d/A simplified drawing of
Joule’s paddlewheel experiment.e/The heating of the tire
and floor in figure c is something
that the average person might
have predicted in advance, but
there are other situations where
it’s not so obvious. When a
ball slams into a wall, it doesn’t
rebound with the same amount of
kinetic energy. Was some energy
destroyed? No. The ball and
the wall heat up. These infrared
photos show a squash ball at
room temperature (top), and after
it has been played with for several
minutes (bottom), causing it to
heat up detectably.Although the story is picturesque and memorable, most books
that mention the experiment fail to note that it was a failure! The
problem was that heat wasn’t the only form of energy being released.
In reality, the situation was more like this:gravitational energy→kinetic energy
→heat energy
+ sound energy
+ energy of partial evaporation.The successful version of the experiment, shown in figures d and
f, used a paddlewheel spun by a dropping weight. As with the
waterfall experiment, this one involves several types of energy, but
the difference is that in this case, they can all be determined and
taken into account. (Joule even took the precaution of putting a
screen between himself and the can of water, so that the infrared
light emitted by his warm body wouldn’t warm it up at all!) The
result^4 is
K=
1
2
mv^2 [kinetic energy].Whenever you encounter an equation like this for the first time,
you should get in the habit of interpreting it. First off, we can tell
that by making the mass or velocity greater, we’d get more kinetic
energy. That makes sense. Notice, however, that we have mass to
the first power, but velocity to the second. Having the whole thing
proportional to mass to the first power is necessary on theoretical
grounds, since energy is supposed to be additive. The dependence
onv^2 couldn’t have been predicted, but it is sensible. For instance,
suppose we reverse the direction of motion. This would reverse the
sign ofv, because in one dimension we use positive and negative signs
to indicate the direction of motion. But sincev^2 is what appears in
the equation, the resulting kinetic energy is unchanged.
separately from the rest of the things to which we now refer as energy, i.e.,
mechanical energy. Separate units of measurement had been constructed for
heat and mechanical of energy, but Joule was trying to show that one could
convert back and forth between them, and that it was actually their sum that
was conserved, if they were both expressed in consistent units. His main result
was the conversion factor that would allow the two sets of units to be reconciled.
By showing that the conversion factor came out the same in different types
of experiments, he was supporting his assertion that heat was not separately
conserved. From Joule’s perspective or from ours, the result is to connect the
mysterious, invisible phenomenon of heat with forms of energy that are visible
properties of objects, i.e., mechanical energy.(^4) If you’ve had a previous course in physics, you may have seen this presented
not as an empirical result but as a theoretical one, derived from Newton’s laws,
and in that case you might feel you’re being cheated here. However, I’m go-
ing to reverse that reasoning and derive Newton’s laws from the conservation
laws in chapter 3. From the modern perspective, conservation laws are more
fundamental, because they apply in cases where Newton’s laws don’t.
Section 2.1 Energy 77