Tag: Newton's third law

A corny teaching analogy

Pop goes the comparison

Keith S. Taber

The order of corn popping is no more random than the roll of a dice.

I was pleased to read about a 'new' teaching analogy in the latest 'Education in Chemistry' (the Royal Society of Chemistry's education magazine) – well, at least it was new to me. It was an analogy that could be demonstrated easily in the school science lab, and, according to Richard Gill (@RGILL_Teach on Twitter), went down really well with his class.

Teaching analogies

Analogies are used in teaching and in science communication to help 'make the unfamiliar familiar', to show someone that something they do not (yet) know about is actually, in some sense at least, a bit like something they are already familiar with. In an analogy, there is a mapping between some aspect(s) of the structure of the target ideas and the structure of the familiar phenomenon or idea being offered as an analogue. Such teaching analogies can be useful to the extent that someone is indeed highly familiar with the 'analogue' (and more so than with the target knowledge being communicated); that there is a helpful mapping across between the analogue and the target; and that comparison is clearly explained (making clear which features of the analogue are relevant, and how).

Read about analogies in science

The analogy is discussed in the July 2022 Edition of Education in Chemistry, and on line.

Richard Gill suggests that 'Nuclear decay is a tough concept' to teach and learn, but after making some popcorn he realised that popping corn offered an analogy for radioactive decay that he could demonstrate in the classroom.

Richard Gill describes how

"I tell the students I'm going to heat up the oil; I'm going to give the kernels some energy, making them unstable and they're going to want to pop. I show them under the visualiser, then I ask, 'which kernel will pop first?' We have a little competition. Why do I do this? It links to nuclear decay being random. We know an unstable atom will decay, but we don't know which atom will decay or when it will decay, just like we don't know which kernel will pop when."

Gill, 2022

In the analogy, the corn (maize) kernels represents atoms or nuclei of an unstable isotope, and the popped corn the decay product, daughter atoms or nuclei. 1

'Parents' before 'decay
(Image by Paulo Marcos pmarcos6821 from Pixabay)
'Daughters' after 'decay'
(Image by Leonardo Alvarado from Pixabay)

Richard Gill homes in on a key feature of radioactive decay which may seem counter-intuitive to learners, but which is actually a pattern found in many different phenomena – exponential decay. The rate of radioactive decay falls (decays, confusingly) over time. Theoretically the [radioactive] decay rate follows a very smooth [exponential] decay curve. Theoretically, because of another key feature of radioactive decay that Gill highlights – its random nature!

It may seem that something which occurs by random will not lead to a regular pattern, but although in radioactivity the behaviour of an individual nucleus (in terms of when it might decay) cannot be predicted, when one deals with vast numbers of them in a macroscopic sample, a clear pattern emerges. Each different type of unstable atom has an associated half-life which tells us when half of a sample will have decayed. These half-lives can vary from fractions of a second to vast numbers of years, but are fixed for a particular nuclide.

Richard Gill notes that he can use the popping corn demonstration as background for teaching about half-life,

I usually follow this lesson with the idea of half-lives. The concept of half-lives now makes sense. Why are there fewer unpopped kernels over time? Because they're popping. Why do radioactive materials become less radioactive over time? Because they're decaying.

Gill, 2022

Perhaps he could even develop his demonstration to model the half-life of decay?

Modelling the popcorn decay curve

The Australian Earth Science Education blog suggests

"Popcorn can be used to model radioactive decay. It is a lot safer than using radioactive isotopes, as well as much tastier"

and offers instructions for a practical activity with a bag of corn and a microwave to collect data to plot a decay curve (see https://ausearthed.blogspot.com/2020/04/radioactive-popcorn.html). Although this seems a good idea, I suspect this specific activity (which involves popping the popping corn in and out of the oven) might be too convoluted for learners just being introduced to the topic, but could be suitable for more advanced learners.

However, The Association of American State Geologists suggests an alternative approach that could be used in a class context where different groups of students put bags of popcorn into the microwave for different lengths of time to allow the plotting of a decay curve by collating class results (https://www.earthsciweek.org/classroom-activities/dating-popcorn).

Another variants is offered by The University of South Florida's' Spreadsheets Across the Curriculum' (SSAC) project. SSAC developed an activity ("Radioactive Decay and Popping Popcorn – Understanding the Rate Law") to simulate the popping of corn using (yes, you guessed) a spreadsheet to model the decay of corn popping, as a way of teaching about radioactive decay!

This is more likely to give a good decay curve, but one cannot help feeling it loses some of the attraction of Richard Gill's approach with the smell, sound and 'jumping' of actual corn being heated! One might also wonder if there is any inherent pedagogic advantage to simulating popping corn as a model for simulating radioactive decay – rather than just using the spreadsheet to directly model radioactive decay?

Feedback cycles

The reason the popping corn seems to show the same kind of decay as radioactivity, is because it can be represented with the same kind of feedback cycle.

This pattern is characteristic of simple systems where

  • a change is brought about by a driver
  • that change diminishes the driver

In radioactive decay, the level of activity is directly proportional to the number of unstable nuclei present (i.e., the number of nuclei that can potentially decay), but the very process of decay reduces this number (and so reduces the rate of decay).

So,

  • when there are many unstable nuclei
  • there will be much decay
  • quickly reducing the number of unstable nuclei
    • so reducing the rate of decay
    • so reducing the rate at which unstable nuclei decay
      • so reducing the rate at which decay is reducing
      • …

and so forth.

Exponential decay is a characteristic of systems with a simple negative feedback cycle
(source: ASCEND project)

Recognising this general pattern was the focus of an 'enrichment' activity designed for upper secondary learners in the Gatsby SEP supported ASCEND project which presented learners with information about the feedback cycle in radioactive decay; and then had them set up and observe some quite different phenomena (Taber, 2011):

  • capacitor discharge
  • levelling of connected uneven water columns
  • hot water cooling

In each case the change driven by some 'driver' reduced the driver itself (so a temperature difference leads to heat transfer which reduces the temperature difference…).

Read about the classroom activity

In Richard Gill's activity the driver is the availability of intact corn kernels being heated such that water vapour is building up inside the kernel – something which is reduced by the consequent popping of those kernels.

A negative feedback cycle

Mapping the analogy

A key feature of an analogy is that it can be understood as a kind of mapping between two conceptual structures. The making popcorn demonstration seems a very simple analogue, but mapping out the analogy might be useful (at least for the teacher) to clarify it. Below I present a representation of a mapping between popping corn and radioactive decay, suggesting which aspects of the analogue (the popping corn) map onto the target scientific concept.

