1. 1 A tugboat, left, is a small but powerful ship used primarily to tow larger ships in harbors or inland waterways. How could such a small boat moves a large object?

2. 2 Major Concepts  Konsep daya  Newton's First Law of Motion  Jisim (intersia, graviti)  Newton's Second Law of Motion  Newton's Third Law of Motion  Applikasi Hukum Newton  Daya normal  Daya geseran

3. 3  Daya adalah agen yang menyebabkan perubahan dalam halaju sesuatu objek Dalam kata lain, daya adalah agen yang menyebabkan pecutan kepada sesuatu objek Dalam kata lain, daya adalah agen yang menyebabkan pecutan kepada sesuatu objek

4. 4 Contoh-contoh daya yang bertindak. Objek dalam kota adalah objek yang ditindak oleh daya. Daya yang bertindak itu pula berasal daripada agent luar daripada kotak itu (persekitaran)

5. 5 Daya yang bertindak ke atas objek boleh jadi tolak atau tarik

6. 6 Daya bersih  Daya bersih ialah hasiltambah vektor kesemua daya yang bertindak pada sesuatu objek  Ia juga dikenali daya jumlah (total force), daya hasil (resultant force) atau daya tak terseimbangkan (unbalanced force)

7. 7 Oleh kerana daya bersifat vektor, dua daya yang bertindak secara simultaneously (F 1,F 2 ) setara dengan daya bersih R (dan vice versa)

8. 8 Peleraian daya kepada komponen- komponen

9. 9 Contoh bergambah F x dan F y adalah komponen-konponen leraian daya F yang selari dan berserenjang dengan satah condong

10. 10 Daya bersih sifar  Bila daya bersih ialah sifar: pecutan sifar pecutan sifar Halaju malar Halaju malar Keseimbangan berkalu jika daya bersih ialah sifar Keseimbangan berkalu jika daya bersih ialah sifar Jika objek dalam keadaan rehat akan kekal rehat Jika objek dalam keadaan rehat akan kekal rehat Jika objek bergerak, it kekal bergerak pada halaju malar Jika objek bergerak, it kekal bergerak pada halaju malar

11. 11 Contoh: Blok di atas meja yang pegun F up F down F bersih = 0  kekal tak bergerak

12. 12 Kelas daya  Daya kontak (misalnya, tendangan bola) melibatkan kontak secara fizikal anta dua objek untuk interaksi berlaku  Daya medan bertindak melalui ruang (misalnya: daya graviti) tak payah ada kontak fizikal tak payah ada kontak fizikal

13. 13 Cara sukat daya  Neraca spring boleh digunakan untuk menentukurkan magnitud sesuatu daya   Unit daya ialah Newton N = kg.m/s 2

14. 14 Vektor nature of force manifested via its exertion on a spring scale

15. 15 Rangka inersia  Apa-apa objek atau proses fizikal boleh diperhatikan daripada mana-mana rangka rujukan yang dipilih  Misalnya, dari kamar kamu ke, dari atas motosikal (laju malar) ke, atau dari kapalterbang yang sedang takeoff  Misalnya, memerhatikan seorang gadis cantik yang sedang tidur nyenyak dari rangka-rangka rujukan yang berlainan  rangka-rangka seperti kamar, motosikal laju malar adalah rangka yang berbeza berbanding dengan kapalterbang yang sedang take off  Dalam rangka rujukan kapalterbang, gadis tidur itu tidak kelihatan halaju malar tapi memecut relatif kepada rangka rujukan  Dalam rangka rujukan kamar, motosikal laju malar, gadis tidur itu kelihatan berhalaju malar relatif kepada rangka rujukan  Jadi, ada bezanya di antara rangka yang memecut berbanding dengan rangka yang tidak memecut  Rangka yang tidak memecut (relatif kepada rangka yang memecut) dipanggil rangka inersia

16. 16  Apa-apa rangka inersia yang bergerak dengan halaju malar relatif kepada suatu rangka inersia yang diketahui, mereka juga merupakan rangka- rangka inersia.  Secara praktiknya tiada rangka rujukan inersia yang mutlak  Rangka rujukan yang bergerak dengan halaju malar relatif kepada bintang jauh adalah penghampiran rangka inersia terbaik Bumi dianggap suatu rangka inersia yang baik walaupun terdapat suatu pecutan memusat hasil daripada gerakan kisaran di sekitar paksinya Bumi dianggap suatu rangka inersia yang baik walaupun terdapat suatu pecutan memusat hasil daripada gerakan kisaran di sekitar paksinya

17. 17 Quick quiz  (a) Fikirkan suatu rangka bukan inertial yang you pernah ‘berehat’ di dalam  (b) Apakah pemerhatian dalam rangka tersebut yang membawa anda kepada kesimpulan bahawa rangka itu bukan inersial?

