The Force Is Zero With This One

There is nothing absurd about perpetual motion; everywhere we lookโ€”at the planets wheeling around the Sun, or the electrons circling the heart of the atomโ€”we see examples of it. Where there is no friction, as in airless space, an object can keep moving forever.

Arthur C. Clarke, Things That Can Never Be Done (1972)

So, according to Arthur C. Clarke, famous author and originator of the idea of the geosynchronous communications satellite, perpetual motion is no big deal. What is a big deal, of course, is arranging for such perpetual motion to occur on Earth. This is a near impossibilty, although we can get close: Clarke suggests magnetically suspending a heavy flywheel in a vacuum. (He also goes on to make the point that perpetual motion machines that can do useful external work while they run are, in fact, utterly impossible.)

The lack of visible examples of perpetual motion on Earth is, I think, why getting students to accept Newton’s First Law of Motion is such a perpetual struggle.

Newton’s First Law of Motion

Every body continues in its state of rest or uniform motion in a straight line, except insofar as it doesn’t.

A. S. Eddington, The Nature Of The Physical World (1958)

I think Sir Arthur Eddington was only half-kidding when he mischieviously rewrote the First Law as above. There is a sense where the First Law is superfluous.

It is superfluous because, technically, it is subsumed by the more famous Second Law which can be stated as F=ma where F is the resultant (or total) force acting on an object. Where the acceleration a is zero, as it would be for ‘uniform motion in a straight line’, then the resultant force is zero.

However, the point of the First Law is to act as the foundation stone of Newtonian dynamics: any deviation of an object from a straight line path is taken as implying the existence of a resultant force; if there is no deviation there no force and vice versa.

The First Law is an attempt to reset our Earth-centric intuition that a resultant force is needed to keep things moving, rather than change the perpetual motion of an object. In other words, our everyday, lived experience that to make (say) a box of books move with uniform motion in a straight line we need to keep pushing is wrong

Newton’s First Law, for real this time

A more modern formulation of Newton’s First Law might read:

An object experiencing zero resultant force will either: (a) remain stationary; or, (b) keep moving a constant velocity.

In my experience, students generally have no difficulty accepting clause (a) as long as they understand what we mean by a ‘zero resultant force’. As in so many things, example is possibly the best teacher:

The meaning of zero and non-zero resultant force

Clause (b) uses the concept of ‘constant velocity’ to avoid the circuitous ‘uniform motion in a straight line’. It is this second clause which gives many students difficulty because they hold the misconception that force is needed to sustain motion rather than change it.

And, truth be told, bearing in mind what students’ lived experience of motion on Earth is, it’s easy to see why they find clause (b) so uncongenial.

Is there any way of making clause (b) more palatable to your typical GCSE student?

Galileo, Galileo — magnifico!

Galileo, Galileo,
Galileo, Galileo,
Galileo Figaro - magnifico!

Queen, Bohemian Rhapsody

Galileo Galilei was one of the giants on whose shoulders Newton stood. His principle of inertia anticipated Newton’s First Law by nearly a century.

What follows is a variation of a ‘thought experiment’ that Galileo advanced in support of the principle of inertia; that is to say, that objects will continue moving at a constant velocity unless they are acted on by a resultant force. (A similar version from the IoP can be found here.)

Galileo’s U-shaped Track for the principle of inertia

Picture a ball placed at point A on the track and released.

Galieo’s U-shaped track (1/4): what we see in the real world…

What we see is the ball oscillating back and forth along the track. However, what we also observe is that the height reached by the ball gradually decreases. This is because of resistive forces that slow down the ball (e.g. friction between the track and the ball and air resistance).

What would happen if we stretched out one side of the curve to make a flat line?

Galieo’s U-shaped track (2/4): an extrapolation from what we see in the real world…

We surmise that the ball would come to a stop at some distant point B because of the same resistive forces we observed above.

