The Acceleration Required Practical Without Light Gates PART DEUX

I have written about completing the acceleration practical without light gates before but I thought I’d share a slight variation on the original method that I have found to work well with my teaching groups. Links to some digital resources (spreadsheet, powerpoint and worksheet) will be included.

The method does not require light gates or a data logger. In fact, the only measuring instruments needed are a metre rule and a stop clock. The other items are standard laboratory equipment (dynamic trolley, bench pulley, string. 4 x 10 g masses on a hanger, 4 x 100 g masses on a hanger, and wooden runway). If your class can access IT then a rather clever spreadsheet is included, but this is not essential.

We use small 10 g masses to accelerate the trolley so the time it takes to travel a certain distance (between 0.50 to 0.90 m) can be timed manually with a stop clock (typical time for the 10 g mass is between 3 and 5 seconds).

This works well as a class practical, especially if you follow Adam Boxer’s excellent ‘Slow Practical’ method.

The Powerpoint that I use to run this practical can be downloaded here.

Set up a friction-compensated slope

The F in Newton’s Second Law stands for the resultant force (or total force) so ideally we should eliminate any frictional force tending to slow down the trolley. This can be done by tilting the runway slightly as shown.

Using one or two 100 g slotted masses propped under one end of the runway provides enough of a slope so that the trolley continues moving at a steady speed when given a short, gentle push. Use trial and error to find the precise angle of the slope needed.

Students should mark START and STOP lines on the runway and measure the distance s between them and record it on the worksheet (or in the spreadsheet).

Make sure the weight stack does not hit the ground before the trolley crosses the stop line, otherwise the results will be unreliable as the trolley will not be accelerating over the full distance.

Use a system of constant mass

Increase the mass of the trolley, but keep F fixed

Calculate the acceleration

The force of the weight stack on the trolley can be calculated using W=mg where m is the mass in kilograms and g is the gravitational field strength of 9.81 N/kg, although the approximation 10 g = 0.10 N can be useful if students are performing the calculations and plotting the graph manually.

Students can use the formula a = 2s/t2 to calculate the acceleration manually. Note that the units of this expression are m/s2 as we would expect for a valid equation for acceleration.

A derivation of this expression suitable for GCSE students is outlined on Slide 5 of the Powerpoint.

If students have access to tablets or computers, they can use this spreadsheet to automatically calculate the results and plot the graph. Students can print the graph if they click on the relevant tab. (The line of best fit is not included as all students generally benefit from practicing this skill!)

Evaluate the results

Students can evaluate the results using Slide 7 of the Powerpoint.

Note that in the graph shown, although there is a convincing straight line of best fit, there is also a noticeable systematic error: the acceleration is slightly too small for the indicated force. This would suggest that the runway was not tilted steeply enough to eliminate all frictional forces.

If you find this blog and resources useful, please leave a comment and/or share it on Twitter 🙂

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Filed under Forces, physics, Practical Work

Cornell versus Ebbinghaus

Most of us are only too familiar with the mordant truth of Shakespeare’s observation that “Old men forget, yet all shall be forgot”. In fact, things are generally even worse than the Bard suggests: everyone forgets, all the time.

In time, all shall indeed be forgot.

This was established experimentally by Hermann Ebbinghaus in 1880. The graph below shows Ebbinghaus’ original results with some more recent replications (from Murre and Dros 2015).

Diagram from https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0120644

However, there is a workaround or “hack” that allows us to beat the Ebbinghaus curve of forgetfulness.

The Power of Review

Diagram from Chun and Heo 2018. (Top annotations with coloured circles added to original.)

If the content is reviewed at regular intervals, not only do we remember more but the review process also slows down the rate at which knowledge decays.

Cornell notes as a structure for regular review

‘Cornell notes’ is a two column note-taking system developed by Cornell University Professor of Education Walter Pauk (1974). (See also this link.)

I developed its use in Physics classes with a mind to defeating the Ebbinghaus forgetting curve using this template (click on the link to download a blank printable pdf version).

Example of Cornell style notes on the photoelectric effect

Step 1 Students write notes

In the lesson, students complete the sections highlighted in red but they should leave the other sections blank. This can be a bit of struggle with some students, but is actually a vital part of the process.

Then the students wait 24 hours.

The first couple of times you try this with a class, it might be worth insisting that all students hand in their incomplete Cornell notes at this point just to make sure they follow the process correctly. As students learn to appreciate the effectiveness of the process, you can trust them to follow it without taking control of their work (hopefully!)

Step 2 Students complete the Questions / Key Words section

After a pause of 24 hours, students then complete the section highlighted in green. Of course, they have to thoroughly review and think hard about the material in the notes section to do this, and in Daniel Willingham’s resonant phrase: “Memory is the residue of thought.”

Then, wait a further 48 hours. (Again, the first couple of times you do this with a class, you may want to take in the incomplete Cornell notes to make sure the process is followed correctly: many students seem to find it impossible to “let it be”!)

Step 3 Students complete the summary section

48 hours after completing the Questions / Key Words section, students complete the Summary section.

Students often find writing the Summary the hardest part of the process and usually need the most support with this section. The limited space forces concision and an intense focus on the most important concepts — which, of course, is no bad thing in itself!

As an addition to step 3 and following Cho (2011), writing a Reflection on the back of the Cornell notes sheet can be useful to encourage retention. The Reflection is intended to elicit or memorialise an emotional reaction to the content. The context of this could be “Big Picture”, professional, historical or personal.

Students are encouraged to select one context and write something that has emotional resonance for them. Examples relevant to the photoelectric effect (see above) might be:

  • “Big picture”: The photoelectric effect is the basis of all light detection technology. Without the science of the photoelectric effect, the fibre optic data networks on which our interconnected society depends would be not only impossible but unthinkable.
  • Professional: As an electronic engineer, I would use the photoelectric effect to design super-sensitive electronic cameras that can be used with large aperture telescopes to build up — photon by photon — images of galaxies that are so distant that their light left them four and a half billion years before the Sun formed.
  • Historical: Einstein’s 1905 paper on the photoelectric effect was one of the trio of papers published in his “Annus Miriablis” (“Miracle Year”). In the other two he outlined the theory of Special Relativity and used Brownian motion to prove the existence of atoms. Historians of science say that any one of the three would have been enough to secure his reputation as one of the most important physicists of the 20th Century!
  • Personal: I thought this was one of the most mathematically challenging topics that we have covered so far in Physics. I am really pleased that I can successfully handle the algebra but also have a good understanding of the physical meaning of all the terms.

