Should we legislate against actions and reactions in introductory physics?
Keith S. Taber
Even apparently authoritative sources can sometimes encourage alternative conceptions (misconceptions). I've recently been reading entries in John Gribbin's 'Companion to the Cosmos'. This 'Companion' is a large book styled as a reference book – like a dictionary or encyclopaedia in that it is a series of entries arranged alphabetically – so, something that presents as an authoritative source. That may not sound like a good read, but (even though is is now quite dated, being published in 1996) actually it contains a lot of really fascinating material. I have come across a good deal of intriguing and interesting detail in its pages.
John Gribbin's 'Campanion to the Cosmos': a worthy companion
I did not expect to learn anything new from the entry on 'Newton's laws of motion', but I did find something to take note of. The statement of the third law was presented as follows:
"Whenever a force (or, as Newton put it, an action) is applied to an object, the object pushes back with an equal and opposite reaction. So, for example, gravity pulls me downwards with a force equal to my weight, and the chair I am sitting on pushes back with an equal and opposite reaction, leaving me sitting still, not accelerating downwards (as I would if there were no intervening chair or floor) to the centre of the Earth. And while gravity pulls me towards the centre of the Earth, the mass of my body is pulling the Earth towards me with an equal force."
Gribbin's presentation of Newton's Third Law
Now if I had been an editor asked to comment on this I would have suggested some deletions to give a much more focused treatment:
"Whenever a force (or, as Newton put it, an action) is applied to an object, the object pushes back with an equal and opposite reaction. So, for example, gravity pulls me downwards with a force equal to my weight…and while gravity pulls me towards the centre of the Earth, the mass of my body is pulling the Earth towards me with an equal force."
An edited version of Gribbin's account less likely to confuse a novice?
I am not sure I like the 'mass' doing the pulling, rather than perhaps the 'matter' of my body. But this edited version does seem to reflect the law: Gribbin's body is pulled towards the centre of the earth and also pulls the earth with an equal force. Two bodies, Gribbin's and the earth, are attracted towards each other, and the same magnitude of forces acts on both. Gribbin is pulled towards the earth with a force of perhaps 700N in which case the earth is also being pulled with a force of 700N towards Gribbin.
Action and delayed reaction?
But I think the terms 'action' and 'reaction' are unhelpful as it suggests a sequence of actions: A attracts (or repels) B, and in response, B then attracts (or repels A). But it is more helpful to think not of a pair of forces, but rather as a force as being something (singular) which acts between (and so on) two bodies – such as an attractive force between John Gribbin and planet Earth.
A common misconception
There are a number of common alternative conceptions concerning the area of forces, acceleration and motion that Newton's laws of motion describe. One of these common 'misconceptions' involves misidentifying the 'action' – 'reaction' pair as both acting on the same body, and determining that because the forces are 'opposite and equal' they must cancel.
Read about conceptions of Newton's third law
So, for example, consider an apple hanging securely from a tree (as Newton once did). There is a downwards force on the apple (due to its weight) but it does not fall as there is also a balancing upwards force provided by the stem (stalk) from which the apple hangs. This is a fair description, BUT this does not describe the so-called 'action' and 'reaction' of Newton's third law. If it did, and we generalised this, we would end up with a situation where we ascribe balanced forces to every body (as there must always be an equal and opposite force acting, Newton said so). This would mean no acceleration.
In that universe (assuming Newton's first law still applied), every stationary body must remain stationary, and every moving body must continue to move in the same direction at the same speed. That would not be a very interesting universe. It would be a universe with no need for Newton's second law which tells us how a body is accelerated under net forces, as there would be no net forces if every force was balanced by its reaction! If that universe exists, it is not our universe.
Formulations of the law
The more wordy "if [or perhaps, 'whenever' is better] a body A exerts a force on a body B, then body B exerts a force on body A that is equal in magnitude and opposite in direction" is perhaps more difficult for some learners to unpick – but has the advantage of making it clear the force[s] act[s] on two different bodies. If the apple is pulled down by the earth, then the earth is pulled up by the apple. Simultaneously: While the apple is pulled down by the earth, the earth is pulled up by the apple.
