Download Paper

THE CONCEPT OF FORCE
V. G. Jadhao
Regional Institute of Education, Bhopal – 462013
B. K. Parida
Regional Institute of Education, Bhubaneswar – 751022
The concept of Force is the most fundamental yet the most misunderstood concept in
physics especially by the students up to higher secondary level. Learning materials in
print form which discuss the formation of these concepts technically known as
cognition or in Piagetian terminology, schemata, are rarely available to a practicing
teacher or to learners. Here we present what special and technical meaning the
concept of force has in the realm of pre-relativisitic classical physics and review the
existence of various alternative conceptions of the learners. We discuss here ways
and means to find out alternative conceptions of students at senior secondary level
regarding the concept of force. Some exemplar teaching and testing strategies are
illustraed. The teachers as well as self-learners can profitably use this in their
attempts to develop correct concept about force.
INTRODUCTION
There are a large number of books titled as or on “Conceptual Physics”, which
attempt to state in clear-cut terms the concepts of physics appropriate to the level they
are meant for. Some books elucidate the concepts, and some others like Fundamentals
of Physics by Halliday1, Resnick and Walker give sets of thought-provoking
questions to help the development of correct concepts in their readers. But, materials
in print form, which discuss the formation of these concepts, technically known as
cognition or in Piagetian terminology, schemata, are rarely available to a practising
teacher or to learners. At senior secondary level, the students, for the first time, learn
physics as a separate discipline. Up to the secondary level, they learn physics as part
of a general science curriculum. Notwithstanding all this, physics is perceived to be
very vast and complicated. Therefore, it is necessary to introduce students to the
excitement of physics, to give them that thrill which the early physicists like Newton
experienced while discovering or propounding the concepts.
PARK
That’s my Nuton over
there. He is about to
discover a law of
Nature!
The two aspects that can together be termed the method of physics or, for that
matter, the scientific method, are ‘logical thinking’ and ‘curiosity to experiment’. This
scientific method has created all physics and all science, and should as well be utilized
to understand the fundamental concepts of any discipline of science including physics.
The concept of force is dealt in physics and sciences at all levels of school education.
It is also a term which is frequently used in daily conversation between people. Here
we elucidate what special and technical meaning the concept of force has in the realm
of physics and explain the existence of various alternative conceptions learners have
due to use of this term by people at large.
The concept of ‘force’ has been chosen here to illustrate the use of logical
thinking and interpretation of experiments and thought experiments (which are
themselves dependent on logical thinking) for developing correct concepts by the
learner. The term ‘force’ is familiar to all of us in the sense that we use it in our dayto-day life while describing things and events happening all around us. For example,
we say: “Water is coming out of the tap with a great force”; “Force within the earth
pulls the stone down”; “The police forced the door open”; “In spite of applying so
much force the lid of the tin is not opening”; “The earth keeps us tied down to itself
by gravitational force”, so on and so forth.
In the discipline of physics, the term ‘force’ has a very clear-cut meaning that
is at variance with the meaning of the term in every day usage. Many times it is found
that the usage of the term is biased by the Aristotelian way of thinking according to
which “The state of rest is the most preferred state and, therefore, a state of motion,
even that of uniform motion in a straight line, must have a continuous cause for it.”
This cause is misconstrued as ‘force’. These ideas are contrary to the formal concept
of force, which is based on the validity of the Newton’s laws of motion.
These Aristotelian ideas and some other misconceptions (alternative
conceptions, alternative frameworks) about force do persist in students and teachers
alike. This can be made evident by administration of a simple question following the
description of Osborne’s thought experiment described later in this article. We discuss
here ways and means to find out alternative conceptions of students at senior
secondary level regarding the concept of force. Possible causes for this are also
outlined.
Some exemplar teaching and testing strategies are illustrated. The teachers can
profitably use these in their attempts to develop correct concept about force in their
students.
ALTERNATIVE CONCEPTIONS RELATED TO FORCE
It is found by many research studies that students in schools as well as in
colleges/universities possess a number of alternative conceptions with regard to force.
