The Force Is Zero With This One

There is nothing absurd about perpetual motion; everywhere we look—at the planets wheeling around the Sun, or the electrons circling the heart of the atom—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.

6 thoughts on “The Force Is Zero With This One

  1. paulmartin42 February 1, 2021 / 4:51 am

    Hot wheels: Forty two million – Hornby: Nil

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