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Weight and gravity: teachers’

ambiguity and students’ confusion
about the concepts
a
Igal Galili
a
The Amos De‐Shalit Science Teaching Center in Israel,
Hebrew University of Jerusalem, Jerusalem 91904, Israel
Version of record first published: 25 Feb 2007.

To cite this article: Igal Galili (1993): Weight and gravity: teachers’ ambiguity and students’
confusion about the concepts, International Journal of Science Education, 15:2, 149-162

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 INT. J. sci. EDUC., 1993, VOL. 15, NO. 2, 149-162

Weight and gravity: teachers' ambiguity and

students' confusion about the concepts
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Igal Galili, The Amos De-Shalit Science Teaching Center in Israel,

Hebrew University of Jerusalem, Jerusalem 91904, Israel

An existing dichotomy in teaching the concept of weight in junior high and high school might cause a
misunderstanding of this basic physics concept and related physics phenomena. The reported results
show a great deal of uncertainty as to the relationship between the concepts of weight and gravity, causing
widespread confusion among high school students and preservice teachers. The results could be
interpreted as support for a specific way of presenting the weight concept, hitherto employed only in a
minor fraction of existing introductory physics textbooks in the USA, although it is the dominant approach
practised in current textbooks in the former USSR.

Introduction
Convincing evidence has been accumulated concerning widespread confusion
among students of different ages and training background about gravity and related
concepts. For instance, elementary (7-8 years of age) schoolchildren's naive ideas
about Earth's gravity were investigated by Nussbaum and Novak (1976). Ruggiero
et al. (1985) investigated these ideas among middle school pupils (12-13 years of age)
while Mayer (1987) carried out research with secondary school pupils (14—18 years of
age). First-year university pre-instruction physics students were researched by
Gunstone and White (1981). A broad sample of subjects including primary school
children, secondary school pupils, university students and adult non-experts in
physics were investigated by Noce et al. (1988). Primary school teachers' under-
standing of the concepts of gravity were investigated by Kruger et al. (1990). Many
naive preconceptions and novice misconceptions in the domain of the understanding
of gravity were reported. One of them, which seems to us of special importance,
provides the basis of the present research. This was the interrelationship between the
concepts of weight and gravity.
Not all physics teachers seem to be aware of the dichotomy appearing in physics
textbooks regarding the way to define the concept of weight in mechanics. For years it
has continued to be an issue of discussion between those physics teachers who define
weight or 'weight force' as a synonym for gravitational force, and those who define
weight as a result of weighing, which implies a force exerted by something against
support (or pivot) and equal to the contact, elastic, normal force exerted by the
support (or pivot) on the object. Figure 1 illustrates both approaches. In the first
approach, weight is the result of interaction with the Earth only, while in the second
approach weight is the result of interaction with its support (or pivot) and could be
influenced by a number of dynamic and kinematic factors (gravitational force might
be, and often is, among them).
0950-0693/93 $10·00 © 1993 Taylor & Francis Ltd.
 150 RESEARCH REPORTS

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Figure 1. Two possible definitions of weight.

It appears from a study of the literature that most physics educators hold strong
opinions on these definitions (see Appendix 1). The interesting point is that the
separation between the upholders of each approach is not only 'ideological' but also
geographical: most (but not all) of the authors in the physics textbooks available in
the USA adopt the first approach, while the traditionally employed approach in the
former USSR is the second.*
The first approach to teaching weight and gravity has more of a historical
tradition, starting from Newton himself. Most available physics textbooks employ
this approach (from a very long list, e.g., Resnick and Halliday 1966). One can find
the employment of the second, alternative approach in a small minority of physics
textbooks outside the USSR (from a very short list, e.g., Marion and Hornyack 1982,
French 1971). This alternative approach seems to be more elaborate philosophically,
being in the spirit of Mach's approach to science philosophy and science teaching
(Matthews 1990) or of 'operativists' like Bridgman (1952). Methodologically, the
second approach also seems to be better supported as a teaching-learning procedure
(Arons 1984). Still, the situation is far from simple. In methodological physics
literature, there have been some efforts to compare these two approaches and to
review the arguments in favour of each of them (e.g., Mario Iona 1975).
Unfortunately, the discussion took on a completely academic character, and
sometimes seemed of only semantic significance. The topic is a relevant problem for
any physics instructor facing his students in an introductory physics course.
It seems important to check the results of the currently accepted teaching
strategy, by enquiring into the subject knowledge shown by 'novice', post-
instructional students. The issue might be resolved by new science teaching research
rather than by logical arguments in favour of either approach. In our research we
wanted to attain this goal by speculating about possible origins of physics
misconceptions and misunderstandings related to the concept of weight, which
might be traced to the currently employed teaching strategy. The results could
present an unbiased basis for necessary recommendations for changes in the teaching
strategy of the subject-matter. Another product of this research might be better
understanding of the interrelations between the three main aspects of science