Step 4 Independent Review

This can be as simple as covering the red section 1 with a piece of paper and using the Questions and Key Words section as a cue to recall the hidden content.

Conclusion

This was run as a pilot project in Y12 with A-level Physics students. In Y13, they were taught by different teachers who did not use the adapted system. About one quarter of the students who had been taught the process were still using it for Y13 revision and were enthusiastic about how much they felt it boosted their recall of content and understanding.

Some research (e.g. Ahmad 2019) suggests learning gains for students who use the traditional (non-adapted) Cornell notes system. Interestingly, Jacobs (2008) suggests a large improvement in “higher level question” scores for Cornell notes students (again, not the adapted Cornell notes version outlined above).

References

Ahmad, S. Z. (2019). Impact of Cornell Notes vs. REAP on EFL Secondary School Students’ Critical Reading Skills. International Education Studies12(10), 60-74.

Cho, J. (2011). Improving science learning through using interactive science notebook (ISN). In P. Gouzouasis (Ed.), Pedagogy in a new tonality (pp. 149-166). Rotterdam, the Netherlands: Sense Publishers. https://doi.org/10.1007/978-94-6091-669-4_10

Chun, B. A., & Heo, H. J. (2018). The effect of flipped learning on academic performance as an innovative method for overcoming Ebbinghaus’ forgetting curve. In Proceedings of the 6th International Conference on Information and Education Technology (pp. 56-60).

Jacobs, K. (2008). A comparison of two note taking methods in a secondary English classroom. Proceedings of the 4th Annual GRASP Symposium, Wichita State University, 2008 (pp. 119-120).

Murre, J. M., & Dros, J. (2015). Replication and analysis of Ebbinghaus’ forgetting curve. PloS one10(7), e0120644.

Pauk, W. (1974). How to study in college. Boston: Houghton Mifflin.

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Filed under Education, Physics

Physics Six Mark Calculation Question? Give it the old FIFA-One-Two!

Batman gives a Physics-Six-Marker the ol’ FIFA-One-Two,

Many students struggle with Physics calculation questions at KS3 and KS4. Since 40% of the marks on GCSE Physics papers are for maths, this is a real worry for their teachers.

The FIFA system (if that’s not too grandiose a description) provides a minimal and flexible framework that helps students to successfully attempt calculation questions.

Since adopting the system, we encounter far fewer blanks on test and exam scripts where students simply skip over a calculation question. A typical student can gain 10-20 marks.

The FIFA system is outlined here but essentially consists of:

  • Formula: students write the formula or equation
  • Insert values: students insert the known data from the question.
  • Fine-tune: rearrange, convert units, simplify etc.
  • Answer: students state the final answer.

The “Fine-tune” stage is not — repeat, not — synonymous with re-arranging and is designed to be “creatively ambiguous” and allow space to “do what needs to be done” and can include unit conversion (e.g. kilowatts to watts), algebraic rearrangement and simplification.

The FIFA-One-Two

Uniquely for Physics, instead of the dreaded “Six Marker” extended writing question, we have the even-more-dreaded “Six Marker” long calculation question. (Actually, they can be awarded anywhere between 4 to 6 marks, but we’ll keep calling them “Six Markers” for convenience.)

The “FIFA-one-two” strategy can help students gain marks in these questions.

Let’s look how it could be applied to a typical “Six mark” long calculation question. We prepare the ground like this:

FIFA-one-two: the set up. (Note that since the expected unit of the final answer is given, this is actually a five marker not a six marker; however, the system works equally well in both cases.)

Since the question mentions the power output of the kettle first, let’s begin by writing down the energy transferred equation.

Next we insert the values. It’s quite helpful to write in any “non standard” units such as kilowatts, minutes etc as a reminder that these need to be converted in the Fine-tune phase.

And so we arrive at the final answer for this first section:

Next we write down the specific heat capacity equation:

And going through the second FIFA operation:

Conclusion

I think every “Six Marker” extended calculation question can be approached in a productive way using the FIFA-One-Two approach.

This means that, even if students can’t reach the final answer, they will pick up some method marks along the way.

I hope you give the FIFA-One-Two method a go with your students.

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Reducing Cognitive Overload in Practicals by graphing with Excel

Confession, they say, is good for the soul. I regret to say that for far too many years as a Science teacher, I was in the habit of simply ‘throwing a practical’ at a class in the belief that it was the best way for students to learn.

However, I now believe that this is not the case. It is another example of the ‘curse of the expert’. As a group, Science teachers are (whether you believe this of yourself and your colleagues or not) a pretty accomplished group of professionals. That is to say, we don’t struggle to use measuring instruments such as measuring cylinders, metre rules (not ‘metre sticks’, please, for the love of all that’s holy), ammeters or voltmeters. Through repeated practice, we have pretty much mastered tasks such as tabulating data, calculating the mean, scaling axes and plotting graphs to the point of automaticity.

But our students have not. The cognitive load of each of the myriad tasks associated with the successful completion of full practical should not be underestimated. For some students, it must seem like we’re asking them to climb Mount Everest while wearing plimsols and completing a cryptic crossword with one arm tied behind their back.

One strategy for managing this cognitive load is Adam Boxer’s excellent Slow Practical method. Another strategy, which can be used in tandem with the Slow Practical method or on its own, is to ‘atomise’ the practical and focus on specific tasks, as Fabio Di Salvo suggests here.

Simplifying Graphs (KS3 and KS4)

If we want to focus on our students’ graph scaling and plotting skills, it is often better to supply the data they are required to plot. If the focus is interpreting the data, then Excel provides an excellent tool for either: a) providing ready scaled axes; or b) completing the plotting process.

Typical exam board guidance states that computer drawn graphs are acceptable provided they are approximately A4 sized and include a ‘fine grid’ similar to that of standard graph paper (say 2 mm by 2 mm) is used.

Excel has the functionality to produce ‘fine grids’ but this can be a little tricky to access, so I have prepared a generic version here: Simple Graphs workbook link.