18. 18 Hukum Newton pertama  Dalam ketidakhadiran daya luar, jika diperhatikan dari suatu rangka inersia, sesuatu objek dalam keadaan rehat tetap akan berehat dan objek dalam gerakan tetap akan bergerak pada halaju malar Hukum pertama memerihalkan apa yang berlaku dalam ketidakhadiran daya bersih Hukum pertama memerihalkan apa yang berlaku dalam ketidakhadiran daya bersih Ia juga mengatakan bahawa jika tiada daya bersih bertidak pada suatu objek pecutannya mestilah sifar Ia juga mengatakan bahawa jika tiada daya bersih bertidak pada suatu objek pecutannya mestilah sifar Nota: hukum ini hanya beraplikasi dalam rangka inersia saje, tidak dalam rangka bukan inersia Nota: hukum ini hanya beraplikasi dalam rangka inersia saje, tidak dalam rangka bukan inersia

19. 19 Ada daya luar daya luar hampir sifar, gerak halaju malar daya luar kurang tapi masih ada

20. 20 Figure 3-4, cummings

21. 21 Quick Quiz 5.1 Which of the following statements is most correct? (a) It is possible for an object to have motion in the absence of forces on the object. (b) It is possible to have forces on an object in the absence of motion of the object. (c) Neither (a) nor (b) is correct. (d) Both (a) and (b) are correct.

22. 22 Answer: (d). Choice (a) is true. Newton’s first law tells us that motion requires no force: an object in motion continues to move at constant velocity in the absence of external forces. Choice (b) is also true. A stationary object can have several forces acting on it, but if the vector sum of all these external forces is zero, there is no net force and the object remains stationary. Quick Quiz 5.1

23. 23 Jisim dan inersia  Kecenderungan suatu objek untuk menentang usaha mengubah halajunya dikenali inersia  Jisim ialah sifat sesuatu jasad/objek yang menentukan berapa banyak penentangan objek itu terhadap perubahan dalam halajunya  Lebih jisim lebih enggan ia berubah halajunya terhadap daya luar

24. 24 Nota tambahan tentang jisim  Jisim ialah sifat hakiki sesuatu jasad  Jisim suatu jasad tidak bergantung persekitaran yang ia berada  Jisim tidak bergantung kepada cara ia disukat  Jisim suatu kuantiti skalar  Unit SI jisim ialah kg

25. 25 Jisim vs. berat  Jisim dan berat adalah dua jenis kuantiti yang berlainan  Berat adalah bersamaan dengan magnitud daya graviti bertindak ke atas sesuatu objek Berat berubah-ubah mengikut lokasi, tapi jisim tidak Berat berubah-ubah mengikut lokasi, tapi jisim tidak

26. 26 1 kg standard beratnya 9.8 N di bumi tapi 1.6 N aje di bulan

27. 27 Hukum Newton kedua  Jika diperhatikan/dicerap daripada suatu rangka inersia, pecutan suatu objek adalah berkadar terus dengan daya bersih yang bertindak padanya, dan berkadar songsang dengan jisimnya Daya ialah sebab perubahan dalam pergerakan, yang diukur oleh pecutannya Daya ialah sebab perubahan dalam pergerakan, yang diukur oleh pecutannya  Secara algebra,  F = m a

28. 28 Arah pecutan mengikut arah daya bersih

29. 29 Pecutan berkadar dengan daya bersih

30. 30 Untuk daya bersih yang sama, pecutan adalah berkadar songsang dengan jisim a 1 =  F/m 1 a 2 =  F/m 2 a 3 =  F/(m 1 +m 2 )

31. 31 Superbike dengan Newton II  rekaan superbike mengaplikasikan hukum newton kedua: utk memaksimumkan pecutan ke depan motosikal dicipata seringan yang mingkin (supaya m kecil) dan menggunakan engin seberkuasa yang mungkin (supaya daya memecut ke depan lebih besar)

32. 32 Hukum Newton dalam sebutan komponen  Hukum Newton juga terexpres dalam sebutan komponennya:  F x = m a x  F x = m a x  F y = m a y  F y = m a y  F z = m a z  F z = m a z

33. 33 Quick Quiz 5.2 An object experiences no acceleration. Which of the following cannot be true for the object? (a) A single force acts on the object. (b) No forces act on the object. (c) Forces act on the object, but the forces cancel.