Even teachers are not immune to them. The situation is not peculiar to any particular
country or region and seems to be universal. In 1983, Watts2 studied the ideas of a
number of pupils aged between 11 and 17 years, from schools in the Greater London
urban area, in the context of force. He identified the following 8 alternative
frameworks used by the pupils when describing common phenomena in terms of their
concept of force.
a) Forces are obligations to complete an action against some resistance.
(Affective forces)
b) Objects restrained in a position have force. (Configuration forces)
c) Forces are designated to those objects that are causing or will cause events to
occur. (Designated forces)
d) When two or more forces come together they can be combined to change the
movement of an object. (Encounter forces)
e) Moving objects are a force, which is made manifest when the object collides
with some other body. (Impact forces)
f) If a body is moving, there is force acting upon it in the direction of the
movement. If a body is not moving there is no force acting upon it. (Motive
forces)
g) Force is an action. The amount of force is proportional to the amount of
activity taking place. (Operative forces)
h) Forces are positive actions that are effective when they come into contact with
objects. (Substantial forces)
Different forms of the ideas about force possessed by the various learners may
be noted here. They, however, seem to be aware of the fact that the ‘neutral’ language
of physics uses force as a noun (not as a verb). In the Indian context, Datta3 and
Prabhakara identified the following misconceptions of advanced students and student
teachers with regard to the laws of motion.
i. If a ball is thrown vertically up by the hand, the push force exerted at the
time of throw remains in the body during the entire flight. The same is
also true for a projectile (in parabolic motion) throughout its flight.
ii. When a ball is projected upwards vertically, its acceleration keeps
changing continuously, being directed upwards when the ball is moving
up, zero when the ball reaches the highest point, directed downwards
when it is falling down.
iii. A projectile moves along a parabolic trajectory because a tangential force
is acting on it. Equivalently, force, velocity and acceleration are always
in the same direction.
iv. The force that ‘propels’ a satellite around the earth (in uniform circular
motion) is a tangential force either acting all by itself, or in combination
with other forces.
v. There is no force of gravity on a satellite.
vi. The uniform circular motion of a satellite involves a centripetal and a
centrifugal force, which according to Newton’s third law of motion, are
equal and opposite, and hence cancel each other.
vii. An object moves up or down depending on whether either the velocity or
the kinetic energy is larger or smaller than the force of gravity.
The sample in this case comprised students from higher secondary and student
teachers or pre-service teachers from B. Sc. Ed., M. Sc. Ed. and B. Ed. courses.
Connections between these and Watts’ findings as above may be seen. Results of
similar nature may also be found in (Watts4 and Zylbersztajn, 1981; Sadanand5 and
Kess, 1990; Witelock6, 1991; Galili7 and Bar, 1992; Thijs8, 1992; Kumar9, 1997;
Palmer10 and Flanagan, 1997; Parasnis11, 1998; Heywood12 and Parker, 2001). A list of
alternative conceptions in the context of Newton’s laws of motion and related
domains is further available in a paper by Kane13 (1998).
Here we would like to consider the following alternative conceptions culled
from the above sources.
1.
2.
3.
4.
5.
6.
7.
8.
Force is associated with the body till it is in motion.
When a body is at rest the force acting on it is zero.
Force is always in the same direction as the velocity of the body.
If the velocity is changing then force is also changing.
Centripetal and centrifugal forces both act on a body moving in a circle.
The action-reaction forces act on the same body.
The product of mass and acceleration is a force.
Only animate things like people and animals exert forces; passive ones like
tables, floors do not exert forces.
9. A force applied by, say a hand, still acts on an object after the object leaves the
hand.
We shall mostly refer to this list in what follows.
TEACHING STRATEGY
ORIGIN AND REMEDY OF ALTERNATIVE CONCEPTIONS
Can I ever ‘force’ them to
learn the concept of ‘force’ ?
In order to realize the fact that alternative conceptions are a part of schemata of the
students, one may use Osborne’s thought experiment as a teaching episode. We shall
describe the situation as under.
Consider an elastic ball. If we just drop the ball, it will go down.
On its journey downward, if it meets a perfectly elastic horizontal
floor, it’ll return to the same spot from where we dropped it, and
this process would continue forever. After describing the situation
we encourage the participants to ask for any clarifications. We may
satisfy them by stating facts such as we can neglect air resistance,
or air resistance can be completely eliminated by conducting the
experiment in vacuum. It may also be told that the correct answer
to the question to follow does not really depend on all these
clarifications. After this the following question is asked with
reference to Fig. 1.
