Download "Horse and Wagon Problem"?

Chapter Seven Notes:
Newton’s Third Law of Motion – Action and
Reaction
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A force is always part of a mutual action that involves
another force.
 A mutual action is an interaction between one thing
and another
 Ea: A hammer strikes a nail, however the nail exerts
a force on the hammer! There are a pair of forces!
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Newton’s third law states that whenever one object
exerts a force on a second object, the second object
exerts an equal and opposite force on the first object.
 First force –
 Other force –
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To identify a pair of action – reaction forces,
first identify the interaction objects A and B,
and if the action is A on B, then the reaction
is B on A.
Ea: A falling boulder! The interaction during
the fall is between the boulder and Earth. So
if we call the action Earth exerting a force on
the boulder, then the reaction is the boulder
simultaneously exerting a force on Earth.
 Newton's Third Law of Motion
 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. 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 and
are the subject of Newton's third law of motion.
Formally stated, Newton's third law is:
 For every action, there is an equal and opposite
reaction.
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The statement means that in every
interaction, there is a pair of forces acting on
the two interacting objects. The size of the
forces on the first object equals the size of
the force on the second object. The direction
of the force on the first object is opposite to
the direction of the force on the second
object. Forces always come in pairs - equal
and opposite action-reaction force pairs.
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According to Newton's third law, for every action
force there is an equal (in size) and opposite (in
direction) reaction force. Forces always come in
pairs - known as "action-reaction force pairs."
Identifying and describing action-reaction force
pairs is a simple matter of identifying the two
interacting objects and making two statements
describing who is pushing on who and in what
direction. For example, consider the interaction
between a baseball bat and a baseball.
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The baseball forces the bat to the left; the bat
forces the ball to the right. Together, these
two forces exerted upon two different objects
form the action-reaction force pair. Note that
in the description of the two forces, the
nouns in the sentence describing the forces
simply switch places.
Consider the following three examples. One
of the forces in the mutual interaction is
described; describe the other force in the
action-reaction force pair. Click the Mouse to
view the answer.
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Baseball pushes glove leftwards.
Answer: The glove pushes the baseball
rightward.
 Bowling ball pushes pin leftwards.
Answer: Pin pushes bowling ball rightward.
 Enclosed air particles push balloon wall
outwards.
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Answer: Balloon wall pushes enclosed air
particles inwards.
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1. Consider the interaction depicted below
between foot A, ball B, and foot C. The three
objects interact simultaneously (at the same
time). Identify the two pairs of action-reaction
forces. Use the notation "foot A", "foot C", and
"ball B" in your statements. Click the button to
view the answer.
Answer: The first pair of action-reaction force
pairs is: foot A pushes ball B to the right; and ball
B pushes foot A to the left. The second pair of
action-reaction force pairs is: foot C pushes ball
B to the left; and ball B pushes foot C to the
right.
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2. Identify at least six pairs of action-reaction force
pairs in the following diagram.
Answer: The elephant's feet push backward on the
ground; the ground pushes forward on its feet. The
right end of the right rope pulls leftward on the
elephant's body; its body pulls rightward on the right
end of the right rope. The left end of the right rope
pulls rightward on the man; the man pulls leftward on
the left end of the right rope. The right end of the left
rope pulls leftward on the man; the man pulls
rightward on the right end of the left rope. The
tractor pulls leftward on the right end of the left rope;
the left end of the left rope pulls rightward on the
tractor. etc., etc.
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Consider a cannon and cannon ball.
According to Newton’s second law we must
consider the masses.
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Cannon ball:
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Cannon:
F/m
F/m
=
a
= a
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Whenever one object exerts a force on a
second object, the second object exerts an
equal and opposite force on the first. Actionreaction pairs never act on same body.
 Defining your System
Two objects define a system for a Newton’s
third law interaction.
We are not considering (necessarily) the net
force acting on an object.
