c/As in figure b, an infrared
camera distinguishes hot and
cold areas. As the bike skids to
a stop with its brakes locked, the
kinetic energy of the bike and
rider is converted into heat in
both the floor (top) and the tire
(bottom).
a new form of invisible “mystery energy” that patches things up?
This would be like balancing your checkbook by putting in a fake
transaction that makes your calculation of the balance agree with
your bank’s. If we could fudge this way, then conservation of energy
would be untestable — impossible to prove or disprove.
Actually all scientific theories are unprovable. A theory can
never be proved, because the experiments can only cover a finite
number out of the infinitely many situations in which the theory is
supposed to apply. Even a million experiments won’t suffice to prove
it in the same sense of the word “proof” that is used in mathematics.
However, even one experiment that contradicts a theory is sufficient
to show that the theory is wrong. A theory that is immune to
disproof is a bad theory, because there is no way to test it. For
instance, if I say that 23 is the maximum number of angels that
can dance on the head of a pin, I haven’t made a properly falsifiable
scientific theory, since there’s no method by which anyone could even
attempt to prove me wrong based on observations or experiments.
Conservation of energy is testable because new forms of energy
are expected to show regular mathematical behavior, and are sup-
posed to be related in a measurable way to observable phenomena.
As an example, let’s see how to extend the energy concept to include
motion.2.1.3 Kinetic energy
Energy of motion is calledkinetic energy. (The root of the word
is the same as the word “cinema” – in French, kinetic energy is
“ ́energie cin ́etique.”) How does an object’s kinetic energy depend
on its mass and velocity? Joule attempted a conceptually simple
experiment on his honeymoon in the French-Swiss Alps near Mt.
Chamonix, in which he measured the difference in temperature be-
tween the top and bottom of a waterfall. The water at the top of
the falls has some gravitational energy, which isn’t our subject right
now, but as it drops, that gravitational energy is converted into ki-
netic energy, and then into heat energy due to internal friction in
the churning pool at the bottom:gravitational energy→kinetic energy→heat energyIn the logical framework of this book’s presentation of energy, the
significance of the experiment is that it provides a way to find out
how an object’s kinetic energy depends on its mass and velocity. The
increase in heat energy should equal the kinetic energy of the water
just before impact, so in principle we could measure the water’s
mass, velocity, and kinetic energy, and see how they relate to one
another.^3(^3) From Joule’s point of view, the point of the experiment was different. At
that time, most physicists believed that heat was a quantity that was conserved
76 Chapter 2 Conservation of Energy