Data is entered on the DATA1 tab. (BTW if you wish to access the locked non-green cells, go to Review > Unlock sheet)

The data is automatically plotted on the ‘CHART1 (with plots)’ tab.

Please note that I hardly ever use the automatic trendline drawing functionality of Excel as I think students always need practice at drawing a line of best fit from plotted points.

Alternatively, the teacher can hand out a ‘blank’ graph with scaled axes using the ‘CHART1 (without) plots’ tab.

Using the Simple Graph workbook with a class

I have used this successfully with classes in a number of ways:

  • Plotting the data of a demo ‘live’ and printing out a copy of the completed graph for each student.
  • Supplying laptops or tablet so that students can enter their own data ‘live’.
  • Posting the workbook on a VLE so that students can process their own data later or for homework.

Adjusting the Simple Results Graph workbook for different ranges

But what if the data range you wish to enter is vastly different from the generic values I have randomly chosen?

It may look like a disaster, but it can be resolved fairly easily.

Firstly, right click (or ctrl+click on a Mac) on any number on the x-axis. Select ‘Format Axis’ and navigate to the sub-menu that has the ‘Maximum’ and ‘Minimum’ values displayed.

Since my max x data value is 60 I have chosen 70. (BTW clicking on the curved arrow may activate the auto-ranging function.)

I also choose a suitable value of ’10’ for the “Major unit’ which is were the tick marks appear. And I also choose a value of ‘1’ for the minor unit (Generally ‘Major unit’/10 is a good choice)

Next, we right click on any number on the y-axis and select ‘Format Axis’. Going through a similar process for the y-axis yields this:

… which, hopefully, means ‘JOB DONE’

Plotting More Advanced Graphs at KS4 and KS5

The ‘Results Graph (KS4 and KS5)’ workbook (click on link to access and download) will not only calculate the mean of a set of repeats, but will also calculate absolute uncertainties, percentage uncertainties and plot error bars.

Again, I encourage students to manually draw a line of best fit for the data, and (possibly) calculate a gradient and so on.

And finally…

If you find these Excel workbooks useful, please leave a comment on this blog or Tweet a link (please add @emc2andallthat to alert me).

Happy graphing, folks 🙂

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Filed under Data, Practical Work, Science, Uncategorized

Keep Calm and Draw Free Body Force Diagrams (Part 2)

You can read Part 1 which introduces the idea of free body force diagrams here.

Essentially the technique we will use is as follows:

  1. Draw a situation diagram with NO FORCE ARROWS.
  2. ‘Now let’s look at the forces acting on just object 1’ and draw a separate free body diagram (i.e. a diagram showing just object 1 and the forces acting on it)
  3. Repeat step 2 for some or all of the other objects at your discretion.
  4. (Optional) Link all the diagrams with dotted lines to emphasise that they are facets of a more complex, nuanced whole

The Wheel Thing

Let’s consider a car travelling at a constant velocity of 20 miles per hour.

NOT a force diagram. (Note: whilst force arrows on situation diagrams should be discouraged, there is no equivalent argument for speed arrows)

’20 m.p.h.’ is such an uncivilised unit so let’s use the FIFA system to change it into more civilised scientific S.I. units:

NOT a force diagram! (Note: it is fine to draw speed/velocity/acceleration arrows on a situation diagram, but not force arrows.)

Note that point A on the car tyre is moving at 8.9 m/s due to the rotation of the wheel, as well as moving at 8.9 m/s with the rest of the car. This means that point A is moving at 8.9 + 8.9 = 17.8 m/s relative to the ground.

More strangely, point B on the car tyre is moving backwards at speed of 8.9 m/s due to the rotation of the wheel, as well as moving forwards at 8.9 m/s with the rest of the car. Point B is therefore momentarily stationary with respect to the ground.

The tyres can therefore ‘grip’ the road surface because the contact points on each tyre are stationary with respect to the road surface for the moment that they are in position B. If this was not the case, then the car would be difficult to control as it would be in a skid.

(Apologies for emphasising this point — I personally find it incredibly counterintuitive! Who says wheels are not technologically advanced!)

Forces on a tyre

Situation diagram (note: no force arrows) and free body diagrams for road and tyre. Note also different style of arrow for speed and force.

Assuming the car in the diagram is a four wheel drive, the total force driving it forward would be 4 x 330 N = 1320 N. Since it is travelling at a constant speed, this means that there is zero resultant force (or total force). We can therefore infer that the total resistive force acting on the car is 1320 N.

It is can also be slightly disconcerting that the force driving the car forward is a frictional force because we usually speak of frictional forces having a tendency to ‘oppose motion’.

And so they are in this case also. The movement they are opposing is the relative motion between the tyre surface and the road. Reduce the frictional force between the road with oil or mud, and the tyre would not ‘lock’ on the surface and instead would ‘spin’ in place. It’s worth bearing in mind (and communicating to students) that the tread pattern on the tyre is designed to maximise the frictional force between the tyre surface and the road

And then a step to the right…

It’s just a jump to the left

And then a step to the right

The Time Warp, Rocky Horror Picture Show
Situation diagram for a person taking a step to the right; and free body diagrams for the person and the floor

We can see how important friction is for taking a step forward in the above diagrams. Again, it is worth pointing out to students how much effort goes into designing the ‘tread’ on certain types of footwear so as to maximise the frictional force. On climbing boots, the ‘tread’ extends on to the upper surface of the boot for that very reason.

Amazon.com | La Sportiva Men's TC Pro Climbing Shoe | Climbing
A climbing boot

One step beyond

Let’s apply a similar analysis to the case of a person stepping off a boat that happens not be tied to the mooring.

Situation diagram for a person stepping off an unmoored boat; and free body force diagrams for the person and the boat. Note different style of arrow for forces and acceleration.

The person pushes back on the boat (gripping the boat with friction as above). By Newton’s Third Law, this generates an equal an opposite force on the boat. There is no horizontal force to the right due to the tension in the rope, since there is no rope(!) This means that there is a resultant force on the boat to the left so the boat accelerates to the left.

The forces on the person and the boat will be equal in magnitude, but the acceleration will depend on the mass of each object from F = ma.

