Bab 4

1
Bab 4 Hukum-hukum gerakan
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
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
Daya

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

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
Daya yang bertindak ke atas objek boleh jadi
tolak atau tarik
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
Oleh kerana daya bersifat vektor, dua daya yang
bertindak secara simultaneously (F1,F2)setara
dengan daya bersih R (dan vice versa)
8
Peleraian daya kepada komponen-komponen
9
Contoh bergambah
Fx dan Fy adalah komponen-konponen leraian daya F
yang selari dan berserenjang dengan satah condong
10
Daya bersih sifar

• Bila daya bersih ialah sifar
• pecutan sifar
• Halaju malar
• Keseimbangan berkalu jika daya bersih ialah sifar
• Jika objek dalam keadaan rehat akan kekal rehat
• Jika objek bergerak, it kekal bergerak pada
  halaju malar

11
Contoh Blok di atas meja yang pegun
Fup
Fbersih 0 ?kekal tak bergerak
Fdown
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

13
Cara sukat daya

• Neraca spring boleh digunakan untuk menentukurkan
  magnitud sesuatu daya
• Unit daya ialah NewtonN kg.m/s2

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

• 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

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
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
• 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

19
daya luar hampir sifar, gerak halaju malar
Ada daya luar
daya luar kurang tapi masih ada
20
Figure 3-4, cummings
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
Quick Quiz 5.1
Answer (d). Choice (a) is true. Newtons 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.
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
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
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

26
1 kg standard beratnya 9.8 N di bumi tapi 1.6 N
aje di bulan
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
• Secara algebra, SF m a

28
Arah pecutan mengikut arah daya bersih
29
Pecutan berkadar dengan daya bersih
30
Untuk daya bersih yang sama, pecutan adalah
berkadar songsang dengan jisim
a1 ?F/m1
a2 ?F/m2
a3 ?F/(m1m2)
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
Hukum Newton dalam sebutan komponen

• Hukum Newton juga terexpres dalam sebutan
  komponennya
• SFx m ax
• SFy m ay
• SFz m az

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
Quick Quiz 5.2
Answer (a). If a single force acts, this force
constitutes the net force and there is an
acceleration according to Newtons second law.
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
Quick Quiz 5.3
Answer (c). Newtons second law relates only the
force and the acceleration. Direction of motion
is part of an objects velocity, and force
determines the direction of acceleration, not
that of velocity.
37
Quick Quiz 5.4
You push an object, initially at rest, across a
frictionless floor with a constant force for a
time interval ?t, 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) 4?t (b) 2?t (c) ?t (d) ?t/2 (e)
?t/4
38
Quick Quiz 5.4
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.
39
Contoh biji carom yang memecut (dalam satah
2-D)
40
Daya graviti

• Daya graviti, Fg, 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 Fg mg
• pecutan yang terhasil akibat tindakan graviti ke
  atas apa-apa objek adalah sama, g

41
Pecutan objek jatuh bebas disebabkan oleh graviti
adalah malar dan universal, g
a g
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
• Berat bukannya sifat hahiki sesuatu objek

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
Jisim graviti vs. jisim inersia, samb

• Manakala, dalam daya tarikan graviti ke atas
  suatu jasad oleh bumi,
• Fg mgg
• Jisim mg ialah ialah pemalar kadar yang
  menentukan berapa kuatnya daya graviti bertindak
  di antara objek dengan Bumi
• Lebih besar mg lebih kuatlah tarikan graviti oleh
  bumi ke atas jasad itu

45
Jisim graviti diukur

• Cummings 3-9, 3-10

46
Jisim inersial diukur

• Fig 3.11 cumming

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
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
Quick Quiz 5.5
Answer (a). The gravitational force acts on the
ball at all points in its trajectory.
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
Quick Quiz 5.6
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!
52
Contoh konsep berapakan berat badan anda dalam
lif?
53
Newtons Third Law

• If two objects interact, the force F12 exerted by
  object 1 on object 2 is equal in magnitude and
  opposite in direction to the force F21 exerted by
  object 2 on object 1
• F12 - F21
• Note on notation FAB is the force exerted by A
  on B

54
Newtons 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
• It doesnt 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

55
Action-Reaction Examples, 1

• The force F12 exerted by object 1 on object 2 is
  equal in magnitude and opposite in direction to
  F21 exerted by object 2 on object 1
• F12 - F21

