Download FORCES AND NEWTON`S LAWS OF MOTION

Chapter 4
FORCES AND
NEWTON’S LAWS OF
MOTION
Sir Isaac Newton
1642 – 1727
Formulated basic
laws of mechanics
Discovered Law of
Universal
Gravitation
Invented form of
calculus
Many observations
dealing with light
and optics
4.1 The Concepts of Force and
Mass
• Force is a push or pull; the cause of an
acceleration, or a change in an object’s velocity.
• Kinds of forces:
• 1. contact forces- arise from the physical contact
between 2 objects.
• Examples:
• Frictional Force, Tensional Force, Normal
Force, Air Resistance Force, Applied Force
Spring Force
• e.g. in basketball, the player launches a shot
and pushed the ball when he shoot.
Kinds of forces
• 2. non contact forces are also called action
at a distance force because they arise
without physical contact between two
objects.
• e.g. when a skydiver is pulled toward the
earth because of the force of gravity.
Gravitational Force, Electrical Force,
Magnetic Force
Classes of Forces
Contact and Field forces
Forces cause changes in velocity
•
•
•
•
Force can cause object to:
A. start moving
B. stop moving
C. change direction
C
A
B
Fundamental Forces
•Gravitational force
– Between objects
•Electromagnetic forces
– Between electric charges
•Nuclear force
– Between subatomic particles
•Weak forces
– Arise in certain radioactive decay processes
•Note: These are all field forces.
Give at least 3 examples of each of
the following
• 1. force causing an object to start moving
• 2. force causing an object to stop moving
• 3. force causing an object to change
direction.
Mass is a property of matter that
determines how difficult it is to
• accelerate or decelerate an object. It is a
scalar quantity.
• There are 3 important laws that deal with
force and mass and they are called
Newton’s Laws of Motion.
Inertia and Mass
• Inertia is the natural tendency of an object
to remain at rest or in motion at a constant
speed along a straight line.
• Mass of an object is a quantitative
measure of inertia.
• The larger the mass, the greater is the
inertia.
• SI unit: kilogram (kg)
4.2 Newton’s First Law of Motion
(Law of Inertia)
• An object continues in a state of rest or in the
state of motion at a constant speed along a
straight line, unless compelled to change that
state by a net force.
• Example: If friction and other opposing forces
are absent, a car could travel forever at 60km/hr
in a straight line, without using any gas after it
has come up to speed.
• When an object moves at a constant speed
along a straight line, its velocity is constant.
More About Mass
•Mass is an inherent property of an object.
•Mass is independent of the object’s
surroundings.
•Mass is independent of the method used to
measure it.
•Mass is a scalar quantity.
– Obeys the rules of ordinary arithmetic
•The SI unit of mass is kg.
Newton’s 1st law indicates that a
state of rest (zero velocity) and
• a state of constant velocity are completely
equivalent, in the sense that neither one
requires the application of a net force to
sustain it.
• Consider a car traveling at a constant
velocity, Newton’s FLM tells us that the
external force on the car must be equal to
zero.
Units of mass, acceleration and
force
System
Mass
Acceleration
Force
SI
kg
m/s2
N= kg.m/s2
Cgs
g
cm/s2
dyne=g.cm/s2
ft/s2
lb=slug.ft/s2
avoirdupois slug
4.3 Newton’s Second Law of
Motion
• Newton’s First Law indicates that if no net force
acts on an object, then the velocity of the object
remains unchanged.
• The 2nd law deals with what happens when a net
force does act on it.
• The 2nd law: The acceleration a, of an object is
directly proportional to the net external force F,
acting on an object and inversely proportional to
the object’s mass, m
• a = ΣF= ma or a = ΣF/m
Units for Mass, Acceleration and
Force
System Mass
Acceleration
Force
SI
Kilogram
(kg)
meter/sec2
(m/s2)
Newton (N)
CGS
Gram (g)
centimeter/sec2 Dyne (dyn)
(cm/s2)
BE
Slug (sI)
foot/sec2 (ft/s2) Pound (lb)
Example 3:
• An airplane has a mass of 3.1 x 104 kg
and take off under the influence of a
constant net force of 3.7 x 104 N. What is
the net force that acts on the plane’s 78 kg
pilot?
• Solution:
• a = ΣF/m
ΣF = ma
More About Newton’s Second
Law
• is the net force
– This is the vector sum of all the forces acting on the
object.
• May also be called the total force, resultant force,
or the unbalanced force.
•Newton’s Second Law can be expressed in terms of
components:
ΣFx = m ax
ΣFy = m ay
ΣFz = m az
•Remember that ma is not a force.
– The sum of the forces is equated to this product of the
mass of the object and its acceleration.
Conceptual Challenge
• 1. A truck loaded with sand accelerates at 0.5
m/s2 on the highway. If the driving force on the
truck remains constant, what happens to the
truck’s acceleration if sand leaks at a constant
rate from a hole in the truck bed?