* The country of the author, Israel, could be generally included in the first group that identifies weight
with the gravitational force, partly due to the fact that us physics textbooks are dominant at the college
level and, hence, are widely used by school physics teachers too. High-school students traditionally use
translations of the same textbooks (e.g., Sears et al. 1987).
 WEIGHT AND GRAVITY 151

education: scientific method, didactics and the quality of students' acquired

knowledge.

Instruments
A paper-and-pencil test was administered to students of high-school/college level
groups of different ages and educational background. T h e questionnaires were
administered in a regular class environment. The tasks, in the form of open
questions, were qualitative and concerned two possible physical situations involving
the state of weightlessness. The decision to invoke only the phenomena called
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weightlessness has its definite rationale. The context of this physical state provides
fertile soil for probing the genuine understanding of gravity, from its straightfor-
ward aspects to its subtle ones. Students were invited to articulate the views they held
on two particular physical situations. The situations are commonly discussed both
during the classroom presentation of dynamics and in most introductory physics
textbooks (for examples see any from the list in Appendix 1). The tasks were
supported with illustrative drawings which we do not reproduce here, due to their
obvious character.

Task 1. An elevator with a person inside is considered in a state of free fall. The
subjects were asked to identify the forces experienced by the person
only, and to describe what is happening inside the elevator regarding the
sensations of the person immediately after the cable was broken and
before its impact.
Task 2. The task considered an astronaut in a satellite coasting around the
Earth. Two questions, if the astronaut in the satellite experienced
weight and if he experienced gravitational force, were asked. The
subjects were required to justify their answers.

Besides the data accumulated from the responses to these two tasks, some data from
our previous research (Galili and Bar 1991) on problems in teaching mechanics were
used, though the scope of that research was different. We used, for comparison, part
of the pertinent data concerning the situation in an elevator moving with a constant
velocity upwards and downwards, where the subjects were asked a question similar
to Task 1, to identify and comment on the forces exerted on the passenger.

Sample
Our sample included five main groups.
The first group, HS-10 (HS-High School), consisted of 33 10th grade students
(aged approximately 15 years) all from the same class in a prestigious city school.
This control group was to give us, if not verification, then at least a feeling for the
naive ideas students hold at this age just before they start serious study of weight and
gravity concepts in mechanics.
The second group, H S - 1 1 , consisted of 60 11th grade students (aged approxi-
mately 16 years) from three different classes in two schools; Hsl - a n ordinary urban
school, and H S 2 - a prestigious urban school. We will distinguish between these two
subgroups, H S 1 - 1 1 and H S 2 - 1 1 respectively. These were novice students having just
 152 RESEARCH REPORTS

studied the pertinent topics in mechanics from a standard physics curriculum. Their
answers thus reflected the status of knowledge following instruction.
The third group, HS-12, included 36 12th grade students (aged approximately 18
years) from the same prestigious school. The results of that group should show if
students change their relevant acquired knowledge and understanding while they
progress through the physics curriculum.
Our fourth group, UPS (University Pre-academic School), included 27 students
aged 23 and older. These 'novice' students were taught from a shortened and
conceptually oriented physics curriculum.
The fifth group, PTTTC (Preservice Teachers in a Technology Teachers College),
included 42 students, aged 23 and older, from three classes. The students were in
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their fourth year of the training programme which was mainly technologically
oriented. Their high school physics background was heterogeneous. The test took
place around three years after they last partook of a physics course.
All the 'novice' subjects were exposed to the kind of instruction we previously
labelled as the first approach in teaching the weight concept, where no difference is
taught between weight and gravitational force.