Mapping an analogy between making pop-corn and radioactive decay

In this mapping I have used colour to highlight differences between the two (conceptual) structures. Perhaps the most significant difference is represented by the blue (target concept) versus red (analogue) features.

Most analogies only map to a limited extent

There will be aspects of an analogue that do not map onto anything on the target, and sometimes there will be an important feature of the target which has no analogous feature in the analogue. There is always the possibility that irrelevant features of an analogue will be mapped across by learners.

As one example, the comparison of the atom with a tiny solar system was once an image often used as a teaching analogy, yet it seems learners often have limited understandings of both analogue and target, and may be transferring across inappropriately – such as assuming the electrons are bound to the atom by gravity (Taber, 2013a). Where students have an alternative conception of the analogue (the earth attracts the sun, but not vice versa) they will often assume the same pattern in the target (the nucleus is not attracted to the electrons).

Does this matter? Well, yes and no. A teaching analogy is used to introduce a technical scientific concept by making it seem familiar. This is a starting point to be built upon (so, Richard Gill tells us that he will build upon the diminishing activity of cooking corn in his his popcorn demonstration to introduce the idea of half-life), so it does not matter if students do not fully understand everything immediately. (Indeed, it is naive to assume most learners could acquire a new complex set of ideas all at once: learning is incremental – see Key ideas for constructivist teaching).

Analogies can act as 'scaffolds' to help learners venture out from their existing continents of knowledge towards new territory. Once this 'anchor' in learners' experience is established one can, so to speak, disembark from the scaffolding raft the onto the more solid ground of the shore.

Read about scaffolding learning

However, it is important to be careful to make sure

  • (a) learners appreciate the limitations of models (such an analogies) – that they are thinking and learning tools, and not absolute accounts of the natural word; and that
  • (b) the teacher helps dismantle the 'scaffolding' once it is not needed, so that it is not retained as part of the learners 'scientific' account.
Weak anthropomorphism

An example of that might be Gill's use of anthropomorphism.

…unstable atoms/nuclei need to become stable…

…I'm going to give the kernels some energy, making them unstable and they're going to want to pop…

Anthropomorphism

This type of language is often used to offer narratives that are more readily appreciated by learners (making the unfamiliar familiar, again) but students can come to use such language habitually, and it may come to stand in place of a more scientific account (Taber & Watts, 1996). So, 'weak' anthropomorphism used to help introduce something abstract and counter-intuitive is useful, but 'strong' anthropomorphism that comes to be adopted as a scientific explanation (e.g., nuclei decay because they want to be stable) is best avoided by seeking to move beyond the figurative language as soon as students are ready.

Read about anthropomorphism

The 'negative' analogy

The mapping diagram above may highlight several potential teaching points that may be considered (perhaps not to be introduced immediately, but when the new concepts are later reinforced and developed).

Where does the energy come from?

One key difference between the two systems is that radioactive decay is (we think) completely spontaneous, whereas the corn only pops because we cook it (Gill used a Bunsen burner) and left to its own devices remains as unpopped kernels.

Related to this, the source of energy for popping corn is the applied heat, whereas unstable nuclei are already in a state of high energy and so have an 'internal' source for their activity. This a key difference that will likely be obvious to some, but certainly not all learners in most classes.

When is random, random?

A more subtle point relates to the 'random' nature of the two events. I suggest subtle, because there are many published reports written by researchers in science education which suggests even supposed experts can have a pretty shaky ideas of what counts as random (Taber, 2013b).

Read 'Nothing random about a proper scientific evaluation?'

Read about the randomisation criterion

As far as scientists understand, the decay of one unstable nucleus in a sample of radioactive material (rather than another) is a random process. It is not just that we are not yet able to predict when a particular nucleus will decay – according to current scientific accounts it is not possible to predict in principle. This is an idea that even Einstein found difficult to accept.

That is not true with the corn. Presumably there are subtle differences between kernels – some have slightly more water content, or slightly weaker casings. Perhaps more significantly, some are heated more than others due to their position in the pan and the position of the heat source, or due differential exposure to the cooking oil… In principle it would be possible to measure relevant variables and model the set up to make good predictions. (In principle, even if in practice a very complex task.) The order of corn popping is no more random than…say…the roll of a dice. That is, physics tells us it follows natural laws, even if we are not in a position to fully model the phenomenon.

(We might suggest that a student who considered the corn popping as a random event because she saw apparently identical kernels all being heated in the same pan at the same time is simply missing certain 'hidden variables'. Einstein wondered if there were also 'hidden variables' that science had not yet uncovered which could explain random events such as why one nucleus rather than another decays at a particular moment.)

On the recoil

Perhaps a more significant difference is what is observed. The corn are observed 'jumping' (more anthropomorphic language?) Physics tells us that momentum must always be conserved, and the kernels act like tiny jet propelled rockets. That is, as steam is released when the kernel bursts, the rest of the kernel 'jumps' in the opposite direction. (That is, by Newton's third law, there is a reaction force to the force pushing the steam out of the kernel. Momentum is a vector, so it is possible for a stationary object to break up into several moving parts with conservation of momentum.)

Something similar happens in radioactive decay. The emitted radiation carries away momentum, and the remaining 'daughter' nucleus recoils – although if the material is in the solid state this effect is dissipated by being spread across the lattice. So, the radioactivity which is detected is not analogous to the jumping corn, but to the steam it has released.

Is this important? That likely depends upon the level being taught. If the topics is being introduced to 14-16 years-olds, perhaps not. If the analogy is being explored with post-compulsory students doing an elective course, then maybe. (If not in chemistry; then certainly in physics, where learners are expected to to apply the principle of conservation of momentum across various scenarios.)

Will this be on the exam?

When I drafted this, I suspected most readers might find my caveats above about the limitations of the analogy, a bit pernickety (the kind of things an academic who's been out of the school classroom too long and forgotten the realities of working with pupils might dream up), but then I found what claims to be an Edexcel GCE Physics paper from 2012 (paper reference 6PH05/01) on line. In this paper, one question begins:

"In a demonstration to her class, a teacher pours popcorn kernels onto a hot surface and waits for them to pop…".

Much to my delight, I found the first part of this question asked learners:

"How realistic is this demonstration as an analogy to radioactive decay?