34. 34 Answer: (a). If a single force acts, this force constitutes the net force and there is an acceleration according to Newton’s second law. Quick Quiz 5.2

35. 35 Quick Quiz 5.3 An object experiences a net force and exhibits an acceleration in response. Which of the following statements is always true? (a) The object moves in the direction of the force. (b) The acceleration is in the same direction as the velocity. (c) The acceleration is in the same direction as the force. (d) The velocity of the object increases.

36. 36 Answer: (c). Newton’s second law relates only the force and the acceleration. Direction of motion is part of an object’s velocity, and force determines the direction of acceleration, not that of velocity. Quick Quiz 5.3

37. 37 Quick Quiz 5.4 You push an object, initially at rest, across a frictionless floor with a constant force for a time interval Δt, resulting in a final speed of v for the object. You repeat the experiment, but with a force that is twice as large. What time interval is now required to reach the same final speed v? (a) 4Δt (b) 2Δt (c) Δt (d) Δt/2 (e) Δt/4

38. 38 Answer: (d). With twice the force, the object will experience twice the acceleration. Because the force is constant, the acceleration is constant, and the speed of the object (starting from rest) is given by v = at. With twice the acceleration, the object will arrive at speed v at half the time. Quick Quiz 5.4

39. 39 Contoh: biji “ carom ” yang memecut (dalam satah 2-D)

40. 40 Daya graviti  Daya graviti, F g, adalah daya yang dikenakan ke atas suatu objek oleh bumi  Daya itu berarah ke bawah dan menuju ke pusat bumi  Magnitudnya dikenali sebagai berat objek itu  Berat = |F g |= mg  pecutan yang terhasil akibat tindakan graviti ke atas apa-apa objek adalah sama, g

41. 41 Pecutan objek jatuh bebas disebabkan oleh graviti adalah malar dan “universal”, g a = g

42. 42 Nota tambahan berkenaan berat  Disebabkan kesandarannya pada g, berat berubah dengan lokasi g, dan seterusnya berat, menjadi makin kurang pada altitud yang lebih tinggi g, dan seterusnya berat, menjadi makin kurang pada altitud yang lebih tinggi  Berat bukannya sifat hahiki sesuatu objek

43. 43 Jisim graviti vs. jisim inersia  Jisim memainkan dua peranan yang berasing dalam mekanik  Jisim dalam hukum Newton ialah jisim inersia yang mengukur rintangan  Jisim inersia ditakrifkan sebagai pemalar kadar (constant of proportionality) antara pecutan dengan daya yang menyebabkannya.  Inilah apa yang dimaksudkan oleh m dalam F = ma

44. 44 Jisim graviti vs. jisim inersia, samb  Manakala, dalam daya tarikan graviti ke atas suatu jasad oleh bumi, F g = m g g  Jisim m g ialah ialah “ pemalar kadar ” yang menentukan berapa kuatnya daya graviti bertindak di antara objek dengan Bumi  Lebih besar m g lebih kuatlah tarikan graviti oleh bumi ke atas jasad itu

45. 45 Jisim graviti diukur  Cummings 3-9, 3-10

46. 46 Jisim inersial diukur  Fig 3.11 cumming

47. 47 Kesetaraan antara jisim inersia dan jisim graviti  Eksperimen yang paling jitu telah menentukan, setakat yang dibenarkan oleh teknologi hari ini, bahawa jisim graviti bagi suatu objek adalah sama nilai dengan jisim inersia objek itu  Penting kerana inilah titik tolak Einstein mengemukakan teori kerelatifan amnya

48. 48 Quick Quiz 5.5 A baseball of mass m is thrown upward with some initial speed. A gravitational force is exerted on the ball (a) at all points in its motion (b) at all points in its motion except at the highest point (c) at no points in its motion

49. 49 Answer: (a). The gravitational force acts on the ball at all points in its trajectory. Quick Quiz 5.5