Results
Task 1. (Elevator during free fall)
The answers given were categorized in different, not mutually exclusive, categories
(figure 2).
The first category ('mg only') includes correct answers which presumed that the
only real force exerted on the person in the state of free fall is the downward force of

80

• HS-10
HS2-11
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• HS1-11
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Figure 2. Responses to task 1 (Free-falling elevator).

 WEIGHT AND GRAVITY 153

the gravitational attraction, usually mentioned as 'mg'. The rate of correct responses
was not high, about 60% for all groups, and was not improved by educational
background. The adult groups (PTTTC and UPS) had slightly lower success rates than
the naive group (HS-10).
The second category ('AT exists') included answers in which N, the normal,
contact, or elastic force from the elevator floor, is still being exerted on the person
during free fall.
The third category ('No force shown') includes the answers of those students
who only mentioned the forces while refraining from graphically presenting them.
The high rate of naive students (majority of HS-10) and the considerable number of
novice students entering this category (about one-third in the novice groups HS2-11,
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H S - 1 2 and PTTTC, and about 20% of UPS) illustrate a great deal of uncertainty about
applied forces when a free fall state is concerned.
Those answers included in 'Additional force' relate to any reference to a third
force in addition to 'mg' and W . The majority of responses here were from the naive
group, HS-10, and the novice group, PTTTC. In their answers, the subjects, in a variety
of ways, referred to an intuitively experienced force that could be reminiscent of an
inertial force acting opposite to the movement.
The 'Weight changes' category includes those answers in which any change of
weight, or apparent weight, (either its increase or decrease) was mentioned. Though
the free fall situation is expected to be a famous and common example of
weightlessness, our subjects' answers generally did not support this. Very few novice
subjects mentioned or described the state of weightlessness (category 'Man flies').
The next category of answers ('Man moves relatively') includes those mentioning
the retarded relative movement of the person who moved upwards and stopped when
reaching the elevator ceiling. This kind of response, which might reveal vestiges of
Aristotelian understanding of free fall, was rare.
The next category ('No movement break') indicates the students' correct
notation that the person and the elevator do not start to move downwards
immediately with the cable break, but first gradually reduce the upward velocity and
finally change direction. This point was mentioned only by a minority of subjects
(about a third in groups H S 2 - 1 1 , H S - 1 2 and UPS and even less in other groups).

Task 2. {Coasting Satellite)

The first four categories of answers given (figure 3) are mutually exclusive, and
reflect different views on gravitation force (G) and weight (W) experiences:
1. 'G-yes, W-yes'-both are experienced by the astronaut;
2. 'G-yes, PF-no'-the Earth's gravitational force acts on the astronaut, but
weight is not experienced;
3. 'G-no, W-no'-ihe gravitational force and weight are both absent or of
negligent effect in the situation;
4. 'G-no, W-yes'-the gravitational force does not act on the astronaut but
weight is experienced.
Our general impression was that the subjects were not comfortable being asked to
differ between gravity and weight. The majority in all groups answered in favour of
the equivalence between the concepts, which is the way students were taught.
 154 RESEARCH REPORTS

uu -

• HS-10
HS2-11
y HS-12 =
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=j

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UPS
PTTTC i
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=
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1 "
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O
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W-n
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yes,

B 8"
G-y

O 6 5
u II

Figure 3. Responses to task 2 (Coasting Satellite).

The answers of the second category were similarly rare for young naive (HS-10)
and some adult novice students (PTTTC). This kind of answer was more pronounced
in the HS2-1 1 group (about 40%). The other groups gave a rate of about 20% for this
category of answers.
The third category, which denied both gravity and weight in the situation, was
not uncommon for young naive ( H S - 1 0 - 3 0 % ) and some adult novice students
(PTTTC-36%).
The fourth category answer, stating the existence of weight contrary to the
greatly diminished gravitational force was most often expressed by naive students
(HS-10, about 20%).
A final category ( ' G = W decreased') is not mutually exclusive with the others.
We incorporated here all answers in which the subjects explicitly mentioned that the
gravitational force and weight, being the same, decrease in magnitude with the
increasing distance from the Earth and that this fact explains the diminished or zero
weight experienced by the astronaut in a coasting satellite. Such an opinion was
favoured by about half of the subjects, with the rate reaching more than 80% for the
UPS group.
We also reproduce here (figure 4) that part of the data involving a constant speed
elevator. The categories shown are not mutually exclusive. The category 'Forces:
mg + N' includes all answers in which subjects succeeded in identifying correctly the
forces exerted on the person in the elevator. It comprised the answers mentioning
either balanced (correct) or unbalanced (incorrect) forces. Only a small fraction of
our naive students and about half of the PTTTC group succeeded in identifying the
exerted forces correctly. Other novice students, though better, still did not exhibit
satisfactory results. The lack of the normal force N ('No N force') exerted on the
person by the elevator was favoured by a majority of naive students and by some
novice subjects ( H S 2 - 1 1 and HS-12). These data look like a generalization of
 WEIGHT AND GRAVITY 155