Consider aspects of the demonstration that are similar to radioactive decay and aspects that are different"

Examination paper asking physics students to identify positive and negative aspects of the analogy.

Classes of radioactivity

One further difference did occur to me that may be important. At some level this analogy works for radioactivity regardless of what is being emitted from an excited nucleus. However, the analogy seems clearer for the emission of an alpha particle, or a beta particle, or a neutron, than in the case of gamma radiation.

Although in gamma decay an excited nucleus relaxes to a lower energy state emitting a photon, it may not be as obvious to learners that the nucleus has changed (arguably, it has not 'substantially' changed as there is no change of substance) – as it has the same mass number and charge as before. This may be a point to be raised if moving on later to discuss different classes of radioactivity.

Or, perhaps, with gamma decay one can use a different version of the analogy?

Another corny analogy

Although I do not think I had never come across this analogy before reading the Education in Chemistry piece (perhaps because I do not make myself popcorn), Richard Gill does not seem to be the only person to have noticed this comparison. (They say 'great minds think alike' – and not just physicist Henri Poincaré thinking like Kryten from'Red Dwarf'). When I looked around the world-wide web I found there were two different approaches to using corn kernels to model radioactivity.

Some people use a similar demonstration to Mr Gill.2 However, there was also a different approach to using the corn. There were variations on this 3, but the gist was that

  • one starts with a large number of kernels
  • they are agitated (e.g., shaken in a box with different cells, poured onto the bench…)
  • then inspected to see which are pointing in some arbitrary direction designated as representing decay
  • the 'decayed' kernels are removed and counted
  • the rest of the sample is agitated again
  • etc.
Choose a direction to represent decay, and remove the aligned kernels as the 'activity' in that interval.
(Original image by Susie from Pixabay)

This lacks the excitement of popping corn, but could be a better model for gamma decay where the daughter nucleus is at a different energy after decay, but is otherwise unchanged.

Perhaps this version of the analogy could be improved by using a tray with an array of small dips (like tiny spot tiles) just the right size to stand corn kernels in the depressions with their points upwards. Then, after a very gentle tap on the bench next to the tile, those which have 'relaxed' from the higher energy state (i.e., fallen onto their sides) would be considered decayed. This would more directly model the change in potential energy and also avoid the need to keep removing kernels from the context (just as daughter atoms usually remain in a sample of radioactive material), as further gentle tapes are unlikely to excite them back to the higher energy state. 4

Or, dear reader, perhaps I've just been thinking about this analogy for just a little too long now.

Sources:
Notes

1 Referring to the nuclei before and after radioactive decay as 'parents' and 'daughters' seems metaphorical, but this use has become so well established (in effect, these are now technical terms) that these descriptors are now what are known (metaphorically!) as 'dead metaphors'.

Read about metaphors in science

2 Here are some examples I found:

Jennifer Wenner, University of Wisconsin-Oshkosh uses the demonstration in undergraduate geosciences:

"I usually perform it after I have introduced radioactive decay and talked about how it works. It only takes a few minutes and I usually talk while I am waiting for the "decay" to happen 'Using Popcorn to Simulate Radioactive Decay'"

https://serc.carleton.edu/quantskills/activities/popcorn.html

The Institute of Physics (IoP) include this activity as part of their 'Modelling decay in the laboratory Classroom Activity for 14-16' but suggest the pan lid is kept on as a safety measure. (Any teacher planing on carrying out any activity in the lab., should undertake a risk assessment first.)

I note the IoP also suggests care in using the term 'random':

Teacher: While we were listening to that there didn't seem to be any fixed pattern to the popping. Is there a word that we could use to describe that?

Lydia: Random?

Teacher: Excellent. But the word random has a very special meaning in physics. It isn't like how we think of things in everyday life. When do you use the word random in everyday life?

Lydia: Like if it's unpredictable? Or has no pattern?

https://spark.iop.org/modelling-decay-laboratory

Kieran Maher and 'Kikibooks contributors' suggests readers of their 'Basic Physics of Nuclear Medicine' could "think about putting some in in a pot, adding the corn, heating the pot…" and indeed their readers "might also like to try this out while considering the situation", but warn readers not to "push this popcorn analogy too far" (pp.20-21).

3 Here are some examples I found:

Florida High School teacher Marc Mayntz offers teachers' notes and student instructions for his 'Nuclear Popcorn' activity, where students are told to "Carefully 'spill' the kernels onto the table".

Chelsea Davis (a student?) reports her results in 'Half Life Popcorn Lab' from an approach where kernels are shaken in a Petri dish.

Redwood High School's worksheet for 'Radioactive Decay and Half Life Simulation' has students work with 100 kernels in a box with its sides labelled 1-4 (kernels that have the small end pointed toward side 1 after "a sharp, single shake (up and down, not side to side)" are considered decayed). Students are told at the start to to "Count the popcorn kernels to be certain there are exactly 100 kernels in your box".

This activity is repeated but with (i) kernels pointing to either side 1 or 2; and in a further run (ii) any of sides 1, 2, or 3; being considered decayed. This allows a graph to be drawn comparing all three sets of results.

The same approach is used in the Utah Education network's 'Radioactive Decay' activity, which specifies the use of a shoe box.

A site called 'Chegg' specified "a square box is filled with 100 popcorn kernels". and asked "What alteration in the experimental design would dramatically change the results? Why?" But, sadly, I needed to subscribe to see the answer.

The 'Lesson Planet' site offers 'Nuclear Popcorn' where "Using popcorn kernels spread over a tabletop, participants pick up all of those that point toward the back of the room, that is, those that represent decayed atoms".

'Anonymous' was set a version of this activity, but could not "seem to figure it out". 'Jiskha Homework Help' (tag line: "Ask questions and get helpful responses") helpfully responded,

"You ought to have a better number than 'two units of shake time…'

Read off the graph, not the data table."

(For some reason this brought to mind my sixth form mathematics teacher imploring us in desperation to "look at the ruddy diagram!")

4 Consider the challenge of developing this model to simulate nuclear magnetic resonance or laser excitation!

Plus ça change – balancing forces is hard work

Confusing steady states and equilibrium?