Since the boat (e.g. a rowing boat) is likely to have a smaller mass than the person, its acceleration to the left will be higher in magnitude than the acceleration of the person to the right — which will lead to the unfortunate consequence shown below.

The effect of stepping off an unmoored boat

The acceleration of the person and the boat happens only when the person and boat are in contact with each other, since this is the only time when there will be a resultant force in the horizontal direction.

Note that although force arrows on a situation diagram should be discouraged for the sake of clarity, there is an argument for drawing velocity and acceleration arrows on the situation diagram as a form of dual coding. Further details can be found here, and an explanation of why acceleration is shown as a double headed arrow.

The velocity to the left built up by the boat in this short instant will be greater than the velocity to the right built up by the person, because the acceleration of the boat is greater, as argued above.

The outcome, of course, is that the person falls in the water, which has been the subject of countless You’ve Been Framed clips.

Next post…

In the next post, I will try to move beyond horizontal forces and take account of the normal reaction force when an object rests on both horizontal surfaces and inclined surfaces.

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Filed under Dual Coding, FIFA, Forces, Free Body DIagrams

Fear of Forces? Keep Calm and Draw Free Body Diagrams

Why do so many students hold pernicious and persistent misconceptions about forces?

Partly, I think, because of the apparent clash between our intuitive, gut-level knowledge of real world physics. For example, a typical student might find the statement ‘If I push this box, it will stop moving shortly after I stop pushing because force is needed to move things‘ entirely unobjectionable; whilst in the theoretical, rarefied world of the physicist the statement ‘The box will keep moving at a constant velocity after I stop pushing it, unless it is acted on by a resultant force such as friction‘ would get a tick whereas the former would get a big angry X and and a darkly muttered comment about ‘bloody Aristotleans.’

After all, ‘pernicious’ is in the eye of the beholder. Physics teachers have to remember that they suffer mightily under the ‘curse of knowledge’ and have forgotten what it’s like to look at the world through anything than the lens of Newtonian mechanics.

We learn about the world through the power of example. Human beings are ‘inference engines’: we strive to make sense of the world by constructing general rules based on the examples presented to us.

Many of the examples of forces in action presented to students are in the form of force diagrams; and in my experience, all too many force diagrams add to students’ confusion.

A bad force diagram

Force Diagram 1: version 1 (really bad)

Over the years, I have seen many versions of this diagram. To my own chagrin, I must admit that I, personally, have drawn versions of this diagram in the past. But I now recognise it has one major, irredeemable flaw: the arrows are drawn hanging in mid-air.

OK, let’s address this. Is this better?

Force Diagram 1: version 2 (still bad)

No, it isn’t because it is still unclear which forces are acting on which object. Is the blue 75 N arrow the person pushing the cart forward or the cart pulling the person forward? Is the red 75 N arrow the cart pushing back on the person or the person pulling back on the cart?

From both versions of this diagram shown above: we simply cannot tell.

As a consequence, I think the explanatory value of this diagram is limited.

Free Body Diagrams to the Rescue!

A free body diagram is simply one where we consider the forces on each object in the situation in turn.

Force Diagram 1: version 3 (much better!)

We begin with a situation diagram. This shows the relationship between the objects we are considering. Next, we draw a free body diagram for each object; that is, we draw each object involved and consider the forces acting on it.

From version 3 of Force Diagram 1, we can see that it was an attempt to illustrate Newton’s Third Law i.e. that if body A exerts a force on body B then body B exerts an equal and opposite force on body A.

Another bad force diagram

Force Diagram 2: version 1 (very bad)

This is a bad force diagram because it is unclear which forces are acting on the cart and which are acting on the person. Apart from a very general ‘Well, 50 N minus 50 N means zero resultant force so zero acceleration’, there is not a lot of information that can be extracted from this diagram.

Also, the most likely mechanism to produce the red retarding force of 50 N is friction between the wheels of the cart and the ground (and note that since the cart is being pushed by an external body and the wheels are not powered like those of a car, the frictional force opposes the motion). Showing this force acting on the handle of the cart is not helpful, in my opinion.

Free body diagrams to the rescue (again)!

The Newton 3 pairs are colour coded. For example, the orange 50 N forward force on the person (object A) is produced as a direct result of Newton’s 3rd Law because the person’s foot is using friction to grip the floor surface (object B) and push backwards on it (the orange arrow in the bottom diagram).

This diagram shows a complete free body diagram body analysis for all three objects (cart, person, floor) involved in this simple interaction.

I’m not suggesting that all three free body diagrams always need to be discussed. For example, at KS3 the discussion might be limited at the teacher’s discretion to the top ‘Forces on Cart’ diagram as an example of Newton’s First Law in action. Or equally, the teacher may wish to extend the analysis to include the second and third diagrams, depending on their own judgement of their students’ understanding. The Key Stage ticks and crosses on the diagram are indicative suggestions only.

At KS3 and KS4, there is not a pressing need to explicitly label this technique as ‘free body force diagrams’. Instead, what I suggest (perhaps after drawing the situation diagram without any force arrows on it) is the simple statement that ‘OK, let’s look at the forces acting on just the cart’ before drawing the top diagram. Further diagrams can be introduced with a similar statements such as ‘Next, let’s look at the forces acting on just the person’ and so on. Linking the diagrams with dotted lines as shown is, I think, useful in not losing sight of the fact that we are dealing piecemeal with a complex and nuanced whole.

Conclusion

The free body force diagram technique (whether or not the teacher decides to explicitly call it that) offers a useful tool that will allow us all to (fingers crossed!) draw better force diagrams.

  1. Draw a situation diagram with NO FORCE ARROWS.
  2. ‘Now let’s look at the forces acting on just object 1’ and draw a separate free body diagram (i.e. a diagram showing just object 1 and the forces acting on it)
  3. Repeat step 2 for some or all of the other objects at your discretion.
  4. (Optional) Link all the diagrams with dotted lines to emphasise that they are facets of a more complex, nuanced whole

In the next post, I hope to show how the technique can be used to explain common problems such as how a car tyre interacts with the ground to drive a car forward.

You can read Part 2 here.

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Filed under Dual Coding, FIFA, Forces, Free Body DIagrams, Physics

SHM and the Top Gear Challenge

There are three things that everyone should know about simple harmonic motion (SHM).

