Download Newton`s 3rd Law

Cat Falls Off a Building
Why is it that a cat that falls from the top of a 50
story building will hit the ground no faster than if
it fell from the 20th story?
The cat reaches terminal velocity in a 20 story
fall, so falling the extra distance doesn’t affect
the speed.
The low terminal velocities of small creatures
enables them to fall without harm from heights
that would kill larger creatures.
Falling is favored by their higher ratio of surface
area/mass.
Humans boost this ratio by using parachutes.
Newton’s 3rd Law
Drop a sheet of tissue paper in front of the
heavyweight boxing champion of the world and
challenge him to hit it in midair with a force of
only 50 pounds (222 N).
Sorry, the champ can't do it. In fact, his best
punch couldn't even come close. Why is this?
We'll see in this chapter that the tissue has
insufficient inertia for a 50-pound interaction with
the champ's fist.
Forces and Interactions
So far we have treated force in its simplest sense—as a
push or pull.
In a broader sense, a force is not a thing in itself but
makes up an interaction between one thing and another.
If you push on a wall with your fingers, more is
happening than you pushing on the wall. The wall is also
pushing on you.
How else can you explain the bending of your fingers?
Your fingers and the wall push on each other.
There is a pair of forces involved: your push on the wall
and the wall's push back on you.
These forces are equal in magnitude and opposite in
direction and comprise a single interaction. In fact, you
can't push on the wall unless the wall pushes back.
Boxer
Consider a boxer's fist hitting a massive punching bag.
Fist hits the bag (and dents it) while the bag hits back on
the fist (and stops its motion).
In hitting the bag there is an interaction with the bag that
involves a pair of forces. The force pair can be quite
large.
But what of hitting a piece of tissue paper, as discussed
earlier? The boxer's fist can only exert as much force on
the tissue paper as the tissue paper can exert on the fist.
Furthermore, the fist can't exert any force at all unless
what is being hit exerts the same amount of force back.
An interaction requires a pair of forces acting on two
objects.
In the interaction between the hammer
and the stake, the hammer exerts a force
against the stake, but is itself brought to a
halt in the process. Such observations led
Newton to his third law of motion.
Forces and Interactions
The impact forces between the blue and
yellow balls move the yellow ball and stop
the blue ball.
Which exerts the force and which receives the
force?
Isaac Newton's answer to this was that neither
force has to be identified as “exerter” or
“receiver”; he concluded that both objects must
be treated equally.
For example, when you pull the cart, the cart
simultaneously pulls on you.
This pair of forces, your pull on the cart and the
cart's pull on you, makes up the single
interaction between you and the cart.
Action and reaction forces. Note that when
action is “A exerts force on B,” the reaction is
then simply “B exerts force on A.”
Newton’s 3rd Law
Whenever one object exerts a force on a second
object, the second object exerts an equal and
opposite force on the first.
Newton's third law is often stated thus: “To every action
there is always opposed an equal reaction.”
In any interaction there is an action and reaction pair of
forces that are equal in magnitude and opposite in
direction.
Neither force exists without the other—forces come in
pairs, one action and the other reaction.
The action and reaction pair of forces makes up one
interaction between two things.
You interact with the floor when you walk on it. Your push
against the floor is coupled to the floor's push against
you.
The pair of forces occurs simultaneously.
Likewise, the tires of a car push against the road while
the road pushes back on the tires—the tires and road
push against each other.
In swimming you interact with the water that you push
backward, while the water pushes you forward—you and
the water push against each other.
In each case there is a pair of forces, one action and the
other reaction, that make up one interaction. The
reaction forces are what account for our motion in these
cases.
These forces depend on friction; a person or car on ice,
for example, may not be able to exert the action force to
produce the needed reaction force.
Which force we call action and which we call reaction
doesn't matter. The point is that neither exists without the
other.
Defining a System
An interesting question often arises; since
action and reaction forces are equal and
opposite, why don't they cancel to zero?