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
• The action (Fg, 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
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
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
Quick Quiz 5.7
Answer (c). In accordance with Newtons third
law, the fly and bus experience forces that are
equal in magnitude but opposite in direction.
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
Quick Quiz 5.8
Answer (a). Because the fly has such a small
mass, Newtons 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.
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
Quick Quiz 5.9
Answer (c). The reaction force to your weight is
an upward gravitational force on the Earth due to
you.
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
Contoh konsep lu tolak gua dan gua tolau lu
66
Quick Quiz 5.10
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.
67
Applications of Newtons Law

• Assumptions
• Objects can be modeled as particles
• 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 rope
• Interested only in the external forces acting on
  the object
• can neglect reaction forces
• Initially dealing with frictionless surfaces

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
Equilibrium, Example 1a

• A lamp is suspended from a chain of negligible
  mass
• The forces acting on the lamp are
• the force of gravity (Fg)
• the tension in the chain (T)
• Equilibrium gives

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
Equilibrium, Example 2a

• Example 5.4
• Conceptualize the traffic light
• Categorize as an equilibrium problem
• No movement, so acceleration is zero

72
Equilibrium, Example 2b

• Analyze
• Need two free-body diagrams
• Apply equilibrium equation to the light and find
  T3
• Apply equilibrium equations to the knot and find
  T1 and T2

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 Newtons Second Law in component form

74
Newtons Second Law, Example 1a

• Forces acting on the crate
• A tension, the magnitude of force T
• The gravitational force, Fg
• The normal force, n, exerted by the floor

75
Newtons Second Law, Example 1b

• Apply Newtons 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
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 Fg

77
Inclined Planes

• Forces acting on the object
• The normal force, n, acts perpendicular to the
  plane
• The gravitational force, Fg, 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
Contoh5.6Gen2 that runs away
79
Multiple Objects

• When two or more objects are connected or in
  contact, Newtons 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
Multiple Objects, Example 1

• First treat the system as a whole
• Apply Newtons Laws to the individual blocks
• Solve for unknown(s)
• Check P21 P12

81
Multiple Objects, Example 2

• Forces acting on the objects
• Tension (same for both objects, one string)
• Gravitational force
• Each object has the same acceleration since they
  are connected
• Draw the free-body diagrams
• Apply Newtons Laws
• Solve for the unknown(s)

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 Newtons Laws
• Solve for the unknown(s)

83
Problem-Solving Hints Newtons Laws

• Conceptualize the problem draw a diagram
• Categorize the problem
• Equilibrium (SF 0) or Newtons Second Law (SF
  m a)
• Analyze
• Draw free-body diagrams for each object
• Include only forces acting on the object

84
Problem-Solving Hints Newtons Laws, cont

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

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 resistance is called the force of friction

86
Forces of Friction, cont.

• Friction is proportional to the normal force
• ƒs µs n and ƒk µk n
• 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
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
Static Friction

• Static friction acts to keep the object from
  moving
• If F increases, so does ƒs
• If F decreases, so does ƒs
• ƒs ? µs n where the equality holds when the
  surfaces are on the verge of slipping
• Called impending motion

89
Kinetic Friction

• The force of kinetic friction acts when the
  object is in motion
• Although µk can vary with speed, we shall neglect
  any such variations
• ƒk µk n

90
Some Coefficients of Friction
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
Quick Quiz 5.11
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.
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
Quick Quiz 5.12
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.
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
Quick Quiz 5.13
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.
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
Quick Quiz 5.14
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.
99
Friction in Newtons Laws Problems

• Friction is a force, so it simply is included in
  the SF in Newtons Laws
• The rules of friction allow you to determine the
  direction and magnitude of the force of friction

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 q
• For µs, use the angle where the block just slips
• For µk, use the angle where the block slides down
  at a constant speed

101
Friction, Example 2

• Draw the free-body diagram, including the force
  of kinetic friction
• Opposes the motion
• Is parallel to the surfaces in contact
• Continue with the solution as with any Newtons
  Law problem

102
Friction, Example 3

• Friction acts only on the object in contact with
  another surface
• Draw the free-body diagrams
• Apply Newtons Laws as in any other multiple
  object system problem

103
Applikasi Automobile Antilock Braking Systems
(ABS)
104
Ringkasan

• 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)

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