100
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Figure 4. Pertinent portion of data concerning the elevator in a constant

speed movement.

Minstrell's 'at rest' discussion (1982). Some of the subjects (about half in the PTTTC
group) introduced the additional force to differentiate between the elevator
downwards or upwards ('Additional force' category).

Discussion and inferences

Keeping clearly in mind that all our novice subjects had been taught to identify
weight with gravitational force, we now consider the data presented in the previous
section.
It has been reported that the identification of the supporting normal force N,
(figure 1) is problematic for novice students (e.g., Minstrell 1982). We too observed
the problem: AT was omitted where it should be mentioned (figure 4) and mentioned
where it should be omitted (figure 2). In addition, our data show that considerably
fewer students had a problem in identifying the mg force (figure 4). Why? Our
interpretation is that, in light of the current method for teaching the concept of
weight (the first approach), there is no formal connection between weight and
contact, elastic force. When standing on the floor, a person attributes his sense of
burden, load, heaviness or what we also call weight, to the gravitational force exerted
by the Earth. This interpretation is not unique and was not made naturally; we are
educated to make it. Historically, we find an alternative interpretation in the
Aristotelian science, the 'orderliness', as attributing the cause of natural occurrences
to a natural tendency to reach the definite order of the four basic elements.
We therefore assume that our subjects' interpretation was the result of their
present formal and informal education about the Earth as the origin of weight. Thus,
just AT-force 'disappeared', as no room had been left in their perceptual knowledgefor an
 156 RESEARCH REPORTS

additional force -the normal force from the support. As many of our subjects stated:
' We feel a force downwards... this is gravity...'. They looked no further for, after all,
how many forces do you need to explain the same sensation?
With the alternative definition of weight as a contact force something exerts
against the support, the presence of normal force JV, as the reaction to weight force,
might be much easier to comprehend. The identification of the mg force in this case
should not 'suffer', as the awareness of mg force, as we noted, is much less
problematic for students.
Further, it was evident how in a constant speed elevator context (figure 4) some
students invoked an additional third force to resolve the competition between weight
(they labelled it 'mg') and the reaction force JV, in favour of one which showed the
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direction of'real' movement (Galili and Bar 1991). If weight was defined as equal to
JV-force then we could assume there should be no question which of the two prevails.
Ultimately, one cannot avoid the use of Newton's laws in order to infer the equality
of gravitational force and normal forces (zero net force) in this case as well, but weight,
being equal to the normal force, would not be involved in the other important
mechanical misconception 'Motion-itnplies-force'. In some 'free fall elevator' re-
sponses (figure 2) the additional third force was also 'drafted' by students. This was
done to explain the strange sensations experienced by the falling person and
sometimes to 'neutralize' the normal force JV in order to 'sponsor' the fall.
Commonly, discussing free fall, physics textbooks (e.g., Sears et al. 1982, p. 73)
use the often 'misleading' term of 'weightlessness', which may cause confusion.
Actually, it should not come as a surprise since in the same textbook, only a page
earlier, weight is equalized to gravity. The solution proposed to escape from the
logical trap (if weight is gravity then no weight means no gravity) is usually an
introduction of an additional concept-'apparent weight', 'sensation of weight' or
'real weight'. In theory, this is fairly legitimate, but in practice additional labels, not
always properly understood, have a tendency, over time, to disappear from students'
memories when the classroom instruction ends - and absence of weight is probably too
strongly associated for many with the term 'weightlessness'.
For the physics community, the 'falling elevator' is the famous Gedankenexperi-
ment constantly used while presenting an introduction to both classical and
relativistic physics. Still, few of us have actually experienced the situation of the
falling elevator. This might explain why students cannot appeal to their perceptual
experiences in this case, and have to rely exclusively on theoretical considerations.
The current way to define weight, as mg, is invariant to the situation and cannot help.
To expect that the gravitational pull disappears when the cable breaks seems to be a
strange idea. So, if the weight coincides with the gravitational pull there is no
'appealing' reason to think in the direction of possible changes in weight or of
weightlessness. More sophistication is needed to employ the 'apparent weight'
concept.
In the frame of the alternative definition (weight is equal to the force exerted on
the floor), there is no automatic answer to the question about the value of weight. The
problem becomes physics-context dependent. Looking for the value of JV, a student
discovers its zero value and assesses from that fact that weight, W, is zero too. To
consider the weight changes becomes a routine procedure of dynamic problem
solving. Weightlessness in 'the free fall elevator' becomes real and strongly
connected to the absence of JV-force: JV vanished together with W, being always equal
to it.
 WEIGHT AND GRAVITY 157