50. 50 Quick Quiz 5.6 Suppose you are talking by interplanetary telephone to your friend, who lives on the Moon. He tells you that he has just won a newton of gold in a contest. Excitedly, you tell him that you entered the Earth version of the same contest and also won a newton of gold! Who is richer? (a) You (b) Your friend (c) You are equally rich

51. 51 Answer: (b). Because the value of g is smaller on the Moon than on the Earth, more mass of gold would be required to represent 1 newton of weight on the Moon. Thus, your friend on the Moon is richer, by about a factor of 6! Quick Quiz 5.6

52. 52 Contoh konsep: berapakan berat badan anda dalam lif?

53. 53 Newton ’ s Third Law  If two objects interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F 21 exerted by object 2 on object 1  F 12 = - F 21 Note on notation: F AB is the force exerted by A on B Note on notation: F AB is the force exerted by A on B

54. 54 Newton ’ s Third Law, Alternative Statements  Forces always occur in pairs  A single isolated force cannot exist  The action force is equal in magnitude to the reaction force and opposite in direction One of the forces is the action force, the other is the reaction force One of the forces is the action force, the other is the reaction force It doesn ’ t matter which is considered the action and which the reaction It doesn ’ t matter which is considered the action and which the reaction The action and reaction forces must act on different objects and be of the same type The action and reaction forces must act on different objects and be of the same type

55. 55 Action-Reaction Examples, 1  The force F 12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to F 21 exerted by object 2 on object 1  F 12 = - F 21

56. 56 Action-Reaction Examples, 2  The normal force (table on monitor) is the reaction of the force the monitor exerts on the table Normal means perpendicular, in this case Normal means perpendicular, in this case  The action (F g, Earth on monitor) force is equal in magnitude and opposite in direction to the reaction force, the force the monitor exerts on the Earth

57. 57 Free Body Diagram  In a free body diagram, you want the forces acting on a particular object  The normal force and the force of gravity are the forces that act on the monitor

58. 58 Quick Quiz 5.7 If a fly collides with the windshield of a fast-moving bus, which object experiences an impact force with a larger magnitude? (a) the fly (b) the bus (c) the same force is experienced by both

59. 59 Answer: (c). In accordance with Newton’s third law, the fly and bus experience forces that are equal in magnitude but opposite in direction. Quick Quiz 5.7

60. 60 Quick Quiz 5.8 If a fly collides with the windshield of a fast-moving bus, which object experiences the greater acceleration? (a) the fly (b) the bus (c) the same acceleration is experienced by both

61. 61 Answer: (a). Because the fly has such a small mass, Newton’s second law tells us that it undergoes a very large acceleration. The huge mass of the bus means that it more effectively resists any change in its motion and exhibits a small acceleration. Quick Quiz 5.8

62. 62 Quick Quiz 5.9 Which of the following is the reaction force to the gravitational force acting on your body as you sit in your desk chair? (a) The normal force exerted by the chair (b) The force you exert downward on the seat of the chair (c) Neither of these forces

63. 63 Answer: (c). The reaction force to your weight is an upward gravitational force on the Earth due to you. Quick Quiz 5.9

64. 64 Quick Quiz 5.10 In a free-body diagram for a single object, you draw (a) the forces acting on the object and the forces the object exerts on other objects (b) only the forces acting on the object

65. 65 Contoh konsep: lu tolak gua dan gua tolau lu

66. 66 Answer: (b). Remember the phrase “free-body.” You draw one body (one object), free of all the others that may be interacting, and draw only the forces exerted on that object. Quick Quiz 5.10

67. 67 Applications of Newton ’ s Law  Assumptions Objects can be modeled as particles Objects can be modeled as particles Masses of strings or ropes are negligible Masses of strings or ropes are negligible When a rope attached to an object is pulling it, the magnitude of that force, T, is the tension in the ropeWhen a rope attached to an object is pulling it, the magnitude of that force, T, is the tension in the rope Interested only in the external forces acting on the object Interested only in the external forces acting on the object can neglect reaction forcescan neglect reaction forces Initially dealing with frictionless surfaces Initially dealing with frictionless surfaces

68. 68 Objects in Equilibrium  If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium  Mathematically, the net force acting on the object is zero

