carrying a passenger on your bike, then it takes more "work" to reach the same
speed.It turns out that these intuitive relationships among the "work" done on
a system, its mass, and changes in its speed can be sharpened into a precise
statement, called the work-energy theorem. (One caution, though: the technical
definition of work needed for this precise statement is different from its everyday
usage and physiological meanings; e.g., you do no work on a heavy box by merely
holding it still.) As you will begin to see in the present lesson, this relationship
between work and mechanical energy gives you a new and powerful tool for the
solution of many problems, a tool that is often easier to use than a direct
application of Newton's second law.The assigned reading for this lesson in the
Halliday and Resnick text deals exclusively with energy in the context of
Newtonian mechanics. The text's definitions of work and kinetic energy are
chosen to be useful in mechanical theory, and therefore may sound very abstract
to you. Actually, the concept of energy is much broader than this, and your
understanding will be helped if you are aware of other scientific uses of the
energy concept. If your background from previous physics courses is somewhat
sketchy, you may find it useful to review a more general treatment of energy in
an introductory physics text or good encyclopedia.
Imagine a bicycle rider coasting without pedaling along a road that is very
smooth but has a lot of small hills. As he coasts up a hill, the force of gravity will
slow him down, but it speeds him up again as he goes down the other side. We
say that gravity is a conservative force because it gives back as much kinetic
energy to the cyclist when he returns to a lower level as it took away when he
ascended to the top. We therefore assign a gravitational potential energy of Ug to
the cyclist, which depends only on his elevation. The lost kinetic energy K is
converted into this Ug. We then find to our delight that total energy represented
by the sum E = K + Ug is (approximately) constant: Ug is larger at the top of each
hill, and smaller at the bottom, in just such a way that its change compensates for
the change in the kinetic energy K! This is an example of the conservation of
mechanical energy.If we watch the cyclist for some time, however, we are
disappointed to find that K + Ug is only approximately conserved: frictional
forces gradually slow the cyclist down and after awhile he starts pedaling again,
thereby increasing K + Ug. But still, all is not lost. The energy-conservation law
can be saved by defining other kinds of energy (for example, chemical, thermal,
and nuclear) that are produced by the action of so-called non-conservative forces.
If we call these non-mechanical energy forms Enc, then E = K + U + Enc is exactly
conserved. In fact, energy conservation is one of the most general principles of
physics, and one that holds even outside the domain where Newton's laws are
valid.Another example of energy transformation is provided by hydroelectric
power production, beginning with the water stored behind a high dam. As the
water rushes down the intake pipes it gains kinetic energy, then does work on
the turbine blades to set them in motion; and, finally, the energy is transmitted
electrically to appear as heat in the oven in your kitchen. Experience with energy
transformations of this kind led to the formulation of the law of conservation of
energy in the middle of the nineteenth century: energy can be transformed, but
neither created nor destroyed. This law has survived many scientific and