State the direction of force acting on the ball when it passes
through the point B midway between points C and A as it travels
(i)
(ii)
Upwards.
Downwards.
C
C
B
B
A
A
(i) Ball moving upwards
(ii) Ball moving downwards
Fig. 1
First, the opinion of each and every participant should be recorded. Sometimes
the participants really do not give the response they feel like giving, but just give that
which they think might be correct, or just because some ‘bright’ participant has given
one, they tend to repeat the same. The later kind is known as a ‘band wagon’ response,
which can be discovered with a little experience. Afterwards, they should be asked to
justify their responses on the basis of answers to such questions as to who is applying
the force. Varying answers and very interesting justifications are expected form the
participants. This process of having a dialogue with the participants is very important.
At some stage, they may be told that their responses are quite contrary to each other,
and that both the options such as direction of the force in a particular situation is
downward as well as upwards couldn’t be correct. We may then discuss with them the
various ways in which one can arrive at the unique and correct answer to the question
posed.
Before we discuss how to arrive at the correct response to the question in
Osborne’s thought experiment, let us just state, without further explanation, that the
correct answer is that the direction of force in both the cases (i) and (ii) is downwards.
It is seen that many students, and sometimes teachers too, say that when the ball is
going upwards/downwards, the force is accordingly upwards/downwards. We may
conclude that such participants think that the direction of force is the same as that of
the velocity. We have to impress upon them the fact that the direction of force can be
obtained by noting the direction of acceleration or the direction of change of
momentum as stated by Newton’s second law. Of course, this is a longer route to
arrive at the correct answer. The shorter route is to consider the cause or the origin of
the force. This is of course the earth, which is always situated below the ball and it
pulls the ball towards itself and produces acceleration or change of momentum of the
ball in the same direction as well. Thinking of another interesting example, to many
the Alternative Conception No. 7 (The product of mass and acceleration is a force)
may not appear to be a misconception at all. One may argue – after all this is all that
Newton’s second law tells us about force. We will just leave the issue as such and
clarify it later.
Now, specifically we shall discuss the possible reasons that create the
misconceptions that force is always associated with a body in motion, force would be
zero if the velocity of the body were zero, and the direction of force is that of the
velocity (Alternative Conception Nos. 1, 2 and 3). When we teachers introduce the
concept of force, we invariably give the example of a stationary object like a duster or
a piece of chalk, and impress upon the students that it will remain so as long as we do
not apply a force on it. So, the student reverses the argument in his mind and thinks
that as ‘force is required to have motion in an object at rest’, whenever the object is in
motion, force must also be present there. This could be the genesis of the alternative
conception under discussion. The learner is further helped in his thinking by our
inability to show him examples of such motions that do not require any steady force to
act on an object to keep it in uniform motion because of the ubiquitous presence of
frictional force in every case of motion we are familiar with. We should emphasize
while giving the above example that force is needed only to change the velocity of the
body, and no force is needed to maintain its constant velocity. In every day life, we do
need a steady force to maintain a constant velocity of our bicycle or moped in order to
counterbalance the frictional force arising due to the relative motion of the two
surfaces in contact. An interesting and instructive account of friction, suitable for
higher secondary level, is available in a recent article by Popli14 (2002).
Fundamentally, even these forces are the result of interaction between the atoms and
molecules of the surfaces in contact. This brings us to the crux of the problem. Force
acting on any object in any situation is always the result of its interaction with
another object as is implied by Newton’s third law of motion. This being so, one
cannot associate a force with one object alone whether it is at rest or in motion. A
force may act on an object but its cause is always external to the object. Naturally, the
direction of force will depend upon the location and nature of the other object. This
then takes care of the misconception that the direction of force is that of the velocity.