Keith S. Taber

"…I am older than I once was
And younger than I'll be
But that's not unusual
No, it isn't strange
After changes upon changes
We are more or less the same
After changes we are more or less the same…"

From the lyrics of 'The Boxer' (Simon and Garfunkel song) by Paul Simon

In a recent post I discussed the treatment of Newtonian forces in a book (Thomson, 2005) about the history of natural theology (a movement which sought to study the natural world as kind of religious observance – seeking to glorify God by the study of His works) and its relationship to the development of evolutionary theory.

The book was written by a prestigious scientist, who had held Professorships at both Yale in the US and at Oxford. Yet the book contained some erroneous physics – 'howlers' of the kind that are sometimes called 'schoolboy errors' (as presumably most schoolgirls would be careful not to make them?)

Read 'Even Oxbridge professors have misconceptions'

'The Watch on the Heath'

by Prof. Keith Thomson

My point is not to imply that this is a poor read – the book has much to commend it, and I certainly thought it was worth my time. I found it an informative read, and I have no reason to assume that the author's scholarship in examining the historical sources was was not of the highest level – even if his understanding of some school physics seemed questionable. I think this highlights two features of science:

  1. Science is so vast that research scientists setting out to write 'popular' science books for a general readership risk venturing into areas outside their specialist knowledge – areas where they may lack expertise 1
  2. Some common alternative conceptions ('misconceptions') are so insidious that we confidently feel we understand the science we have been taught whilst continuing to operate with intuitions at odds with the science.

Out of specialism

In relation to the first point, I previously highlighted a reference to "Einstein's relativity theory" being part of quantum physics, and later in the book I found another example of a non-physicist confusing two ideas that may seem similar to the non-specialist but which to a physicist should not be confused:

"In the 1930s, Arthur Holmes worked out the geology of the mechanism [underpinning plate tectonics] and the fact that the earth's inner heat (like that of the sun) comes from atomic fission."
p.190

Thomson, 2005: 190

The earth contains a good deal of radioactive material which, through atomic fission, heats up the earth from within. This activity has contributed to the, initially hot, earth cooling much more slowly than had once been assumed – most notably according to modelling undertaken by Thomson's namesake, Lord Kelvin.2 Kelvin did not know about nuclear fission.

But the sun is heated by a completely different kind of nuclear reaction: fusion. The immense amount of energy 'released' during this process enables stars to burn for billions of years without running out of hydrogen fuel.3

Lord Kelvin did not know about that either, leading to him suggesting

"…on the whole most probable that the sun has not illuminated the earth for 100,000,000 years, and almost certain that he has not done so for 500,000,000 years"

Thomson, 1862

Kelvin suggested this was 'almost' but not 'absolutely' certain – a good scientist should always keep an open mind to the possibility of having missed something (take note, BBC's Nick Robinson).

We now think the sun has been 'illuminating' for about 4 600 000 000 years, almost ten times as long as Kelvin's upper limit. It may seem strange that a serious scientist should refer to the sun as 'he', but this kind of personification was once common in scientific writings.

Read about personification in science

The first atomic weapons were based on fission processes of the kind used in nuclear power stations.

Hydrogen bombs are much more devastating still, making use of fusion as occurs deep in the sun.

(Image by Gerd Altmann from Pixabay)

A non-scientist may feel this conflation of fission and fusion is a minor technical detail. But it is a very significant practical distinction.

For one thing the atomic bombs that were used to devastate Hiroshima and Nagasaki were fission devices. The next generation of atomic weapons, the 'hydrogen bombs' were very much more powerful – to the extent that they used a fission device as a kind of detonator to set off the main bomb! It is these weapons, fusion weapons, which mimic the processes at the centre of stars such as the sun.

…The rusty wire that holds the cork that keeps the anger in
Gives way and suddenly it's day again
The sun is in the east
Even though the day is done
Two suns in the sunset, hmph
Could be the human race is run…

From the lyrics of 'Two suns in the sunset' (Pink Floyd song) by Roger Waters

In terms of peaceful technologies, fission-based nuclear power stations, whilst not using fossil fuels, have been a major concern because of the highly radioactive waste which will remain a high health risk for many thousands of years, and because of the dangers of radiation leaks – very real risks as shown by the Three Mile Island (USA) and Windscale (England) accidents, and much more seriously at Fukushima (Japan) and, most infamously, Chernobyl (then USSR, now Ukraine). There are also serious health and human rights issues dogging the mining of uranium ore, which is, of course, a declining resource.

For decades scientists have been trying to develop, as an alternative, nuclear fusion based power generation which would be a source of much cleaner and sustainable power supplies. This has proved very challenging because the conditions under which fusion takes place are so much more extreme. Critically, no material can hold the plasma at the extreme temperatures, so it has to be magnetically suspended well away from the containment vessel 'walls'.

The tenacious nature of some misconceptions

My second point, the insidious nature of some common alternative conceptions, is a challenge for science teachers as simply giving clear, accurate presentations with good examples may not be enough to bring about change in well-established and perhaps intuitive ways of thinking, even when students study hard and think they have learnt what has been taught.

I suggested this was reflected in Prof. Thomson's text (Keith, that is, not Sir William) in his use of references to Newton's ideas about force and motion. Prof. Thomson was not as a biologist therefore seeking to avoid referring to physics, but rather actively engaging with Newton's notions of inertia and the action of forces to make his points. Yet, also, seemingly misusing Newtonian mechanics because of a flawed understanding. Likely, as with many students, Prof. Thomson's intuitive physics was so strong that although he had studied Newton's laws, and can state them, when he came to apply them his own 'common-sense' conceptions of force and motion insidiously prevailed.

The point is not that Prof. Thomson has got the physics wrong (as research suggests most people do!) but that he was confident enough in his understanding to highlight Newtonian physics in his writing and, in effect, seek to teach his readers about it.

Newton's laws

What are commonly known as 'Newton' three laws of motion' can be glossed simply as:

N1: When no force is acting, an object does not change its motion: if stationary, it remains stationary; if moving, it carries on moving at the same speed in the same direction.

Indeed, this is also true if forces are acting, but they cancel because they are balanced, i.e.,

N1': When no net (overall, resultant) force is acting, an object does not change its motion: if stationary, it remains stationary; if moving, it carries on moving at the same speed in the same direction.

N2: When a net force is acting on a body it changes its motion in a way determined by the magnitude and direction of the force. (The change in velocity takes place in the direction of the force, and at a rate depending on the magnitude of the force).

So, if the force acts along the direction of motion, then the speed will change but not direction; but if the force acts in any other direction it will lead to a change in direction.

