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Analysing the Motion of Material Objects: usual ways of reasoning

Analysing the Motion of Material Objects: usual ways of reasoning

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Laws for quantities at time t



63



But in the situations presented, the velocities and, more generally, the

motions, differ. This results in a surprisingly high frequency of answers like:

“The forces are different because the motions are,” or, “The force is zero

because the velocity is zero.” These students establish a relationship between

force and motion, or, more specifically, between force and velocity.

Other comments also deserve our attention. They reveal:

a delocalisation of physical quantities in space and time: “At the top of

the trajectory, gravity and the force of the movement of the thrower are

at work” (although the thrower is no longer accomplishing any action

when the object reaches peak height);

an attribution of force to the object: “The force of the mass upwards”,

“the mass has a force” (whereas in correct physics, mass is subjected to a

force, exerts another force, but does not have a force of its own). This

encourages the idea of a storage capacity, and of a temporal gap between

cause and effect: “A supply of upward force”, “the force the fellow gave

it” (whereas only energy or linear momentum can be stored);



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an indiscriminate use of the terms “force,” “impetus,” “velocity,”

“energy,” “inertia,” etc. (sometimes, diagrams are added in which a

“force” and a “velocity” are added vectorially, in defiance of what

physicists call “homogeneity”);

a certain vagueness about the ideas introduced: it is not clear whether

these are represented by a (scalar) number or by a vector: “... a supply ...

upwards” (force and velocity are vectors, but kinetic energy is a scalar,

which has no “direction”).

These characteristics, often found in situations involving “forcevelocity”, appear to indicate a view of physical phenomena that will require

more to change it than the simple substitution of one relation (force-velocity)

for another (force-acceleration).



Chapter 4



66



2.2



Selective occurrence of some types of answer

(Pendulum questionnaire)



Our previous hypothesis is supported by the fact that the frequency with

which reasoning of the “force-velocity” type appears depends largely on

certain theoretically irrelevant aspects of the situation proposed. These errorinducing factors are to be found in the questions cited above:

- The motion is “salient”, i.e., it is presented in a form easily accessible to

the imagination;

- It seems “incompatible” with the forces of interaction at work in the

given situation: the known force does not have the same direction as the

motion; or one of the two quantities, force and velocity, is zero, but not the

other.

In other questions, where motion is presented in analytical form at the

outset, or where only the forces are given, there are far fewer errors of this

type.

An additional question (box 3) illustrates precisely the selective

application of erroneous aspects of common reasoning. It presents four

different kinematic situations for the same device: a simple pendulum, i.e., a

small mass at the end of a string, the other end of which is attached. The

forces acting on the mass in these four situations are considered. In all four

cases, only the weight and the tension3 of the string could possibly act on this

mass.

These four situations do not result in the same proportion of “forcevelocity” errors. Cases of “invented” force, aligned with velocity, become

more frequent when real forces of interaction are less often mentioned (see

columns 2 and 3 of the table in box 3). It would appear that the forces of

interaction that one knows are more or less acceptable depending on the

kinematic situation. The most perturbed case is when the mass is at the top

of a complete circular trajectory, and experiences only downward forces: the

tension of the string and the weight of the mass. Then, to a much greater

extent than for the other three situations, the students feel a centrifugal force

is necessary4 to “balance” the weight. If the tension of the string is shown in

the wrong direction, the desired radial balance can be obtained: “Zero radial

velocity, therefore zero radial force.”



3



4



If the velocity is not zero, there is a centripetal acceleration and therefore also a centripetal

component of force: the tension of the string adapts itself accordingly.

These “centrifugal forces” cannot be interpreted by changing the frame of reference, as their

occurrence is selective. Moreover, no change in frames of reference has ever “reversed”

the tension of a string. The interpretation of the “optimistic physicist,” who gives students

credit for a correct justification (see box 7 below), does not hold.



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Conversely, the case least favourable to error is when the mass is at its

height, in maximum simple oscillation. True, the velocity is zero while the

resulting force is not. Yet this force will soon have an effect: a slight gap in

time between cause and effect is not a problem for common reasoning.



3.



AN INTERPRETATION OF COMMON WAYS OF

REASONING IN DYNAMICS



How can all these intuitions be combined to form a coherent whole? Here

is one possible interpretation, based on simple ideas:

First, in the absence of motion, no questions arise.5 But if there is an

obvious motion, it has to be accounted for (see also Andersson, 1986).