The second framework of weight definition would also provide a great ideological
contribution to students' physics comprehension by calling their attention to the
point of Einstein's initial thinking about gravitation: actually, we do not feel gravity]
The origin of our sensation of burden is actually our effort to prevent the falling, and
not the pull of the gravitational force; this feeling exists due to our muscles working
against the resisting force from the support or pivot. Take away the support (or cut
the pivoting rope) and the sense of burden will disappear. There will be no weight
feeling as well as no reaction force; in short, there will be weightlessness. The fact
that in the context of a falling elevator only a small minority of our subjects
mentioned the phenomena of weightlessness ('Man flies') or any 'weight changes'
(figure 2) illustrates, to our mind, that students do not even consider the problem of
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weight or apparent weight changes.

The data show that the Aristotelian view ('Man moves relatively') was also not
popular among our students. This fact could be interpreted as further support of the
statement that many of our subjects didn't identify the task 1 situation as a free fall,
similar to the fall of a thrown stone in Galili and Bar (1991). The difference is in the
context of the task: a stone falls alone while the person falls within the elevator box.
This way, the students avoided the relevant discussion, missed support force
disappearance, and did not exhibit the Aristotelian view on free fall, even if they held
it.
Further related conclusions could be made observing the data on the Coasting
Satellite task (figure 4). The combination of these questions in one task may have
sounded a little strange to some of the students. To be consistent with the classroom
instruction (equating weight with gravity), the subject had to give the same
affirmative answer to both questions (G-yes, W-yes). Yet, many of the subjects did
not so answer. The highest rate in novice groups was about 60%, and most were
around 50%. It is important to note that naive students' results were less - 40%. What
influenced them, as the situation in the satellite was no more experienced by any
student than that of the free falling elevator? In contrast to the previous task, all the
students had observed, and not just once, pictures of astronauts 'flying' inside
Skylab. They had all observed the weightlessness and heard the descriptions of this
curious 'space experience'. The problem was, of course, their interpretation.
Some of the subjects, in spite of the current instruction, kept gravity acting but
discarded weight ('G-yes, W-no'). These students could be guided by the intuitive
association of weight as a sense of burden. Many previous researchers (Gunstone and
White 1981, Mayer 1987, Ruggiero et al. 1985, Kruger et al. 1990) have pointed to
the widespread confusion between the two concepts, weight and gravity, in different
populations and different ages of students and primary teachers. People commonly
mean different things by these concepts. In this sense we could see, at least partly, in
the responses 'G-yes, W—no1 and 'G-no, PF-yes' of novice students, a resonance with
their pre-instruction beliefs. For those, the alternative definition of weight (II)
would be more educationally effective, as it represents a more natural way to reflect
their intuitive considerations.
Other students, perhaps influenced by the images of objects flying in space,
dismissed both gravity and weight ('G-no, W-no'). We could interpret their
rationale as an attempt to be 'consistent' with their learning experience, as they
understood it. That understanding could be presented in the following logical
sequence: weight is gravity, => in the state of weightlessness, 'obviously', there is no
weight, => weightlessness occurs in space, => so, there is no (or little) gravity in space.
 158 RESEARCH REPORTS