69. 69 Equilibrium, Example 1a  A lamp is suspended from a chain of negligible mass  The forces acting on the lamp are the force of gravity (F g ) the force of gravity (F g ) the tension in the chain (T) the tension in the chain (T)  Equilibrium gives

70. 70 Equilibrium, Example 1b  The forces acting on the chain are T ’ and T ”  T ” is the force exerted by the ceiling  T ’ is the force exerted by the lamp  T ’ is the reaction force to T  Only T is in the free body diagram of the lamp, since T ’ and T ” do not act on the lamp

71. 71 Equilibrium, Example 2a  Example 5.4  Conceptualize the traffic light  Categorize as an equilibrium problem No movement, so acceleration is zero No movement, so acceleration is zero

72. 72 Equilibrium, Example 2b  Analyze Need two free-body diagrams Need two free-body diagrams Apply equilibrium equation to the light and find T 3 Apply equilibrium equation to the light and find T 3 Apply equilibrium equations to the knot and find T 1 and T 2 Apply equilibrium equations to the knot and find T 1 and T 2

73. 73 Objects Experiencing a Net Force  If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it.  Draw a free-body diagram  Apply Newton ’ s Second Law in component form

74. 74 Newton ’ s Second Law, Example 1a  Forces acting on the crate: A tension, the magnitude of force T A tension, the magnitude of force T The gravitational force, F g The gravitational force, F g The normal force, n, exerted by the floor The normal force, n, exerted by the floor

75. 75 Newton ’ s Second Law, Example 1b  Apply Newton ’ s Second Law in component form:  Solve for the unknown(s)  If T is constant, then a is constant and the kinematic equations can be used to more fully describe the motion of the crate

76. 76 Note About the Normal Force  The normal force is not always equal to the gravitational force of the object  For example, in this case  n may also be less than F g

77. 77 Inclined Planes  Forces acting on the object: The normal force, n, acts perpendicular to the plane The normal force, n, acts perpendicular to the plane The gravitational force, F g, acts straight down The gravitational force, F g, acts straight down  Choose the coordinate system with x along the incline and y perpendicular to the incline  Replace the force of gravity with its components

78. 78 Contoh5.6:Gen2 that runs away

79. 79 Multiple Objects  When two or more objects are connected or in contact, Newton ’ s laws may be applied to the system as a whole and/or to each individual object  Whichever you use to solve the problem, the other approach can be used as a check

80. 80 Multiple Objects, Example 1  First treat the system as a whole:  Apply Newton ’ s Laws to the individual blocks  Solve for unknown(s)  Check: |P 21 | = |P 12 |

81. 81 Multiple Objects, Example 2  Forces acting on the objects: Tension (same for both objects, one string) Tension (same for both objects, one string) Gravitational force Gravitational force  Each object has the same acceleration since they are connected  Draw the free-body diagrams  Apply Newton ’ s Laws  Solve for the unknown(s)

82. 82 Multiple Objects, Example 3  Draw the free-body diagram for each object One cord, so tension is the same for both objects Connected, so acceleration is the same for both objects  Apply Newton ’ s Laws  Solve for the unknown(s)

83. 83 Problem-Solving Hints Newton ’ s Laws  Conceptualize the problem – draw a diagram  Categorize the problem Equilibrium (  F = 0) or Newton ’ s Second Law (  F = m a) Equilibrium (  F = 0) or Newton ’ s Second Law (  F = m a)  Analyze Draw free-body diagrams for each object Draw free-body diagrams for each object Include only forces acting on the object Include only forces acting on the object

84. 84 Problem-Solving Hints Newton ’ s Laws, cont  Analyze, cont. Establish coordinate system Establish coordinate system Be sure units are consistent Be sure units are consistent Apply the appropriate equation(s) in component form Apply the appropriate equation(s) in component form Solve for the unknown(s) Solve for the unknown(s)  Finalize Check your results for consistency with your free- body diagram Check your results for consistency with your free- body diagram Check extreme values Check extreme values

85. 85 Forces of Friction  When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions between the object and its environment This is due to the interactions between the object and its environment  This resistance is called the force of friction

86. 86 Forces of Friction, cont.  Friction is proportional to the normal force ƒ s  µ s n and ƒ k = µ k n ƒ s  µ s n and ƒ k = µ k n These equations relate the magnitudes of the forces, they are not vector equations These equations relate the magnitudes of the forces, they are not vector equations  The force of static friction is generally greater than the force of kinetic friction  The coefficient of friction ( µ ) depends on the surfaces in contact