Sometimes, the idea that an object adheres to, or is part of, another moving

object seems sufficient.6 In some cases, drag is mentioned (see chapter 3) but

it is not deemed necessary to identify the driving force acting on the object.

It often happens, too, that a cause is found, such as “this pulls it... and it

comes,” “this pushes it... and it goes,” “the weight brings it down... and it

comes down” – then everything is all right.7 But if “it goes up” when weight

5



Séré (1982, 1985) has shown that this is especially true for gases: at the start of secondary

education, teenagers cannot easily imagine the action of a gas on a wall.

6

Gutierrez and Ogborn, 1992; see also the study on friction by Caldas, 1994.

7

A variant of this type of analysis consists in interpreting by means of a single force of

interaction what the physicists associate with the vector sum of two forces in opposite

directions. The “suction force” so often alluded to in sailing manuals ought to make one

wonder how molecules colliding on a wall, on a sail, or on the wing of a plane could ever

cause anything but “push.” To understand this so-called “suction,” a difference between



Laws for quantities at time t



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is the only force acting, then there is panic. The same thing occurs in the

case of the pendulum which “stays up in the air” even though two known

forces are pulling the mass downwards.

What can continue to make things move, or make them “stay up in the

air” in the absence of known forces? Their dynamism. This term might be

used for the single notion to which the students haphazardly apply the more

or less scientific terms enumerated above: “force,” “impetus”, “velocity”,

“energy”, “inertia”... What matters is not so much the precise elements

involved in the notion as its explanatory function. This ”dynamism“ is also

attributed to the object: “The force of....”

Let us now examine the temporal aspect, which is very correctly

connected with the idea of cause.

Cause ordinarily means the reason why things happen. If causes were

persons, one might say they were responsible for events. In the definition of

“physical causality,” there is another element to be considered: cause

precedes effect in time. In this sense, one cannot say that the fundamental

relationship of dynamics, F=ma, presents force as the cause of acceleration,

as it concerns quantities measured at the same time. A law associating

simultaneous quantities is, to put it briefly... a law, not a story where causes

precede effects.

But to speak of “the force of the thrower’s movement, which acts at the

top of the trajectory,” corresponds to another type of logic, involving an

initial cause. The idea of storage allows a previous cause to remain the

reason for motion, or for the absence of falling, when one is needed: there is

a delocalisation in time of the implicated quantities, for the purposes of the –

causal – common explanation.

This type of temporal gap between quantities that should, in theory, “be

taken at the same time” is very common in students’ reasoning. In appendix

1, this tendency and its consequences are discussed further, in relation to a

slightly more complex situation (concerning propulsion by a spring).

Sometimes, too, the history of the motion manifests itself inappropriately

through the trajectory, as though the circular or rectilinear nature of the

preceding movement had been stored in the moving object (appendix 2).

The history of ideas contains traces of such conceptions. The preGalilean theories of impetus mentioned in chapter 3 are, by far, the most

similar to these conceptions (Viennot, 1979). In most versions, a supply of

“impetus” is stored within the object, which is thereby endowed with a

greater or lesser “capacity for impetus,” and this explains otherwise

inexplicable movements. These coincidences are not raised here to support

the simplistic thesis of a strict parallelism between the respective

two pushes should be envisaged. But one would then have to be willing to take two causal

agents into account. (See the following chapter on the difficulties this entails.)



Chapter 4



70



developments of the individual (ontogeny) and of the species (phylogeny).

But they do throw some light on the strength of the trends of reasoning

analysed in this book (Saltiel and Viennot, 1985).

The reductionist interpretation of physical phenomena, centred on

representations of objects and the characteristics that one attributes to them

–in this case, a dynamic supply of force which explains motion – is a

familiar aspect of common reasoning. This may well be due, to a great

extent, to our basic anthropomorphism.



4.



COHERENCE AND RANGE OF COMMON WAYS

OF REASONING IN DYNAMICS



Let us now examine how these aspects of natural reasoning extend to

areas of physics which, from the point of view of accepted theory, have

nothing in common with those dealt with so far. Common thought, however,

establishes a link.

Such is the case with the propagation of mechanical waves, an issue

introduced here through two examples: the propagation of a “bump” on a

rope, and the propagation of sound.



4.1



Bumps on ropes



From Maurines (1986); see also Maurines and Saltiel (1988a).