• 2. Gravity and Rocks. The force of gravity is
twice as great as on a 2 kg rock as it is on a 1 kg
rock. Why doesn’t the 2 kg rock have a greater
free fall acceleration?
Gravitational Force
•The gravitational force, Fg , is the force
that the earth exerts on an object.
•This force is directed toward the center of
the earth.
•From Newton’s Second Law:
•Its magnitude is called the weight of the
object.
Weight = Fg= mg
4.4 The Vector Nature of Newton’s
Second Law of Motion
• Application of Newton’s 2nd law always
involve the net external force which is the
vector sum of all the external forces that
act on an object. Each component of the
net force leads to a corresponding
components of the acceleration.
• ΣFx= max
ΣFy = may
Example 2
• A vector force has a magnitude of 720 N
and a direction of 380 north of east.
Determine the magnitude and direction of
the components of the force that point
along the north-south line and along the
east-west line?
Equilibrium, Example
•A lamp is suspended from a chain of
negligible mass.
•The forces acting on the lamp are:
– the downward force of gravity
– the upward tension in the chain
•Applying equilibrium gives
∑F
y
= 0 → T − Fg = 0 → T = Fg
Section 5.7
4.5 Newton’s Third Law of Motion
• Whenever one body exerts a force on a second
body, the second body exerts an oppositely
directed force of equal magnitude on the first
body.
• This law is often called “action-reaction”.
Example: The Acceleration Produced
by Action Reaction Forces
• Suppose that the mass of the spacecraft is
ms = 11000 kg and that the mass of the
astronaut is ma = 92 kg. Assume that the
astronaut exerts a force of P = + 36 N on
the spacecraft. Find the acceleration of the
spacecraft and the astronaut?
Analysis: According to Newton’s 3rd
law, when the astronauts applies
• The force P = + 36 N to the spacecraft, the
spacecraft applies the reaction
• force –P = -36N to the astronaut.
• Therefore, the spacecraft and the astronaut
accelerate in opposite directions. Although the
action and reaction forces have the same
magnitude, they don’t have the same
acceleration because they don’t have the same
mass. (smaller mass, larger acceleration)
•
There is a clever application of Newton’s third law in
some rental trailer.
• The tow bar connecting the trailer to the rear bumper of
a car contains a mechanism that can automatically
actuate brakes on the trailer wheels.
• When the driver applies the car brakes, the car slows
down. Because of inertia, the trailer continues to roll
forward and begins pushing against the bumper. In
reaction, the bumper pushes back on the tow bar. The
reaction force is used by the mechanism in the tow bar
to “ push the brake pedal” for the trailer.
4.6 Types of Forces: An Overview
• Newton’s law of motion make it clear that
forces play a central role in determining
the motion of an object.
• 3 Fundamental force:
• 1. Gravitational force• 2. Strong nuclear force- stability of the
nucleus in atom (Chapter 31)
• 3. Electroweak force- single force that
manifests itself in 2 ways (Chapter 32)
•Homework: p 125127, # 1 - 14
4.7 The Gravitational Force Newton’s
Law of Universal Gravitation
• Objects fall down because of gravity.
• Every particle in the universe exerts an attractive force on
every other particle. A particle is a piece of matter, small
enough in size to be regarded as a mathematical point.
For 2 particles that have masses m1 and m2 and are
separated by distance r, the force that each exerts on the
other hand is directed along the line joining the particles
and has a magnitude given by
F
=
G
m
1
r
m
2
2
• The symbol G denotes the universal gravitational
constant, whose value is found experimentally to be
• G= 6.673 x 10-11 N.m2/kg2
Example: Gravitational Attraction
• What is the magnitude of the gravitational
force that acts on earth particle assuming
m1 = 12 kg (approximately the mass of a
bicycle), m2 = 25 kg, and r = 1.2 m?
• Solution:
Weight
• The weight of an object arises because of the
gravitational pull of the earth.
• The weight of an object on or above the earth is
the gravitational force that the earth exerts on
the object. The weight always acts downward,
toward the center of the earth. On or above
another astronomical body, the weight is the
gravitational force exerted on an object by that
body.
• SI Unit: newton (N)
The gravitational force that each uniform sphere of matter exerts
On the other is the same as if each sphere were a particle with
Its mass concentrated at its center. The earth (mass ME) and
The moon (mass MM) approximate such uniform spheres.
W =G
•
•
•
•
M Em
r2
W= weight
m = mass of the object
ME= mass of the earth
r = radius
Example: The Hubble Space
Telescope
• The mass of the Hubble Space Telescope is
11600 kg. Determine the weight of the telescope
• (a) when it was resting on the earth
(b) as it is in its orbit 598 km above the earth’s
surface. (Earth’s radius = 6.38 x106m and
Earth’s mass = 5.98 x 1024 kg))
The weight of the Hubble telescope decreases as the telescope gets
further from the earth. The distance from the center of the earth to
The telescope is r.
