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A tugboat, left, is a small but powerful ship used primarily to tow larger ships in
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harbors or inland waterways. How could such a small boat moves a large object?
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
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 Daya
adalah agen yang menyebabkan
perubahan dalam halaju sesuatu objek

Dalam kata lain, daya adalah agen yang
menyebabkan pecutan kepada sesuatu objek
3
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)
4
Daya yang bertindak ke atas objek
boleh jadi tolak atau tarik
5
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)
6
Oleh kerana daya bersifat vektor,
dua daya yang bertindak secara
simultaneously (F1,F2)
setara dengan daya bersih R
(dan vice versa)
7
Peleraian daya kepada komponenkomponen
8
Contoh bergambah
Fx dan Fy adalah komponen-konponen leraian daya
F yang selari dan berserenjang dengan satah
9
condong
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
10
Contoh: Blok di atas meja yang
pegun
Fup
Fbersih = 0
kekal tak bergerak
Fdown
11
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
12
Cara sukat daya

Neraca spring boleh
digunakan untuk
menentukurkan magnitud
sesuatu daya
 Unit daya ialah Newton
N = kg.m/s2
13
Vektor nature of force manifested
via its exertion on a spring scale
14
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
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memecut) dipanggil rangka inersia

Apa-apa rangka inersia yang bergerak dengan
halaju malar relatif kepada suatu rangka inersia
yang diketahui, mereka juga merupakan rangkarangka 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
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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?
17
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
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Ada daya luar
daya luar
kurang tapi
masih ada
daya luar hampir sifar,
gerak halaju malar
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Figure 3-4, cummings
20
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.
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Quick Quiz 5.1
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.
22
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
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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
24
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
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1 kg standard beratnya 9.8 N di
bumi tapi 1.6 N aje di bulan
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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
27
Arah pecutan mengikut arah daya
bersih
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Pecutan berkadar dengan daya
bersih
29
Untuk daya bersih yang sama,
pecutan adalah berkadar songsang
dengan jisim
a1 = F/m1
a2 = F/m2
a3 = F/(m1+m2)
30
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)
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Hukum Newton dalam sebutan
komponen
 Hukum
Newton juga terexpres dalam
sebutan komponennya:



SFx = m ax
SFy = m ay
SFz = m az
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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.
33
Quick Quiz 5.2
Answer: (a). If a single force acts, this force constitutes the
net force and there is an acceleration according to Newton’s
second law.
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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.
35
Quick Quiz 5.3
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.
36
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
37
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.
38
Contoh: biji “carom” yang memecut
(dalam satah 2-D)
39
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
40
Pecutan objek jatuh bebas
disebabkan oleh graviti adalah
malar dan “universal”, g
a=g
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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
42
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
43
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
44
Jisim graviti diukur
 Cummings
3-9, 3-10
45
Jisim inersial diukur
 Fig
3.11 cumming
46
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
47
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
48
Quick Quiz 5.5
Answer: (a). The gravitational force acts on the ball at all
points in its trajectory.
49
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
50
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!
51
Contoh konsep: berapakan berat
badan anda dalam lif?
52
Newton’s 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
53
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
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
54
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
55
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
56
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
57
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
58
Quick Quiz 5.7
Answer: (c). In accordance with Newton’s third law, the fly
and bus experience forces that are equal in magnitude but
opposite in direction.
59
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
60
Quick Quiz 5.8
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.
61
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
62
Quick Quiz 5.9
Answer: (c). The reaction force to your weight is an upward
gravitational force on the Earth due to you.
63
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
64
Contoh konsep: lu tolak gua dan
gua tolau lu
65
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.
66
Applications of Newton’s 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
67
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
F  0
 F  0 and  F
x
y
0
68
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
F
y
 0  T  Fg  0
T  Fg
69
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
70
Equilibrium, Example 2a

Example 5.4
 Conceptualize the
traffic light
 Categorize as an
equilibrium problem

No movement, so
acceleration is zero
71
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
72
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
73
Newton’s 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
74
Newton’s Second Law, Example
1b

Apply Newton’s Second Law in component form:
 F  T  ma
 Solve for theFunknown(s)
 y  n  Fg  0  n  Fg
x

x
If T is constant, then a is constant and the
kinematic equations can be used to more fully
describe the motion of the crate
75
Note About the Normal Force


The normal force is not
always equal to the
gravitational force of the
object
For example, in this case
F
y

 n  Fg  F  0
n may and
alsonbe
than
 Fless

F
g
Fg
76
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
77
Contoh5.6:Gen2 that runs away
78
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
79
Multiple Objects, Example 1

First treat the system as a
whole:
F
 msystemax
Apply Newton’s Laws to
the individual blocks
Solve for unknown(s)
Check: |P21| = |P12|
x



80
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 Newton’s Laws
Solve for the unknown(s)
81
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)
82
Problem-Solving Hints
Newton’s Laws
 Conceptualize
the problem – draw a
diagram
 Categorize the problem

Equilibrium (SF = 0) or Newton’s Second Law
(SF = m a)
 Analyze


Draw free-body diagrams for each object
Include only forces acting on the object
83
Problem-Solving Hints
Newton’s 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 freebody diagram
Check extreme values
84
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
85
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
86
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
87
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
88
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
89
Some Coefficients of Friction
90
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
91
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.
92
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.
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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.
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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
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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.
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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
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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.
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Friction in Newton’s Laws
Problems
 Friction
is a force, so it simply is included
in the SF in Newton’s Laws
 The rules of friction allow you to determine
the direction and magnitude of the force of
friction
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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
100
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
Newton’s Law
problem
101
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
102
Applikasi: Automobile Antilock
Braking Systems (ABS)
103










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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