CONCEPTUAL PHYSICS › CHAPTER 5, NEWTON’S THIRD LAW
You Cannot Push Without Being Pushed Back
Chapter 4 asked what decides how much something accelerates. This chapter asks where the push came from in the first place, and the answer forces a change in how you talk about forces at all: a force is never something one object has. It is something two objects do to each other.
5.A Name both forces in an interaction, in the form A pushes on B, and say which object each one acts on.
5.B Explain why the two forces of a pair never cancel each other, and use that to say why anything is able to move at all.
5.C Find the outside push that gets a thing going, whether it is a foot on the ground or gas leaving a rocket.
1. A force is not something an object has
You cannot push on something without it pushing back on you. Lean on a wall and the wall leans back, with exactly the force you gave it. Punch it and it punches your hand, which is not a figure of speech, it is why your hand hurts.
So a force is never a possession. Nobody has a force the way they have a mass. A force is what happens between two things, and if you can name a force you can always name two objects and draw two arrows.
2. Naming the partner correctly
The two forces in a pair are always the same size, always point opposite ways, always act on different objects, and are always the same kind of force. If one of them is gravity, so is the other.
That last rule catches the most common wrong answer in the chapter. The partner to the Earth pulls down on you is you pull up on the Earth. It is not the floor pushes up on you. The floor pushing up on you is a real force and it is a perfectly good answer to a different question; it belongs to a different pair, the one whose other half is you push down on the floor.
Two students face each other on rolling chairs and one of them pushes. Change how heavy each of them is and push again. The two arrows are the forces they exert on each other, and they stay the same length no matter what you do to the masses. What changes is what each person does about it.
Notice what the simulation refuses to let you do. There is no setting of the sliders that makes one arrow longer than the other. The heavier person is not pushed harder; the heavier person is harder to push, which is Chapter 4 arriving to finish the sentence Chapter 5 started.
3. Why the two forces do not cancel
Here is the argument that stops most students, and it is worth taking slowly because every part of it is true except the conclusion. A horse pulls a cart. The cart pulls back on the horse just as hard. Equal and opposite, so they cancel, so the cart can never move.
The word doing the damage is cancel. Two forces cancel only when they act on the same object. The two members of a pair never do, because being on different objects is what makes them a pair in the first place. So they can be equal, and opposite, and cancel nothing whatsoever.
The same horse and cart, drawn three ways. Slide across to change which object you are looking at, and the picture shows only the forces acting on that object. The pair the argument worries about appears in full only in the first view, where the two halves are on different bodies and nothing cancels.
4. So what actually moves the horse and cart
Draw the cart alone and there is one forward force on it: the horse. Draw the horse alone and there are two horizontal forces, the cart pulling it backward and something pushing it forward. That something is the ground.
The horse pushes backward on the ground with its hooves, and by everything in section 2 the ground pushes forward on the horse. That forward push is what gets the whole business moving, and it is the force students almost always leave out, because the ground is scenery rather than a participant.
The quickest way to see that it matters is to remove it. On frictionless ice you cannot push backward on anything, so nothing pushes you forward, and you stay exactly where you are however hard you move your legs.
5. Rockets, balloons, and recoil
A rocket does not push against the air. It throws gas backward, and the gas pushes the rocket forward. That is a pair like any other, and it is why a rocket works in space, where there is nothing outside to push against at all. The air is in fact a nuisance to a rocket, which is part of why they are built to get out of it quickly.
Let go of an untied balloon and you have the same physics in your hand. The air rushes out one way and the balloon goes the other. So does a rifle into a shoulder, and so do you when you step out of a small boat and the boat slides away behind you.
One question always follows: if the forces are equal, why does the gas move so much faster than the rocket, and the bullet so much faster than the rifle? Because equal forces do not mean equal results. The force is the same on both, and the acceleration each one gets also depends on how much there is of it. Chapter 5 says the forces match. Chapter 4 says the outcomes do not have to.
Check yourself
1. A book rests on a table. Write the two forces of the pair that involves the table and the book, each in the form A pushes on B.
The table pushes up on the book, and the book pushes down on the table. Both are contact forces, both the same size, each acting on a different object. Note what is not in this pair: the Earth pulling down on the book. That is a real force on the book, but its partner is the book pulling up on the Earth.
2. A student says the pair for a ball resting on the ground is gravity pulls the ball down and the ground pushes the ball up. Say what is wrong, and give the correct partner for each.
Both of those forces act on the same object, the ball, so they cannot be a pair. They happen to be equal here only because the ball is not accelerating. The partner to the Earth pulls the ball down is the ball pulls the Earth up. The partner to the ground pushes the ball up is the ball pushes the ground down. Two separate pairs, four forces, and only two of them are drawn on the ball.
3. Explain in one sentence the difference between two forces are equal and opposite and two forces cancel.
Equal and opposite is a statement about the two arrows; cancelling is a statement about what they do to one object, and it requires both of them to be acting on that object. Every action and reaction pair is equal and opposite, and no action and reaction pair ever cancels.
4. Rank these by how easily a person can start moving forward, most easily first, and say why: on dry pavement in trainers; on wet ice in smooth shoes; on a loose gravel path; standing in a canoe on still water.
Dry pavement, then gravel, then the canoe, then wet ice. The question is really how hard you can push backward on something without it giving way. Pavement holds, gravel slides a little, the canoe simply moves off behind you and takes most of your push with it, and the ice gives you almost nothing to push against at all. In every case the force that moves you forward is the other thing pushing back on you.
5. A student says a rocket cannot work in space, because there is no air for the exhaust to push against. Say what is wrong, and give the right explanation in one sentence.
The rocket never pushes on the air. It pushes on its own exhaust gas, and the gas pushes back on the rocket, which is a complete pair needing nothing outside the rocket at all. Air would only get in the way. The student has confused a rocket with a swimmer, who genuinely does need something to push against.
Chapter 6, Momentum. This chapter said that the two forces in an interaction are always equal. The next one follows that through to what the two objects end up doing, and gets a rule that holds for collisions, explosions and every recoil on this page.