An object cannot exert a force on itself to
cause an acceleration.
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 What is the "Horse and Wagon Problem"?
Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK,
Old Dobbin, let's go!"
Old Dobbin turns to Farmer Brown and says, "Do you remember back in
high school, when we took Physics together?"
"Yes, I do. We were lab partners in that class, and we had a lot of fun."
says Farmer Brown.
"Ah, yes! Those were the good old days, all right!", says Old Dobbin,
"You do remember Newton's Three Laws, of course, which tell how all
objects move?"
"Yes, I do! I remember that Newton's Laws of Motion are the cornerstone
of mechanics. Now, let's get this wagon moving!"
"Do you remember how Newton's Third Law says that every action force
has an equal and opposite reaction force?", says Old Dobbin, ignoring
Farmer Brown's impatience.
"Yes, I do." says Farmer Brown, sensing trouble.
"Newton's Third Law says that if I pull on the wagon, the wagon exerts
an equal and opposite force on me. Don't you agree?", asks Old Dobbin.
"Yes... but..."
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What is the "Horse and Wagon Problem"?
 (Continued…)
"If these two forces are equal and opposite, they will cancel, so that the
net force is zero, right?", argues Dobbin.
"Well, I suppose so," stammers Farmer Brown.
"The net force is always the important thing. If the net force is zero, then
Newton's Second Law (and Newton's First Law, too) says that the
acceleration of the wagon must be zero."
"Yes, I remember Newton's Second Law very well, Old Dobbin.", says
Farmer Brown, hopefully. "This physics discussion is certainly
interesting, but let's get going!"
"But that's the point!", objects Old Dobbin, "If the wagon's pull is always
equal and opposite of my pull, then the net force will always be zero, so
the wagon can never move! Since it is at rest, it must always remain at
rest! Get over here and unhitch me, since I have just proven that
Newton's Laws say that it is impossible for a horse to pull a wagon!"
At this point, Farmer Brown throws up his hands in dismay and turns to
you. "Please help me!" he says, "I really should have paid more attention
in physics class! I know that Newton's Laws are correct, and I know that
horses really can pull wagons. There has to be an error in Old Dobbin's
argument, but what is it? How can I convince Old Dobbin that if he pulls
on the wagon, it will move?"
So, what is your reply?
Physics Notes – Dynamics
The Horse and Wagon Explained
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(No Friction Case)
Preliminaries
I have to admit that few physics questions have provided
as much entertainment for me over the years as the "Horse
and Wagon Question" - the answers that students come up
with are just hilarious! (What is the "Horse and Wagon
Problem"?)
The fact is, however, if you can come up with a clear,
logical answer to the "Horse and Wagon Question", you
have a very good grasp of Newton's Laws of Motion and
their application, and if you can't, you don't.
After some study and thought, I hope that you will find
answers like "The wagon moves because it's attached to
the horse." or "If the horse pushes harder on the ground
than the wagon pulls on the horse, then the wagon
accelerates." as entertaining as your physics teacher does!
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The Key
Even though a complete answer to the Horse and
Wagon Question can get rather involved, a clear
explanation only hinges on a couple of simple points:
An object accelerates (or not) because of the forces
that push or pull on it. (Newton's 2nd Law)
Only the forces that act on an object can cancel.
Forces that act on different objects don't cancel after all, they affect the motion of different objects!
(See "Why Don't Action & Reaction Forces Cancel".)
The Forces - No Friction
The diagram at right shows the
horizontal forces that act on
the horse, the wagon, and the
earth. The convention for
drawing the forces in the diagram is:
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The force is drawn as an arrow pointing in the
direction of the force.
The force is drawn on the object getting
pushed or pulled.
The force is labeled with the object doing the
pushing or pulling.
For example, the yellow arrow labeled
"wagon" is a force exerted by the wagon on
the horse. The blue arrow labeled "horse" is a
force exerted by the horse on the ground.
