Good morning. We have talked a lot about work and energy in this class. Now it is time to discuss
the most general equation we have which relates work and energy. This equation states that the
change in energy of the system equals the net energy transferred into or out of the system.
To be clear, delta E sub system is the change in energy of the system and sigma T is the sum of
the energy transferred into or out of the system. So, the change in energy of the system is equal to
the amount of energy that is put into or taken out of the system. That seems kind of obvious, right?
Yeah. Sure.
Right, this may seem a little obvious, however, it is a great place to start and
we are going to derive equations from this relatively obvious starting place. Okay,
let’s talk about specific ways energy can be transferred into or out of a system.
Mechanical waves: Sound waves are a great example of energy transferring from one system to another
through a disturbance of a medium, in this case
that medium is the air. ♪ Flipping Physics ♪
Work: A force applied can transfer energy to a system by doing work on the system.
For example, here, work done by the force applied
is adding gravitational potential energy to the Earth-book system.
Heat: Heat is a way to transfer energy from one system to another via a difference in temperature.
For example, this space heater disguised as a fireplace transfers energy to the system
by increasing the temperature of the system. Electricity: Electrical current can transfer
energy from one system to another, consider the electric motor of this power drill converting
electric potential energy to kinetic energy in the rotating power drill.
Radiation: Electromagnetic waves like visible light, ultraviolet light,
radio waves, and microwaves can add energy to a system. For example,
this microwave oven added energy to this water via microwave radiation so I can have tea.
(Are you going to keep teaching us or what?) Okay.
For a long time in this class, the only source of energy transfer into or out of a system we
will consider will be via work. For now, let’s consider the net energy transferred into or out
of the system to be done by the work done by a force applied. We will learn about those other
modes of energy transfer later. Also, the change in energy of a system is equal to the
change in mechanical energy of the system plus the change in internal energy of the system.
That means that our equation shows us that the change in mechanical energy of the system plus the
change in internal energy of the system equals the work done by the force applied on the system. And,
if there is no force applied transferring energy into or out of the system via work,
then we get that the change in mechanical energy of the system plus the change in internal energy
of the system equals zero. The change in internal energy of the system is caused by the work done
by nonconservative forces like friction. In other words, the work done by nonconservative
forces on a system converts mechanical energy into internal energy of the system.
You should recognize this because when you rub your hands together,
they get warmer. The kinetic energy of the motion of your hands is being converted,
via work done by friction, into internal energy in your hands, your hands get warmer.
{rubbing hands} They do get warmer. {rubbing hands} Yeah, they do!
Yea. That’s fun.
The equation for that is that the change in internal energy of the system equals the negative
of work sub NC where NC stands for nonconservative forces. From there you can see that the general
equation about energy transfer we started with, if there is zero work done by a force applied
on the system, gives us that the work done by nonconservative forces on the system equals
the change in mechanical energy of the system. Hey, is that the work done by friction equals
change in mechanical energy equation we’ve used before? It looks almost identical to that.
It is close. It is work done by nonconservative forces on the
system equals the change in mechanical energy of the system, which is not exactly the same.
Right. When we learned the work due to friction equals change in mechanical energy equation
we had not yet learned about conservative and nonconservative forces. Now that we understand
conservative and nonconservative force, we can use the more general work done by nonconservative
forces on the system equals the change in mechanical energy of the system equation.
Makes sense. Okay. Sure. Let's go one step further and say there is zero
work done on the system by nonconservative forces. When that is true, the change in mechanical energy
equals zero. Change in mechanical energy equals mechanical energy final minus mechanical energy
initial. And that means mechanical energy initial equals mechanical energy final.
What do we call mechanical energy initial equals mechanical energy final?
Conservation of mechanical energy! Exactly. We have just shown that, if there is
no work done on a system by applied forces and no work done on a system by nonconservative forces,
the mechanical energy of the system is conserved. We may have known that before, however, now
we have derived it! Yeah! Yea. Cool.
Okay. Let’s do a quick review. Starting after the general concept that the change in energy of the
system equals the net energy transferred into or out of the system, I would like the three of you
to review what we just learned today. Please. Okay. Uh, well the work done by nonconservative
forces on a system converts mechanical energy into internal energy of the system.
In other words, the change in internal energy of a system equals the negative of the work done by
nonconservative forces on the system. From there we were able to prove that,
when there is no force applied doing work on the system, that the work done
by nonconservative forces on the system equals the change in mechanical energy of the system.
And if there is also no work done by nonconservative forces on the system,
mechanical energy of the system is conserved. Very nice. And please, please, please,
I beg you to remember that whenever you use these equations you have to identify your initial and
final points. (We will.)
(Of course we will.) And you need to identify
what object or objects are a part of the system. (Oh yeah. Right. Sure)
I will clarify the importance of identifying what object or objects are a part of the system in my
next video “Energy Systems Clarified”. (Cool. Yeah. Okay.)
Thank you very much for learning with me today, I enjoyed learning with you.