Strictly, the law relates to the 'rate of change of momentum' but assuming the mass of the body is fixed, we can think in terms of changes of velocity. 4

N3: Forces are interactions between two bodies/objects (that attract or repel each other): the same size force acts on both. (This is sometimes unfortunately phrased as 'every action having an equal and opposite reaction') 5.

These (perhaps) seem relatively simple, but there are complications in applying them. Very simply, the first law,when applied to moving bodies does not seem to fit our experience (moving bodies often seem to come to a stop by themselves – due to forces that we do not always notice).

The second law relates an applied force to a process of change, but it is very easy to instead think of the applied force directly leading to an outcome. That is people often equate the change in direction with the final direction. The change occurs in the direction of the force: that does not mean the final direction is the direction of the force.

The third law is commonly misapplied by assuming that if 'forces come in pairs' these will be balanced and cancel out. But they cannot cancel out because they are acting on the two bodies. (If your friend hits you in the eye after one too many pedantic complaints about her science writing you cannot avoid a black eye simply by hitting her back just as hard!)

A N3 force 'pair' does not balance out!

Often objects are in equilibrium because the forces acting on them are balanced. But they are never in equilibrium just because a force on them is also acting on another body! An apple hangs from a tree because the branch pulls it up the same amount as its weight pulls it down: these are two separate forces, each of which is also acting on the other body involved (the branch, and the earth, respectively).

Read about learning difficulties and Newton's third law

Thomson's 'Newtonian Physics'

In the previous posting I noted that Prof. Thomson had written

  • "Any trajectory other than a straight line must be the result of multiple forces acting together."
  • "the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun…
  • "a Newtonian balance of forces… rocks: gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again"

The first two statements are simply wrong according to conventional physics. Curved paths are often the result of a single force acting. The earth and moon orbit because they are both the subject of unbalanced forces.

Those two statements are contrary to N1 and N2.

The third statement seemed to suggest that a balance of forces was somehow considered to bring about changes. The suggestion appeared to be that a cycle of changes might be due to a balance of forces. But I acknowledged that "this reference to Hutton's ideas seems to preview a more detailed treatment of the new geology in a later chapter in the book (that I have not yet reached), so perhaps as I read on I will find a clearer explanation of what is meant by these changes being based on a theory of balance of forces".

Now I have finished the book, I wanted to address this.

A sort of balance

Prof. Thomson discusses developing ideas in geology about how the surface of the earth came to have its observed form. Today we are familiar with modern ideas about the structure of the earth, and continental drift, and most people have seen this represented in various ways.

Image by Venita Oberholster from Pixabay
Image by Clker-Free-Vector-Images from Pixabay
Original images by by Michel Müller from Pixabay

However, it was once widely assumed that the earth's surface was fairly static , but had been shaped by violent events in the distant past – a view sometimes called 'catastrophism'. One much referenced catastrophe was the flood associated with the biblical character Noah (of Ark fame) that was sometimes considered to have been world-wide deluge. (Those who considered this were aware that this required a source of water beyond normal rainfall – such as perhaps vast reservoirs of water escaping from underground).

The idea that the earth was continually changing, and that forces that acted continuously over vast periods of time could slowly (much too slowly for us to notice) lead to the formation of, for example, mountain ranges seemed less feasible.

Yet we now understand how the tectonic plates float on a more fluid layer of material and how these plates slowly collide or separate with the formation of new crust where they move apart. Vast forces are at work and change is constant, but there are cyclic processes such that ultimately nothing much changes.

Well, nothing much changes on a broad perspective. Locally of course, changes may be substantial: land may become submerged, or islands appear from the sea; mountains or great valleys may appear – albeit very, very slowly. But crust that is subsumed in one place will be balanced by crust formed elsewhere. And – just as walking from one side of a small boat to another will lead to one side rising out of the water, whilst the opposite side sinks deeper into the water – as land is raised in one place it will sink elsewhere.

This is the kind of model that scientists started to develop, and which Prof. Thomson discusses.

"[Dr John Woodward (1665-1728) produced] "an ingenious theory, parts of it quite modern, parts simply seventeenth century sophistry within a Newtonian metaphor. Woodward's earth, post deluge, is stable, but not in fact unchanging. This is possible because it is in a sort of balance – a dynamic balance between opposing forces."

Thomson, 2005: 156

Plus ça change, plus c'est la même chose

James Hutton (1726 – 1797) was one of the champions of this 'uniformitarianism',

"Hutton's earth is in a constant state of flux due to processes acting over millions of years as mountains are eroded by rain and frost. In turn, the steady raising up of mountains, balances their steady reduction through erosion.

…for Hutton the evidence of the rocks demonstrated a cyclic history powered by Newtonian steady-state dynamics: the more it changed, the more it stayed the same."
p.181

Thomson, 2005: 181

The more it changed, the more it stayed the same: plus ça change, plus c'est la même chose. This, of course, is an idiom that has found resonance with many commentators on the social, as well as the physical, world,

"…A change, it had to come
We knew it all along
We were liberated from the fold, that's all
And the world looks just the same
And history ain't changed
'Cause the banners, they all flown in the last war
…
There's nothing in the street
Looks any different to me
And the slogans are effaced, by-the-bye
And the parting on the left
Is now parting on the right
And the beards have all grown longer overnight…"

From the lyrics of 'Won't get fooled again' (The Who song), by Pete Townsend

Steady states

So, there are vast forces acting, but the net effect is a planet which stays substantially the same over long periods of time. Which might be considered analogous to a body which is subject to very large forces, but in such a configuration that they cancel.

Where Prof. Thomson is in danger of misleading his reader is in confusing a static equilibrium and a macroscopic overall steady state that is the result of many compensating disturbances. This is an important difference when we consider energy and not just the forces acting.

A steady state can be maintained by nothing happening, or by several things happening which effectively compensate.

If we consider a very heavy mass sitting on a very study table, then the mass has a large weight, but does not fall because the table exerts a balancing upward reaction force. Although large forces are acting, nothing happens. In physics terms, no work is done. 6

Now consider a sealed cylinder, perfectly insulted and shielded from its surroundings, containing some water, air and too much salt to fully dissolve. It would reach a stead state where the

  • the mass of undissolved salt is constant
  • the height of the solution in the tube is constant

On a macroscopic level, nothing then happens – it is all pretty boring (especially as if the cylinder was perfectly insulated we would not be able to monitor it anyway!)