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What are the Newton's Third Law Force Pairs?
The two forces colored yellow in the diagram
are a Newton's Third Law force pair - "horse
pulls wagon" and "wagon pulls horse". They
are equal in magnitude and opposite in
direction.
The two forces colored blue in the diagram
are a Newton's Third Law force pair - "horse
pushes ground" and "ground pushes horse".
They are also equal in magnitude and
opposite in direction.
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Why does the wagon accelerate?
Newton's 2nd Law says that an object
accelerates if there is a net (unbalanced) force
on it. Looking at the wagon in the diagram
above, you can see that there is just one force
exerted on the wagon - the force that the
horse exerts on it. The wagon accelerates
because the horse pulls on it! The amount of
acceleration equals the net force on the
wagon divided by its mass (Newton's Second
Law).
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Why does the horse accelerate?
There are 2 forces that push or pull on the horse
in the diagram above. The wagon pulls the horse
backwards, and the ground pushes the horse
forward. The net force is determined by the
relative sizes of these two forces.
If the ground pushes harder on the horse than
the wagon pulls, there is a net force in the
forward direction, and the horse accelerates
forward.
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If the wagon pulls harder on the horse than the
ground pushes, there is a net force in the backward
direction, and the horse accelerates backward. (This
wouldn't happen on level ground, but it could happen
on a hill...)
If the force that the wagon exerts on the horse is the
same size as the force that the ground exerts, the net
force on the horse is zero, and the horse does not
accelerate.
In any case, the acceleration of the horse equals the
net force on the horse divided by the horse's mass
(Newton's Second Law).
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Why does the ground push on the horse,
anyway?
The force "ground pushes horse" is the
Newton's Third Law reaction force to "horse
pushes ground". These 2 forces are exactly
the same size. If the horse wants the ground
to push him forward, he just needs to push
backwards on the ground.
These two forces do not cancel because they
act on different objects. The force "ground
pushes horse" tends to accelerate the horse,
and the force "horse pushes ground" tends to
accelerate the ground.
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What about the ground?
Looking at the force diagram at the top of the
page, you see that there is one horizontal
force pushing on the ground - the horse
pushes on the ground. Therefore, there is an
net force on the ground, so the ground
should accelerate. Does it?
Of course it does! However the amount of
acceleration equals the size of the net force
divided by the mass of the Earth - and the
mass of the earth is about 6 x 1024 kg. This
means that the acceleration of the ground is
much, much too small to notice.
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Summary:
So, it is possible for horses to pull wagons! It
is true that the force that the horse exerts on
the wagon is the same size as the force that
the wagon exerts on the horse, but these
forces do not combine to produce a zero net
force. The force exerted on the wagon (by the
horse) affects the motion the wagon, and the
force exerted on the horse affects the motion
of the horse.
Physics Notes - Dynamics
 The Horse and Wagon Explained
 (Friction Case)
Before you read this, be sure that you
understand how the horse and wagon works
without friction.
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The Forces:
Compared to the previous diagram, you can
see that two new forces have been added to
the diagram at the right. The friction force
acting on the wagon (colored red) tries to
oppose the motion of the wagon. It is exerted
by the ground. Its Newton's Third Law force
partner is the force "wagon pushes ground".
Note that the force pushing the wagon is
drawn on the wagon, and the force pushing
the ground is drawn on the ground.
As always, these two forces don't cancel
because they act on different objects.
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Here is an analysis in table form.
Force
By
On
Direction
Affects the
Motion of
Horse pulls
Wagon
horse
wagon
right
wagon
wagon
horse
left
horse
horse
ground
left
ground
ground
horse
right
horse
ground
wagon
left
wagon
wagon
ground
rignt
ground
Horse pushes
Ground
Friction
Coments
Action/Reaction
Pair
Action/Reaction
Pair
Action/Reaction
Pair
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Why does the wagon accelerate?
