Forms of Energy: Kinetic, Thermal, & Potential (RP12)

Forms of Energy: Kinetic, Thermal, & Potential (RP12)

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Now we’re ready to use the physics definition
of WORK to develop ideas about — and formulas for — some important FORMS of energy. By “forms of energy,” I don’t mean anything
anthropocentric (like enthusiasm, or spirit). And I don’t mean anything BIOcentric (like
a mysterious life energy, or the Chinese Qi). It turns out that nature’s deepest interpretation
of energy TYPES — that is, FORMS of energy — seems to come from applying the definition
of work in supremely simple situations. By the way, I’m now indulging in what philosophers
call reductionism: reducing issues to their SIMPLEST elements. This is often the way of
science. I don’t know if reductionism is the road to ULTIMATE truth. But it certainly has
given us PRICELESS insights. Consider THE SIMPLEST case of a force doing
work: a CONSTANT force acting on a FREE — i.e., unattached — object that is initially at
rest. For example, let gravity act on a mass over
a short distance near Earth’s surface (pretend Earth is down there), and ignore the tiny
effect of air resistance: [drop … thud] The force of gravity, F, does work, W, on
mass, m, through a distance, d. [Draw it!] Another way of drawing this situation would
focus on the constant acceleration, a, and the resulting speed, v, acquired at time,
t, just before impact. [Draw it!] The definition of work tells us that work
equals force times distance. N2, Newton’s second law, allows us to rewrite
this single force F as m times a, so that W=Force times distance=mad And simple linear kinematics tells us how
“distance traveled” is related to the constant acceleration: d=one-half a t^2. So… W=ma-times-one-halfat^2 … which equals…
one-half times m times the quantity (at)-squared And, finally, from the very definition of
acceleration, we know that constant acceleration times the elapsed time gives the speed acquired.
That is, a is defined as: delta-v over delta-t, which
becomes, when initial time and speed are zero, simply v=at. So, W=one-half m times v-squared This equation says that the work done on a
free mass is manifested as SPEED. This “one-half m v-squared” is so useful in physics that
we give it a special name and its own symbol: one-half mv^2 is called KINETIC ENERGY, capital
K, the energy of MOTION. This is our first FORM of energy. A 1-kilogram object moving
at 1 meter-per-second (ordinary walking speed) has one-half joule of kinetic energy. Notice that the v in the formula for kinetic
energy is speed, not velocity. Direction is not involved. This will remind us that kinetic
energy — like ALL energies — is NOT a vector quantity. Our 1-kilogram object has exactly the same
energy whether it moves to the right at 1 meter per second, or to the left at 1 meter
per second. And notice that the speed v is SQUARED in
the formula. This means that speed determines kinetic energy in a BIG way. If, for example,
we double a BULLET’s speed, then we quadruple its energy. This is an important — and perhaps
scary — insight. Capital K is defined as one-half mv^2. Remember
that. The work done on the mass has given it kinetic
energy. If the mass had already been moving, then the work would just have CHANGED the
kinetic energy. In other words, we can generalize our result to become a VERY useful law of
physics: capital W-sub-net=delta-(capital-K) The work done by the net force on a mass equals
the mass’s CHANGE in kinetic energy. If the work is a POSITIVE number of joules, then
the kinetic energy increases by that many joules, and the mass speeds up. If the work
is NEGATIVE, then capital-K decreases, and the mass slows down. This very general law of physics has acquired
a strange name. It’s called the work–kinetic-energy THEOREM, as if we had proven it mathematically. We sure DID use math to help derive this relationship,
but, in the end, we BELIEVE the so-called “Work–Kinetic-Energy Theorem” because EXPERIMENT
— and every-day life — confirm it again and again and again. Perhaps you noticed that little n-e-t subscript
that I slipped-in alongside the W in the Work–kinetic-energy theorem. As I said, W-sub-net is the work done by the
NET force acting on the mass. Or, equivalently, by the SUM of the works (positive and negative)
done by EACH of the forces acting on the mass. We’ll come back to the Work–Kinetic-Energy
Theorem in another Radical Physics episode. But, for now, let’s remember what we originally
set out to do: to learn about different FORMS of energy by seeing work done in simple situations. When episode RP11 first introduced the concept
of work, I said, “WORK is the TRANSFER of ENERGY from one object to another by means
of a FORCE.” Let’s take that seriously. Look, again, at the mass that simply falls
through a distance d. The work done by a force (gravity) is transferring energy (kinetic
energy) to THIS object. But as this kilogram strikes the ground, is
