Chapter 4
Newton’s Laws:
Explaining Motion
Newton’s Laws of
Motion
The
concepts of
force,
mass, and
weight play
critical
roles.
A Brief History
! Where do our ideas and theories about
motion come from?
! What roles were played by Aristotle,
Galileo, and Newton?
Will the chair continue to move when
the person stops pushing?
!How did
Newton’s theory
come about?
!What does it
tell us about
motion?
!Can we trust
our intuition?
Aristotle’s View
"A force is
needed to keep
an object moving.
"Air rushing
around a thrown
object continues
to push the
object forward.
Galileo’s Contribution
" Galileo challenged Aristotle’s ideas that
had been widely accepted for many
centuries.
" He argued that the natural tendency of
a moving object is to continue moving.
No force is needed to keep an object
moving.
# This goes against what we seem to
experience.
#
Newton’s Contribution
" Newton built on Galileo’s
work, expanding it.
" He developed a
comprehensive theory of
motion that replaced
Aristotle’s ideas.
" Newton’s theory is still
widely used to explain
ordinary motions.
Newton’s First and
Second Laws
! How do forces affect the motion of an
object?
! What exactly do we mean by force? Is
there a difference between, say, force,
energy, momentum, impulse?
! What do Newton’s first and second laws
of motion tell us, and how are they
related to one another?
Newton’s First Law of Motion
An object
remains at rest,
or in uniform
motion in a
straight line,
unless it is
compelled to
change by an
externally
imposed force.
Newton’s Second Law of Motion
The acceleration of an
object is directly
proportional to the
magnitude of the imposed
force and inversely
proportional to the mass
of the object.
The acceleration is the
same direction as that of
the imposed force.
Newton’s Second Law of Motion
$Note that a force is proportional to an object’s
acceleration, not its velocity.
$We need some precise definitions of some
commonly used terms:
$The mass of an object is a quantity that tells us how much
resistance the object has to a change in its motion.
$This resistance to a change in motion is called inertia.
F = ma
units : 1 newton = 1 N = 1 kg " m s2
Fstring = 10 N (to the right)
$It is the total force or net force
ftable = 2 N (to the left)
that determines an object’s
acceleration.
Fnet = 10 N " 2 N
$If there is more than one
= 8 N (to the right)
vector acting on an object, the
forces are added together as
F
8N
vectors, taking into account
a = net =
m 5 kg
their directions.
= 1.6 m s2 (to the right)
!
Two equal-magnitude horizontal
forces act on a box. Is the object
accelerated horizontally?
a)
b)
c)
Yes.
No.
You can’t tell from
this diagram.
Since the two forces are equal
in size, and are in opposite
directions, they cancel each
other out and there is no
acceleration.
Is it possible that the box is
moving, since the forces are equal
in size but opposite in direction?
a)
a)
Yes, it is possible for
the object to be moving.
No, it is impossible for
the object to be moving.
Even though there is no
acceleration, it is possible the
object is moving at constant
speed.
Two equal forces act on an object
in the directions shown. If these
are the only forces involved, will
the object be accelerated?
a)
b)
c)
Yes.
No.
It is impossible to determine
from this figure.
The vector sum of the two forces results in a
force directed toward the upper right corner.
The object will be accelerated toward the
upper right corner.
Two forces act in opposite directions
on a box. What is the mass of the
box if its acceleration is 4.0 m/s2?
a)
b)
c)
d)
e)
5 kg
7.5 kg
12.5 kg
80 kg
120 kg
The net force is 50 N - 30 N = 20 N,
directed to the right. From F=ma,
the mass is given by:
m = F/a
= (20 N) / (4 m/s2)
= 5 kg.
A 4-kg block is acted on by three
horizontal forces. What is the net
horizontal force acting on the block?
a)
b)
c)
d)
e)
10 N
20 N
25 N
30 N
40 N
The net horizontal force is:
5 N + 25 N - 10 N = 20 N
directed to the right.
A 4-kg block is acted on by three
horizontal forces. What is the
horizontal acceleration of the block?
a)
b)
c)
d)
e)
10 N
20 N
25 N
30 N
40 N
From F=ma, the acceleration is given by:
a = F/m
= (20 N) / (4 kg)
= 5 m/s2
directed to the right.
Mass and Weight
! What exactly is mass?
! Is there a difference between mass and
weight?
! If something is weightless in space,
does it still have mass?
Mass, Weight, and Inertia
$A much larger force
is required to produce
the same acceleration
for the larger mass.
$Inertia is an object’s
resistance to a change
in its motion.
$Mass is a measure of
an object’s inertia.
$The units of mass are
kilograms (kg).
Mass, Weight, and Inertia
$An object’s weight is
the gravitational force
acting on the object.
$Weight is a force,
measured in units of
newtons (N).
$In the absence of
gravity, an object has
no weight but still has
the same mass.
Mass, Weight, and Inertia
$Objects of different mass
experience the same
gravitational acceleration on
Earth:
g = 9.8 m/s2
$By Newton’s 2nd Law, F = ma,
the weight is W = mg.
$Different gravitational forces
(weights) act on falling objects
of different masses, but the
objects have the same
acceleration.
A ball hangs from a string
attached to the ceiling. What is
the net force acting on the ball?
a)
b)
c)
The net force is downward.
The net force is upward.
The net force is zero.
Since the ball is hanging from the
ceiling at rest, it is not
accelerating so the net force is
zero. There are two forces acting
on the ball: tension from the string
and force due to gravitation.