Consulting the diagram, notice that there are
now two forces acting on the wagon. The net
force on the wagon equals the force the horse
exerts minus the friction force the ground exerts.
If the horse pulls harder on the wagon than the
friction force, there will be a forward-pointing
net force, and the wagon will accelerate forward.
If the pull of the horse exactly balances the
friction force, then the net force on the wagon
will be zero, and the wagon will not accelerate.
(This is the situation when the horse is pulling
the wagon at constant velocity.)
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Why does the horse accelerate?
The situation for the horse is the same as in the
previous (no friction) situation.
Does the ground accelerate?
There are now 2 forces acting on the ground - the
horse pushes it backwards and the wagon pushes it
forward. The net force on the ground equals the force
that the horse exerts on the ground minus the force
that the ground exerts on it. If the horse pushes
harder, there will be a backward net force on the
ground. If the wagon pushes harder, there will be a
forward net force on the ground. If they push equally,
the net force on the ground will be zero. In any case,
the acceleration of the ground will not be noticeable,
due to the enormous mass of the earth.
Why Don't Action & Reaction
Forces Cancel?
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The Problem:
Often people have the following difficulty
with Newton's Third Law:
"If A pushes B, then B pushes A with an equal
and opposite force. If these forces are equal
and opposite, they cancel, producing a net
force of zero. This means that neither object
can accelerate, which means that Newton's
Laws predict that nothing can ever move."
(See The Horse & Cart Problem.) What's going
on?
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The Key Ideas:
Object A accelerates (or not) because of the
forces that push or pull on it. (Newton's 2nd
Law) Forces that push or pull on some other
object have no effect on object A's motion even if object A exerts them.
Only the forces that act on an object can
cancel. Forces that act on different objects
don't cancel - after all, they affect the motion
of different objects!
The Solution:
 Newton's Third Law really does say that if A
pushes B, then B pushes A with an equal and
opposite force. However, these forces DO
NOT CANCEL because they influence the
motion of different objects. The force that A
exerts on B influences B's motion, and the
force that B exerts on A influences A's
motion. The force on B can cancel with other
forces on B - but NOT with forces on A (and
vice versa).
Internal Forces
Now you know why Newton's Third Law action and
reaction forces don't cancel - it seems pretty obvious
once you get it. The problem is that sometimes
Newton's Third Law action and reaction forces DO
cancel...
You Can't Bully Yourself...
 Have you ever noticed that you can't push yourself?
You can push a book and it accelerates, and you can
push another person and they accelerate, but you
can't accelerate yourself by pushing yourself.
 You can lift a book off the table, and you can lift
another person off the ground, but you can't lift
yourself off the ground. (A person can't literally "pull
themselves up by the bootstraps" as the old saying
says...)
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Because:
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Suppose that one part of an object is pushing on another part your right hand is pushing on your left hand. Newton's Third Law
tells you that both hands exert forces, and that the force on your
right hand is equal and opposite to the force on your left.
Previously, you saw that the force that your right hand exerts on
your left hand accelerates your left hand, and that the force your
left hand exerts on your right hand accelerates your right hand and you can see and feel that happening.
Notice, though, that no matter how hard you push, the forces
your hands exert on one another will not accelerate your body as
a whole.
Forces exerted by one part of an object on another part of the
same object are called internal forces - and
internal forces never influence the motion of an object.
Newton's Third Law action/reaction forces between objects do
not cancel - but internal forces (Newton's Third Law
action/reaction forces within an object) do cancel.
Forces between distinct, separate objects are called external
forces, and external forces DO influence the motion of objects.
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Hold a sheet of paper in midair and tell a
friend that the heavyweight champion of the
world could not strike the paper with a force
of 200N (45 pounds). You would be correct,
unless you held the paper against the wall,
which would gladly assist the paper!
For every interaction between things, there is
always a pair of oppositely directed forces
that are equal in strength