The second misconception arises because the student is unable to distinguish between
the two situations, namely, the object permanently at rest and the object momentarily
at rest. To prevent this from happening, we have to first explain the concepts of
average velocity and instantaneous velocity and the fact that unlike position, velocity
is linked with two instants rather than one. The displacement suffered by the body
divided by the time interval between the two instants gives us the average velocity
during the interval. The mathematical concept of the derivative of a function then
gives us the instantaneous velocity at a particular instant of time as the limit of the
average velocity as the time interval around the instant tends to zero. What holds good
for velocity also holds good for acceleration. When we come across a situation where
the velocity of the particle is zero at some instant, we must enquire what was its
velocity just before that instant. If it was zero, then the acceleration can be inferred to
be zero at that instant. If not, the instantaneous acceleration would not be zero
although the instantaneous velocity is zero. Thus we find that some of the
misconceptions about force are related to students’ misconceptions in kinematics,
namely the concepts of velocity and acceleration.
The misconceptions referred to above and other ones as well can be avoided if
we impress on the students that the first and foremost thing one ought to keep in mind,
while learning the concept of force, is that there does not exist any definition of force
independent of Newton’s laws of motion. The first law gives us the qualitative
definition of force. It just tells us how to conclude from our observation on the body
whether any force is acting on it or not. If one finds that the momentum of the body is
changing with time, which is equivalent to saying that the body with a constant mass
is having acceleration, then some force must be acting on it.
A Limerick on First Law of Newton
Doin’ its Own Thing
The first Law of Newton I sing
My voice has a relevant ring:
“An object left free
Of hassles will be
Engrossed in just doing its thing.”
(Composed by Edward H. Green)
(Source: Online APS News, March 1997 Edition)
The second law quantitatively defines the force as mass times acceleration,
and thereby defines the unit of force as well. This can be used to correctly understand
the concept of force. Here it should also be recognized that the second law not only
defines the force but also the mass of the body in terms of force. This is called the
inertial mass. So the first and second laws give us a technique based on a study of
kinematics to find out
i.
ii.
whether some unbalanced external force is acting on the body (first law),
and
if yes, how much (second law).
Two things have to be understood at this stage: the two laws do not say
anything even remotely about the cause of the force; they just talk of the net effect in
terms of the net force. We would illustrate it by giving two examples. If we study the
kinematics of the moon of mass ‘m’say, we would come to know about its
acceleration ‘amoon’ both in direction and magnitude. So we can conclude that a net
force F given by mass times this acceleration, ‘mamoon’ should act on it. Now, this
force may be provided by the pull of the earth as well as that of the sun on it. So, this
product ‘mamoon’ is not the force that we instinctively think as push/pull by any one
well-defined object. In this sense, ‘mamoon’ is not a force (Alternative Conception No.
7). Another example is that of a stone thrown. We can study its acceleration and know
what is the net force acting on it. But the cause of that force could be the pull with
which the earth attracts the stone, the frictional force that the air around applies on it
and the force applied by the wind on it. All these causes together would determine the
net force given so simply by the expression F = ma. Clearly, ‘ma’ is no independent
force acting on the stone; in this sense this is a misconception.
Related to the teaching of Newton’s first and second laws is the concept of
inertia and that too, inertia of rest and inertia of motion. Frankly, in this discussion,
we would have liked to avoid the concept of inertia altogether. The reasons for so
disregarding this concept are as follows. Firstly, in modern day physics, whenever we
define some quantity, it is believed that we should also give an experimental way of
measuring it. Definitions related to this aspect are known as ‘operational definitions’.
In this sense, mass of a body is considered as a measure of its inertia. So, if we can
discuss things with the help of mass, why talk about inertia? Secondly, certain
prevalent definitions of inertia and force also generate misconceptions about them.
One such definition of inertia is ‘the resistance that a body offers to change in its state
of motion’. Now, the term ‘resistance’ in the minds of the students is already related
to some kind of opposing force. So, he starts relating inertia with force, which gives
rise to some other misconceptions. Thirdly, we talk of inertia of rest and inertia of
motion. It has been reported in certain studies that, according to students, inertia of
motion is larger than the inertia of rest, which is contrary to the meaning correct
concept.
