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Newton’s Laws of Motion
• tiga hukum newton : merupakan dasar dari
hukum mekanik
• mendeskripsikan semua kejadian yang
bergerak dengan kecepatan biasa / normal
Among other accomplishments, Sir Isaac Newton
(1642-1727) invented calculus, developed the laws of
motion, and developed the law of gravitational
attraction.
Newton's First Law of Motion
(The Law of Inertia)
• objects tend to remain either at rest or in uniform straight
line motion (i.e., motion with constant velocity) until acted
upon by an unbalanced force
• inertia: concept introduced by Galileo
– an object’s tendency to resist changes in its motion
– mass of an object: a measure of the amount of inertia the
object has
• an object with a larger mass has more inertia (i.e., more
resistance to a change in its motion)
• an object with a small mass has less inertia
Top view of a person standing in the aisle of a bus.
(A) The bus is at rest, and then starts to move forward. Inertia
causes the person to remain in the original position, appearing
to fall backward.
(B) The bus turns to the right, but inertia causes the person to
retain the original straight line motion until forced in a new
direction by the side of the bus.
Newton's Second Law of Motion
• A net force acting on an object produces an
acceleration (a change in the motion of the object)
F = ma
m = mass of the object
a = acceleration
F = net force acting on the object
– the acceleration is:
• directly proportional to the net force acting on the
object
• inversely proportional to the mass of the object
If the force of tire
friction (F1) and
the force of air
resistance (F2)
have a vector sum
that equals the
applied force (Fa),
the net force is
zero. Therefore,
the acceleration is
zero (i.e., velocity
is constant)
More mass results in less
acceleration when the same
force is applied. With the
same force applied, the
riders and the bike with
twice as much mass will
have half the acceleration
(with all other factors
constant). Note that the
second rider is not pedaling.
More about: F = ma
• the unit of force in the metric system is: Newton (N)
1N = 1 kg m/s2
• the unit of force in the English system is: pound (lb)
1 lb = 1 slug x 1 ft/s2 (slug is the unit of mass in the English
system)
• The Weight of an object:
– the downward pulling force of the Earth on that object (the force of
gravity on the object)
– is equal to the mass of an object (m) times the acceleration due to
gravity (g)
W = mg
A parallel between the mass and the
weight of an object
mass
• Jumlah materi yang terkandung
dalam suatu benda
• a scalar quantity (no direction)
• metric unit: kg
• the same everywhere in the
universe
– ex.: mass of an object on the Moon
is the same as on the Earth
weight
• Gaya gravitasi yang bekerja
pada benda
• a vector ( direction: vertically
down)
• metric unit: N (English unit: lb)
• calculated as: W = mg
(g = gravitational acceleration)
• changes with location (with
change in g)
– on the Moon: gMoon = 1.6 m/s2
– weight of an object on the Moon is
about six times less than on the
Earth
Semakin besar benda maka
semakin besar hambatan dari massa
benda tersebut untuk dipercepat
Buzz Aldrin  “perangkat penunjang hidup kami yang bisa
dibawa dipunggung terlihat sederhana tetapi sulit dibawa dan
licin. Dibumi, gabungan perangkat penunjang dan baju
memiliki berat 190 pound, tetapi dibulan beratnya hanya 30
pound”
Newton's Third Law of Motion
Whenever two objects
interact, the force exerted
by the first object on
second is equal in size and
opposite in direction to the
force exerted by the second
object on the first.
F1 = F2
F2
F1
Examples
Solusi :
Centripetal force
• Gaya yang menarik benda kedalam suatu lintasan
lingkaran yang menghasilkan suatu percepatan
• produces an acceleration: centripetal acceleration
ac = v2/r
m = mass
v = velocity
r = radius of the circle
– Substitute ac into the force equation F = ma to get an equation for
the centripetal force
Fc = mv2/r
A ball is swung on the end of a string in a horizontal circle.
The pulling force of the string on the ball acts as centripetal
force and causes the ball to change direction continuously, or
accelerate into a circular path. Without the unbalanced force
acting on it, the ball would continue in a straight line.
Examples :
Seorang anak mengikat batu bermassa
50 g dengan seutas benang. Kemudian
batu diputar diatas kepalanya pada
radius 79,6 cm dengan kecepatan
tetap dua putaran tiap detik.
Tentukanlah tegangan pada benang
(gravitasi diabaikan)
Solusi
To Be Continue
Next Week
Universal Law of Gravitation
– Every object in the universe is attracted to every other
object in the universe by a force that is directly
proportional to the product of their masses and inversely
proportional to the square of the distances between them.
