration Push on an empty shopping cart. Then push equally hard on a heavily loaded shopping cart. The loaded shopping cart will accelerate much less than the empty cart. Acceleration depends on the mass being pushed. 39

40 The same force applied to twice as much mass results in only half the acceleration. The acceleration is inversely proportional to the mass. α Inversely means that the two values change in opposite directions. As the denominator increases, the whole quantity decreases by the same factor. 40

41 Newton s Law of Force and Acceleration (Newton's Second Law of Motion) The acceleration of an object as produced by a net force is: directly proportional to the magnitude of the net force in the same direction as the net force inversely proportional to the mass of the object α 41

42 The acceleration is equal to the net force divided by the mass. α = If the net force acting on an object doubles, its acceleration is doubled. If the mass is doubled, then acceleration will be halved. If both the net force and the mass are doubled, the acceleration will be unchanged. Newtons Second Law 42

43 Sample Problems An object is accelerating at 2.0 m/s 2 east. 1. If the net force is tripled, what is the object's new acceleration? 2. If the net force is halved, what is the object's new acceleration? 3. If the net force is tripled and the mass is quadrupled, what is the object's new acceleration? 43

44 Sample Problems An object is accelerating at 2.0 m/s 2 east. 1. If the net force is tripled, what is the object's new acceleration? a = Net F m The new acceleration is also tripled. 2. If the net force is halved, what is the object's new acceleration? a = Net F m The new acceleration is also halved. 3. If the net force is tripled and the mass is quadrupled, what is the object's new acceleration? a = Net F m The new acceleration will be 3/4 or 75% of the original acceleration. 44

45 Example A 1300 kg car is moving at a constant speed when the brakes are applied, providing a frictional force of 6500 N. What is the acceleration? 45

46 Check Your Understanding A race car has a mass of 710 kg. It starts from rest and travels 40.0 m in 3.0 s. What net force is applied to it? 46

47 Lesson Summary In this lesson you have learned that Newton's Second Law The net force needed to accelerate an object is a product of the object's mass and acceleration F net = ma or The acceleration of an object as produced by a net force is: directly proportional to the magnitude of the net force in the same direction as the net force inversely proportional to the mass of the object or a = F net m 47

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50 5. The weight of the object is 80 N. F N F f F A F g 50

51 a = Net F m = 30.0 N = 30.0 Kg.m/s kg kg. = 3 m/s 2 The acceleration of the object is 3.0 m/s 2 south v= at a = v t a = Net F m v t = The net force during acceleration is 6.3 Newtons west. 51

52 north a = Net F m north The mass of this object is 1.9 kilograms m = 1.08 x 10 3 kg. t = 12.0 s d = 132 m north Net Force =find a =? 132 m = 0 x 12.0 s +1/2 a (12.0s) 2 a = 1.8 m/s 2 a = Net F m 1.8 m/s 2 = Net F 1.08 x 10 3 kg. Net F = 1.94 N north The net force acting on the car during the acceleration is 1.94 N north. 52

53 5. The weight of the object is 80 N. F N F f F A F g The vertical forces of gravity and the normal force balance one another, resulting in no vertical acceleration. The weight of the object, 80 N is due to the force of gravity, so because F g = ma, 80 N = m x 9.8m/s 2. Therefore m = 80N = 8.2 kg 9.8 m/s 2 The acceleration is horizontal to the right. Using Newton's Second Law (and using the right as the positive) a = Net Force = (50 N 10N) = 4.9 m/s 2 m 8.2 kg The Normal Force is 80 N upward, the Net Force is 40 N to the right, the mass is 8.2 kg, and the acceleration is 4.9 m/s 2 to the right. 53

54 The Third Law of Motion For every force, there is an equal and opposite force. 54

55 A force is always part of a mutual action that involves another force. Examples When you push on the wall, the wall pushes on you. 55

56 A hammer exerts a force on the nail and drives it into a board. Newton reasoned that while the hammer exerts a force on the nail, the nail exerts a force on the hammer. In the interaction, there are a pair of forces, one acting on the nail and the other acting on the hammer. 56