Actually, all the time,

  1. salt is dissolving
  2. salt is precipitating
  3. gases from the air are dissolving in the solution
  4. gases are leaving the solution
  5. water is evaporating into the air
  6. water vapour is condensing

But the rates of 1 and 2 are the same; the rates of 3 and 4 are the same; and the rates of 5 and 6 are the same. In terms of molecules and ions, there is a lot of activity – but in overall terms, nothing changes: we have a steady state, due to the dynamic equilibria between dissolving and precipitating; between dissolving and degassing; and between evaporation and condensation.

This activity is possible because of the inherent energy of the particles. In the various interactions between these particles a molecule is slowed here, an ion is released from electrical bonds – and so. But no energy transfer takes place to or from the system, it is only constantly redistributed among the ensemble of particles. No work is done.

Cycling is hard work

But macroscopic stable states maintained by cyclic processes are not like that. A key difference is that in the geological cycles there are significant frictional effects. In our sealed cylinder, the processes will continue indefinitely as the energy of the system is constant. In the geological systems, change is only maintained because there is source of power – the sun drives the water cycle, radioactive decay in effect drives the rock cycle.

Work is done in forming new crust under the sea between two plates. More work is done pushing one plate beneath another at a plate boundary. It does not matter if the compensating changes were produced by identical magnitude forces pushing in opposite directions – these are not balanced forces in the sense of cancelling out (they act on different masses of material) – if they had been, nothing would have happened.

You cannot move tectonic plates around without doing a great deal of work – just as you cannot cycle effortlessly by using a circular track that brings you back to where you started, even though when cycling in one direction the ground was pushing you one way, and on the way back the ground was pushing you in the opposite direction! (Your tyres pushed on the track, and as Newton's third law suggests, it pushed back on the tyres in the opposite direction – but those equal forces did not cancel as they were acting on different things: or you would not have moved.)

Perhaps Prof. Thomson understands this, but his language is certainly likely to mislead readers:

"Hooke realised that there was a balance of forces: while the geological strata were being formed and mountains were raised up, at the same time the land was constantly being eroded…"

Thomson, 2005: 179

No, there was not a balance of forces.

It could be that Prof. Thomson's use of the phrase 'balance of forces' is only intended as a metaphor or an analogy. 7 However, he also repeats errors he had made earlier in the book

  • "the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun"
  • "any trajectory other than a straight line must be the result of multiple forces acting together"

which suggests a genuine confusion about how forces act.

One of these mistakes is that planetary orbits (which require a net {unbalanced} force), are due to 'opposing forces',

"…Paley's tortured dancing on the heads of all these metaphysical pins is pre-shadowing of modern ecological thinking and a metaphysical extension of Hooke and Newton's explanation of planetary orbits in terms of opposing forces, or Woodward's theory of matter, or Hutton's geology – it is the living world as a dynamic system of force and counterforce, of checks and balances."
p.242

Thomson, 2005: 242 (my emphasis)

The other was that a single force cannot lead to a curved path,

"…the philosophical concept of reduction, namely that any complex system can be reduced to the operation of simple causes. Thus the parabolic trajectory of a projectile is the product of two straight-line forces acting on each other [sic];…"
p.264

Thomson, 2005: 264 (my emphasis)

Forces are interactions between bodies, they are abstractions and do not act on each other. The parabolic path is due to a single constant force acting on a body that is already moving (but not in the direction of the applied force). It can be seen as the result of the combination of a force (acting according to N2) and the body's existing inertia (i.e., N1). Prof. Thomson seems to be thinking of the motion itself as corresponding to a force, where Newton suggested that it is only a change of motion that corresponds to a force.

However, whilst Prof. Thomson is wrong, he is in good company – as one of the most common alternative conceptions reported is assuming that a moving body must be subject to a force. Which, as I pointed out last time, is not so daft as in everyday experience cars and boats and planes only keep on moving as long as their propulsion systems function (to balance resistive forces); and footballs and cricket balls and javelins that do not have a source of motive power (to overcome resistive forces) soon fall to earth. So, these are understandable and, in one sense, very forgiveable slips. It is just unfortunate they appear in an otherwise informative book about science.

Sources cited:
  • Thomson, K. (2005). The Watch on the Heath: Science and religion before Darwin. HarperCollins.
  • Thomson, W. (1862). On the Age of the Sun's Heat. Macmillan's Magazine, 5, 388-393.
  • Thorn, C. E., & Welford, M. R. (1994). The Equilibrium Concept in Geomorphology. Annals of the Association of American Geographers, 84(4), 666-696. http://www.jstor.org/stable/2564149
Notes

1 Although there are plenty of 'academic' books in many fields of scholarship (usually highly focused so the author is writing about their specialist work), the natural sciences tend to be communicated and debated in research journals. Most books written by scientists tend to be for a more general audience – and publishers expect popular science books to appeal to a wide readership, so these books are likely to have a much broader scope than academic monographs.

2 When he was ennobled, William Thomson chose to be called Baron Kelvin – after his local river, the river Kelvin. So the SI unit of temperature is named, indirectly, after a Scottish River.

Kelvin's reputation was such that when he modelled the cooling earth and suggested the planet was less that a 100 000 000 years old, this caused considerable concerns given that geologists were suggesting that much longer had been needed for it to have reached its present state.

3 For a brief discussion regarding energy changes during processes of this kind, see 'How much damage can eight neutrons do?'

4 The rate of change of momentum is proportional to the magnitude of the applied force and takes place in the direction of the applied force.

As momentum is mv, and as mass is usually assumed fixed (if the motion is well below light speeds) 'the rate of change of momentum' is the mass times the rate of change of the velocity – or ma. (F=ma.)

The key point about direction is that it is not that the body moves in the direction of the force, but the change of momentum (so change of velocity) is in the direction or the force.

As the body's momentum is a vector, and the change in momentum is a vector, the new momentum is the vector sum of these two vectors: new momentum = old momentum + change in momentum.

The object's new direction after being deflected by a force is in the direction of the new momentum

5 When there is force between two bodies (let's call them A, B) the force acting on body B is the same size as the force acting on body A, but is anti-parallel in direction.

The force between the earth and the sun acts on both (not shown to scale)

6 This is an ideal case.

A real table would not be perfectly rigid. A real table would initially distort ever so slightly with the area under the mass being ever so slightly compressed, and the weight dropping to an ever so slightly lower level. The very slight lowering of the weight does a tiny amount of work compressing the table surface.

