Section 3.2
Newton’s Laws of Motion
Objectives
• Analyze relationships between forces and motion
• Calculate the effects of forces on objects
• Identify force pairs between objects
New Vocabulary
•
•
•
•
•
•
Newton’s first law of motion
Inertia
Mass
Newton’s second law of motion
Newton’s third law of motion
Force pairs
What do you think of when you think of a law? Whether they concern traffic,
the environment, or the economy, laws set a limit on what can and cannot be
done. There are laws in physics as well. The laws of physics govern the
concepts of energy, matter, heat, and more. There are three major laws that
govern linear motion. These laws, based on force and acceleration, describe
the behavior and detail the limits of standard motion.
Figure 3.1
3.2 - Newton’s Laws of Motion
Law of Inertia
Newton’s first law of motion states that an object will maintain its current state of motion unless it is acted upon by an unbalanced force. This law is often called
the law of inertia. Inertia is a property of matter that describes its tendency to resist a change in motion.
Jump to Net Force
Mass is a measurement of the quantity of matter and is also
related to inertia. A more massive object has more inertia. For
example, a rock has mass and also inertia. If a rock is at rest
on the ground, it does not experience an unbalanced force and
will remain at rest. The downward pull of gravity is balanced
by the upward normal force. If an additional unbalanced
force, like the force from being kicked, were applied to the
rock, the rock would no longer remain at rest. If the rock were
more massive, it would have more inertia, so a more powerful
kick is needed to make the larger rock begin moving with the
same velocity as the less massive rock.
The law of inertia also applies to objects in motion. An object
in motion will continue moving at a constant velocity until it
is acted upon by an unbalanced force. For example, if a
bowling ball rolled across a completely frictionless surface
with no other obstacles in the way, it would continue to roll at
the same velocity forever. More force would be necessary to
abruptly stop the bowling ball than the force required to stop
Figure 3.2-1 The cooler that was attached to the roof of a vehicle continues in motion after the vehicle is
stopped by the force from a wall.
a marble traveling with the same velocity. Another example of
the law of inertia is shown in Figure 3.2-1. The vehicle and the cooler on the roof were traveling at a certain velocity, until the vehicle experienced the unbalanced
force from the wall. The force from the wall is great enough to drastically change the velocity of the vehicle, causing it to stop. At the moment of impact, the
cooler, which does not experience the force of the wall, continues moving forward with the same velocity that it had when it was attached to the roof.
Jump to Velocity
Chapter 3 - Forces
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Section continues
3.2 - Newton’s Laws of Motion
In everyday life, it often seems as if objects slow
down on their own without a force being applied. If
a book is initially pushed across a table and then
released, it will slow down and stop. However, the
book still obeys Newton’s first law of motion,
because the unbalanced force acting on the book is
the frictional force. The book can move at a constant
velocity while the applied force is equal to the
frictional force opposing its motion, as shown in the
free-body diagram in Figure 3.2-2. Objects traveling
on near frictionless surfaces, such as a hockey puck
on the ice, will slow down at a much slower rate than
objects traveling on higher friction surfaces.
Jump to Free-Body Diagrams
Figure 3.2-2 A book is pushed across a table by an applied force. The net force on the book is zero so the book
moves with a constant velocity.
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Section continues
3.2 - Newton’s Laws of Motion
Force & Acceleration
When a non-zero net force acts on an object it causes the object to accelerate in the direction of the net
force. Newton’s second law of motion states that the acceleration of an object is directly related to the
net force acting on the object and inversely related to the mass of the object. This means that when the
net force on the object is increased, the acceleration of an object will also increase and if the net force on
an object is decreased, the acceleration of the object will also decrease. Also, a net force applied to an
object with a smaller mass will cause it to accelerate more than if the same net force was applied to an
object with a larger mass.