87. 87 Forces of Friction, final  The direction of the frictional force is opposite the direction of motion and parallel to the surfaces in contact  The coefficients of friction are nearly independent of the area of contact

88. 88 Static Friction  Static friction acts to keep the object from moving  If F increases, so does ƒ s  If F decreases, so does ƒ s  ƒ s  µ s n where the equality holds when the surfaces are on the verge of slipping Called impending motion Called impending motion

89. 89 Kinetic Friction  The force of kinetic friction acts when the object is in motion  Although µ k can vary with speed, we shall neglect any such variations  ƒ k = µ k n

90. 90 Some Coefficients of Friction

91. 91 Quick Quiz 5.11 You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall

92. 92 Answer: (b). The friction force acts opposite to the gravitational force on the book to keep the book in equilibrium. Because the gravitational force is downward, the friction force must be upward. Quick Quiz 5.11

93. 93 Quick Quiz 5.12 A crate is located in the center of a flatbed truck. The truck accelerates to the east, and the crate moves with it, not sliding at all. What is the direction of the friction force exerted by the truck on the crate? (a) to the west (b) to the east (c) No friction force exists because the crate is not sliding.

94. 94 Answer: (b). The crate accelerates to the east. Because the only horizontal force acting on it is the force of static friction between its bottom surface and the truck bed, that force must also be directed to the east. Quick Quiz 5.12

95. 95 Quick Quiz 5.13 You place your physics book on a wooden board. You raise one end of the board so that the angle of the incline increases. Eventually, the book starts sliding on the board. If you maintain the angle of the board at this value, the book (a) moves at constant speed (b) speeds up (c) slows down (d) none of these

96. 96 Answer: (b). At the angle at which the book breaks free, the component of the gravitational force parallel to the board is approximately equal to the maximum static friction force. Because the kinetic coefficient of friction is smaller than the static coefficient, at this angle, the component of the gravitational force parallel to the board is larger than the kinetic friction force. Thus, there is a net downhill force parallel to the board and the book speeds up. Quick Quiz 5.13

97. 97 Quick Quiz 5.14 You are playing with your daughter in the snow. She sits on a sled and asks you to slide her across a flat, horizontal field. You have a choice of (1) pushing her from behind, by applying a force downward on her shoulders at 30° below the horizontal (part a below), or (2) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal (part b below). Which would be easier for you and why? (a) #1, because the normal force between the sled and the snow is increased (b) #1, because the friction force between the sled and the snow is decreased (c) #2, because the normal force between the sled and the snow is increased (d) #2, because the friction force between the sled and the snow is decreased

98. 98 Answer: (b). When pulling with the rope, there is a component of your applied force that is upward. This reduces the normal force between the sled and the snow. In turn, this reduces the friction force between the sled and the snow, making it easier to move. If you push from behind, with a force with a downward component, the normal force is larger, the friction force is larger, and the sled is harder to move. Quick Quiz 5.14

99. 99 Friction in Newton ’ s Laws Problems  Friction is a force, so it simply is included in the  F in Newton ’ s Laws  The rules of friction allow you to determine the direction and magnitude of the force of friction

100. 100 Friction Example, 1  The block is sliding down the plane, so friction acts up the plane  This setup can be used to experimentally determine the coefficient of friction  µ = tan  For µ s, use the angle where the block just slips For µ s, use the angle where the block just slips For µ k, use the angle where the block slides down at a constant speed For µ k, use the angle where the block slides down at a constant speed

101. 101 Friction, Example 2  Draw the free-body diagram, including the force of kinetic friction Opposes the motion Opposes the motion Is parallel to the surfaces in contact Is parallel to the surfaces in contact  Continue with the solution as with any Newton ’ s Law problem

102. 102 Friction, Example 3  Friction acts only on the object in contact with another surface  Draw the free-body diagrams  Apply Newton ’ s Laws as in any other multiple object system problem

103. 103 Applikasi: Automobile Antilock Braking Systems (ABS)

104. 104  students should understand each of the following and be able to demonstrate their understanding in problem applications as well as in conceptual situations.  Force  Vector nature of force  Weight  Normal force  Mass  Newton's laws  First law (law of inertia)  Second law (F = ma)  Third law (action-reaction force pairs)

105. 105