To answer this question we must consider
the system involved. Consider the force
pair between the apple and orange.
When the apple pulls on the orange, the
orange accelerates. At the same time, the
orange pulls on the apple. Do the forces
cancel to zero?
When the orange is the system (within the
dashed line) an external force provided by
the apple acts on it. Action and reaction
forces do not cancel and the system
accelerates.
When both the orange and apple compose
the system (both within the dashed line)
no external force acts on it. Action and
reaction are within the system and do
cancel to zero. Zero net force means no
acceleration of the system.
If, however, we consider the system to enclose both the
orange and apple, the force pair is internal to the orangeapple system. Then the forces do cancel each other.
The apple and orange move closer together but the
system's “center of gravity” is in the same place before
and after the pulling.
There is no net force and therefore no net acceleration.
Similarly, the many force pairs between molecules in a
golf ball may hold the ball together into a cohesive solid,
but they play no role at all in accelerating the ball.
A force external to the ball is needed to accelerate the
ball.
So a force external to both the apple and orange is
needed to produce acceleration of both (like friction of
the floor on the apple's feet).
In general, when Body A inside a system interacts with
Body B outside the system, each can experience a net
force.
Action and reaction forces don't cancel. You can't cancel
a force acting on Body A with a force acting on Body B.
Forces cancel only when they act on the same body, or
on the same system.
Action and reaction forces always act on different
bodies.
When action and reaction forces are internal to a
system, they cancel each other and produce no
acceleration of the system.
Check Yourself
If this is confusing, it may be well to note that Newton
had difficulties with the third law himself.
1. On a cold rainy day your car battery is dead and you
must push the car to move it and get it started. Why can't
you move the car by remaining comfortably inside and
pushing against the dashboard?
2. Why does a book sitting on a table never accelerate
“spontaneously” in response to the trillions of interatomic forces acting within it?
3. Does a speeding missile possess force?
4. We know that the Earth pulls on the moon. Does it
follow that the moon also pulls on the Earth?
5. Can you identify the action and reaction forces in the
case of an object falling in a vacuum?
Horse and Cart Problem
Action and Reaction
on Different Masses
As strange as it may first seem, a falling object
pulls upward on the Earth as much as the Earth
pulls downward on it.
The downward pull on the object seems normal
because the acceleration of 10 meters per
second each second is quite noticeable.
The same amount of force acting upward on the
huge mass of the Earth, however, produces
acceleration so small that it cannot be noticed or
measured.
The Earth is pulled up by the boulder with
just as much force as the boulder is pulled
downward by the Earth.
We can see that the Earth accelerates slightly in
response to a falling object by considering the
exaggerated examples of two planetary bodies.
The forces between bodies A and B are equal in
magnitude and oppositely directed in each case.
If acceleration of planet A is unnoticeable in a, then it is
more noticeable in b where the difference between the
masses is less extreme.
In c, where both bodies have equal mass, acceleration of
object A is as evident as it is for B.
Continuing, we see the acceleration of A becomes even
more evident in d and even more so in e.
So strictly speaking, when you step off the curb, the
street comes up ever so slightly to meet you.
Which falls toward
the other,
A or B?
Do the accelerations
of each relate
to their relative masses?
Interaction
Between Rifle and Bullet
The role of different masses is evident in a
fired rifle
The force exerted against the recoiling rifle
is just as great as the force that drives the
bullet. Why then, does the bullet
accelerate more than the rifle?
If we extend the idea of a rifle recoiling or
“kicking” from the bullet it fires, we can
understand rocket propulsion.
Consider a machine gun recoiling each time a
bullet is fired. If the machine gun is fastened so it
is free to slide on a vertical wire , it accelerates
upward as bullets are fired downward. A rocket
accelerates the same way.
It continually “recoils” from the ejected exhaust
gas. Each molecule of exhaust gas is like a tiny
bullet shot from the rocket .
