Chapter Seven Notes: Newton’s Third Law of Motion – Action and

Reaction

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!

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 –

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.

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.

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.

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.

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.

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.

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.

Consider a cannon and cannon ball. According to Newton’s second law we must consider the masses.

Cannon ball: F/m = a Cannon: F/m = a

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 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.

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..."

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

(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!

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:

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.

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.

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).

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.

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).

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.

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.

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.

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.

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 wagon horse left horse

Horse pushes

Ground

horse ground left ground Action/Reaction

Pair ground horse right horse

Friction ground wagon left wagon Action/Reaction

Pair wagon ground rignt ground

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.)

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?

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?

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...)

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.

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