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Newton’s
Laws of Motion
I. Law of Inertia
II. F=ma
III. Action-Reaction
Describing Motion
- Motion is one of the more common events in your
surroundings. You can see motion in natural events (clouds
moving, rain falling), and you can see motion in everyday
activities (walking, running).
- Consider a ball you notice one morning in the middle of a
lawn. Later in that afternoon, you notice that the ball is at
the edge of the lawn, against a fence, and you wonder if the
wind or some person moved the ball. All you know for sure
is that the ball has been moved because it is in a different
position after some time passed.
There are two important aspects of motion:
(1) change of position and (2) the passage of time.
Measuring Motion
- Since motion involves a change of position and the
passage of time, the motion of objects can be described by
using combinations of the fundamental properties of length
and time. These measurements describe three main
properties of motion: speed, velocity, and acceleration.
Describing Motion: Speed
- Suppose you are in a car moving over a straight road. How
could you describe your motion? You need at least two
measurements: (1) the distance you have traveled and (2) the
time that has elapsed while you covered the distance.
- Such measurements
can be expressed as a
ratio called speed,
which is a measure of
how fast you are
moving. Speed is
defined as a distance
over a unit of time.
Calculating Speed
Practice Question 1: Jim travels 45 miles at 15 mph.
How long does it take him?
It takes 3 hours. (45 miles / 15 mph = 3 hours)
Practice Question 2: Jake walks at 4 mph for 2.5 hours.
How far does he walk?
He walked 10 miles. (4 miles x 2.5 hours = 10 miles)
Practice Question 3: Jenny drives at a constant speed. In
the first 3 hours she travels 81 miles. How far will she
have traveled after 5 hours?
She will travel 135 miles. (27 mph x 5 hours
= 135 miles)
Velocity
- The word velocity is sometimes used interchangeably with
the word speed, but there is a difference. Velocity describes
the speed and direction of a moving object. Velocity is
often represented graphically with arrows. The lengths of the
arrows are proportional to the magnitude, and the arrowheads
indicate the direction.
Acceleration
- Motion can be changed in three different ways: (1) by
changing the speed, (2) by changing the direction of travel,
and (3) combining both of these by changing speed and
direction at the same time.
- You need at least one additional
measurement to describe a change
of motion, which is how much time
has elapsed while the change was
taking place. The change of
velocity and time can be
combined to define the rate at
which the motion was changed.
This rate is called acceleration.
Calculating Acceleration
Practice Question 1: A skater goes from a standstill to a
speed of 6.7 m/s in 12 seconds. What is the acceleration of
the skater?
Step 1: Write the equation.
a = vf – vi
t
=
Dv
t
Step 2: Insert the known measurements into the equation.
a = 6.7m/s – 0 m/s
12s
=
6.7 m/s
12s
The initial speed of the skater was zero since he was not
in motion. The skater finally reached a speed of 6.7m/s in
12 seconds, which is the final speed or velocity.
Step 3: Solve. The SI unit for acceleration is meters per
second squared (m/s2).
a = 6.7m/s – 0 m/s
12s
As with any
formula, if you
know one
variable, you can
rearrange to
solve for another.
=
6.7 m/s
12s
= 0.56 m/s2
Velocity Formulas
velocity
acceleration
Where
v
=
time
v0 =
a =
initial velocity
t
=
final velocity
initial velocity
acceleration
time
Newton’s Laws of Motion
• 1st Law – An object at rest will stay at rest,
and an object in motion will stay in motion
at constant velocity, unless acted upon by an
unbalanced force.
• 2nd Law – Force equals mass times
acceleration.
• 3rd Law – For every action there is an equal
and opposite reaction.
st
1
Law of Motion
(Law of Inertia)
- Place a coin on a flat, level surface.
- Let it sit there for 5 minutes,
watching it carefully.
- Notice whether or not it starts
moving all by itself.
You have just demonstrated the first part of
Newton’s first law, which is that objects
tend to remain at rest unless you hit them.
More Fun With
st
1
Law
Now let’s introduce the second part of Newton’s
first law, which is that objects in motion tend to
stay in motion until something hits them.
An example of this is what
happens if an astronaut throws
something while in outer
space. The item will continue
in the same direction and at
the same speed unless some
force (like a planet’s gravity)
acts upon the item thrown.
MORE Fun With 1st Law
- It can be a real pain to say things like, “Hey, looks to
me like that thing over there tends to keep on doing what
it’s doing more so than that other thing over there.”
- To make things easy, there’s a special term that refers to
an object’s tendency to keep on doing what it’s doing –
called inertia.
- It’s hard to change the motion of an object with lots of
inertia (like elephants, mountains, or perhaps
government-run agencies). It’s easy to change the motion
of an object with very little inertia (like mosquitoes, lima
beans, or dust bunnies).
Putting It All Together
Remember when we talked
about something staying in
motion unless something else
“hits” it? That term is a bit
restrictive.
It turns out that you can
change an object’s motion by
pushing it or pulling it or
nudging it or blowing on it or
any number of things, all of
which are referred to as forces.
First Law Explained
Sooo … if Newton’s First
Law says that objects in
motion will stay in motion,
why then, do we observe
every day objects in motion
slowing down and becoming
motionless seemingly
without an outside force?