I think from the teaching perspective I would prefer a law definition something like 'A force is an interaction between two bodies and always acts on both with equal magnitude (along a line joining the centres of the bodies)'. Perhaps there is some good reason we do not always teach it that way, but I suspect it is more a matter of Newton's first law (of teaching) acting – that is, inertia. The terms 'action' and 'reaction' have become established. And perhaps by deference to Newton (who like everyone else had to come to terms with his own laws: having previously suggested that, as it was moving around the sun rather than being attracted into it, a comet may be directed by magnetism as well as being attracted to the Sun).
The apple is not falling (and the earth is not rising – though to be fair it is rather hard to notice the earth rising even when the apple does fall *) so the forces on the apple are balanced – but these are not an 'action-reaction' pair. Rather we have a pair of such 'pairs' ,and we are equating across these pairs. (This is much mote obvious if we avoid talk of 'reactions' and 'action-reaction' pairs and just define a force as acting between two different bodies as then two forces acting on the same body should not get confused in this way – as Newton's third law refers and applies separately to each individual interaction/force).
The apple hangs form the branch by a connecting stem (also known as the stalk). The apple pulls down on the stem with the same magnitude force that the stem pulls the apple up (Newton's third law), and the earth pulls down on the apple with the same force as the apple pulls up on the earth (Newton's third law); AND as the full weight of the apple is supported by the stem – as it is robust enough: not due to Newton's third law but simply as a fact about the tree structure at this point in time – and so the stem is pulling up with a force that happens to be equivalent to the apple's weight . This means there is no net force on the apple, and so it goes nowhere (Newton's first law).
But one day the stem, the apple's connection to the branch, will have changed such that it can no longer support the weight of the apple and the apple will fall; while Newton's third law continues to apply to the apple, the earth, the tree, and everything else. An area of the stem called the abscission zone becomes changed by the changing pattern of plant hormones triggered by the environment such that the cells in this part of the stem become less strongly adhered together. (Crudely, the tree physiology includes a system which dissolves the 'glue' holding cells together in this region of the stalk once the fruit has matured.)
For a moment the stem will be pulling up on the apple, but now with a force less than the apple's weight. (And by Newton's third law, at that moment the apple will be pulling the stem with an equal force that is somewhat less than its weight.) The apple's weight has not changed, and so the force between the apple and and earth is still the same – and the net force on the apple is no longer balanced, so it starts to accelerate towards the ground in the manner that Newton noticed.
In the simplified case, we can imagine the stem slowly changing, and its tensile strength very gradually diminishing from a value more than sufficient to support the apple to reaching a critical point where it just drops below what can support the weight of the apple – at which point the stem structure fails, and the apple falls. Realistically, this 'ideal' scenario is unlikely, as winds (as well as birds, squirrels and naughty children) lead to branches moving about, such that the fruit is subject to various forces – so the stalk will likely reach breaking point earlier, when subject to the apple's weight plus some additional stress due to some incidental momentary contingency. But the principle is sound even if the actual situation is likely more complex because the apple may well fall during a dynamic episode rather than when hanging in an equilibrium state. When the stem cannot support the apple, it will fall.
A misleading account?
The point is that Newton' third law is very simple, but it is easily (and often) misunderstood and misapplied. So, as I started to read Gribbin's presentation of the law, I though 'whoa (or something equivalent), that's not right!'
"Whenever a force (or, as Newton put it, an action) is applied to an object, the object pushes back with an equal and opposite reaction. So, for example, gravity pulls me downwards with a force equal to my weight, and the chair I am sitting on pushes back with an equal and opposite reaction, leaving me sitting still, not accelerating downwards (as I would if there were no intervening chair or floor) to the centre of the Earth."
