It's professor dave, I want to tell you
about kinetic and potential energy.
We now understand a more
rigorous scientific definition of the
word energy as being the capacity to do
work, but as we said, there are a few
different kinds of energy, so we must
talk about all of these varieties. First
we will discuss kinetic energy and
potential energy. Kinetic energy is the
energy an object possesses by virtue of
its motion. If we recall Newton's second
law, we know that the application of some
net force will move an object with some
mass at some constant acceleration. We
also know that work is equal to force
times distance, so if we account for the
distance travelled by this object we get
that W equals Fd equals mad or simply
W equals mad. We also know of this
kinematic equation for an object
experiencing constant acceleration. If we
solve for ad we get this expression
which can be plugged into the above
equation for work. After some
simplification, we arrive here, thus
deriving the work-energy theorem. This
term, one-half mass times velocity
squared, represents the kinetic energy of
a system. So now we can express the
work-energy theorem by saying that when
an external force does work on a system
the amount of work will be equal to the
change in kinetic energy of the system.
If w is positive, the system increases
its kinetic energy, and the change will
be equal to the work done on the system.
If w is negative, the system decreases
its kinetic energy, and this change will
represent the work that is done by the system.
Note the presence of mass in the kinetic
energy expression. This means that if two
objects with different masses are moving
at the same velocity, the more massive
object will necessarily have more
kinetic energy. Now let's discuss
potential energy, which is forever
intertwined with kinetic energy.
Potential energy is the energy an
object possesses by virtue of its
position in a field, whether that is a
gravitational field, an electromagnetic
field, or any other type of field.
If you lift a ball up into the air, you're
increasing its gravitational potential
energy as it moves farther away from the
ground. If you release the ball, that
potential energy is converted into the
kinetic energy of motion as it falls. The
closer an object is to the center of
gravity of the earth, the less potential
energy it has, and as you pull it up and
away from the ground it gains potential
energy because it has an increasing
potential to fall some distance to the
ground. It may seem strange to bestow an
object with more energy just by lifting
it into the air, but remember that we
have to eliminate our prior conceptions
of the word energy in favor of more
rigorous definitions. The potential
energy of a compressed spring or an
arrow ready to be released from a bow
is where the kinetic energy of motion
comes from. It is like a kind of stored
energy. In this course we will frequently
be discussing gravitational potential
energy for objects on earth, and for any
object this will be equal to the mass of
the object in kilograms, times the
freefall acceleration due to gravity for
the earth, times the height of the object
in meters. The greater the height, the
greater the potential energy, as this
represents the work that can be done by
gravity to produce the motion of a
falling object. There is also elastic
potential energy, such as with the spring
or the bow and arrow, and we will discuss
this later as well. For now, we just need
to understand kinetic energy as the
energy of motion and potential energy as
the energy of location.
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