Professor Dave again, let's learn about
conservation of energy.
We now know about kinetic and potential energy and
we know that these quantities can be
altered as an object moves, like the way
potential energy is converted into
kinetic energy when an object
experiences free fall towards the ground.
But energy can be transformed in a
variety of other ways as well, so we must
learn about all the kinds of energy and
how they can transform from one to
another.
We also must understand that while
energy can change forms, the total energy
of a closed system will always be
conserved, that is to say, there will
always be conservation of energy. As an
object falls, potential energy is
converted into kinetic energy, but the
sum of the potential and kinetic
energies of the object will be the same
at every instant during the free fall. We
can call this sum the mechanical energy
of the system. This is more easily
visualized using the simple harmonic
motion of a mass-spring system which
utilizes elastic potential energy, but we
can also use the pendulum of a
grandfather clock, which will use
gravitational potential energy. At the
top of the swing, the pendulum possesses
its maximum potential energy and zero
kinetic energy. At the very bottom of the
swing it possesses its minimum potential
energy and its maximum kinetic energy. As
these two forms interchange again and
again and again, there is conservation of
energy, and the total mechanical energy
which again is the sum of the two, is
constant. This concept can be described
mathematically by the following equation.
If mechanical energy is the sum of
kinetic energy and potential energy
which are in turn represented by these
expressions, and this value is conserved
then one-half mv squared initial plus
mgh initial will be equal to one-half mv
squared final plus mgh final. It shows
that the sum of the kinetic and
potential energy of a system like the
pendulum will be the same at every point
in its motion. This equation will be
used frequently in physics when we want
to assess the kinetic or potential
energy of an object at a particular
moment, and if we have enough information
about a system we will be able to
algebraically solve for some unknown.
This only works when there is no
friction present, but for systems like a
swinging pendulum we can use it anyway
as the force of friction will be negligible.
Once again, the label of mechanical
energy is just a way of categorizing
energy. It distinguishes kinetic energy
of motion and gravitational or elastic
potential energy from other forms of
energy, which we call non mechanical energy.
This includes things like chemical
energy, thermal energy, nuclear energy,
electrical energy, acoustic energy, and
more. These are also some kind of kinetic
or potential energy as they involve the
motion of tiny vibrating particles, the
energy stored in an atomic nucleus, or
some other form of energy associated
with either motion or storage. But they
differ in nature from mechanical energy.
As we said, energy can be transformed
from one form to another but it is
always conserved. A car engine converts
chemical energy stored in gasoline
through a series of steps to eventually
produce the kinetic energy that is the
movement of the car. When we metabolize
food we are converting chemical energy
within the food into the chemical energy
in ATP which can then be used as kinetic
energy to move our bodies around.
If while moving around you decide to slap
your hand down on the table, all that
kinetic energy is transformed into
thermal energy by heating up the table
slightly, as well as acoustic energy
which is the sound we will hear. As we
progress through the 21st century we
will continue to try to find more
efficient ways to convert energy from
natural sources like solar and wind
energy into the energy that our
civilization needs to operate all of our
technology, but for now there's much more
physics to discuss, so let's check comprehension.
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