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Chapter 4
The Laws of Motion
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4.1 Classes of Forces

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Contact forces 接
觸力
involve physical
contact between
two objects
Field forces 場力
act through empty
space

No physical contact
is required
Fig 4.1
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More About Forces
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A spring can be
used to calibrate the
magnitude of a force
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
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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4.2 Newton’s First Law
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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This is also called the law of inertia慣性定律
It defines a special set of reference frames
called inertial frames慣性座標系,
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We call this an inertial frame of reference
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Isaac Newton (1642-1727)
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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

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
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
Also tells us that 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 that property of an object that
specifies how much resistance an
object exhibits to changes in its velocity
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More About Mass
Mass is
 an inherent property of an object
 independent of the object’s
surroundings
 independent of the method used to
measure it
 a scalar quantity
The SI unit of mass is kg
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Mass vs. Weight 質量 vs 重量

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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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Weight will vary with location
The mass of an object is the same
everywhere
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4.4 Newton’s Second Law
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

 F 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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
F
F
F
x
 max
y
 may
z
 maz
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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

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
Weight is not an inherent property of the
object
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Gravitational Mass vs. Inertial
Mass
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In Newton’s Laws, the mass is the inertial
mass and measures the resistance to a
change in the object’s motion
In the gravitational force, the mass is
determining the gravitational attraction
between the object and the Earth
Experiments show that gravitational mass
and inertial mass have the same value
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4.6 Newton’s Third Law
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

Note on notation:
by A on B
is the force exerted
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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 and 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, 1

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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Action-Reaction Examples, 2
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The normal force (table on
monitor) is the reaction of
the force 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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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
Fig 4.6(b)
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CONCEPTUAL EXAMPLE Third law clarification. Michelangelo’s assistant has
been assigned the task of moving a block of marble using a sled. He says to his boss,
“When I exert a forward force on the sled, the sled exerts an equal and opposite force
backward. So how can I ever start it moving? No matter how hard I pull, the
backward reaction force always equals my forward force, so the net force must be
zero. I’ll never be able to move this load.” Is this a case of a little knowledge being
dangerous? Explain.
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4.7 Applications of Newton’s Law
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Assumptions
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Objects can be modeled as particles
Masses of strings or ropes are negligible
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When a rope attached to an object is pulling it, the
magnitude of that force, , is the tension in the
rope, along the rope away from the object
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Objects in Equilibrium
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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
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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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Problem-Solving Hints
Newton’s Laws, cont
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Analyze, cont.
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Establish coordinate system
Be sure units are consistent
Apply the appropriate equation(s) in component
form
Solve for the unknown(s)
Finalize
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Check your results for consistency with your freebody diagram
Check extreme values
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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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A traffic light weighing 122 N hangs from a
cable tied to two other cables fastened to a
support, as in Figure 4.10a. The upper cables
make angles of 37.0° and 53.0° with the
horizontal. These upper cables are not as
strong as the vertical cable and will break if
the tension in them exceeds 100 N. Does the
traffic light remain in this situation, or will
one of the cables break?
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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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A child on a sled is released on a frictionless hill of angle , as
in Figure 4.11a.
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A Determine the acceleration of the sled after it is released.
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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
x along the incline and y
perpendicular to the incline
Replace the force of gravity
with its components
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From (2) we conclude that the
n = mg cos  .
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B Suppose the sled is released from rest at the top of the hill and
the distance from the front of the sled to the bottom of the hill is d.
How long does it take the front of the sled to reach the bottom, and
what is its speed just as it arrives at that point?
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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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When two objects with unequal masses are hung vertically over
a light, frictionless pulley as in Active Figure 4.12a, the
arrangement is called an Atwood machine. The device is
sometimes used in the laboratory to measure the free-fall
acceleration. Calculate the magnitude of the acceleration of the
two objects and the tension in the string.
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Active Figure
4.12
NEXT
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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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To finalize the problem, let us consider some special cases.
(a) m1 = m2,
(b) m2 >> m1
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Two blocks of masses m1 and m2, with m1 > m2, are placed in contact
with each other on a frictionless, horizontal surface, as in Active
Figure 4.13a. A constant horizontal force F is applied to m1 as shown.
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Active Figure
4.13
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A Find the magnitude of the acceleration of the system of two
blocks.
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First treat the system as a whole:
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B Determine the magnitude of the contact force between
the two blocks.
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Apply Newton’s Laws to the individual blocks
Solve for unknown(s)
Check: |P21| = |P12|
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C Imagine that the force F in Active Figure 4.13 is applied
toward the left on the right-hand block of mass m2. Is the magnitude
of the force P12 the same as it was when the force was applied
toward the right on m1?
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A person weighs a fish on a spring scale attached to the ceiling of
an elevator, as shown in Figure 4.14. Show that if the elevator
accelerates, the spring scale reads an apparent weight different
from the fish’s true weight.
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Solution An observer on the accelerating elevator is not in an inertial
frame. We need to analyze this situation in an inertial frame, so let us
imagine observing it from the stationary ground.
Newton’s second law applied to the fish in the vertical direction
gives us
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For example, if the weight of the fish is 40.0 N and is a upward
with ay = 2.00 m/s2, the scale reading is
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4.8 Forces on Automobiles
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The force that accelerates an
automobile is the friction force from the
ground
The engine applies a force to the
wheels
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The bottom of the tires apply forces
backward on the road surface and the
reaction (road on tires) causes the car to
move forward
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Automobile Performance
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