Let us follow the course on a stretched rope of a bump caused by flicking

it once with one’s hand. The phenomenon is startling: the shape is

maintained throughout its course; fragments of thread inform one another in

turn, so as to reproduce the initial curve time after time. Physics teaches us

that the speed of propagation of the signal depends solely on the rope and on

its tension. But more important is the idea that what is moving is not a

material object, made up of the same particles from start to finish.

How does common reasoning deal with this?

If students are asked if a bump moving along a rope can be made to move

faster (box 4), many reply with the following type of comment:

“You have to shake your hand harder, the bump will have more force, it

will move faster.” A sketch reproduced in box 4 confirms that the force in

question is in the bump, and directed forwards.



Laws for quantities at time t



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Première scientifique.



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Chapter 4



72



Again, considering two bumps travelling on the same rope, many

students predict that the bigger one will overtake the smaller because “it has

more force”. Other remarks on bumps and ropes sound oddly familiar:

“The bump flattens, it has less and less force, so it moves more and more

slowly”; and sometimes a student adds: “... because of friction.”

Reading these statements, we can really see the “common dynamics” of

solids at work. Here, an object first had to be invented: the bump. Then a

cause had to be found for a bizarre, unexplained motion – the movement of

the bump along the rope. It is the force stored within the bump, which wears

out little by little. This force is “the force of the initial movement.” Past

cause and present reason are fused, a dynamic supply of force being

attributed to the object: a surreptitious temporal delocalisation appears in the

analysis.



4.2



Fast and slow sounds



From Maurines (1993)

The author of the preceding investigation completed it with a study on

sound.9 In view of the first results, it is easy to predict those of the second

study.

Sound is another signal which moves with a speed that depends only on

the state of the medium that it travels through. This medium may be a gas, a

liquid or a solid, with various characteristics (density, temperature...), but

certainly not a vacuum.

Yet, if sound is thought of as being an object, why shouldn’t it propagate

in a vacuum? That is, in fact, what a lot of students think: “In steel, sound

does not propagate, whereas in a vacuum, there is nothing to impede its

propagation”; or: “If there is an explosion on the moon, an astronaut in orbit

will be able to hear it” – although there is no air on the moon. We should

acknowledge, of course, that the vocabulary used to describe



9



For more detail, see chapter 8.



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73



communications between space shuttles, space laboratories, and the Earth

can easily lead to confusion: they can be “listened to,” or “heard”.

In view of the logic illustrated twice so far, it comes as no surprise that

the students should have decided that the louder one shouts, the faster the

sound will travel: “If Pierre shouts louder than Jean, the sound will have

more force, it will travel faster”. Once again, it is to the initial cause – the

source – that the subsequent property of the signal is attributed: it travels

faster (than one sent off with less energy). The future tense, so often used in

these explanations, is not merely a stylistic device. It stresses the idea of

causality, in the physical sense of the term: cause precedes effect.

Pedagogically speaking, some definite conclusions can be reached.10

When teaching the propagation of waves, it is not enough to repeat the

refrain (which students easily learn by rote): “For a given medium, the speed

of the signal is a constant.” One must at least point out that this is surprising,

even shocking: “The speed with which the bump moves does not depend on

the initial motion”; the same goes for sound. The first statement implies the

second, some readers will say. Logically, perhaps, but this is not the

students’ reasoning: the first statement is a refrain learnt at school, whereas

the second one addresses – and, what is more, curbs – a natural tendency of

thought (see also chapter 8). It gives meaning to the refrain learnt at school.

The predictive power of our analysis as a whole is confirmed here. The

answers to these problems on propagation observed are comparable to those

obtained on the dynamics of solids whenever the problem requires students

to explain a very obvious motion without any obvious “cause.” The initial

cause is then seen as determining: it is stored in the object to allow it to catch

up with its effect in time, through a temporal delocalisation that is never very

explicit.

The deviations from accepted theory are not, however, the same in the

analysis of signals as in the dynamics of ordinary objects. The solutions

arrived at through natural reasoning are even more incorrect, so to speak, for

situations involving propagation, where the motion predicted is wrong (the

wave speed of the signal does not depend on the source), than for situations

involving the motion of solids, where only the interpretation of the motion is

missing.

But the rationale behind all the comments is surprisingly similar, whether

the topic is a stone, a bump, or a sound. Though no school ever consciously

teaches anything of this sort, these forms of reasoning are extremely

enduring!

Returning to the dynamics of ordinary objects, we will now explore some

further repercussions of these typical aspects of natural reasoning. This time,

10



See also Maurines and Saltiel (1988a).



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