The significance of the third law of Newton is much deeper than the action
and reaction it talks about. It states a very important characteristic of force, namely
that forces always occur in pairs. When we are interested in the accelerated motion of
only one body, we may not consider the other paired force, but it does exist. Thus, the
third law states that a force is the result of interaction between two bodies. This is
stated clearly in some books at the higher secondary level, but few books do so at the
secondary level. So, the third law hints at the physical cause of the force acting on a
body and the fact that this cause is external to the body. The misconception often
quoted is students’ thinking that the action and reaction forces act on the same body
(Alternative Conception No. 6). The most effective way of curbing this misconception
is not to give the third law in its briefest form, namely “Action and reaction are equal
and opposite”. It should rather be stated as “Mutual action and reaction between two
bodies are equal and opposite”. The book ‘Fundamentals of Physics’ (Halliday1,
Resnick and Walker, 1994) gives a good number of examples illustrating actionreaction pairs of forces. The common examples given, while teaching this law, are
‘ball and bat’, ‘bullet and rifle’ etc. Even in these cases, forces are neither properly
identified nor described verbally in a pedagogically correct manner. For example, it is
stated that the bullet goes forward and the gun comes backward; one is action and the
other is the reaction. We forget that action and reaction refer to forces and not motion.
If we persist in this way, the misconception of the students equating force with motion
is likely to be strengthened. We should rather say that “The rifle acts on the bullet”
(action) and “The bullet reacts on the rifle” (reaction). So, whatever example we give
of action-reaction pair, we must identify ‘by whom’ and ‘on what’. In the case of ballbat example, stating the pair won’t be enough. The bat either does not seem to move
or move in a direction opposite to that in which the force due to the ball is exerted on
the bat. One comes to know of the existence of this reaction as an experience of the
batsman who feels a pain in his hand.
More interesting and also more confusing in terms of students’ responses are
situations where nothing moves but action-reaction forces are present. In this category
let us cite the example of a boy sitting on a chair. The boy acts on the chair and the
chair reacts on the boy. The physical cause for the boy’s action on the chair is the
gravitational pull of the earth on the boy. This is also an action the opposite paired
reaction for which is the force with which the boy attracts the earth. The ‘pair’ of
forces acting on the boy by ‘the earth and the chair’ is equal and opposite (why?) but
is not an action-reaction pair because both members of the pair are acting on the same
object that is the boy! And in this case three objects are involved: the earth, the chair
and the boy. So, it should be clear that the action and reaction, which the third law
talks about, describe in fact the physical interactions between objects taken two at a
time. Now, let us explain the reason for giving the example of the boy rather than, say
that of an object resting on a table. The point we are trying to make here is that usually
teachers shy away from giving examples of animate beings while teaching Newton’s
laws. May be because they mistakenly think that the laws do not apply to animate
beings! In this connection let us do the following. Let us tell our students, if a
paperweight kept on a table suddenly jumps, we would be surprised and would start
asking who lifted it; but if a rat sitting on the table jumps, we won’t be surprised. If
asked how the rat jumped, we would coolly say that it did so itself. After this we call a
student and make him stand before the class in attention position and ask him whether
he is a living being. Naturally the whole class breaks into a laugh! Then we ask the
same student to jump without coming down. The message is immediately sent to the
class that Newton’s laws apply even to animate beings. In the technical jargon, when
the rat jumped, the legs of the rat pushed the table down (action) and the table pushed
the rat up (reaction). In such examples, there is another facet of force as ‘push and
pull’. In normal circumstances, when an object pushes another, it moves in the same
direction as the pushed object (example: a hammer driving a nail into a wall). But, in
examples of action-reaction, an object moves in one direction but applies force on the
other object in the opposite direction. Lastly, in connection with the third law, we
would like to mention that the action and reaction are interchangeable and
simultaneous unlike the social connotation of “Reaction of A to B’s bad behaviour”.
In the context of Newton’s third law there is no ‘delayed’ causality involved.
The Alternative Conception No. 5 regarding centripetal and centrifugal forces
is related to the concept of ‘pseudo-force’, which is postulated in order to be able to
apply Newton’s laws of motion to non-inertial or accelerated frames of reference. This
needs some elaboration. The equation F = ma has two sides. The right hand side is
obtained by studying the kinematics of the body. The left hand side, on the other hand,
gives the physical cause, which we call interaction of the body with something
external. For example, in the case of the earth moving around the sun, the physical
cause is the gravitational pull of the sun on the earth. For a revolving stone attached to
a string, the tension in the string provides the force that produces the necessary
centripetal acceleration. Now suppose, you are sitting on a stool in a room and seeing
the other things around you at rest. Then suddenly the stool starts vibrating with a
small amplitude. You would now find that the other things around you are vibrating.
