Transcript Newton’s Laws of Motion

Objectives
• The students will be able to:
– Identify the conditions under which an object will
obey Newton’s First Law.
– Calculate force, mass and acceleration using
Newton’s Second Law
– Describe forces as they apply to Newton’s Third
Law.
“If I have ever made any valuable discoveries, it
has been owing more to patient attention, than
to any other talent.”
-Sir Isaac Newton
Newton’s Laws of Motion
Now that we have learned how to describe
motion, how do we cause the motion that
we want?
We apply forces on an object!
But what do forces directly affect:
location? velocity? acceleration? jerk?
Newton answered these questions by
postulating three laws of motion.
Units
The units of mass are kilograms.
Acceleration is measured in meters per second
squared or m/s2
The units of force will be kg*m/s2 or Newtons
(N)
– remember F = ma
– where a force of 1 N will give a mass of 1 kg an
acceleration of 1 m/s2 .
Forces
In order to work with forces, we have to identify
the common forces we find, both as to
magnitude and direction:
• gravity (near earth’s surface, this is called
weight, W) magnitude = m*g; direction =
down
Note that mass is involved in the force of gravity!
This is a separate property from that of inertia,
so we give this property the name
gravitational mass.
Newton’s Laws of Motion
• An object in motion tends to stay in
motion and an object at rest tends to
stay at rest unless acted upon by an
unbalanced force.
• Force equals mass times acceleration
(F = ma).
• For every action there is an equal and
opposite reaction.
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.
Newton’s First Law
An object at rest tends to stay at rest
and an object in motion tends to stay
in motion unless acted upon by an
unbalanced force.
1st Law of Motion
(Law of Inertia)
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.
Newton’s First Law
•
•
•
•
An object at rest will stay at ______
An object in motion will stay in _______
UNLESS a force acts upon that object
Ex. Your sister will continue to sit on the sofa
unless you kick her. Then, she will get up and
beat the snot out of you.
What does this mean?
Basically, an object will “keep doing what it
was doing” unless acted on by an
unbalanced force.
If the object was sitting still, it will remain
stationary. If it was moving at a constant
velocity, it will keep moving.
It takes force to change the motion of an
object.
Newton’s First Law of Motion
When we look at the planets and moon,
however, it is easier to see that they just keep
right on going!
Also, when we remove or reduce a lot of the
forces on an object, it does tend to keep right
on going. Consider a ball rolling on a smooth
floor. We don’t need forces to keep the
motion going!
What is meant by unbalanced
force?
If the forces on an object are equal and opposite, they are said
to be balanced, and the object experiences no change in
motion. If they are not equal and opposite, then the forces are
unbalanced and the motion of the object changes.
Some Examples from Real Life
A soccer ball is sitting at rest. It
takes an unbalanced force of a kick
to change its motion.
Two teams are playing tug of war. They are both
exerting equal force on the rope in opposite
directions. This balanced force results in no
change of motion.
Newton’s First Law is also called
the Law of Inertia
Inertia: the tendency of an object to
resist changes in its state of motion
The First Law states that all objects
have inertia. The more mass an object
has, the more inertia it has (and the
harder it is to change its motion).
More Examples from Real Life
A powerful locomotive begins to pull a
long line of boxcars that were sitting at
rest. Since the boxcars are so massive,
they have a great deal of inertia and it
takes a large force to change their
motion. Once they are moving, it takes
a large force to stop them.
On your way to school, a bug
flies into your windshield. Since
the bug is so small, it has very
little inertia and exerts a very
small force on your car (so small
that you don’t even feel it).
If objects in motion tend to stay in motion, why
don’t moving objects keep moving forever?
Things don’t keep moving forever because
there’s almost always an unbalanced force
acting upon it.
A book sliding across a table slows
down and stops because of the force
of friction.
If you throw a ball upwards it will
eventually slow down and fall
because of the force of gravity.
In outer space, away from gravity and any
sources of friction, a rocket ship launched
with a certain speed and direction would
keep going in that same direction and at that
same speed forever.
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.
What is this unbalanced force that acts on an object in motion?
• There are four main types of friction:
– Sliding friction: ice skating
– Rolling friction: bowling
– Fluid friction (air or liquid): air or water resistance
– Static friction: initial friction when moving an
object
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.
• In the absence of a force of friction, the book
would continue in motion with the same
speed and direction - forever! (Or at least to
the end of the table top.)
1st Law
• Inertia is the
tendency of an
object to resist
changes in its
velocity:
whether in
motion or
motionless.
These pumpkins will not move unless acted on
by an unbalanced force.
1st Law
• Once airborne,
unless acted on
by an
unbalanced
force (gravity
and air – fluid
friction), it
would never
stop!
1st Law
• Unless acted
upon by an
unbalanced
force, this golf
ball would sit on
the tee forever.
Newtons’s 1st 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 80 km/hour is stopped
by the brick wall, your body keeps moving at 80 m/hour.