Then, nothing more happens, and no more work is done.

7 Thorn and Welford (1994) have referred to "the fuzzy and frequently erroneous use of the term…equilibrium in geomorphology" (p.861), and how an 1876 introduction of the "concept of dynamic equilibrium resembles the balance-of-forces equilibrium that appears in dynamics, but by analogy rather than formal derivation" (p.862).

Resistance is how much something is being slowed down

Image by Dimitris Doukas from Pixabay 

"Resistance is how much something is being slowed down or is stopped going round"

Adrian was a participant in the Understanding Science Project. When I interviewed him in Y12 when he was studying Advanced level physics he told me that "We have looked at resistance and conductance and the formulas that go with them". However, when asked about the formula, he suggested, without conviction, that "resistance is current over voltage". So, I asked him how he might go about explaining resistance to a younger student:

We will come back to the formula in a minute then, so let us say you had a younger brother or sister who hasn’t done much physics.

Yes.

And doesn’t do, doesn’t like maths, doesn’t like formulas.

Okay.

So what does it mean though? Why is it important? What’s resistance about?

Erm – I would say it was how much something is being slowed down, or erm how much it is being stopped going round. If it is in electric¬… electricity then it is in a circuit. If it’s in like the wide open range of things it's like erm how resistant is something if you push it? How much force does it give back?

So Adrian was aware of electrical resistance, and also aware of resistance in the context of mechanics.

Oh I see, so, erm if I asked you to push that table over there

Yes.

There might be resistance to that?

Yes.

And that’s different to if we were talking about meters and wires and things?

Yes.

Are they similar in some way?

They have got the same name. {laughs}

Got the same name, okay.

They probably are similar. I've never really thought about it.

So although Adrian associated electrical resistance with 'resistance' in mechanical situations, the similarity between the two types of resistance seemed primarily due to the use of the same linguistic label. This was despite him describing the two forms of resistance in similar terms – "how much something is being slowed down… how much it is being stopped going round" cf. "how resistant is something if you push it".

To a physicist, a property such as resistance should be defined precisely, and therefore preferably mathematically – and so operationally in the sense that there is no ambiguity in how it would be measured. However when students are learning, definitions and formulae may be abstract and have little meaning or connection to experience, so qualitative understanding is important. Students' initial suggestions of what technical terms mean when they first learn about them may be vague and flawed, but if this is linked to a feeling for the concept this may ultimately be a better starting point than a formula which cannot be interpreted meaningfully – as seemed to be the case with Adrian.

Arguably, understanding a relationship in qualitative terms can support later formalising the relationship in mathematical terms, whereas trying to learn a formulae by rote may lead to misremembering and algorithmic application (and so, for example, not noticing when non-feasible results are calculated).

Adrian's suggestion that resistance might be"how resistant is something if you push it? How much force does it give back?" presumably linked to his own experiences of pushing and pulling objects around. However, it seemed to confuse notions of inertia and reaction force (as well as possibly frictional forces). If Adrian were to push with a force of 100N on the wall of a building, a puck on an ice rink, or on a sledge on gravel the reaction force would be 100N in each case (cf. Newton's third law) – although the subjective experience of resistance would be very different in the different situations – as would the outcome on the object pushed.

In these situations it may be difficult for a teacher to know if a vague or confused description reflects conceptual confusion (and/)or limited expression. Yet, students need time and opportunities to be able to explore concepts in their own terms to link the abstract scientific ideas with the 'spontaneous conceptions' they have developed based on their own experiences of acting in the world.

The teacher should offer feedback, and model clear language, but needs to recognise that understanding abstract scientific ideas takes time. After all, Aristotle would be considered to have alternative conceptions of mechanics by comparison with today's science, but Aristotle was clearly highly intelligent and gave the matter a lot of thought!

After this there was extended discussion on the way resistance related to current and voltage, following Arian's comment that resistance is current over voltage. As part of this he was asked about ⚗︎ an example where different voltages were needed in different circuits to allow the same current to flow. ⚗︎ He suggested that the circuit with the higher resistance would be the one where "there is more voltage being put in, if you like, to the circuit, and you are getting less current flowing in, and therefore resistance must be more to stop the rest of that".

Adrian's way of talking about the current in the circuits did not seem to reflect a view of current as driven by a given p.d. across a circuit and limited by a certain resistance, but almost as a fixed potential flow, some of which would be permitted to pass, but some of which would be stopped by the resistance ("how much it is being stopped going round", "resistance … to stop the rest of that"). Yet, as suggested above, it can take time, and opportunities for exploration and discussion, for students' concepts and ways of talking about them to mature towards canonical science.

That Adrian could talk of "more voltage…less current…therefore resistance must be more" seemed promising, although ⚗︎ Adrian could not relate his qualitative description to the mathematical representation of the formula. ⚗︎

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

Iodine's got a larger force that lithium, so it will pull towards the lithium more 

Keith S. Taber

Annie was a participant in the Understanding Chemical Bonding project. She was interviewed near the start of her college 'A level' course (equivalent to Y12 of the English school system). Annie was shown, and asked about, a sequence of images representing atoms, molecules and other sub-microscopic structures of the kinds commonly used in chemistry teaching.

When she was shown an image representing the electron cloud around an iodide ion polarised by an adjacent lithium ion Annie interpreted this as the iodine exerting a greater force on the lithium than vice versa.

Focal figure presented to Annie

What about this, any idea about this?

It's the same sort of thing again – the lithium combines with the iodine – to make a stable outer shell between the two, by sharing electrons, but the lithium has a smaller charge, or smaller pull than the iodine, so the actual shape of it goes in towards. It sort of goes inwards because its attracting the lithium, whereas if the lithium was attracting it, it would be like a reverse picture.

So, so the iodine's attracting what, sorry?

The lithium.

The iodine's attracting the lithium, and the lithium is not attracting the iodine?

Yeah, they're both attracting each other but because this one's got a larger force, then it will pull towards the lithium more.

The iodine's got a larger force,

Yeah.

so it will pull towards the lithium more?

Yeah.

Any image used to represented chemical bonding is necessarily a kind of model, and a partial representation – and there are a range of types of representations students meet. It is perhaps not surprising if students cannot always 'guess what the teacher (or textbook author or researcher) is thinking, and what they intend by a particular type of image.