Since vibration means acceleration, it would mean that, in your frame of reference,
these objects are accelerating in directions opposite to your own. If you believe in
Newton’s laws, you would immediately conclude that some force must be acting on
these objects. But, in fact, you know that these ‘vibrating’ objects are not having any
physical interaction with anything external. Hence in this case, we cannot apply the
equation F = ma. But if we wish this equation to remain valid even in this accelerated
(or non-inertial) frame of reference, then we will have to assume that a force given by
F = ma, where a is the perceived acceleration of the objects is acting upon them. Such
a force is termed ‘pseudo-force’. Interestingly, some prefer to call pseudo-forces
‘inertial forces’ in spite of the fact that their use is perceived in non-inertial frames of
reference.
Centrifugal force is the pseudo-force experienced by the observer in a rotating
frame of reference. In case of the earth it is called Coriolis force (first described by
Gaspard de Coriolis in 1835) because of which an object moving relative to the earth
is deflected from its path (as viewed from the earth) due to earth’s rotation. In case of
a car taking a bend, centrifugal force is experienced by the passenger as an outward
acting force pushing him against the door. Let us consider another interesting
example.
A limerick on Coriolis force
May the Force Be With You
On a merry-go-round in the night,
Coriolis was shaken with fright.
Despite how he walked,
`Twas like he was stalked,
By some fiend always pushing him right.
(Composed by D. Mortin, E. Zaslow, E. Haley, J. Golden and N. Salwen)
(Source: Online APS News, March 1997 Edition)
When one rides a bicycle on a muddy ground at a steady speed, mud particles
are seen to go tangentially off the tyres. For the time being, disregarding the
gravitational pull of the earth, a person on the ground (and even the rider) observes
that the mud particles are moving in straight lines. But an ant sitting on the rim of the
tyre would see the particles move away radially outwards with an acceleration (the
centrifugal acceleration) equal in magnitude but opposite in direction to that of the ant
(the centripetal acceleration). The concept of pseudo-force merits detailed discussion,
as it is sometimes very useful in solving problems. The ideal problem that can be used
to understand this concept is the problem of finding the apparent weight of a body
inside a lift, which is accelerating downwards or upwards with acceleration ‘a’.
Students are in general able to get the correct answer without realizing the relevance
of pseudo-force there. The teacher must ensure that they follow the underlying logic
clearly. The salient points to be kept in mind are the following:
a) Weight should be defined as the negative of the normal reaction suffered by
the object resting on the floor, or mass times acceleration of the falling object
as seen by an observer inside the lift.
b) Reactions like friction and tension are self-adjusting and cannot be assumed to
have any particular value in advance. (In this connection please remind
yourself that ‘friction’, ‘reaction’, ‘tension’ and ‘pressure’ are as troublesome
in physics as in real life when we do not try to understand them correctly!)
c) The problem can be solved as seen from the inertial system and this does not
require the concept of pseudo-force. Application of Newton’s laws is enough.
d) If you want to consider the problem as seen from the accelerated frame,
Newton’s laws cannot be applied as such by considering the forces of
interaction alone, but you have to think as if a force, opposite to the
acceleration of the frame of reference, is applied whose magnitude is equal to
mass of the object times that acceleration.
e) Centrifugal force is a pseudo-force, which explains the position (of rest) of the
object moving uniformly in a circle, in its own frame of reference. It is not one
of the action-reaction pair forces. Remember that action-reaction pair is the
result of interaction. Notwithstanding this, the experience of pseudo-force is
real and not fictitious. The meaning of this statement would be clear if you go
back to the lift problem wherein the lift is accelerating upwards with
acceleration a. A spring balance meant for weighing the object and attached to
the lift would actually record a higher weight m(g+a), where m is the mass of
the object and g is the acceleration due to gravity.