57 Newton s Lawn of Action and Reaction (Newton's Third Law of Motion) Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. 57

58 The third law describes the relationship between two forces in an interaction. One force is called the action force. The other force is called the reaction force. Neither force exists without the other. They are equal in magnitude and opposite in direction. They occur at the same time (simultaneously). Oprahs Life class Note It doesn t matter which force we call action and which we call reaction. 58

59 In every interaction, the forces always occur in pairs. You push against the floor, and the floor simultaneously pushes against you. The tires of a motorcycle interact with the road to produce the motorcycle s motion. The tires push against the road, and the road simultaneously pushes back on the tires. When swimming, you push the water backward, and the water pushes you forward. 59

60 Note The interactions in the previous examples depend on friction. A person trying to walk on ice, where friction is minimal, may not be able to exert an action force against the ice. Without the action force there cannot be a reaction force, and thus there is no resulting forward motion. 60

61 The dog wags the tail and the tail wags the dog. 61

62 Identifying Action and Reaction Pairs of Forces To identify a pair of action reaction forces, first identify the interacting objects A and B. When action is A exerts force on B, the reaction is simply B exerts force on A. 1. Consider the following situations. The action force is stated; determine the reaction force. a) b) c) 2. Identify at least five pairs of action reaction force in the following diagram. Newtons Third Law 62

63 Examples 63

64 Force and Mass When a cannon is fired, there is an interaction between the cannon and the cannonball. The force the cannon exerts on the cannonball is exactly equal and opposite to the force the cannonball exerts on the cannon. You might expect the cannon to kick more than it does. The cannonball moves fast compared to the speed of the cannon. According to Newton s second law, we must also consider the objects' masses. 64

65 The cannonball undergoes more acceleration than the cannon because its mass is much smaller. 65

66 Two Forces We know from our study of vectors that the sum of two equal and opposite forces is zero. Example Two dogs pull on a pillow. One pulls with a force of 2.0 N left and the other pulls with a force of 2.0 N right. The sum of the forces is zero. The pillow will be in a state of static equilibrium. According to the first law of motion, the pillow will not accelerate. Newton's Third Law of Motion (Action-Reaction Law) "Forces come in equal and opposite reaction pairs." "For every action there is an equal and opposite reaction." Examples If I push down on the Earth, the Earth pushes up on me. A football player who makes a tackle experiences the same force that he dishes out. If a hockey stick applies a force to a puck, the puck applies the same amount of force back on the stick. One of the most important conceptual questions of physics is: "If all forces cause reaction forces, then how can anything ever accelerate? In other words, won't F net always equal zero? 66

67 The force pairs referred to in Newton's third law must act on different objects. They can NEVER cancel each other. Reconsider the situation with the hockey stick and puck. The only horizontal force the puck experiences is the force the stick applies. This force is therefore equal to the net force. The puck will accelerate in the direction of the net force. The stick will experience a force from the puck. Why doesn't it accelerate? Summary Action reaction forces are: 1. EQUAL in magnitude 2. OPPOSITE in direction 3. act on DIFFERENT objects Newtons Laws Newtons Three Laws 67

68 Example Suppose you are floating around in space (many km from any planet so that you feel no gravity) outside of your spaceship. You get frustrated and decide to kick your spaceship. Does your foot hurt? 68

69 Check Your Understanding A 60.0 kg boy and a 40.0 kg girl use an elastic rope while engaged in a tug of war on a frictionless icy surface. If the acceleration of the girl towards the boy is 3.0 m/s 2, what is the acceleration of the boy towards the girl? 69

70 Lesson Summary In this lesson you have learned that In every interaction, the forces always occur in pairs. Newton's Third Law For every action force, there is an equal and opposite reaction force. How to identify a pair of interacting forces by first identifying the interacting objects. The force pairs in Newtons's Third Law must interact on different objects they can NEVER cancel each other out. 70

71 Module Summary In this module you have learned that 71

72 1) 2) 3) 72

73 Attachments Why are Astronauts Weightless in Space? Weightless In Space Newtons Laws Newtons First Law of Motion Newtons Three Laws Newtons Second Law Newtons Third Law Oprahs Life class