  • Firstly, it is simple;
  • Secondly, it is harmonic;
  • Thirdly, it is a type of motion.

There, my work here is done. H’mmm — it looks like this physics teaching lark is much easier than is generally acknowledged…

Screenshot 2020-05-04 at 17.00.00.png

[The above joke courtesy of the excellent Blackadder 2 (1986), of course.]

Misconceptions to the left of us, misconceptions to the right of us…

In my opinion, the misconceptions which hamper students’ attempts to understand simple harmonic motion are:

  • A shallow understanding of dynamics which does not differentiate between ‘displacement’ ‘velocity’ and ‘acceleration’ but lumps them together as interchangeable flavours of ‘movement’
  • The idea that ‘acceleration’ invariably leads to an increase in the magnitude of velocity and that only the materially different ‘deceleration’ (which is exclusively produced by resistive forces such as friction or drag) can result in a decrease.
  • Not understanding the positive and negative direction conventions when analysing motion.

All of these misconceptions can, I believe, be helpfully addressed by using a form of dual coding which I outlined in a previous post.

Screenshot 2020-05-04 at 18.12.42.png

Top Gear presenters: Assemble!

Screenshot 2020-05-10 at 11.10.37.png

The discussion context which I present is that of a rather strange episode of the motoring programme Top Gear. You have been given the opportunity to win the car of your dreams if — and only if — you can drive it so that it performs SHM (simple harmonic motion) with a period of 30 seconds and an amplitude of 120 m.

This is a fairly reasonable challenge as it would lead to a maximum acceleration of 5.3 m s-2. For reference, a typical production car can go 0-27 m/s in 4.0 s (a = 6.8 m s-2)) but a Tesla Model S can go 0-27 m/s in a scorching 2.28 s (a = 11.8 m s-2). BTW ‘0-27 m/s’ is the SI civilised way of saying 0-60 mph. It can also be an excellent extension activity for students to check the plausibility of this challenge(!)

Timing and the Top Gear SHM Challenge

Screenshot 2020-05-10 at 10.06.48.png

  • At what time should the car reach E on its outward journey to ensure we meet the Top Gear SHM Challenge? (15 s since A to E is half of a full oscillation and T should be 30 seconds according to the challenge)
  • At what time should the car reach C? (7.5 s since this is a quarter of a full oscillation.)

All physics teachers, to a greater or lesser degree, labour under the ‘curse of knowledge’. What we think is ‘obvious’ is not always so obvious to the learner. There is an egregiously underappreciated value in making our implicit assumptions and thinking explicit, and I think diagrams like the above are invaluable in this process.

But what is this SHM (of which you speak of so knowledgeably) anyway?

Simple harmonic motion must fulfil two conditions:

  1. The acceleration must always be directed towards a fixed point.
  2. The magnitude of the acceleration is directly proportional to its displacement from the fixed point.

In other words:

Screenshot 2020-05-04 at 21.33.31.png

Let’s look at this definition in terms of our fanciful Top Gear challenge. More to the point, let’s look at the situation when t = 0 s:

Screenshot 2020-05-10 at 10.08.29.png

Questions that could be discussed here:

  • Why is the displacement at A labelled as ‘+120 m’? (Displacement is a vector and at A it is in the same direction as the [arbitrary] positive direction we have selected and show as the grey arrow labelled +ve.)
  • The equation suggests that the value of a should be negative when x is positive. Is the diagram consistent with this? (Yes. The acceleration arrow is directed towards the fixed point C and is in the opposite direction to the positive direction indicated by the grey arrow.)
  • What is the value of v indicated on the diagram? Is this consistent with the terms of the challenge? (Zero. Yes, since 120 m is the required amplitude or maximum displacement so if v was greater than zero at this point the car would go beyond 120 m.)
  • How could you operate the car controls so as to achieve this part of simple harmonic motion? (You should be depressing the gas pedal to the floor, or ‘pedal to the metal’, to achieve maximum acceleration.)

Model the thinking explicitlyScreenshot 2020-05-10 at 10.17.49.png

Hands up who thinks the time on the second clock on the diagram above should read 3.75 seconds? It makes sense, doesn’t it? It takes 7.5 s to reach C (one quarter of an oscillation) so the temptation to ‘split the difference’ is nigh on irresistible — except that it would be wrong — and I must confess, it took several revisions of this post before I spotted this error myself (!).

The vehicle is accelerating, so it does not cover equal distances in equal times. It takes longer to travel from A to B than B to C on this part of the journey because the vehicle is gaining speed.

So what is the time when x = 60 m

Screenshot 2020-05-10 at 10.40.24.png

So we can redraw the diagram as follows:

Screenshot 2020-05-10 at 10.41.24

Some further questions that could be asked are:

  • Is the acceleration arrow at B smaller or larger than the acceleration arrow at A? Is this consistent with what we know about SHM? (Smaller. Yes, because for SHM, acceleration is proportional to displacement. The displacement at B is +60 m; the acceleration at B is half the value of the acceleration at A because of this. Note that the magnitude of the acceleration is reduced but the direction of a is still negative since the displacement is positive.)
  • Is the velocity at B positive or negative? (Negative, since it is opposite to the positive direction selected on the diagram and shown by the grey ‘+ve’ arrow.)
  • Is the magnitude of the velocity at B smaller or larger than at A, and is this consistent with a negative acceleration? (Larger. Yes, since both acceleration and velocity are in the same direction. Note that this is an important point to highlight since many students hold the misconception that a negative acceleration is always a ‘deceleration’.)
  • How could you operate the car controls so as to achieve this part of simple harmonic motion? (You should have eased off the gas pedal at this point to achieve half the acceleration obtained at A.)

Next, we move on to this diagram and ask students to use their knowledge of SHM to decide the values of the question marks on the diagram.

Screenshot 2020-05-10 at 10.44.43.png

Which hopefully should lead to a diagram like the one below, and realisation that at this point, the driver’s foot should be entirely off the gas pedal.

Screenshot 2020-05-10 at 10.46.00.png

‘Are we there yet?’