Class work: Do exercises on page
127
• # 18, 19, 21, 23, 25, 27, 29, 31, 33
Relation Between Mass and
Weight
• Mass is an intrinsic
property of matter and
does not change as an
object is moved from one
location to another while
• Weight is the gravitational
force acting on an object
and can vary, depending
on how far the object is
above the earth’s surface
or whether it is located
near another body such
as the moon.
M Em
W =G 2
r
W = mg
• The weight of an object whose mass is m
depends on the values for the universal
gravitational constant G, the mass ME of the
earth and the distance r. These 3 parameters
together determine the acceleration g due to
gravity (g= 9.8 m/s2).
• The g decreases as the distance r increases
means that the weight likewise decreases. The
mass of the object however, does not depend on
these effects and does not change.
4.8 The Normal Force
• The normal force FN
is one component of
the force that a
surface exerts on an
object with which it is
in contact- namely,
the component that is
perpendicular to the
surface.
• The normal force is the support force
exerted upon an object which is in contact
with another stable object. For example, if
a book is resting upon a surface, then the
surface is exerting an upward force upon
the book in order to support the weight of
the book. On occasion, a normal force is
exerted horizontally between two objects
which are in contact with each other.
The magnitude of these 2 forces are
equal accdg. to Newton’s 3rd law
• If other forces in
addition to weight W
and normal force Fn
act in the vertical
direction, the
magnitudes of the
normal force and the
weight are no longer
equal.
Example: Balancing Act
• In a circus balancing act, a woman performs a
headstand on top of the man’s head. The
woman weights 490N, and the man’s head and
neck weigh 50N. It is primarily the seventh
cervical vertebra in the spine that supports all
the weight above the shoulders. What is the
normal force that this vertebra exerts on the
neck and head of the man (a) before the act
• (b) during the act?
Fn
Solution:
x
50N
• A) The only forces acting are the FN and
50N weight. These 2 forces must be
balance for the man’s neck and shoulder
to remain at rest. Therefore, the 7th
cervical vertebra exerts a normal force of
FN = 50 N (BEFORE THE ACT)
• B)W of the 7th vertebrae + weight of the
woman (DURING THE ACT)
• Fn = 50 N + 490N = 540 N
Summary:
• 1. The normal force does not necessarily
have the same magnitude as the weight of
the object.
• 2. The value of the normal force depends
on what other forces are present.
• 3. It also depends on whether the objects
in contact are accelerating.
In situation that involves accelerating
objects, the magnitude of the normal force
can be regarded as apparent weight.
• Apparent weight is the force that the object
exerts on the scale with which it is in
contact.
• The discrepancies between true weight
and apparent weight can be understood by
Newton 2nd law. Applying Newton's 2nd law
in the vertical direction gives
• ΣFy = +Fn – mg = ma
When the elevator is not accelerating the true weight registers.
The apparent weight is zero if the elevator falls freely.
Solving for a normal force then will
give us
• Fn = mg + ma
•
•
(Fn is the apparent
weight and mg is the
true weight)
• A free body diagram
showing the forces acting
on the person riding in the
elevator.
4.9 Static and Kinetic Frictional
Forces
• A surface exerts a force on an object with
which it is in contact. The component of
the force perpendicular to the surface is
called the normal force.
• The component parallel to the surface is
called friction.
Static Frictional Force:
• The magnitude fs of the static frictional
force can have any value from zero up to a
maximum value of fsmax, depending on
the applied force. In other words, fs ≤ fsMAX.
The equality holds only when fs attains its
maximum value, which is fsMAX = µsFN.
• µ = coefficient of static friction
• FN = magnitude of the normal force.
Example1 : A Force Needed to
Start a Sled Moving
• A sled is resting on a horizontal patch of
snow, and the coefficient of static friction is
µ= 0.350. The sled and its rider have a
total mass of 38 kg. What is the magnitude
of the maximum horizontal force that can
be applied to the sled before it just begin
to move?
Kinetic Frictional Force
• The magnitude fk of the kinetic frictional
force is given by fk = µkFn
• µk is the coefficient of kinetic friction
• Example: A 24 kg crate initially at rest on a
horizontal floor requires a 75 N horizontal
force to set it in motion. Find the
coefficient of static friction between the
crate and the floor?
4.10 The Tension Force
• Tension is commonly used to mean the
tendency of a rope to be pulled apart due
to forces that are applied at each end.
• Because of tension, a rope transmits a
force from one end to the other. When a
rope is accelerating, the force is
transmitted only if the rope is mass less.
• Tension is the force which is transmitted
through a string, rope, or wire when it is
pulled tight by forces acting at each end.
The tensional force is directed along the
wire and pulls equally on the objects on
either end of the wire.
The force T applied at one end of a mass less rope is transmitted
undiminished to the other end, even when the rope bends
Around a pulley, provided the pulley is also mass less and
Friction is absent.
4.11 Equilibrium Applications of
Newton’s Law
• An object is in equilibrium when it has a
zero acceleration.
• Questions:
• Can an object be in equilibrium if only one
force acts on it?
Prepare for a Chapter Test
• Do exercises on page 125 – Conceptual
Questions:
• # 1, 4, 6, 7, 8, 17