a DIFFERENT force doing work to transfer the KINETIC energy into ANOTHER form of energy?
After all, the mass ends up NOT MOVING. It’s sitting on the ground, so it has zero KINETIC
energy. Evidently, the force of impact DOES do work,
but at the MOLECULAR level. Take a look at this animation that depicts what’s happening
during a slightly bouncy impact. Those gray circles represent MOLECULES within the falling
object. As the impact occurs, the kinetic energy of
the entire falling object is transformed into the kinetic energy of the object’s MOLECULES.
In a SOLID, those molecules can’t go very far, so they just VIBRATE more than usual. This molecular vibrational energy is commonly
called “heat.” But let’s be a little more formal and call it THERMAL ENERGY, capital
T. The KINETIC energy of the falling object has
become THERMAL energy: vibrational kinetic energy of that object’s molecules (AND of
molecules in the object hit, AND even of the surrounding air molecules). Notice that this heat, or thermal energy,
is NOT created by the motions of the molecules. It *IS* the motions — the kinetic energies
— of the molecules. No mysterious stuff called “heat” is created when molecules collide. Collisions tend to turn the kinetic energy
of MACROscopic objects into the RANDOM kinetic energy of MICROscopic objects (the molecules). This miniaturization and randomization of
energy happens virtually EVERYWHERE and at almost every instant. We will come back to
look at this steady disorganization of energy in later RP episodes. The force of impact did work on the falling
object, and transformed its kinetic energy into thermal energy. But where did the original
kinetic energy of the falling object come from? Gravity did work to transfer WHAT form of
energy into kinetic energy? Scientist’s have found a very useful way of
speaking about the work done by gravity, whether the mass is rising or falling. We say that
the mass’s POTENTIAL ENERGY is changing. Unfortunately, potential energy is symbolized
with a capital U. (Think of it as a big bucket — so big, in fact, that it holds most of
the ordinary energy of the universe!) delta-U (the change in potential energy) is
defined as negative W (work done by any force of a special class of forces) One such special force is gravity. So let’s
use the formula for work done by gravity to find the change in potential energy that resulted: ∆U-sub-g=– W-sub-g Remember what the delta means… Ulater – Uearlier=– W-sub-g U-at-the-bottom – U-at-the-top=– m times
g times d Let’s rearrange this: U-at-the-TOP – U-at-the-bottom=mgd This says that the gravitational potential
energy at the top, minus the gravitational potential energy at the bottom, equals mgd. But if we recognize that this distance d is
just the height h above the ground, then U-at-the-bottom is the potential energy of the object when
it can’t fall any farther. So, if we DEFINE U-at-the-bottom to be the
local zero of potential energy, then U-at-the-top=mgh where h, the height, is just the distance
above our DEFINED starting point — the zero point — for gravitational potential energy.
If we want to say that U-sub-g is zero not on the ground, but actually deeper down, that’s
fine. We can even define U-sub-g to be zero at the
center of Earth. However, then our earlier formula F-sub-g=mg wouldn’t apply all the
way down, cuz g (the acceleration due to gravity) changes underground. So our formula U-at-the-top
=mgh would need to be amended. But, for objects near Earth’s surface, U-sub-g
=mgh is just fine. In fact, U-sub-g is defined as mgh is our second form
of energy: local gravitational potential energy. Other types of potential energy will be considered
later, but THIS type is incredibly useful — especially for you humans trapped there
on Earth! The mgh formula tells us that every elevated
object has potential energy. The greater the elevation, the more the joules of potential
energy. But wait, … elevation …as measured from WHERE?! From WHEREVER we have DEFINED
the elevation to be zero! This may seem fishy, but we did something
quite similar for kinetic energy. We said that K=one-half m v-squared, but we didn’t
say “relative to what” that v must be measured! This means that the kinetic energy of an object,
as with its speed, is a REALTIVE quantity. Relative to these stars, I have no kinetic
energy. But relative to a passing comet, I may have a great deal! Likewise, this kilogram, at a height of 1
meter on Earth, has … m times g times h … it has about 10 joules of gravitational
potential energy RELATIVE to the ground. But relative to the center of Earth, it has many
millions of joules. This kind of RELATIVITY of potential and kinetic
energy does not diminish their usefulness. That’s because the incredibly deep law of
physics that employs them deals only with CHANGES in energy, not with absolute values.
That law is the law of ENERGY CONSERVATION, and it is the subject of our next taproot
episode.

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