This interpretation helped lead us to group together, in the category 'G=W

decreased', all responses where subjects explicitly stated that due to the relationship
between weight and gravity the obvious reduction (not necessarily to zero) in weight,
i.e., weightlessness, was inevitably manifested in the diminishing of the gravitational
force exerted by the Earth. Some responses classified in the first three categories
would have entered this category if the subject had explicitly mentioned this kind of
reasoning. The reduction of gravitational force with distance was mentioned as a
possible reason for the state of weightlessness. Let us note here that since the actual
reduction of the gravitational force with distance is only about 5% for the common
heights of satellites' orbits, it seems probable that we observe here the rational way
students assimilate specific learned definitions of weight and gravity.
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To further illustrate what, in our opinion, was our students' thought rationale,
we would like to use and reproduce (see Appendix 2) the views of the famous science-
fiction writer Jules Verne. His hypothetical response to our questions we would
classify in the 'G-yes, PF-yes' and then, regarding some equilibrium point in space,
in the 'G-no, W-no' and, of course, in the 'G= W decreased' categories. In our mind,
he described in an exquisitely elaborate, yet straightforward manner the equivalency
of weight and gravity, in his novel From the Earth to the Moon and Around the Moon
(1970). The fact that makes these data especially valuable is that the writer himself
(as is true of all his generation, of course) did not observe the free fall reality in a
spaceship. All other initial theoretical knowledge he possessed (in the 19th century)
was identical to that of our subjects.
The last possible error was to deprive the flying man of gravity but to keep his
weight active ('G-no, W-yes'). One could speculate that those responses might be
motivated by the well-known confusion between weight and mass. The fact that it
almost did not occur with our novice students might reflect that this confusion is
usually explicitly addressed in most textbooks and relevant papers. This provides the
necessary guidance for teachers and students, and so this kind of misconception did
not characterize the post-instructional knowledge of novice students in our case.
This kind of confusion might be more prevalent in earlier stages of educational
progression, as demonstrated by our subjects from the naive reference group HS-10.
Lastly, we would like to note that the alternative definition of weight is in
correspondence with the constructivist approach to the teaching-learning process
(Driver and Oldham 1986). This would appear to provide a number of advantages.
First, it is coherent with the fact that people differ in their pre-instructional
knowledge between the concepts of weight and gravity (an important factor from the
constructivist point of view). We observed that they continue to differ between the
concepts even after their physics classroom instruction. Moreover, the teaching of
the concept weight and the concept/orce are separated for different age ranges in the
science curriculum (e.g. Harlen 1977): weight 'for earlier development [very roughly
5-9]' and force 'for later development [very roughly 9-13]'. This separation has also
been reported in numerous articles, some of them mentioned in the introduction. It
would therefore appear to be more educationally effective not to 'fight' this
separation if possible.
Second, the alternative weight definition, being pedagogically flexible, permits
the student to progress in his understanding of weight, parallel with his progress in
learning mechanics, from primitive situations (gravitational force equals the
supporting force-the book on the table iV=mg) to more sophisticated ones (the
accelerated rectilinear and circular movement).
 WEIGHT AND GRAVITY 159

Third, further progress in learning physics brings the advanced student to study
the basis of general relativity - the Einstein Equivalence Principle. For those
students who view weight as equal to the supporting force, it should be quite natural
to equate gravitational force to any inertial force. For them, weight is not solely the
prerogative of gravitational force; inertial force could also cause the weight effect no
less successfully, and this is an exact personification of Einstein's Equivalence
Principle in General Relativity. There need be no great conceptual change or
reconciliation, as multiple contributions to the body's weight was a familiar situation
in their previous learning experience. We will further elaborate the second and third
statements in a separate article as they, especially the third, do not explicitly follow
from the experiment we performed.
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Summary and implications