F = G(m1m2)/d2
G = 6.67 x 10-11 Nm2/kg2 (proportionality constant)
– forces of attraction between everyday objects:
• unnoticeably small
• overshadowed by the large gravitational force of the Earth
F = G (m1m2) / d2
The force of attraction (F) is proportional to the product of the
masses (m1, m2) and inversely proportional to the square of the
distance (d) between the centers of the two masses.
Deriving the Weight of an object from
the Universal Law of Gravitation
• Weight: force of attraction by the Earth on an object:
W = F = G (mEm) / d2
mE = mass of the earth
m = mass of the object
d = distance from the center of the earth to the object
• but the weight of an object is: W = mg
• therefore:
mg = G (mEm) / d2
which gives:
g = G mE / d2
• Therefore: the gravitational acceleration (g) does not depend on the
mass of the object
The force of
gravitational
attraction decreases
inversely with the
square of the distance
from the center of the
earth. Note the
weight of a 70.0 kg
person at various
distances above the
surface of the earth.
Gravitational attraction
acts as a centripetal
force that keeps the
Moon from following
the straight-line path
shown by the dashed
line to position A. It
was pulled to position
B by gravity and thus
"fell" toward Earth the
distance from the
dashed line to B,
resulting in a
somewhat circular
path.
Energy
Work
• the result of the force applied to an object and the
distance the object moves due to the force
• The work done on an object: the magnitude of the
applied force multiplied by the parallel distance
through which the force acts.
Work = force x distance
Work = Fd
– Something must move when work is done.
– The movement must be in the same direction as the
applied force.
Examples of work
Remember: work is done on an
object by a force that moves the
object
Work is done against
gravity when lifting
an object. Work is
measured in joules
or foot-pounds.
The force on the
book moves it
through the vertical
distance from the
second shelf to the
fifth shelf, and the
work done is
Work = Fd.
Motion, Position, and Energy
Energy: the ability to do work
Mechanical energy is of two types:
• potential energy
• kinetic energy
Potential Energy (PE)
• Gravitational potential energy is the
energy that an object has due to its
position in the gravitational field of the
earth
• PE = weight x height
• Since weight is w= mg , PE = mgh
where h = height
Kinetic Energy
– Kinetic energy is the energy that an object has
due to its motion.
kinetic energy = 1/2 (mass) (velocity)2
KE = (1/2) mv2
– Units of Kinetic energy
• In the metric system
unit of KE = kg (m/s)2 = kg m2/s2 =
= (kg m/s2) m =Nm = J
unit of KE = J
• In the English system
unit of KE = ft-lb
The Connection between Work
and Energy
• Work is transfer of energy
• Whenever work is done on an object by an
external force, the energy of the object
changes
• Whenever an object does work its energy
changes
• Every time the change in the energy of the
object is equal to the work done
(A) Work is done on the bowling ball as a force (FB) moves it
through a distance. (B) This gives the ball a kinetic energy
equal to the amount of work done on it. (C) The ball does
work on the pins and has enough remaining energy to crash
into the wall behind the pins.
• Conservation of mechanical energy
– The total amount of mechanical energy of an object
remains constant (in the absence of external forces)
• Law of Conservation of Energy - universal
• Energy is never created or destroyed. Energy can
be converted from one form to another, but the
total energy remains constant.
Example of energy conversion
and conservation
During a free fall an object :
– Loses PE (the height decreases)
– Gains KE (its velocity increases)
PE lost = KE gained
mg(Δh) = (1/2)mv2 ; (initial velocity of the object is
zero)
Δh= distance through which the object falls
Solving for v : v = [2g(Δh)]1/2
This allows you to calculate the velocity of a falling
object using energy conservation principles.
v=0
v=(2g Δh)1/2 = (2 x 9.8 m/s2 x 5m)1/2 = 9.9m/s
v=(2g Δh)1/2 =(2 x 9.8 m/s2 x 10 m)1/2 = 14 m/s
The ball (mass = 1 kg) trades potential energy for kinetic
energy as it falls. Notice that the ball had 98 J of potential
energy when dropped and has a kinetic energy of 98 J just as it
hits the ground (in absence of air resistance)
This pendulum bob loses potential energy (PE) and
gains an equal amount of kinetic energy (KE) as it
falls through as distance h. The process reverses as the
bob moves up the other side of its swing.