The initial section of Gribbin's presentation.
I think Gribbin is meaning that "[as (i)] gravity pulls me downwards with a force equal to my weight, and [ii] the chair I am sitting on [because it is therefore subject to a downwards force from my weight] pushes back with an equal and opposite reaction." At least, that is how I think we need to read this according to physics.
The third law force here is between the chair (pushing upwards on Gribbin) and Gribbin (pushing down on the chair), and this is fine. But my initial reading assumed the intended pairing was between the downward force on Gribbin due to gravity and the upward ('normal') force from the chair. I am sure Gribbin understood this basic physics, but I thought his wording is unhelpful, as he seems to be referring to two forces acting on the same body:
"Whenever a force (or, as Newton put it, an action) is applied to an object, the object pushes back with an equal and opposite reaction. So, for example, gravity pulls me downwards …and the chair I am sitting on pushes back [on me]…"
A misreading of Newton's third law
Moreover, the reference to not accelerating relies on another pair of balanced forces not mentioned in the presentation. For "the chair I am sitting on pushes back with an equal and opposite reaction" only because it is also supported by the ground. Gribbin refers to the floor, and the chair is only able to support him because it is supported by the floor. And that is because it is robust enough to push upwards on a chair with a force that balances the weight of {Gribbin + his chair}. So there are three distinct action-reaction pairs (or if you prefer, simply forces) acting: Gribbin-earth; Gribbin-chair; chair-floor, and Gribbin does not accelerate due his weight because {the floor pushes up on the chair} AND so {the chair pushes up on him}.
Perhaps you might argue that we have to also consider how the floor is supported by the building foundations and those foundations by the ground below…before we can explain why the earth is pulling on Gribbin without him accelerating? But my point is that in introducing Newton's third law, it might be better to focus on one interaction rather than complicate the scenario. Newton's third law tells us that if Gribbin is seated then the chair pushes up on Gribbin as he pushes down in it, but it does not (of itself) – as might seem to be implied by the text – tell us why he is able to sit on the chair or why the chair does not fall through the floor .
Seeing the science at the resolution of the learner
As is often the case, someone who already knows the science can interpret the text in an orthodox way (I wonder how often examiners give the benefit of the doubt to misconceived explanations?) – but if the point is to communicate an idea to someone who has not yet mastered it, then avoiding potentially confusing complications may be the best strategy.
Yes, I am being pedantic about wording, but with reason. We know learners commonly misidentify where the 'action' and 'reaction' are acting, and so come to explain balanced forces as necessarily due to Newton's third law. The law actually tells us that a force always acts (with equal magnitude, if not always equal effect) on a pair of bodies – so can never directly be a valid explanation for why the forces on any single body are balanced. Teachers and authors need to be very careful in their phrasing if they are not to encourage learners to acquire alternative conceptions that many will find convincing, and, indeed, to reinforce such misconceptions where they are already in place.
* That is a whole other common misconception, not distinguishing the force itself from the effect produced – so another common alternative conception is that the larger earth must attract the moon more than the little moon attracts the earth, and the atomic nucleus must (except in hydrogen) attract an electron more than the electron attracts the nucleus.
But, actually, no, the wind-shield experienced just as much force as fly on the wind-shield – but the effect is usually more critical for the poor fly. This is worth thinking about when considering how some footballers respond to tackles: in any interaction both players experience exactly the same force of impact! Of course, the same force can do different levels of damage depending upon where it is applied and at what angle, but it is still interesting just how often one player is floored and pole-axed by another who seems barely to notice any contact.
Me ref? I hardly touched him.
Work cited:
- John Gribbin (1996) Companion to the Cosmos. London: Weidenfeld & Nicolson
The book Student Thinking and Learning in Science: Perspectives on the Nature and Development of Learners' Ideas gives an account of the nature of learners' conceptions, and how they develop, and how teachers can plan teaching accordingly.
It includes many examples of student alternative conceptions in science topics.