What emerges from the analysis of students' responses is that some misunderstand-
ings concerning physical situations involving concepts of weight and gravity might
stem from the improper interpretation of the innocent-looking definition of weight
as a synonym for gravitational force. Alternatively, the other possible definition of
weight, as a force exerted by a body against any support (floor, spring scales) or pivot
(wire, weighing scales), could help students to avoid reported standard confusions
and misunderstandings. In other words, it would be educationally better simply to
define weight as a result of weighing. Some student mistakes which might then
be avoided if gravity and weight were defined as separate concepts are:
• missing the reaction force from the support (the force on an object in rest);
• missing the tension force in the pivoting wire (tension force on a bob of a
pendulum);
• wrong understanding of weightlessness (weightlessness does not mean ab-
sence of gravity but only the absence of a supporting force);
• wrong interpretation of experienced under- and overweight ('some extra g');
• inferrings about sensation or non-sensation of gravity and its distance
dependence;
• exclusion of weight force from the domain of confusion 'motion-implies-
force';
• wrong interpretation of weight loss according to Archimedes' principle;
• interpretation of weight changes and g dependence on geographic latitude due
to the rotation of the Earth;
• missing the possibility of providing astronauts with weight (called sometimes
'artificial gravity') giving, for example, self-rotation to the space station.
A teaching—learning experiment to test this assumption is now in progress.

Acknowledgements
We appreciate the enjoyable interaction with Professor Eric Mendoza on the issue of
science history. We also appreciate the discussions with Dr M. Cohen and Dr V. Bar
who provided a good defence to the current way of teaching the weight concept in
Israel and in this way greatly stimulated the research. We thank Mr R. Zaltsman and
Dr M. Cohen for their help in collecting data. We appreciate the help of Mr A.
Portnoy in preparing the data for publication.
 160 RESEARCH REPORTS

References
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Appendix 1
Below is a list of physics textbooks reviewed for the definitions of weight used. Those books
which employed the second approach to the concept of weight are mentioned by the symbol
(*), all other employing the first approach (see figure 1).
1. ALONSO, M. and FINN, E. J. (1980). Fundamental University Physics. Reading, MA,
Addison Wesley, 150.
2. ATKINS, K. R. (1965). Physics. New York, John Wiley, 88, 95-96.
3. BEISER, A. (1962). The Mainstream of Physics. Reading, MA, Addison-Wesley, 30.
4. ELLIOTT, L. P. and WILCOX, W. F. (1962). Physics: A Modern Approach. New York,
Macmillan, 51.
5. FORD, K. W. (1968). Basic Physics. Waltam, MA, A Division of Ginn and Co, 203.
 WEIGHT AND GRAVITY 161

*6. FRENCH, A. P. (1971). Newtonian Mechanics. New York, W. W. Norton, 129-130.

7. HARWARD PROJECT PHYSICS (1968-9). An Introduction to Physics 1: Concepts of Motion.
New York, Holt, Rinehart and Winston, 79.
8. HEWETT, P. (1989). Conceptual Physics. San Francisco, Scott, Foresman, 141, 144.
*9. MARION, J. B. (1980). Physics and the Physical Universe. New York, John Wiley, 69.
*10. MARION, J. B. and HORNYACK, W. F. (1982). Physics/or Science and Engineering, 1. New
York, Saunders College Publishing, 129.
11. MICHELS, W. C , CORRELL, M. and PATTERSON, A. L. (1968). Foundations of Physics.
Princeton, NJ, Van Nostrand, 105, 256.
12. MILLER, F. J. (1981). College Physics 1977. New York, Harcourt Brace Jovanovich, 60.
13. OHANIAN, H. C. (1989). Physics. New York, W. W. Norton, 126.
*14. OREAR, J. (1967). Fundamental Physics. New York, John Wiley, 82.
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15. PASACHOFF, J. M. (1981). Invitation to Physics. New York, W. W. Norton, 51.

16. RESNICK, R. and HALLIDAY, D. (1966). Physics. New York, John Wiley, 93.
17. PSSC (1965). Physics, 1. Bostin, D. C. Heat, 108.
18. ROGERS, E. M. (1973) Physics for the Inquiring Mind. Princeton, NJ, Princeton University
Press, 117, 131.
19. ROSSEL, J. (1960). Physique Generale. Paris, Grifon.
20. ROWELL, G. and HERBERT, S. (1987). Physics. A Course for GCSE. Cambridge
University Press, 10, 30.
21. SEARS, F. W., ZEMANSKY, M. W. and YOUNG, H. D. (1987). College Physics. Reading, MA,
Addison Wesley, 66.
22. SEARS, F. W., ZEMANSKY, M. W. and YOUNG, H. D. (1982). University Physics. Reading,
MA, Addison Wesley, 66.
23. SWARTZ, C. E. (1981). Phenomenal Physics. New York, John Wiley, 98.
24. SWIFT, D. (1988). Physics for GCSE. Oxford, Basil Blackwell, 9, 35.
25. TIPLER, P. A. (1976). Physics 1. Worth, 83.
26. WILLIAMS, G. A. (1976. Elementary Physics. New York, McGraw-Hill, 48-53.

