Transcript Chapter 5

Chapter 4
The Laws of Motion
1
Force
Force is associated with the change in the stat of
motion of an object.
Force is required to make an object move from
stationay.
What is the relation between the force on an object
and the change in motion of that object?
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4.1 Classes of Forces
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Contact forces
involve physical
contact between two
objects
Field forces act
through empty
space
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No physical contact
is required
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Magnitudes of Forces
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A spring can be
used to calibrate the
magnitude of a force
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Forces are vectors
Forces are vectors, so
you must use the rules
for vector addition to
find the net force
acting on an object
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Fundamental Forces
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All particles in nature are subject to four
fundamental forces
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Strong force
Electromagnetic force
Weak force
Gravitational force
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This list is in order of decreasing strength
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Nature of the four fundamental
forces
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Gravitational forces between objects
with masses
Electromagnetic forces between electric
charges
Strong nuclear forces between
subatomic particles
Weak nuclear forces for certain
radioactive decay processes
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Nuclear Force
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Holds nucleons together
Strongest of all fundamental forces
Very short-ranged
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Less than 10-15 m (1fm)
Negligible for separations greater than this
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31.1 Atoms as
Elementary Particles
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Atoms
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From the Greek for “indivisible”
Were once thought to be the elementary
particles
Atom constituents
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Proton, neutron, and electron
After 1932 (neutrons are found in this year)
these were viewed as elementary for they
are very stable
All matter was made up of these particles
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Discovery of New Particles
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New particles
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Beginning in 1945, many new particles
were discovered in experiments involving
high-energy collisions
Characteristically unstable with short
lifetimes ( from 10-6s to 10-23s)
Over 300 have been cataloged and form a
particle zoo
A pattern was needed to understand all
these new particles
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Elementary Particles – Quarks
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Now, physicists recognize that most particles
are made up of quarks
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Exceptions include photons, electrons and a few
others
The quark model has reduced the array of
particles to a manageable few
Protons and neutrons are not truly
elementary, but are systems of tightly bound
quarks
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Electromagnetic Force
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Responsible for binding atoms and
molecules together to form matter
About 10-2 times the strength of the
nuclear force
A long-range force that decreases in
strength as the inverse square of the
separation between interacting particles
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Weak Force
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To account for the radioactive decay process
such as beta decay in certain nuclei
Its strength is about 10-5 times that of the
strong force
Short-range force
Scientists now believe the weak and
electromagnetic forces are two manifestions
of a single interaction, the electroweak force
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Gravitational Force
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A familiar force that holds the planets,
stars and galaxies together
A long-range force
It is about 10-41 times the strength of the
nuclear force
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Weakest of the four fundamental forces
Its effect on elementary particles is
negligible
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Explanation of Forces
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Forces between particles are often
described in terms of the exchange of
field particles or quanta
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The force is mediated by the field particles
Photons for the electromagnetic force
Gluons for the nuclear force
W+, W- and Z particles for the weak force
Gravitons for the gravitational force
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Forces and
Mediating Particles
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Force and Motions:
Isaac Newton (1642-1727)
Three Newton’s laws of motion
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4.2 Newton’s First Law: The Law
of Inertia
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A moving object can be observed from a
number of reference frame.
Observers in different reference frames may
describe the motion of the object differently.
If an object does not interact with other
objects, it is possible to identify a reference
frame in which the object has zero
acceleration
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Such a reference frame is also called an inertial
frame of reference
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Inertial Frames
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Any reference frame that moves with constant
velocity relative to an inertial frame is itself an
inertial frame
A reference frame that moves with constant
velocity relative to the distant stars is the best
approximation of an inertial frame
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We can consider the Earth to be such an inertial
frame although it has a small centripetal
acceleration associated with its motion
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Newton’s First Law –
Alternative Statement
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In the absence of external forces, when
viewed from an inertial reference frame,
an object at rest remains at rest and an
object in motion continues in motion
with a constant velocity
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Newton’s First Law describes what
happens in the absence of a force
When no force acts on an object, the
acceleration of the object is zero
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4.3 Inertia and Mass
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The tendency of an object to resist any
attempt to change its velocity is called
inertia
Mass is the property of an object that
specifies how much resistance an
object exhibits to change in its velocity
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More About Mass
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An inherent property of an object
Independent of the object’s
surroundings
Independent of the method used to
measure it
Mass is a scalar quantity
The SI unit of mass is kg
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Mass vs. Weight
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Mass and weight are two different
quantities
Weight is equal to the magnitude of the
gravitational force exerted on the object
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The weight of an object will vary with
location
The mass of an object is the same
everywhere
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4.4 Newton’s Second Law
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The acceleration of an object is directly
proportional to the net force acting on it
and inversely proportional to its mass
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Force is the cause of change in motion, as
measured by the acceleration
Algebraically,
F

a
m
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More About Newton’s Second
Law
is the net force
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This is the vector sum of all the forces
acting on the object
Newton’s Second Law can be
expressed in terms of components:
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SFx = m ax
SFy = m ay
SFz = m az
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Units of Force
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Fig 4.4
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4.5 Gravitational Force
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The gravitational force, , is the force
that the earth exerts on an object
This force is directed toward the center
of the earth
Its magnitude is called the weight of the
object
Weight = Fg = mg
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More About Weight
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Because it is dependent on g, the
weight varies with location
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g, and therefore the weight, is less at
higher altitudes
We can compare the masses of two
objects by measuring their weights. At a
given location, the ratio of the weights of
two objects equals the ratio of their
masses.