The rocket recoils from the
“molecular bullets” it fires
and climbs upward
A common misconception is that a rocket is propelled by
the impact of exhaust gases against the atmosphere.
In fact, in the early 1900s before the advent of rockets,
many people thought that sending a rocket to the moon
was impossible because of the absence of an
atmosphere for the rocket to push against.
But this is like saying a gun wouldn't kick unless the
bullet had air to push against.
Not true! Both the rocket and recoiling gun accelerate
not because of any pushes on the air, but because of the
reaction forces by the “bullets” they fire—air or no air.
A rocket works better, in fact, above the atmosphere
where there is no air resistance to oppose its motion.
Newton's 3rd Law
Newton’s 3rd Law is Everywhere
A fish pushes the water backward with its fins,
and the water pushes the fish forward.
The wind pushes against the branches of a tree,
and the branches push back on the wind and we
have whistling sounds.
Forces are interactions between different things.
Every contact requires at least a two-ness; there
is no way that an object can exert a force on
nothing.
Forces, whether large shoves or slight nudges,
always occur in pairs, each of which is opposite
to the other.
Thus, we cannot touch without being touched.
Newton’s 1st Law
An object at rest tends to remain at rest; an
object in motion tends to remain in motion at
constant speed along a straight-line path.
This tendency of objects to resist change in
motion is called inertia.
Mass is a measure of inertia.
Objects will undergo changes in motion only in
the presence of a net force.
Newton’s 2nd Law
When a net force acts on an object, the object will
accelerate.
The acceleration is directly proportional to the net force
and inversely proportional to the mass.
Symbolically, a = F/m.
Acceleration is always in the direction of the net force.
When objects fall in a vacuum, the net force is simply the
weight, and the acceleration is g (the symbol g denotes
that acceleration is due to gravity alone).
When objects fall in air, the net force is equal to the
weight minus the force of air resistance, and the
acceleration is less than g.
If and when the force of air resistance equals the weight
of a falling object, acceleration terminates, and the object
falls at constant speed (called terminal speed).
Newton’s 3rd Law
Whenever one object exerts a force on a
second object, the second object exerts an
equal and opposite force on the first.
Forces come in pairs, one action and the
other reaction, both of which comprise the
interaction between one object and the
other.
Action and reaction always act on different
objects.
Neither force exists without the other.
Problems
How much in newtons does a 20 Kg bag
weigh?
A 350,000 Kg airplane in takeoff uses
25,000 N thrust of each one of its four
engines. What is the acceleration of the
plane during take-off ?
An unbalanced force of 35 N gives an
object an acceleration of 5 m/s . What
force would be needed to give it an
acceleration of 1 m/s ?
A certain unbalanced force gives a 10 Kg
object an acceleration of 2 m/s . What
acceleration would the same force give a
20 Kg object?
A net force of 2N acts on a 3 Kg object,
initially at rest, for 2 seconds. What is the
distance the object moves during that
time?
A 20 Kg block of cement is pulled upward
(not sideways) with a force 300 N. What is
the acceleration of the block?
What is the Pressure on a table when a 12
N book with a .06 meters squared cover
lies flat on it?
Two people have a tug of war on lowfriction ice, One person has 3 times the
mass of the other. Compared to the lighter
person, how many times as fast does the
heavier person accelerate?
What engine thrust (in newtons) is
required for a rocket of mass 30 Kg to
leave the launching pad?
Quiz 1
1. If a man has a mass of 60 Kg, calculate
his weight in Newtons.
2. Calculate in Newtons the weight of a
3 Kg melon.
What is its weight in pounds?
Quiz 2
1. Calculate the acceleration of a
400,000 Kg jumbo jet just before takeoff
when the thrust for each of its 4 engines
is 35,000 N.
2. a. Calculate the acceleration if you push
with a 40 N horizontal force on a 2 Kg
block on a horizontal friction-free air
table.
b. What acceleration occurs if the friction
force is 20 N?