Jump to Acceleration
Jump to Mass
Newton’s second law also takes the form of an equation where the net force acting on an object (Fnet) is
equal to the mass of an object (m) multiplied by its acceleration (a).
net force = (mass)(acceleration)""
"
"
"
Fnet = m a"
Recall that force is measured in newtons, N. Now newtons can be broken down using Newton’s second
law. Since mass is measured in kilograms and acceleration is measured in meters per second squared, a
newton is a kilogram meter per second squared.
N = kg ⋅
Chapter 3 - Forces
m
"
s2
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Section continues
3.2 - Newton’s Laws of Motion
Example problem | A 91 N force causes an object to accelerate at 0.76 m/s2. What is the mass of
the object?
I. Strategy | The problem provides net force and acceleration and asks for the mass of the object.
The mass can be found from the net force and acceleration using the equation for Newton’s
second law.
II. Given and unknown | Fnet = 91 N
"
"
"
"
"
a = 0.76 m /s2
"
"
"
"
"
m = ?
III. Formula | Fnet = m a so m = Fnet
a
IV. Conversions needed? | No. All variables are in standard SI units.
V. Intermediates needed? | No. Since values are given for all of the variables in the equation
except for the one being solved for, no intermediate calculations are needed.
"
"
"
VI. Solve | m = 91 N
= 120 kg
0.76 m /s2
VII. Does the result make sense? | This answer is reasonable because the force is quite large and
the acceleration is relatively small. Also the units involved in the calculation cancel each
other out to yield the correct units for mass.
N
( s2 )
m
Chapter 3 - Forces
= (kg ∙
s2 )
m
( s2 )
m
= kg"
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3.2 - Newton’s Laws of Motion
Example problem | A 250 N net force is applied to a 72 kg object. What is the acceleration of the
object?
I. Strategy | The problem provides net force and mass and asks for the acceleration of the object.
The acceleration can be found from net force and mass by using the equation for Newton’s
second law.
II. Given and unknown | Fnet = 250 N"
"
"
"
"
m = 72 kg
"
"
"
"
a = ?
III. Formula | Fnet = m a so a = "
"
"
Fnet
m
IV. Conversions needed? | No. All variables are in standard SI units.
V. Intermediates needed? | No. Since values are given for all of the variables in the equation
except for the one being solved for, no intermediate calculations are needed.
VI. Solve | a = 250 N
= 3.5 m /s2
72 kg
VII. Does the result make sense? | This answer is reasonable because the units involved in the
calculation cancel each other out to yield the correct units for acceleration.
(kg ∙ s2 )
m
N
= = 2"
kg
kg
s
m
Chapter 3 - Forces
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3.2 - Newton’s Laws of Motion
Example problem | A 5.0 kg object is traveling at a constant velocity of 3.2 m/s. What is the net
force acting on the object?
I. Strategy | The problem provides mass and velocity and asks for the net force. Since the
problem states that the object is traveling at a constant velocity, its acceleration is zero. The net
force can be found from mass and acceleration using the equation for Newton’s second law.
II. Given and unknown | m = 5.0 kg
v = 3.2 m /s
"
"
"
"
"
"
"
"
"
"
a = 0 m /s2
"
"
"
"
"
Fnet = ?
III. Formula | Fnet = m a
IV. Conversions needed? | No. All variables are in standard SI units.
V. Intermediates needed? | No. Since values are given for all of the variables in the equation
except for the one being solved for, no intermediate calculations are needed.
VI. Solve | Fnet = (5.0 kg)(0 m /s2) = 0 N
VII. Does the result make sense? | The answer is reasonable because the object is not accelerating.
Also, the units involved in the calculation combine to yield the correct units for force.
(
m
m
=
kg
∙
= N"
)( s2 )
s2
kg
Chapter 3 - Forces
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Lab - Force & Acceleration
Newton’s second law of motion describes the relationship between the net force applied to an object, the mass of the object, and its acceleration. The following
virtual lab will provide you with the opportunity to vary the force on a ball and the mass of the ball to determine the effects on its acceleration.