Some suggestions about the importance of drawing ‘free body diagrams’ and
drawing them correctly are in order. A free body diagram is drawn because we are
interested in the motion of a particular object, i.e., we would like to find out the
acceleration of the object by applying Newton’s second law of motion. So we must
isolate those forces, which are acting on the object. If we do not, we may commit the
mistake of adding even those forces, which do not act on the object. This is the
difference between mathematics and physics. Mathematics tells us the rule for adding
two vectors. But it cannot tell us whether or what that addition will mean physically.
While drawing free body diagrams students may make the following mistakes.
•
•
•
Showing those forces that do not act on the body
Showing a force and also its resolved components in the same diagram
Assuming in advance the magnitudes of self-adjusting forces like friction, tension,
etc. instead of evaluating them at the end after utilizing all the data.
The teacher ought to make the students aware of these problems and how to take care
of them.
Now we would like to give a list of questions. Finding answers to these and
discussing the thought processes aloud would help in developing the correct concept
about force and also bring the related alternative conceptions of the students to the
fore.
QUESTIONS
Answer the following questions giving your reasons. Be brief and to-the-point.
Draw the diagram showing a body of mass m in projectile motion under gravity. Show
the magnitude and direction of the force acting on the body when it is a)
ascending, b) at the top most position, and c) descending. Give reasons.
1. A simple pendulum is swinging back and forth. The suspension thread suddenly
breaks at the moment when the bob is in the mean position. Draw the diagram and
show the path of the bob after the thread breaks. Give reasons.
2. Consider the pendulum in the above question. Is the tension in the thread always
equal to mg cos θ for any value of θ during the motion of the pendulum? Draw
the free body diagram and explain. The symbols used here have the usual
meanings. (Hint: Think about which physical interaction would provide the so
called centripetal force)
4. We take say 5 identical paperweights and put them on a fairly smooth horizontal
table so that they touch each other and lie on a straight line. Now if we hit this line
of paperweights head on with another identical paperweight moving horizontally
in the same line, it is found that one paperweight at the end of the line moves out
and the moving paperweight comes to rest. Explain this observation on the basis
of the principle of conservation of momentum and in terms of the force acting on
each paperweight. (Hint: Remember that the principle of conservation of
momentum can be applied to an isolated system only. For the second part, ask
questions such as, why the moving paperweight stopped, and then ask similar
questions about the other paperweights)
5. In the Osborne experiment, described earlier, what is the direction and magnitude
of force acting on the ball at the top most position of its journey? Explain
(i) in terms of the concept of force as a result of interaction, and (ii) on the basis of
Newton’s second law (F = ma).
6. Consider a massive simple pendulum at rest. The tension present is just less than
the breaking tension. Suppose this pendulum is set in motion by taking it to one
side and then releasing it. At what position of the swinging pendulum the string is
most likely to break? (Hint: Refer to Question No. 3)
7. The swinging bob of a pendulum meets head on a block of the same mass kept on
a horizontal smooth table. Predict what will happen and give reasons in terms of
momentum conservation and in terms of forces acting on the bob and the block.
(Hint: Refer to Question No. 4)
8. Compare the tension in the string just before and after the collision in Question
No. 7. (Hint: Refer to Question No. 3)
9. In an elevator a heavy steel ball is attached to a vertical spring of force constant k
and is at rest. The elevator is made to go down with acceleration a, greater in
magnitude than g. Compare the condition of the spring when the elevator is at rest
and when it is moving down with acceleration a greater in magnitude than g. Give
reasons for your answer (i) with and (ii) without using the concept of pseudoforce.
CONCLUSION
As spelt out in the introduction, the concept of force is used here as an
illustration to train the students and teachers to talk and think aloud about force and
other related concepts and events. Detailed mathematical analysis of problems has
been deliberately left out. For that any textbook may be referred. What is expected is
to think about, and sometimes even to question, the way we think and interpret events
without being judgmental about ourselves. To illustrate what we are saying, we wish
to discuss a couple of situations.
A spaceship deep in the space, far removed from other objects, is
moving with acceleration a. Some small object just gets detached from
the ship. Neglecting the force of the spaceship on the object, what is
the acceleration of the small object after it gets detached?