It’s a force we sometimes
cannot see – friction!
Types of Friction
• There are four main types of friction:
– Sliding friction (like ice skating)
– Rolling friction: (like bowling)
– Fluid friction (air or liquid): air or water resistance
– Static friction: initial friction when moving an object
Friction Example
Slide a book across a table
and watch it slide to a rest
position.
The book comes to a rest
because of the presence of
a force - that force being
the force of friction which brings the book to a
rest position.
Newton’s First Law and You
Don’t let this be you.
Wear seat belts!
Because of inertia,
objects (including you)
resist changes in their
motion. When the car
going 55 mph/hour is
stopped by the brick
wall, your body keeps
moving at 55 mph/hour.
Newton’s Second Law
While Newton’s first law predicts the behavior of
objects for which all forces are balanced, Newton’s
second law deals with forces that are NOT balanced.
Newton’s Second Law
- Push your friend on a skateboard and your friend
accelerates. Now push equally hard on an elephant on a
skateboard and the acceleration is much less. You’ll see that
the amount of acceleration depends not only on the force but
on the mass being pushed.
- Newton was the first to discover the relationship among the
three basic physical concepts – acceleration, force, and mass.
- Newton’s 2nd law states the acceleration of an object is
directly proportional ( ) to the net force acting on the
object, is in the direction of the net force, and is inversely
proportional ( ) to the mass of the object.
Newton’s Second Law
- In summarized form, the 2nd law says:
Acceleration ~ net force/mass
We use the wiggly line as a symbol meaning “is proportional
to.” We say that acceleration (a) is directly proportional to
the overall net force (F) and inversely proportional to the
mass (m).
By this we mean that, if F increases, a increases by the same
factor (if F doubles, a doubles); but if m increases, a
decreases by the same factor (if m doubles, a is cut in half).
In the metric system, the units for force will be the units for
mass (m) times acceleration (a). The unit for mass is kg and
the unit for acceleration is m/s2. The combination of these
units, (kg)(m/s2), is a unit of force called the newton (N) in
honor of Isaac Newton.
Practice With Second Law
• How much force is needed to accelerate a 1,400
kilogram car 2 meters per second/per second?
• Write the formula
• F=mxa
• Fill in given numbers and units
• F = 1,400 kg x 2 meters per second/second
• Solve for the unknown
• 2,800 kg-meters/second/second or 2,800
N
If mass remains constant, doubling the acceleration, doubles the force. If force remains
constant, doubling the mass, halves the acceleration.
Newton’s 2nd Law proves that different masses
accelerate to the earth at the same rate, but with
different forces.
• We know that objects
with different masses
accelerate to the
ground at the same
rate.
• However, because of
the 2nd Law we know
that they don’t hit the
ground with the same
force.
F = ma
F = ma
98 N = 10 kg x 9.8 m/s/s
9.8 N = 1 kg x 9.8 m/s/s
Check Your Understanding
• 1. What acceleration will result when a 12 N net force applied to a 3 kg object?
12 N = 3 kg x 4 m/s/s
• 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine
the mass.
16 N = 3.2 kg x 5 m/s/s
• 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?
66 kg-m/sec/sec or 66 N
• 4. What is the force on a 1000 kg elevator that is falling freely at 9.8
m/sec/sec?
9800 kg-m/sec/sec or 9800 N
Newton’s Third Law
For every
action, there
is an equal
and opposite
reaction.
Newton’s Third Law
According to Newton,
whenever objects A and
B interact with each
other, they exert forces
upon each other. When
you sit in your chair,
your body exerts a
downward force on the
chair and the chair
exerts an upward force
on your body.
Newton’s Third Law
There are two forces
resulting from this
interaction - a force on
the chair and a force
on your body. These
two forces are called
action and reaction
forces.
Newton’s Third Law
• Consider the propulsion of a
fish through the water. A
fish uses its fins to push
water backwards. In turn,
the water reacts by pushing
the fish forwards, propelling
the fish through the water.
•
The size of the force on the
water equals the size of the
force on the fish; the
direction of the force on the
water (backwards) is
opposite the direction of the
force on the fish (forwards).
Newton’s Third Law
Flying gracefully
through the air, birds
depend on Newton’s
third law of motion.
As the birds push
down on the air with
their wings, the air
pushes their wings up
and gives them lift.
Newton’s Third Law
• Consider the flying motion of birds. A bird flies
by use of its wings. The wings of a bird push air
downwards. In turn, the air reacts by pushing the
bird upwards.
• The size of the force on the air equals the size of
the force on the bird; the direction of the force on
the air (downwards) is opposite the direction of
the force on the bird (upwards).
• Action-reaction force pairs make it possible for
birds to fly.
(More) Newton’s Third Law
The baseball
forces the bat
to the right (an
action); the bat
forces the ball
to the left (the
reaction).
(More) Newton’s Third Law
- The reaction of a rocket is an
application of the third law of
motion. Various fuels are
burned in the engine,
producing hot gases.
- The hot gases push against
the inside tube of the rocket
and escape out the bottom of
the tube. As the gases move
downward, the rocket moves
in the opposite direction.