And thence to this:

Screenshot 2020-05-10 at 10.47.18.png

One of the most salient points to highlight in the above diagram is the question: how could you operate the car controls at this point? The answer is of course, that you would be pressing the foot brake pedal to achieve a medium magnitude deceleration. This is often a point of confusion for students: how can a positive acceleration produce a decrease in the magnitude of the velocity? Hopefully, the dual coding convention suggested in this blog post will make this clearer to students.

‘No, really, ARE WE THERE YET?!!’

Nearly.

Over time, we can build up a picture of a complete cycle of SHM, such as the one show below. This shows the car reversing backwards at t = 25 s while the driver gradually increases the pressure on the brake.

Screenshot 2020-05-10 at 10.48.21.png

From this, it should be easier to relate the results above to graphs of SHM:

Screenshot 2020-05-10 at 10.51.23.png

A quick check reveals that the displacement is positive and half its maximum value; the acceleration is negative and half of its maximum magnitude; and the velocity is positive and just below its maximum value (since the average deceleration is smaller between C and B than it will be between B and A) .

And finally…

I shall leave the final word to the estimable Top Gear team…

Screenshot 2020-05-10 at 11.08.21.png

So there you have it: JOB DONE!

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Magnetism? THERE IS NO MAGNETISM!!!!

Has a school physics experiment or demonstration ever changed the course of human history?

On 21 April 1820, one such demonstration most definitely did. According to physics lore, Hans Christian Øersted was attempting to demonstrate to his students that, according to the scientific understanding of the day, there was in fact no connection between magnetism and electricity.

To this laudable end, he placed a compass needle near to a wire to show that when the current was switched on, the needle would not be affected.

Except that it was affected. Frequently. Each and every time Øersted switched on the electric current, the needle was deflected from pointing North.

Everybody has heard that wise old saw that ‘If it doesn’t work, it’s physics…” except that in this case ‘It did actually work as it was supposed to but in an unexpected way due to a hitherto-unknown-completely-new-branch-of-physics.’

Øersted, to his eternal credit, did not let it lie there and was a pioneer of the new science of electromagnetism.

Push-me-pull-you: or, two current-carrying conductors

One curious consequence of Øersted’s new science was the realisation that, since electric currents create magnetic fields, two wires carrying electric currents will exert a force on each other.

Let’s consider two long, straight conductors placed parallel to each other as shown.

Screenshot 2020-03-22 at 14.39.37.png

In the diagram above, the magnetic field produced by the current in A is shown by the green lines. Applying Fleming’s Left Hand Rule* to conductor B, we find that a force is produced on B which acts towards conductor A. We could go through a similar process to find the force acting on B, but it’s far easier to apply Newton’s Third Law instead: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. Hence, conductor A experiences a force which pulls it towards conductor B.

So, two long, straight conductors carrying currents in the same direction will be attracted to each other. By a similar analysis, we find that two long, straight conductors carrying currents in opposite directions will be repelled from each other.

In the past, this phenomenon was used to define the ampere as the unit of current: ‘The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length.‘ However, the 2019 redefinition of the SI system has ditched this and adopted a new definition in terms of the transfer of the elementary charge, e.

Enter Albert Einstein, pursuing an enigma

What is the connection between magnetism and electricity? It was precisely this puzzle that started Albert Einstein on the road to special relativity. It is one of the unsung triumphs of this theory that it lays bare the connection between magnetism and electricity.

In what follows, we’re going to apply Einstein’s analysis to the situation of two long, straight current-carrying conductors. Acknowledgment: I’m going to following a line of argument laid out in Beiser 1988: 19-22.

It’s gotta be perfect (or ‘idealised’, if you prefer)

Let’s consider two idealised conductors A and B both at rest in the inertial reference frame of the laboratory. The flow of charge in both conductors is made up of positive and negative charge carriers moving in opposite directions with a speed v.

None of the charges in A interact with the other charges in A because we are considering an idealised conductor. However, the charges in A will interact with the charges in B.

Screenshot 2020-03-22 at 16.08.06.png

Two conductors viewed from the inertial frame of the laboratory

Flip the inertial reference frame

Now let’s look at the situation from the inertial reference frame of one of the positive charges in A. For simplicity, we can focus on a single positive charge in A since it does not interact with any of the other charges in A.

With reference to this inertial frame, the positive charge in A is stationary and the positive charges in B are also stationary.

However, the inertial frame of the laboratory is moving right-to-left with a speed v and the negative charges are moving right-to-left with a speed of 2v.

Screenshot 2020-03-22 at 16.13.28.png

The same two conductors viewed from the inertial frame of one of the positive charges in conductor A. Note that all the positive charges are now stationary; the laboratory is moving with speed v right to left, and the negative charges are moving with speed 2v right to left

Since the positive charges in B are stationary with respect to the positive charge in A, the distance between them is the same as it was in the laboratory inertial frame. However, since the negative charges in B are moving with speed 2v with respect to positive charge in A, the spacing between is contracted due to relativistic length contraction (see Lottie and Lorentzian Length Contraction).

Because of this, the negative charge density of B increases since they are closer together. However, the positive charge density of B remains the same since they are stationary relative to the positive charge in A so there is no length contraction.

This means that, as far as the positive charge in A is concerned, conductor B has a net negative charge which means the positive charge experiences an attractive Coulomb’s Law electrical force towards B.

A similar analysis applied to electric currents in opposite directions would show that the positive charge in A would experience a repulsive Coulomb’s Law electrical force. The spacing between the positive charges in B would be contracted but the spacing between the negative charges remains unchanged, so conductor B has a net positive charge because the positive charge density has increased but the negative charge density is unchanged.

Magnetism? THERE IS NO MAGNETISM!!!!

So what we normally think of as a ‘magnetic’ force in the inertial frame of the laboratory can be explained as a consequence of special relativity altering the charge densities in conductors. Although we have just considered a special case, all magnetic phenomena can be interpreted on the basis of Coulomb’s Law, charge invariance** and special relativity.

For the interested reader, Duffin (1980: 388-390) offers a quantitative analysis where he uses a similar argument to derive the expression for the magnetic field due to a long straight conductor.

Update: I’m also indebted to @sbdugdale who points out the there’s a good treatment of this in the Feynman Lectures on Physics, section 13.6.