By increasing the force or decreasing the mass, you should have been able to increase the acceleration of the ball. Since force and acceleration are directly related
and mass and acceleration are inversely related, this is consistent with Newton’s second law of motion.
Chapter 3 - Forces
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Section continues
3.2 - Newton’s Laws of Motion
Friction & Acceleration
Because friction is a force, the amount of friction acting
on an object has an effect on its acceleration. Video
3.2-1 shows two blocks nearly identical in mass and
shape sliding down an inclined plane. The bottom of
one block is covered with a smooth surface, and the
bottom of the other is covered with a rough surface.
The smooth block slides down the ramp from rest in
about 0.6 s, whereas the rough block slides the same
distance down the ramp from rest in about 1.2 s, so the
smooth block has more acceleration. The difference in
acceleration between the two blocks can be accounted
for by the difference in frictional force acting on them.
The smooth block has more acceleration because there
is less friction between it and the inclined plane than
there is between the rough block and the inclined
plane.
Video 3.2-1 The amount of friction acting on each block affects its acceleration. The block with the greater
acceleration has less friction acting on it, whereas the block with less acceleration has more friction acting on it.
Chapter 3 - Forces
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3.2 - Newton’s Laws of Motion
Force Pairs
Newton’s third law of motion states that for every action there is an equal and opposite reaction. This means that whenever a force is applied by one object to
another, the second object applies the same amount of force onto the first object in the opposite direction.
Jump to Force
The equal and opposite forces between two objects are often called force pairs. An example of a force pair occurs when a person pushes against a wall. The
person applies a force to the wall (Fperson on wall) and the wall applies a force equal in magnitude, but opposite in direction, to the person (Fwall on person).
Fperson on wall = − Fwall on person"
For example, if the person applies a force of 300 N on the wall, the wall will apply force of -300 N on the person, where the negative sign denotes the direction of
the force.
A subtle force pair can be observed when a ball is resting on the ground. The force of gravity by the Earth pulls down on the ball, while the ball exerts an equal
but opposite force upward on the Earth. Although these forces do not seem apparent, the world would be very different without them.
The book on the table in Figure 3.2-2 is not accelerating, which means that according to Newton’s second law of motion, the net force on the book is zero. Since
the net force on the book is zero, the normal force (FN) is equal to the force of gravity (Fg) but in the opposite direction. It might be tempting to think that the
normal force on the book and the force of gravity on the book make up a force pair described by Newton’s third law, but this is not the case. There are two force
pairs in this situation. One is the force of gravity by the Earth on the book and the force of gravity by the book on the Earth. The other force pair is the force by the
table on the book and the force by the book on the table. Force pairs are always symmetrical and of the same type, such as gravitational, normal, or applied, to
name a few. Notice that the force by the book on the Earth and the force by the book on the table are not shown on the free-body diagram. This is because a freebody diagram only shows forces acting on the object of interest and not forces by the object of interest.
Jump to Figure 3.2-2
The applied force on the book (FA) and the frictional force (FF) on the book are not considered a force pair as described by Newton’s third law, either. The force
applied to the book creates a force pair with the force applied by the book. Similarly, the frictional force from the surface applied to the book creates a force pair
with the force applied to the surface by the book.
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3.2 - Newton’s Laws of Motion
There are three different force pairs in the example in Figure
3.2-3. One force pair is the downward force of the string on the
ceiling and the upward force of the ceiling on the string. The
second force pair is the upward tension force of the string on the
mass and the downward tension force of the mass on the string.
The third force pair is the downward pull of the gravity by the
Earth on the mass and the upward pull of the gravity by the
mass on the Earth. The force of gravity on the mass and the
tension force on the mass do not make a force pair.
Figure 3.2-3 There are three different force pairs present in this diagram of a
mass suspended from the ceiling by a string.
Chapter 3 - Forces
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Section complete