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Gravitational Mass vs. Inertial
Mass
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In Newton’s first Law, the mass is the inertial
mass and measures the resistance to a
change in the object’s motion
In the gravitational force Fg=mg, the mass is
determined by the gravitational attraction
between the object and the Earth.
The mass of an object obtained in this way is
called the gravitational mass.
Experiments show that gravitational mass
and inertial mass have the same value
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4.6 Newton’s Third Law
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If two objects interact, the force
exerted by object 1 on object 2 is equal
in magnitude and opposite in direction
to the force exerted by object 2 on
object 1
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Note on notation:
by A on B
is the force exerted
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Action-Reaction Examples, 1
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The force
exerted by object 1
on object 2 is equal
in magnitude and
opposite in direction
to
exerted by
object 2 on object 1
Fig 4.5
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Fig 4.5
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Newton’s Third Law,
Alternative Statements
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Forces always occur in pairs
A single isolated force cannot exist
The action force is equal in magnitude to the
reaction force but opposite in direction
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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
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Action-Reaction Examples, 2
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The action force (table on
monitor) is the reaction of
the force that the monitor
exerts on the table
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Normal means perpendicular,
in this case
The action (Earth on
monitor) force is equal in
magnitude and opposite in
direction to the reaction
force (the monitor exerts
on the Earth)
Fig 4.6(a)
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Normal force
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The normal force is a contact force that
is perpendicular to the contact surface.
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Free Body Diagram
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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
The normal force balances
the gravitational force.
Fig 4.6(b)
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Fig 4.7
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4.7 Applications of Newton’s Law
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Objects in equilibrium
If the acceleration of an object is zero,
the object is said to be in equilibrium
Mathematically, the net force acting on
the object is zero
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Fig 4.9
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Problem-Solving Hints
Newton’s Laws
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Conceptualize the problem – draw a
diagram
Categorize the problem
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Equilibrium (SF = 0) or Newton’s Second
Law (SF = m a)
Analyze
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Draw free-body diagrams for each object
Include only forces acting on the object
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Equilibrium, Example 2a
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Example 4.2
Conceptualize the
traffic light
Categorize as an
equilibrium problem
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No movement, so
acceleration is zero
Fig 4.10(a)
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Equilibrium, Example 2b
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Analyze
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Need two free-body
diagrams
Apply equilibrium
equation to the light
and find
Apply equilibrium
equations to the knot
and find and
Fig 4.10(b)(c)
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Objects Experiencing a Net
Force
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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
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Newton’s Second Law,
Example 1a
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Forces acting on the
crate:
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A tension, the
magnitude of force
The gravitational
force,
The normal force, ,
exerted by the floor
Fig 4.8
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Newton’s Second Law,
Example 1b
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Apply Newton’s Second Law in component
form:
Solve for the unknown(s)
If is constant, then a is constant and the
kinematic equations can be used to more fully
describe the motion of the crate
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Inclined Planes
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Forces acting on the object:
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The normal force acts
perpendicular to the plane
The gravitational force 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
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Fig 4.11
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Multiple Objects
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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
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Multiple Objects, Example 1
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Forces acting on the
objects:
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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)
Fig 4.12
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Multiple Objects, Example 2
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First treat the system as
a whole:
Apply Newton’s Laws to
the individual blocks
Solve for unknown(s)
Check: |P21| = |P12|
Fig 4.13
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Fig 4.14
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Exercises of Chapter 4
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7, 14, 17, 25, 29, 31, 33, 46, 49, 51, 56
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Exercise 49
What horizontal force
must be applied to the
cart shown in Figure on
the right so that the blocks
remain stationary relative
to the cart? Assume that
all surfaces, wheels, and
pulley are frictionless.
(Suggestion: Note that the
force exerted by the string
accelerates m1.)
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