They cancel each other.
Two masses connected by a string
are placed on a fixed frictionless
pulley. If m2 is larger than m1, will
the two masses accelerate?
a)
b)
c)
Yes.
No.
You can’t tell
from this diagram.
The acceleration of the two
masses will be equal and will
cause m2 to fall and m1 to rise.
Newton’s Third Law
! Where do forces come from?
! If we push on an object like a chair, does the
chair also push back on us?
! If objects do push back, who experiences the
greater push, us or the chair?
! Does our answer change if we are pushing
against a wall?
! How does Newton’s third law of motion help
us to define force, and how is it applied?
Newton’s Third Law
(“action/reaction”)
For every action
(force),
there is an equal
but opposite
reaction
(force).
It is important to identify the forces acting on an object.
$The forces acting
on the book are W
(gravitational force
from Earth) and N
(normal force from
table).
$Normal force
refers to the
perpendicular force a
surface exerts on an
object.
It is important to identify the forces acting on an object.
It is also important to identify the action-reaction pairs.
$The reaction force
to the Earth’s
attractive force W on
the book, is an equal
attractive force -W
the book exerts on
the Earth.
It is important to identify the forces acting on an object.
It is also important to identify the action-reaction pairs.
$The reaction force
to the table’s normal
force N exerted
upward on the book,
is an equal force -N
the book exerts
downward on the
table.
An uncompressed spring and the same spring
supporting a book.
The compressed spring exerts an upward force on the
book.
Third-Law Action/Reaction Pair
If the cart pulls back on the mule equal and
opposite to the mule’s pull on the cart, how
does the cart over move?
Third-Law Action/Reaction Pair
The car pushes against the road, and the road,
in turn, pushes against the car.
Applications of
Newton’s Laws
! How can Newton’s laws be applied in
different situations such as pushing a
chair, sky diving, throwing a ball, and
pulling two connected carts across the
floor?
What forces are involved in moving a chair?
$The weight W
(gravitational force
from Earth)
$The upward force N
(normal force from
floor).
$The push P (normal
force from hand of
person)
$The frictional force f
exerted by the floor
Does a sky diver continue to accelerate?
$Air resistance R is a force
directed upward, that opposes
the gravitational force W
$R increases as the sky
diver’s velocity increases
$When R has increased to the
magnitude of W, the net force
is zero so the acceleration is
zero
$The velocity is then at its
maximum value, the terminal
velocity
What happens when a ball is thrown?
Three forces act on a thrown ball:
$The initial push P
$Only acts at the beginning; once the ball leaves the hand, P
is no longer acting on the ball.
$The weight W
$Is a constant (does not change) throughout the trajector
$The air resistance R
$Is always directed against the motion
$Is proportional to the speed
What happens when objects are connected?
Two connected carts being accelerated by a force F applied by
a string:
$Both carts must have the same acceleration a which is equal
to the net horizontal force divided by the total mass
$Each cart will have a net force equal to its mass times the
acceleration
What happens when objects are connected?
The interaction between the two carts illustrates Newton’s third
law:
$m1 exerts a pull of 16 N to the right on m2
$m2 exerts an equal and opposite pull of 16 N to the left on m1
Two blocks with the same mass are connected
by a string and are pulled across a frictionless
surface by a constant force. Will the two
blocks move with constant velocity?
a)
b)
c)
Yes, both blocks move
with constant velocity.
No, both blocks move
with constant acceleration.
The two blocks will have
different velocities and/or
accelerations.
The front block will accelerate due to the constant
force F. The rear block is also pulled by a
constant force due to the connecting string, so it
will accelerate with the same acceleration as the
front block. The constant force implies a constant
acceleration. Constant acceleration results in
constantly increasing velocity.
Will the tension in the connecting string be
greater than, less than, or equal to the
force F?
a)
b)
c)
Greater than.
Less than.
Equal to.
The tension in the connecting string is less
than F. Both bodies have the same
acceleration. The force F accelerates a total
mass, 2m. The force in the connecting string
accelerates a mass, m, so it is half of F.
Two blocks tied together by a string are being
pulled across the table by a horizontal force.
The blocks have frictional forces exerted on
them by the table as shown. What is the net
force acting on the entire two-block system?
a)
b)
c)
d)
e)
16 N
36 N
38 N
44 N
46 N
The net horizontal force is:
30 N - 6 N - 8 N = 16 N
directed to the right.
What is the acceleration of this system?
a)
b)
c)
d)
2.00
2.67
5.00
7.50
m/s2
m/s2
m/s2
m/s2
The total mass is:
2 kg + 4 kg = 6 kg
The acceleration of the system is:
Total force ÷ total mass =
16 N ÷ 6 kg = 2.67 m/s2
directed to the right.
What force is exerted on the 2-kg block by
the connecting string?
a)
b)
c)
d)
e)
16 N
36 N
38 N
44 N
46 N
The net horizontal force on the 2-kg block is:
Fnet = ma = 2 kg x 2.67 m/s2 = 5.3 N
So the force due to the string is:
Fstring = Fnet + 6 N = 11.3 N
directed to the right.
What is the acceleration of the 4-kg block?
a)
b)
c)
d)
e)
16 N
36 N
38 N
44 N
46 N
The net horizontal force on the 4-kg block is:
Fnet = 30 N - 8 N - 11.3 N = 10.7 N
So the acceleration of the 4-kg block is:
a = F ÷ m = 10.7 N ÷ 4 kg = 2.67 m/s2
directed to the right.