The answer to this question is zero though one tends to give the
answer as a itself. What is the reason behind this mistake? It could be
our tendency to consider acceleration of the object as its essential
property to be carried on. But, in fact, it is the result of its interaction
with something external. As long as the detached part of the spaceship
was part of the spaceship, it was interacting with the exhaust to derive
its acceleration. But, the moment it got detached, the interaction
vanished and hence the acceleration too vanished!
We all know that when an object is immersed in a fluid it loses weight.
Is there any gain of weight in this situation? Can Newton’s third law
help us in this? To analyze the situation we try to interpret our
observations on the basis of Newton’s laws. We find that the immersed
body does really lose weight as shown by the attached spring balance.
So something must be pushing it up. There cannot be anything other
than the fluid in the container. So we conclude that the fluid must be
pushing the object up. Then it follows from Newton’s third law that
the object must push the fluid downwards. This is really the case as
can be found out by putting the container on a pan balance and by
monitoring its weight as the object is just immersed in it but not
dropped.
At the end, we would like to suggest a few more books/sources for further
reading in this very interesting area of physics. These are by Cooper15 (1969), Pearce16
and Le Roux (2000) and Rankin17 (2001). Those who wish to think harder may revise
their concept of force in relation to relativity by reading the book on Superforce
(Davies18, 1995). So happy thinking and problem solving!
We shall, of course, be pleased to receive thought provoking questions,
interpretations and reactions (not in the sense of misunderstood Newton’s third law!)
from the readers related to fundamentals as well as problem solving situations.
REFERENCES
Halliday, D., Resnick, R., and Walker, J. (1994). Fundamentals of Physics, 4th edition.
Asian books Pvt. Ltd., New Delhi.
Watts, D. M. (1983). A study of schoolchildren’s alternative frameworks of the
concept of force. European Journal of Science Education, 5 (2), pp. 217-230.
Datta, S. and Prabhakara, S. N. (1994). A Preliminary Survey of Misconceptions of
the first Principles of Physics among Advanced Students and Student-teachers.
Physics Education (India), 11(3), pp. 292-303.
Watts, D. M. and Zylbersztajn, A. (1981). A survey of some children’s ideas about
force. Physics Education, 16, pp. 360-365.
Sadanand, N. and Kess, J. (1990). Concepts in force and motion. The Physics
Teacher, 28, pp. 530-533.
Witelock, D. (1991). Investigating a model of commonsense thinking about causes of
motion with 7 to16-year-old pupils. International Journal of Science Education, 13,
pp. 321-340.
Galili, I. and Bar, V. (1992). Motion implies force: where to expect vestiges of the
misconceptions? International Journal of Science Education, 14, pp. 63-81.
Thijs, G. D. (1992). Evaluation of an introductory course on “force” considering
students’ preconceptions. Science Education, 76, pp. 155-174.
Kumar, A. (1997). Pitfalls in Elementary Physics - 1. Velocity, Acceleration and
Force. Resonance, 2(7), pp. 75-81.
Palmer, D. (2001). Students’ alternative conceptions and scientifically acceptable
conceptions about gravity. International Journal of Science Education, 23(7), pp.
691, 704.
Parasnis, A. S. (1998). Motion, Matter, Mass, Laws of Motion, Newton and Einstein.
Physics Education (India), 15(2), pp. 119-116.
Heywood, D. and Parker, J. (2001). Describing the cognitive landscape in learning
and teaching about forces. International Journal of Science Education, 23(11), p.
1177.
Kane, P. R. (1998). An Overview of Techniques for Identifying, Acknowledging and
Overcoming Alternate Conceptions in Physics Education. Joel Klammer Teachers
College – Columbia University 1997/98 Klingenstein Project.
Popli, R. (2002). The Enigma of Friction. IAPT Bulletin, 19(4), p. 112.
Cooper, L. N. (1969). An Introduction to the Meaning and Structure of Physics.
Harper and Row, New York.
Pearce, H. and Le Roux, Pirre (2000). The Force Concept Inventory: its Meaning for
Teaching Physics. ASPECT and Department of Mechanical Engineering, University
of Cape Town. [email protected]
Rankin, W. (2001). Introducing Newton and Classical Physics. ICON Books, UK.
Davies, P. (1995). Superforce: the Search for a Grand Unified Theory of Nature.
Penguin Books.