Next, we return to the U-shaped track and think about what would happen if we lived in a world without any resistive forces.

Galieo’s U-shaped track (3/4): an extrapolation of what we would see in a world with no resistive forces…

The ball would oscillate back-and-forth between A and B. The height would not decrease as there would be no resistive forces.

Finally, what would happen in our imaginary, perfectly frictionless world if we stretched out one side of the ‘U’?

Galieo’s U-shaped track (4/4): a further extrapolation of what we might see in a world with no resistive force…

The ball would keep moving at a constant velocity because there would be no resistive forces to make it slow down.

This, then, is the way things move when no forces are acting on them: when the (resultant) force is zero, in other words.

Conclusion

Galileo framed the argument above (although he used a V-shaped track rather than a U-shaped one) to persuade a ‘tough crowd’ of Aristotleans of the plausibility of the principle of inertia.

In my experience, it can be a helpful argument to persuade even a ‘tough crowd’ of GCSE students to look at the world anew through a Newtonian lens…

Postscript

My excellent edu-Twitter colleague Matt Perks (@dodiscimus) points out that you can model Galileo’s U-shaped track using the PhET Energy Skate Park simulation and that you can even set the value of friction to zero and other values.

Click on the link above, select Playground, build a U-shaped track, set the friction slider to a certain value and away you go!

Using the PhET Energy Skate Park to model Galileo’s U-shaped track
You can even model the decrease in speed because of frictional forces!

This could be a real boon to helping students visualise the thought experiment.

Forces and Inclined Planes

I don’t want to turn the world upside down — I just want to make it a little bit tilty.

In this post, I want to look at the physics of inclined planes, as this is a topic that can trip up students at GCSE and A-level. I believe that one of the reasons for this is that students often have only a fuzzy notion of what we mean by ‘vertical’ and ‘perpendicular’. These terms are often treated as synonymous so I think they could do with some unpicking.

The absolute vertical

The absolute vertical anywhere on the Earth surface is defined by the direction of the Earth’s gravitational field. It will be a radial line connected with the centre of mass of the planet. The direction of the absolute vertical will be shown by line of a plumb line as shown in the diagram.

Using plumb lines to identify the line of the absolute vertical

(As a short aside, A and B indicate why the towers of the Humber Bridge are 3.6 cm further apart at the top than they are at the bottom. Take that, flat-earthers!)

Picture from https://commons.wikimedia.org/wiki/File:Humber_Bridge_From_Air.jpg

The local perpendicular

We define the local perpendicular as a line which is at 90o to the plane or surface or table top we are working on. We can find its direction with a set square as shown in the picture below.

Example of when the local perpendicular is aligned with the absolute vertical

Next we tilt the table so that the local perpendicular and absolute vertical are no longer aligned. (Thanks to my colleague Bruce Pawsey for this idea.)

Example of the local perpendicular and the absolute vertical no longer in alignment.

Forces on a dynamics trolley on an inclined plane (GCSE level analysis)

Next we place a dynamics trolley on a horizontal table top. We observe that it is is equilibrium. This is easy to explain if we draw a free body diagram to show the forces on the trolley.

The forces on a trolley on a horizontal surface

The normal reaction force N on the trolley is equal and opposite to the weight W of the trolley. The resultant (total) force on the trolley is zero so it is not accelerating.

But now note what happens if we tilt the table so that it becomes an inclined plane: the trolley accelerates to the left.

At GCSE, it is probably best to restrict the analysis to what happens in the absolute vertical (shown by the plumb line) and the absolute horizontal (at 90o to the plumb line).

If we resolve the normal reaction force into two components, we see that N has a small horizontal component (see above). This is the resultant force that causes the trolley to accelerate to the left as shown.

Forces on an object on an inclined plane (A level analysis for static equilibrium)

If we flip the trolley so that it is upside down, then there will be a frictional force acting parallel to the slope. This means that, as long as the angle of tilt is not too steep, the object will be in equilibrium.

