Title: Conceptual Physics
1Conceptual Physics
- Chapter Seven Notes
- Newtons Third Law of Motion Action and Reaction
27.1 Forces and Interactions
- 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!
7.2 Newtons Third Law
- Newtons 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 action force !
- Other force reaction force !.
37.3 Identifying Action and Reaction
- 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.
47.3 Identifying Action and Reaction (continued)
- 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.
5- 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.
6Identifying Action and Reaction Force Pairs
- 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.
7- 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.
8- 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. - Answer Balloon wall pushes enclosed air
particles inwards.
9- 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.
10- 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.
117.4 Action and Reaction on Different Masses
Force and Mass
- Consider a cannon and cannon ball. According to
Newtons second law we must consider the masses.
- Cannon ball F/m a
- Cannon F/m a
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137.5 Defining Systems
- Whenever one object exerts a force on a second
object, the second object exerts an equal and
opposite force on the first. Action-reaction
pairs never act on same body. - Defining your System
- Two objects define a system for a Newtons 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.
147.6 The Horse Cart Problem
- 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..."
15- 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?
16- Physics Notes Dynamics
- The Horse and Wagon Explained
- (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!
17- 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
18- 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.
19- 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.
20- 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).
21- 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. -
-
22- 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).
23- 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.
24- 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.
25- 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.
26- 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.
27- 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.
28- Here is an analysis in table form.
Force By On Direction Affects the Motion of Coments
Horse pulls Wagon horse wagon right wagon Action/Reaction Pair
Horse pulls Wagon wagon horse left horse Action/Reaction Pair
Horse pushes Ground horse ground left ground Action/Reaction Pair
Horse pushes Ground ground horse right horse Action/Reaction Pair
Friction ground wagon left wagon Action/Reaction Pair
Friction wagon ground rignt ground Action/Reaction Pair
29- 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.)
30- 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.
31- Why Don't Action Reaction
- Forces Cancel?
-
- 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?
32- 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!
33- 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).
34- 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...)
35- Because
- 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.
367.7 Action Equals Reaction
- 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