Newton's third law

A topic in Learners' conceptions and thinking

Newton's third law is a common source of learning difficulties and alternative conceptions.

(Read about common alternative conceptions.)

Newton-3: The law

Newton's third law considers forces to be interactions between two objects:

• an interaction between an apple and the earth
• an interaction between your feet and the floor you are standing on
• an interaction between the cycle tire and the road surface

and so on.

Newton 3 tells us (in formal phrasing) that when a body (A) exerts a force on another body (B) then the second body (B) also exerts a force on body A, and that this force will be equal in magnitude, opposite in direction ('anti-parallel'), and acting along the same line.

As so often in science, such a statement may seem very obscure and complex, until one really grasps its meaning (after which it may even seem 'obvious' to the expert).

So:

• if the earth's gravity pulls down on the apple, then apple pulls up on the earth with a force that is just as large
• if your feet are pushing down on the floor (because you have weight) then the floor us pushing up on your feet with a force equal to that weight
• if there is a force from the road surface which is pushing the cycle tyre forward, then the tyre is pushing back on the road surface with a force that is the same size.

Once one has acquired this principle, it is fairly simple to apply…but students may find the idea quite counter-intuitive, and there are a number of common alternative conceptions that block students fully understanding and coming to apply the idea.

The nature of our language may act as one impediment to appreciating the basis of the law, as in any expression such as:

"when a body (A) exerts a force on another body (B) then…"

"if the earth's gravity pulls down on the apple…"

"if your feet are pushing down on the floor…"

The even though the meaning of the sentence is that there is a symmetrical interaction, inevitably the way we talk/write (and think verbally) seem to prioritise body A, the earth, the feet, etcetera. over body B, the apple or the floor, etcetera.

This may not be a trivial point as it has been shown that it is very common for people to spontaneously conceptualise many situations in terms of an active agent (body A? the earth?…), acting on a passive patient (body B?, the apple?…). Even in discussing chemical reactions, there is a tendency for learners to think of one substance/species acting on the other (the acid attacks the metal; the water molecule collides with a molecule in solid sugar – there is one active partner).

Reactions?

One aspect of the physics formalism which is unhelpful is that the interaction is commonly referred to as an action and reaction. This suggests two distinct forces, one acting first which provokes the other. This is completely wrong – the interaction acts to the same extent on both objects with exactly the same timing.

In many ways it is better to think of 'a' force acting between (e.g, the apple and the earth), but the 'every actions has an equal and opposite reaction' formulation has wide currency.

Misidentifying the force pair

A common error that students make is to see the 'action-reaction' pair acting on the same object, as in real situations there is rarely only one isolated interaction to consider.

So, if an apple is hanging from a tree a student may suggest that gravity is pulling the apple down, and there is a force from the stalk pulling it up – and the apple does not fall because the two forces balance. So far, so good- but they may think of these two forces as the Newton's third law pair. (If the stalk pulls the apple up, then the apple pulls the stalk down: that is the correct pairing.)

If the 'action=reaction' pairs acted on the same object, then nothing would ever accelerate – movement would never start or end). {As Newton's first law tells us.}

So, if the apple is falling from the tree, there will be gravity pulling the apple down and air resistance pushing it up (as frictional forces always work against the direction of motion), but if the student thinks that these two forces are the Newton 3 pair, then the apple should not be accelerating – indeed, the frictional force should have been large enough to stop the apple falling at all, taking over form the tension in the stalk when the apple was freed from the tree.

[This can lead to a kind of reductio ad absurdum argument: if the frictional force was large enough to balance the apple's weight, then the apple would not fall – but if the apple is not moving then there should be no frictional force acting – so there is an inconsistency which shows something is wrong with (at least) one of our premises.]

Confusing cause and effect

Another aspect is that in physics we distinguish between the force itself, and its effect. Forces of equal magnitude can have different effects when acting on different bodies. So, for example, although when an apple is falling form a tree there is a force acting on both the apple and earth, and the force acting on both is the same , say 1N, the acceleration caused will be very different form the apple (1o ms^-1) and the very much more massive earth (so small as to be practically 0 ms^-1).

Often students do not make the distinction, seeing the size of the effect (or an expected effect) as indicating the magnitude of the force.

Newton-3 errors

In my research, I have commonly found students interpret interactions in ways that are in contradiction to Newton's 3rd law:

1. considering that a larger (or more highly charged) body exerts a force on a smaller (or less charged) body, but not vice versa;
2. considering that a larger (or more highly charged) body exerts a larger force on a smaller (or less charged) body than it 'experiences';
3. considering the forces on both bodies act in the same direction: so if the nucleus pulls on electrons, the electrons push the nucleus away.

Examples of students’ alternative conceptions relating to Newton-3

See the following posts:

Do the forces from the outer shells push the protons and the neutrons together?

The Sun would pull more on the Earth…

They're both attracting each other but this one's got a larger force

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