It now makes sense to resolve W into components parallel and perpendicular to the slope, since it is the only force of the three which is aligned with the absolute vertical. F and W are aligned with the local perpendicular and horizontal to it’s less onerous to use these as the ‘reference’ grid in this instance.

The normal reaction force N is equal to W cos ๐œƒ not W and since cos ๐œƒ is always less than 1 (for angles other than 90o). If we placed the trolley on some digital scales then the reading on the scales would decrease as we increased ๐œƒ.

This effect was used to simulate the lower gravitational field strength on the Moon for training astronauts for the Apollo programme. In effect, they trained on an inclined plane. (‘To attain the Moon’s terrain / One trains mainly on an inclined plane.‘)

See Photos of How Astronauts Trained for the Apollo Moon Missions - HISTORY
Apollo astronauts training for a low gravity environment on an inclined plane.

If the wheels of the trolley were in contact with the table surface so that the frictional force were negligible, then the trolley would accelerate down the slope because of the resultant force of W sin ๐œƒ parallel to the slope. The direction of the acceleration is parallel to the slope (i.e. at 90o to the local perpendicular) and not along the absolute horizontal as suggested by the earlier, simpler GCSE-level analysis in the previous section.

Photosynthesis and Energy Stores

Getting a group of British physics teachers to agree to a new consensus is like herding cats: much easier in principle than in practice.

Herding cats is much easier with CGI… (Screenshot taken from https://www.youtube.com/watch?v=qola8nvoZm4)

However, it seems to be me that, generally speaking, the IoP (Institute of Physics) has persuaded a critical mass of physics teachers that their ‘Energy Stores and Pathways’ model is indeed a Good Thing.

It very much helps, of course, that all the examination boards have committed to using the language of the Energy Stores and Pathways model. This means that the vast majority of physics education resources (textbooks and revision guides and so on) now use it as well — or at least, the physics sections do.

Energy Stores and Pathways: a very brief overview

There’s a bit more to the new model than adding the word ‘store’ to energy labels so that ‘kinetic energy’ becomes ‘kinetic energy store’; although, truth be told, that’s not a bad start.

I have banged on about this model many times before (see the link here) so I won’t go into detail now. For now, I suggest that we stick with the First Rule of the IoP Energy Club….

With apologies to Brad Pitt and Chuck Palahniuk, Image from ‘Fight Club’ (1999)

You can also read the IoP’s own introduction to the Energy Stores and Pathways model (see link here).

The Problem with Photosynthesis

The problem with photosynthesis is that it is often described in terms of ‘light energy’. The IoP Energy Stores and Pathways model does not recognise ‘light’ as an energy store because it does not persist over a significant period of time in a single well-defined location. Rather, light is classified as an ‘energy carrier’ or pathway (see also this link)

A ‘bad’ description of photosynthesis which doesn’t use the Energy Stores and Pathways language

It is possible that the problem is simply one of resource authors using familiar but outdated language. It would seem that exam board specifications are punctilious in avoiding the term ‘light energy’; for example, see below.

From the AQA Combined Science (Trilogy) specification, page 39

How to describe Photosynthesis using the Energy Stores and Pathways model

It’s very simple: just say ‘plants absorb the energy carried by light’ rather than ‘plants absorb light energy’.

In diagram form, the difference can represented as follows:

Conclusion

Over time, I think that the vast majority of physics teachers (in at least in the UK) have come to see the value of the ESP (Energy Stores and Pathways) approach.

I this that I speak for most physics teachers when we hope that biology and chemistry teachers will come to the same conclusion.

H’mmm…if navigating physics teachers towards a consensus is like herding cats, then to what can we liken doing the same for a combined group of physics, biology and chemistry teachers? Perhaps herding a conglomeration of cats, dogs and gerbils across the boundless, storm-wracked prairies of Tornado Alley. In the dark. With both hands tied behind your back.

Wish us luck.