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Conceptual Physics

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Title: Conceptual Physics


1
Conceptual Physics
  • Chapter Seven Notes
  • Newtons Third Law of Motion Action and Reaction

2
7.1 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 !.

3
7.3 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.

4
7.3 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.

6
Identifying 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.

11
7.4 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

12
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13
7.5 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.

14
7.6 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.

36
7.7 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
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