Newton’s Second Law
Force equals mass times acceleration.
F = ma
Acceleration: a measurement of how quickly an
object is changing speed.
2nd Law
What does F = ma mean?
Force is directly proportional to mass and acceleration.
Imagine a ball of a certain mass moving at a certain
acceleration. This ball has a certain force.
Now imagine we make the ball twice as big (double the
mass) but keep the acceleration constant. F = ma says
that this new ball has twice the force of the old ball.
Now imagine the original ball moving at twice the
original acceleration. F = ma says that the ball will
again have twice the force of the ball at the original
acceleration.
NSF North Mississippi GK-8
More about F = ma
If you double the mass, you double the force. If you
double the acceleration, you double the force.
What if you double the mass and the acceleration?
(2m)(2a) = 4F
Doubling the mass and the acceleration quadruples the
force.
So . . . what if you decrease the mass by half? How
much force would the object have now?
NSF North Mississippi GK-8
What does F = ma say?
F = ma basically means that the force of an object
comes from its mass and its acceleration.
Something very massive (high mass)
that’s changing speed very slowly
(low acceleration), like a glacier, can
still have great force.
Something very small (low mass) that’s
changing speed very quickly (high
acceleration), like a bullet, can still
have a great force. Something very
small changing speed very slowly will
have a very weak force.
NSF North Mississippi GK-8
Force
• So what is FORCE
– A push or a pull on an object!
Forces
A. Newton’s 2nd Law
1. A net force acting on an object
causes the object to accelerate in
the direction of the net force.
2. a = FNET / mass or a = F / m
B. Friction
1. Force that opposes motion
between two surfaces in contact.
2. Amount depends on:
a. Kinds of surfaces in
contact.
b. Amount of force pressing
surfaces together. Something that
weighs more will have greater
friction.
3. Friction is caused by microwelds
4. Types of friction:
a. Static (usually the greatest)
b. Sliding
c. Rolling (usually the least)
C. Air resistance (drag force)
1. Force that opposes
motion of objects through air
2. Pushes up on falling
objects
3. Affected by object’s
speed, size, shape
4. Without drag force, all objects
fall at the same rate
5. Terminal velocity is the max
speed at which an object can fall
D. Gravity
1. Attraction between objects
2. Weakest force in universe
3. Farthest range
4. Directly proportional to the
masses of the objects
5. Inversely proportional to the
squares of the distance between
E. Gravitational Acceleration
1. g = 9.8 m/s/s on Earth
2. FWEIGHT = m x g
3. All objects fall with the same g
4. Weight is NOT the same as mass
F. Free Fall (Weightlessness)
1. As long as an object is free falling,
nothing exerts an upward force
2. With no upward force, FW = 0 N
G. Projectile and Circular Motion
1. Projectile motion
a. Follow a curved path
b. Two types of motion are
independent of one another:
1) Horizontal (based on initial
velocity and inertia)
2) Vertical (based on gravity)
c. An object launched horizontally
will land at the same time as an
object simply dropped from the
same height
2. Circular Motion
a. Objects moving in circular paths
accelerate toward the center
b. Centripetal acceleration
c. Centripetal force (FC = m x aC)
d. Centrifugal force is imaginary
e. Weightlessness in orbit exists
because objects are constantly falling
toward Earth, but have enough
forward velocity to keep them in orbit
2nd Law
The net force of an object is
equal to the product of its mass
and acceleration, or F=ma.
2nd Law
• When mass is in kilograms and acceleration is
in m/s/s, the unit of force is in newtons (N).
• One newton is equal to the force required to
accelerate one kilogram of mass at one
meter/second/second.
2nd Law (F = m x a)
• How much force is needed to accelerate a
1400 kilogram car 2 meters per second/per
second?
• Write the formula
• F=mxa
• Fill in given numbers and units
• F = 1400 kg x 2 meters per second/second
• Solve for the unknown
• 2800 kg-meters/second/second or 2800
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? A 6 kg object?
• 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2.
Determine the mass.
• 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?
• 4. What is the force on a 1000 kg elevator that is falling freely at 9.8
m/sec/sec?
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.
NSF North Mississippi GK-8
Newton’s Third Law of Motion
This is sometimes called the law of action and
reaction.
I like to call it: you can’t push yourself! You can
only push on an object and hope that it pushes
back.
Example: when you walk up a stairs, you use
your muscles to push down on the stairs and
you trust that the stairs will push back up on
you lifting you up the stairs.
What does this mean?
For every force acting on an object, there is an equal
force acting in the opposite direction. Right now,
gravity is pulling you down in your seat, but
Newton’s Third Law says your seat is pushing up
against you with equal force. This is why you are
not moving. There is a balanced force acting on
you– gravity pulling down, your seat pushing up.
NSF North Mississippi GK-8
Think about it . . .
