New trends in physics teaching, v.4; The ... - unesdoc - Unesco

New Trends in Physics Teaching IV
into the presentation of the results obtained in calculating kinetic energy, for instance, which
consisted of the dropping of the coefficient ?4 from the expression %mv2 and which caused the
final result to lose its true physical significance.
This method is also used for the introduction of the concept of kinetic energy, which is
characteristic of systems in movement and hence capable of doing mechanical work. The mathematical
aspect of the formulation is based on the experimental study of the variations in the
kinetic energy of the moving body under consideration whose mass is m and whose velocity is v.
This conforms to a current trend in physics teaching which deserves to be stressed and encouraged,
for the use of mathematical language makes it easier to choose models whereby physical reality
can be interpreted. The concept of energy is no exception to this rule.
A similar approach is adopted for dealing with the concept of potential energy, i.e. the energy
that a body possesses by virtue of its position. A body that falls from a height h can do work; a
compressed and immobile spring can do work when it is released. In order to link the mathematical
formulation with the physical reality, emphasis should be laid on the fact that the arbitrary
choice of the origin of potential energy (in the case of a falling body, it is natural to consider that
the potential energy is nil at ground level) leads to far more interest being taken in the potential
energy variation than in the potential energy itself.
To return to the purely physical aspect, it is generally agreed that no concept should be
introduced unless it is accompanied by applications drawing on everyday examples derived as far
as possible from the pupil’s environment.
The concept of the mechanical energy (the sum of the kinetic energy and the potential energy)
of a particular system is then introduced with reference to simple physical systems defined having
regard to their positions in space. Examples: the system ‘spring, mass rn’ where the weight mg is
an external force; and the system ‘spring, mass m, rod, Earth’ where the spring and the mass are
guided without friction along a horizontal rod in such a way as to stretch the spring and where
all the forces that come into play are internal forces.
The conservation of total mechanical energy is studied with reference to a mechanically
isolated system, i.e. a system that is not subject to any external forces or that is subject to
external forces that balance each other out. By way of example, it may be noted here that the
system formed by the mass alone is not mechanically isolated, while the system ‘spring, mass
m, rod, Earth’ is.
This property of total mechanical energy is linked to the work of the conservative forces
within the isolated system. These forces are said to be conservative because their work, from the
initial position to the final position along the path followed when their point of application is
displaced, depends only on those two positions and not on the path followed. In the opposite
case, such forces are said to be non-conservative. As an example, one can refer to the frictional
forces acting upon a moving body as it slides over a plane and whose work depends on the form
of the path. At this stage in the method employed to define the concept of energy, the pupil’s
attention should be drawn to the difficulty of generalizing and extending the calculation of
mechanical energy to a system composed of a very large number of particles (since any material
system can be regarded as a set of particles). It is always possible to define the mechanical energy
of a system on a microscopic (molecular) scale, but it would be very difficult, if not impossible,
to calculate it on the same scale when a large number of particles are involved.
This naturally brings us to the concept of heat energy, introduced on the basis of examples of
the non-conservation of mechanical energy in the case of a mechanically isolated system, where
this non-conservation is linked to the work done by non-conservative forces. The production of
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