Notes and references

* Although you could use a non-FLHR catapult field analysis, of course

** ‘A current-carrying conductor that is electrically neutral in one frame of reference might not be neutral in another frame. How can this observation be reconciled with charge invariance? The answer is that we must consider the entire circuit of which the conductor is a part. Because a circuit must be closed for a current to occur in it, for every current element in one direction that a moving observer find to have, say, a positive charge, there must be another current element in the opposite direction which the same observer finds to have a negative charge. Hence, magnetic forces always act between different parts of the same circuit, even though the circuit as a whole appears electrically neutral to all observers.’ Beiser 1988: 21

Beiser, A. (1988). Concepts of modern physics. Tata McGraw-Hill Education

Duffin, W. J. (1980). Electricity and magnetism. McGraw-Hill.

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Electric Motors Without The Left Hand Rule

There is little doubt that students find understanding how an electric motor works hard.

What follows is an approach that neatly sidesteps the need for applying Fleming’s Left Hand Rule (FLHR) by using the idea of the catapult field.

The catapult field is a neat bit of Physics pedagogy that appears to have fallen out of favour in recent years for some unknown reason. I hope to rehabilitate and publicise this valuable approach so that more teachers may try out this electromagnetic ‘road less travelled’.

Screenshot 2020-02-21 at 09.48.42

(Incidentally, if you are teaching FLHR, the mnemonic shown above is not the best way to remember it: try using this approach instead.)

The magnetic field produced by a long straight conductor

Moving electric charges produce magnetic fields. When a current flows through a conductor, it produces a magnetic field in the form of a series of cylinders centred on the wire. This is usually shown on a diagram like this:

Screenshot 2020-02-21 at 09.59.26.png

If we imagine looking down from a point directly above the centre of the conductor (as indicated by the disembodied eye), we would see a plan view like this:

Screenshot 2020-02-21 at 10.01.22.png

We are using the ‘dot and cross‘ convention (where an X represents an arrow heading away from us and a dot represents an arrow heading towards us) to easily render a 3D situation as a 2D diagram.

The direction of the magnetic field lines is found by using the right hand grip rule.

Screenshot 2020-02-21 at 10.38.32.png

The thumb is pointed in the direction of the current. The field lines ‘point’ in the same direction as the fingers on the right hand curl.

3D to 2D

Now let’s think about the interaction between the magnetic field of a current carrying conductor and the uniform magnetic field produced by a pair of magnets.

In the diagrams below, I have tried to make the transition between a 3D and a 2D representation explicit, something that as science teachers I think we skip over too quickly — another example of the ‘curse of knowledge’, I believe.

Screenshot 2020-02-21 at 11.18.21.png

Magnetic Field on Magnetic Field

If we place the current carrying conductor inside the magnetic field produced by the permanent magnets, we can show the magnetic fields like this:

Screenshot 2020-02-21 at 11.32.31.png

Note that, in the area shaded green, the both sets of magnetic field lines are in the same direction. This leads a to stronger magnetic field here. However, the opposite is true in the region shaded pink, which leads to a weaker magnetic field in this region.

Screenshot 2020-02-21 at 11.33.27.png

The resultant magnetic field produced by the interaction between the two magnetic fields shown above looks like this.

Screenshot 2020-02-21 at 11.37.19.png

Note that the regions where the magnetic field is strong have the magnetic field lines close together, and the regions where it is weak have the field lines far apart.

The Catapult Field

This arrangement of magnetic field lines shown above is unstable and is called a catapult field.

Essentially, the bunched up field lines will push the conductor out of the permanent magnetic field.

If I may wax poetic for a moment: as an oyster will form a opalescent pearl around an irritant, the permanent magnets form a catapult field to expel the symmetry-destroying current-carrying conductor.

Screenshot 2020-02-21 at 11.50.55.png

The conductor is pushed in the direction of the weakened magnetic field. In a highly non-rigorous sense, we can think of the conductor being pushed out of the enfeebled ‘crack’ produced in the magnetic field of the permanent magnets by the magnetic field of the current carrying conductor…

Also, the force shown by the green arrow above is in exactly the same direction as the force predicted by Fleming’s Left Hand Rule, but we have established its direction using only the right hand grip rule and a consideration of the interaction between two magnetic field.

The Catapult Field for an electric motor

First, let’s make sure that students can relate the 3D arrangement for an electric motor to a 2D diagram.

Screenshot 2020-02-21 at 13.42.51.png

The pink highlighted regions show where the field lines due to the current in the conductor (red) are in the opposite direction to the field line produced by the permanent magnet (purple). These regions are where the purple field lines will be weakened, and the clear inference is that the left hand side of the coil will experience an upward force and the right hand side of the coil will experience a downward force. As suggested (perhaps a little fancifully) above, the conductors are being forced into the weakened ‘cracks’ produced in the purple field lines.

The catapult field for the electric motor would look, perhaps, like this:

Screenshot 2020-02-21 at 14.39.36.png

And finally…

On a practical teaching note, I wouldn’t advise dispensing with Fleming’s Left Hand Rule altogether, but hopefully the idea of a catapult field adds another string to your pedagogical bow as far as teaching electric motors is concerned (!)

I have certainly found it useful when teaching students who struggle with applying Fleming’s Left Hand Rule, and it is also useful when introducing the Rule to supply an understandable justification why a force is generated by a current in a magnetic field in the first place.

The catapult field is a ‘road less travelled’ in terms of teaching electromagnetism, but I would urge you to try it nonetheless. It may — just may — make all the difference.

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FIFA for the GCSE Physics calculation win

Student: Did you know FIFA is also the name of a video game, Sir?

Me: Really?

Student: Yeah. It’s part of a series. I just got FIFA 20. It’s one of my favourite games ever.

Me: Goodness me. I had no idea. I just chose the letters ‘FIFA’ completely and utterly at random!

The FIFA method is an AQA mark scheme-friendly* way of approaching GCSE Physics calculation questions. (It is also useful for some Y12 Physics students.)

I mentioned it in a previous blog and @PedagogueSci was kind enough to give it a boost here, so I thought I’d explain the method in a separate blog post.

The FIFA method:

  1. Avoids the use of formula triangles
  2. Minimises the cognitive load on students when approaching calculations.

Why we shouldn’t use formula triangles

Formula triangles are bad news. They are a cognitive dead end.