Annie here demonstrates the common notion that chemical bonding can be based upon 'sharing' electrons (i.e., covalent bonding). At this point in her course Annie would not be expected to appreciate polar bonds or the polarisation of ions, but her prior learning that covalent bonding could be understood as 'sharing' of electrons could potentially act as an impediment to learning that the ionic-covalent bonding distinction should be seen as a spectrum, a continuous dimension, not a dichotomy.

The way forces are understood in physics is that they are interactions between two bodies, and that the same magnitude of force acts of both bodies (i.e., Newton's third law). However, students commonly consider that a 'larger' body (e.g., more massive, more highly charged) exerts a large force on the smaller body. Students do not clearly distinguish the force from its effect, and so this alternative conception seems to draw upon intuitions based on actual experience of the world (i.e., a grounded learning impediment) where larger sources (larger fires, bigger loudspeakers, larger lamps) often seem to have larger effects.

[Read about Newton's third law, and student learning difficulties]

The Sun would pull more on the Earth…

Bert's understanding of the reciprocal nature of forces 

Keith S. Taber

Bert was a participant in the Understanding Science Project. A key idea in school physics is that forces occur in pairs, when two bodies exert an equal magnitude force upon each other (as required by Newton's third law). However, this seems counter intuitive to pupils, who may expect that a larger (more massive, or greater charge etc.) object would exert a greater force on a smaller body than vice versa. In physics a distinction is made between the forces (always equal) and their effects (which depend upon the force applied, and the mass of the object being acted upon). This distinction is not always made by students.

When in Y11, Bert offered an example of one of the common alternative conceptions found among students – that the larger body will exert more force:

What about the Earth going round the Sun, that's an orbit as well is it?

Yeah.

…

So why does it go round?

Why does it go round?

Yeah.

Erm because erm, well one is the gravity of it pulling and the other is, I'm not so sure what the other force is.

That's gravity of what?

The Sun.

So the gravity of the Sun pulling on the Earth?

Yeah.

Do you think the Earth pulls on the Sun?

Yeah, I guess but not strongly enough to move the Sun. Because if there's an object with a small amount of mass then it's not going to give off as much pull as something ten times bigger as it. So the Earth would pull more on the Sun, I mean the Sun would pull more on the Earth.

Whereas the physics perspective is that a force is an interaction between bodies, Bert talks as though a force is something that emanates from one body to another ("give off … pull"), a way of talking quite common among students applying their intuitive understanding of force.

Many students conflate the force acting on a body, and its effect (the acceleration produced) – so here the Sun and Earth are subject to the same force, but the earth is much less massive so will accelerate much more subject to that force than the Sun would. (The Sun's acceleration would actually depend on the net force acting on it considering the various bodies in orbit around it.)

Common experience tells us that in interactions between contrasting bodies (e.g., consider a fly on a windshield) the larger object has more effect, which may seem naturally to mean it applies more force (how much force can the tiny fly impart? – surely the car must apply more force to the fly?) So there is an intuition here, which can act as a grounded learning impediment to learning the physics formalism.


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

Keith S. Taber

Annie was a colearner (participant) in the Understanding Chemical Bonding project. In her first interview, during the first year of her two year 'A level' college course, Annie was asked about a (Bohr type) representation of a (sodium) atom. Annie did not know what held the protons and neutrons together in the atomic nucleus, but suggested it might be due to forces from the electrons "pushing":

Interviewer: Can you identify the different parts of that diagram? What's the blob in the centre?

Annie: It's the nucleus.

I: That's the nucleus. Do you know what's in the nucleus?

A: The protons and, no the electrons and the neutrons, no the protons and the neutrons. The electrons are round the outside.

I: There's protons and neutrons in the centre okay.

A: Yeah.

I: Erm, what holds them together, any idea?

A: Is it the forces from the outer ring? Outer rings or outer shells? The electronic forces?

I: What repelling them in? Holding them

A: Yeah.

I: in the centre? It could be.

A: Pushing them.

I: It's not actually, but that's a sensible suggestion. So you haven't actually done anything about what holds the nucleus together?

A: No.

…

The question of why the nucleons should be held together (given the repulsion between positive protons) is not usually considered in school chemistry lesson, and does not seem to be a question which students tend to spontaneously consider. The interview continued…

I: What holds the electrons in place?

(pause, c.4s)

A: Er (pause, c.9s) Not really sure, but I know there's a set pattern of how many can go in each shell, so if its connected with that?

I: Huh hm, do you think, do you think you need anything to hold the electrons in place, or I mean is it just the way the Universe is, or God's will, or, you know, or just aesthetic, you know nature's aesthetic,

A: Yeah.

I: and it looks pretty? I mean do you think there has to be some physical reason why the electrons are there rather than anywhere else?

A: Probably is to do with the structure of it.

I: But you are not, you're not sure why,

A: No.

I: it should be that the electrons should be in orbitals or orbits?

A: No.

I: Rather than just scattered higgledy-piggledy.

A: No, I don't know that.

In this section of the interview, Annie seems to suggest she is not aware of any forces acting on the electrons, and suggests it may be something inherent in the electronic structure which holds the electrons in place. It seems odd that Annie does not invoke a force from the nucleus, given her comment just earlier about a possible pushing from the outer electron ring/shell onto the nucleons. It seems Annie does not know about, or at least does not bring to mind, an electrical force attracting the electrons and nucleus. However, this was tested by a slightly different question…

Okay. So can you tell me why the electrons don't fall out of the atom? I mean if you imagine that this was sort of, er, an atom that's placed vertically, why don't the electron's just fall out of the bottom?

A: The forces hold them together.

I: What kind of forces are they. Do you know?

(pause, c.5s)

A: The attraction from the nucleus, from the protons.

I: So the protons in the nucleus attract the electrons?

A: Yeah.

I: So what kind of attraction is that. What kind of force is that?

A: Er (pause, c.7s) I don't know

So Annie is aware that the electrons are attracted by the nucleus, and specifically by the protons. Despite this, Annie does not suggest the interaction is electronic, or specially refer to charge. Her suggestion that the outer electron shell may push on the nucleus, holding it together, contradicts Newton's third law in that forces between bodies are either attractive or repulsive, not not a mixture of the two. So if the nucleus attracts electrons, then electrons must attract (not push) the nucleus. Annie's suggestion was also inconsistent with the way forces between charges depend upon separation (by an inverse square law): the repulsion between adjacent protons would be far larger than any force due to the more distant electrons.