What happens if you are standing on a
skateboard or a slippery floor and push against
a wall? You slide in the opposite direction
(away from the wall), because you pushed on
the wall but the wall pushed back on you with
equal and opposite force.
Why does it hurt so much when you stub
your toe? When your toe exerts a force on a
rock, the rock exerts an equal force back on
your toe. The harder you hit your toe against
it, the more force the rock exerts back on your
toe (and the more your toe hurts).
NSF North Mississippi GK-8
Review
Newton’s First Law:
Objects in motion tend to stay in motion
and objects at rest tend to stay at rest
unless acted upon by an unbalanced force.
Newton’s Second Law:
Force equals mass times acceleration
(F = ma).
Newton’s Third
Law:
For every action there is an equal and
opposite reaction.
NSF North Mississippi GK-8
Vocabulary
Inertia:
the tendency of an object to resist changes in
its state of motion
Acceleration:
a measurement of how quickly an object is
changing speed
NSF North Mississippi GK-8
3rd Law
• For every action, there is an
equal and opposite reaction.
3rd 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.
3rd 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 3rd Law in Nature
• 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).
3rd 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.
• 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.
Other examples of Newton’s Third
Law
• The baseball forces the
bat to the left (an
action); the bat forces
the ball to the right (the
reaction).
3rd Law
• Consider the motion of
a car on the way to
school. A car is
equipped with wheels
which spin backwards.
As the wheels spin
backwards, they grip
the road and push the
road backwards.
3rd 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.
Newton’s Third Law
• Forces always act in equal and opposite
_____.
• In pairs, come up with an example of this and
be ready to share it with the class.
Gravitational Force
• Previously we saw that the force of gravity
depended on the mass of an object as well
as the constant acceleration due to gravity, g.
• But we know that objects on the moon fall to
the moon’s surface, not to the earth’s
surface. If objects do have mass, then why
don’t ALL objects fall to the earth?
Gravitational Force
• Newton “discovered” the Law of Gravity by
sitting under an apple tree and getting
conked! Is this correct?
• Imagine sitting under an apple tree and
getting conked by an apple. Also consider that
you see the moon up in the sky. Have you
wondered why the apple falls down but the
moon doesn’t?
Gravitation
• But what makes the moon go around the
earth instead of continuing off into space?
• If the moon is orbiting, there must be some
force causing the circular acceleration for
circular motion. The obvious answer (at least
now) is that the earth’s gravity does cause the
moon to fall - it’s just moving sideways so that
it continues to move and fall - continues in its
circular orbit!
Newton’s Law of Gravity
• In looking at gravity as the cause of the
moon’s circular motion, Newton came to the
conclusion that the force of gravity had to be
weaker at the moon’s distance than it was on
the earth - otherwise the moon would have to
be going much faster to stay in orbit.
Newton’s Law of Gravity
• Newton came up with the following equation
for gravity: any two objects attract one
another based on the mass of each, the
distance apart, and some constant based on
units: Fgravity = G*m1*m2 / r122
where r12 is the distance between m1 and m2
and G = 6.67 x 10-11 Nt*m2 / kg2 which
describes how strong gravity is.
Newton’s Law of Gravity
Do all objects with mass attract all other objects
with mass? Are you attracted to your
neighbor (gravitationally, that is)?
We have done experiments that show the
answer is yes!
Newton’s Law of Gravity
However, because the strength of gravity is very
weak, the force of attraction is very weak. For
one kilogram separated from another
kilogram by one meter:
Fg = Gm1m2/r122 =
(6.67 x 10-11 Nt-m2/kg2)*(1 kg)*(1 kg) / [1 m]2
= 6.67 x 10-11 Nt (a very small force).
Newton’s Law of Gravity
At the earth’s surface, we have
Fgravity = G*Mearth*m / Rearth2
where the distance between an object on the
earth’s surface and the earth (center to
center distance) is the radius of the earth.
Note that G, Mearth and Rearth are all constant, so
that near the earth this reduces to
Fgravity = mg where g = G*Mearth/Rearth2 .
Mass of the Earth
The great gravity we feel on the earth is due to
the huge mass of the earth. Even though
gravity is weak, the huge mass of the earth
combines lots of very weak forces into one
reasonably strong force.
But how much mass does the earth have?
Mass of the Earth
We can use the equation: g = G*Mearth/Rearth2
to solve for Mearth since we know
g = 9.8 m/s2 (from our lab experiment),
G = 6.67 x 10-11 Nt-m2/kg2 (from precise gravity
force experiments), and
Rearth = 6,400 km (since we know the
circumference of the earth = 25,000 miles).
Mass of the Earth
g = G*Mearth/Rearth2 or Mearth = g*Rearth2/G
= 9.8 m/s2 * (6.4 x 106 m)2 / 6.67 x 10-11 Nt-m2/kg2
= 6.0 x 1024 kg .
This value is certainly large as we expect the
mass of the earth to be large. But is there
another way to get the same answer? If there
is, that would greatly add to our confidence in
our answer!