A USSR physics textbook employing the second way to define the concept of weight is:
CHAIKIN, S. E. (1963). The Physical Basis of Mechanics (Gosudarstvenoe Izdatelstvo Fisiko-
Matematicheskoi Literaturi, Moscow) (in Russian).

The following list is of some references to the discussions among physics educators on
issues relevant to the weight concept.
BACHMAN, A. A. (1984). Free fall and weightlessness. Physics Teacher, 22, 482.
BARTLETT, A. A. (1984). Physics from the news. Physics Teacher, 22, 249.
BARTLETT, A. A. (1984). The author replies. Physics Teacher, 22, 482.
BARTLETT, A. A. and HEWITT, P. G. (1987). Why the ski instructor says, 'lean forward!'
Physics Teacher, 25, 28-31.
BARTLETT, A. A. and HEWITT, P. G. (1987). Response. Physics Teacher, 26, 71.
FRENCH, A. P. (1983). Isg really the acceleration due to gravity? ThePhysics Teacher, 528-529.
MARIO IONA (1975). The meaning of weight. The Physics Teacher, 13, 263-274.
MARIO IONA (1987). Weightlessness is real. The Physics Teacher, 25, 418.
MARIO IONA (1988). Weightlessness and microgravity. The Physics Teacher, 26, 72.
MCGOWAN, L. (1987). Down with microgravity! The Physics Teacher, 25, 137.
MCGOWAN, L. (1987). The Physics Teacher, 26, 72.
YOUNG, W. O. (1985). A note on apples, elevators and the space shuttle. Physics Teacher, 23,
103.

Appendix 2

From Verne, J., 1970:

'Yes; provided it possesses an initial velocity of 12,000 yards per second; calculations prove
that to be sufficient. In proportion as we recede from the earth the action of gravitation
 162 WEIGHT AND GRAVITY

diminishes in inverse ratio to the square of the distance; that is to say, at three times a given
distance the action is nine times less. Consequently, the weight of a short will rapidly decrease,
and will become reduced to zero at the instant that the attraction of the moon exactly
counterpoises that of the Earth; that is to say, at 47/52 of its passage. At that instant the
projectile will have no weight whatever; and if it passes that point, it will fall into the moon by
the sole effect of lunar attraction... on account of its weight.' (p. 25)
'From the moment of leaving earth, their own weight, that of the projectile, and the objects
it enclosed, had been subject to an increasing diminution. If they could not feel this loss by the
projectile, a moment had to arrive when it would be appreciate insofar as they themselves and
the utensils and instruments they used were concerned.... We know that the attraction, or
the weight, is in proportion to the densities of bodies, and inversely to the squares of the
distances. Hence this fact: if the earth had been alone in space, if the other celestial bodies had
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been suddenly annihilated, the projectile, according to Newton's laws, would weigh less as it
got farther from the earth, but without ever losing its weight entirely, for the terrestrial
attraction would always make itself felt, at whatever distance.' (p. 290)
... and finally, at some moment, they approached that point where:'... neither themselves
nor the objects enclosed in the projectile would be any longer subject to the laws of weight. Up
to this time, the travelers, while feeling that this action was constantly decreasing, had not yet
become aware of its total absence. But that day, about eleven o'clock in the morning, Nicholl
having accidentally let a glass slip from his hand, the glass, instead of falling, remained
suspended in the air... weight really missing from their bodies. If they stretched out their
arms they did not attempt to drop. Their heads were shaky on their shoulders . . . . They were
like drunks who have no stability... here reality, by neutralization of attractive forces,
produced men in whom nothing had any weight, and who weighed nothing themselves.
... An influence of these attractions lasted scarcely an hour; the travelers felt themselves
insensible drawn toward the floor... by the inverse motion the base was approaching first; the
lunar attraction was prevailing over the terrestrial; the fall toward the moon was
beginning...'. (pp. 29-294)