Screenshot 2019-10-27 at 15.34.54

During a university admissions interview for veterinary medicine, I asked a prospective student to explain how they would make up a solution for infusion into a dog. Part of the answer required them to work out the volume required for a given amount and concentration. The candidate started off by drawing a triangle, then hesitated, eventually giving up in despair. […]

They are a trick that hides the maths: students don’t apply the skills they have previously learned. This means students don’t realise how important maths is for science.

I’m also concerned that if students can’t rearrange simple equations like the one above, they really can’t manage when equations become more complex.

— Jenny Koenig, Why Are Formula Triangles Bad? [Emphases added]

I believe the use of formula triangle also increases (rather than decreases) the cognitive load on students when carrying out calculations. For example, if the concentration c is 0.5 mol dm-3 and the number of moles n required is 0.01 mol, then in order to calculate the volume V they need to:

  • recall the relevant equation and what each symbol means and hold it in working memory
  • recall the layout of symbols within the formula triangle and either (a) write it down or (b) hold it in working memory
  • recall that n and c are known values and that V is the unknown value and hold this information in working memory when applying the formula triangle to the problem

The FIFA method in use (part 1)

The FIFA acronym stands for:

  • FORMULA
  • INSERT VALUES
  • FINE TUNE (this often, but not always, equates to rearranging the formula)
  • ANSWER

Lets look at applying it for a typical higher level GCSE Physics calculation question

Screenshot 2019-10-27 at 16.04.29.png

We add the FIFA rubric:

Screenshot 2019-10-27 at 16.13.00.png

Students have to recall the relevant equation as it is not given on the Data and Formula Sheet. They write it down. This is an important step as once it is written down they no longer have to hold it in their working memory.

Screenshot 2019-10-27 at 16.18.15.png

Note that this is less cognitively demanding on the student’s working memory as they only have to recall the formula on its own; they do not have to recall the formula triangle associated with it.

Students find it encouraging that on many mark schemes, the selection of the correct equation may gain a mark, even if no further steps are taken.

Next, we insert the values. I find it useful to provide a framework for this such as:

Screenshot 2019-10-27 at 16.27.41.png

We can ask general questions such as: “What data are in the question?” or more focused questions such as “Yes or no: are we told what the kinetic energy store is?” and follow up questions such as “What is the kinetic energy? What units do we use for that?” and so on.

Screenshot 2019-10-27 at 16.35.54.png

Note that since we are considering each item of data individually and in a sequence determined by the written formula, this is much less cognitively demanding in terms of what needs to be held in the student’s working memory than the formula triangle method.

Note also that on many mark schemes, a mark is available for the correct substitution of values. Even if they were not able to proceed any further, they would still gain 2/5 marks. For many students, the notion of incremental gain in calculation questions needs to be pushed really hard otherwise they will not attempt these “scary” calculation questions.

Next we are going to “fine tune” what we have written down in order to calculate the final answer. In this instance, the “fine tuning” process equates to a simple algebraic rearrangement. However, it is useful to leave room for some “creative ambiguity” here as we can also use the “fine tuning” process to resolve difficulties with units. Tempting though it may seem, DON’T change FIFA to FIRA.

We fine tune in three distinct steps (see addendum):

Screenshot 2019-10-29 at 12.17.55.png

Finally, we input the values on a calculator to give a final answer. Note that since AQA have declined to provide a unit on the final answer line, a mark is available for writing “kg” in the relevant space — a fact which students find surprising but strangely encouraging.

Screenshot 2019-10-29 at 12.16.46.png

The key idea here is to be as positive and encouraging as possible. Even if all they can do is recall the formula and remember that mass is measured in kg, there is an incremental gain. A mark or two here is always better than zero marks.

The FIFA method in use (part 2)

In this example, we are using the creative ambiguity inherent in the term “fine tune” rather than “rearrange” to resolve a possible difficulty with unit conversion.

Screenshot 2019-10-27 at 17.20.42.png

In this example, we resolve another potential difficulty with unit conversion during the our creatively ambiguous “fine tune” stage:

Screenshot 2019-10-27 at 17.33.05.png

The emphasis, as always, is to resolve issues sequentially and individually in order to minimise cognitive overload.

The FIFA method and low demand Foundation tier calculation questions

I teach the FIFA method to all students, but it’s essential to show how the method can be adapted for low demand Foundation tier questions. (Note: improving student performance on these questions is probably a more significant and quicker and easier win than working on their “extended answer” skills).

For the treatment below, the assumption is that students have already been taught the FIFA method in a number of contexts and that we are teaching them how to apply it to the calculation questions on the foundation tier paper, perhaps as part of an examination skills session.

For the majority of low demand questions, the required formula will be supplied so students will not need to recall it. What they will need, however, is support in inserting the values correctly. Providing a framework as shown below can be very helpful:

Screenshot 2019-10-27 at 17.47.24.png

Also, clearly indicating where the data came from is useful.

Screenshot 2019-10-27 at 17.55.45.png

The fine tune stage is not needed, so we can move straight to the answer.

Screenshot 2019-10-27 at 18.01.07.png

Note also that the FIFA method can be applied to all calculation questions, not just the ones that could be answered using formula triangle methods, as in part (c) of the question above.

Screenshot 2019-10-27 at 18.06.16.png

And finally…

I believe that using FIFA helps to make our thinking and methods in Physics calculations more explicit and clearer for students.

My hope is that science teachers reading this will give it a go. You can read how to use the FIFA-one-two! for extended calculation questions here.

PS If you have enjoyed this, you might also enjoy Dual Coding SUVAT Problems and also Magnification using the Singapore Bar Model.

 

 

*Disclaimer: AQA has not endorsed the FIFA method. I describe it as “AQA mark scheme-friendly” using my professional own judgment and interpretation of published AQA mark schemes.

Addendum

I am embarrassed to admit that this was the original version published. Somehow I missed the more straightforward way of “fine tuning” by squaring the 30 and multiplying by 0.5 and somehow moved straight to the cross multiplication — D’oh!

My thanks to @BenyohaiPhysics and @AdamWteach for pointing it out to me.

Screenshot 2019-10-27 at 16.58.23.png

PS You can read FIFA Part Deux here.

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