Hi. It’s Mr. Andersen and this AP Physics essentials video 81. It is on potential energy.
Let’s say I take this crate right here and I add a cable to it and I raise it up. Does
that crate now have potential energy? It does assuming it is sitting on the earth because
if I cut that cable it is going to fall down to earth. And so I have added energy to the
crate by lifting it up. I have done work on that crate. But let’s say I do this. Let’s
say I take the crate and I slide it across the floor. Does it have potential energy now?
Have I added potential energy to it? No. It is not going to move back to where it was.
And so just adding a force over a given distance, doing work on an object, does not insure there
is going to be potential energy stored in that object. It has to be conservative forces.
And we will talk about what a conservative force is in this video. And so if a system
has internal structure there can be potential energy due to the interactions between the
objects inside that system. And so your basic definition for what is potential energy, it
is energy due to position. Position of the objects within the system. Now this only works
if those interactions between objects are conservative forces. And the three conservative
forces that we will talk about in AP Physics are going to be objects found in an gravitational
field, mass spring oscillators, and then also if we have a charge found within a circuit.
Then that energy is going to be a conservative force and we can store potential energy in
that object. And so potential energy, if you think about it, is energy due to position.
But it has to be positioned where we can get that energy back out again. And so as this
archer pulls back on the arrow, this is a system. What are some of the objects? We have
the string. We have the bow. We have his hand. And so what we are doing is as we are pulling
on that bow, we are applying a conservative force. And when we let it go we are going
to get some of that energy back. Let’s say we take an object like this. Does it have
potential energy due to its position? Well not if it is in space. But if it is on the
earth then the earth is another object, which is applying a gravitational field to it. And
if we let it go we are going to release some of that energy. And so remember this only
works if you are using conservative forces. And so a conservative force is a force where
the work that we are putting into the object is independent of the path by which that object
takes. And so what does that mean? It means we are going to have the same amount of energy
in the object if we move along the pathway of the green or if we move along the pathway
of the blue. And so let’s start with gravity, which we know is a conservative force. So
if I lift this object from here to here we are storing gravitational potential energy
in it. But I could have lifted the ball like this all the way around like this. And it
still is going to have the same amount of energy stored inside it. It is conserved.
And so we know that there is gravitational potential energy. Now let me take that same
diagram and say we are looking at it from above. And now we have this red ball and we
are going to move it across some carpet. So we are looking at it from above. And so when
I apply force to it, to move it from here to here, I am going to do less work then if
I move it all the way around like this. And so we call friction a non-conservative force.
And that is why we are not going to get that energy back out of the system. And let’s
go through these three examples of conservative forces and how you figure out the potential
energy in each. And so our equation for gravitational potential energy is m g times the change in
y, so where we are in that gravitational field. And so if I take that object and lift it up
to 2 meters, how much gravitational potential energy does it have? Well I am going to use
these three things. First I have the mass, plugging that in. We know the gravitational
field strength is -9.8 meters per second. How far did I lift it? 2 meters. And so what
is the work done on the system? It is -39 joules solving for significant digits. And
so if I were to let it go I am going to get that energy back out of the system. It is
conserved. Let’s say I do it in a different way though. Let’s say I lift that ball up
to 3 meters. And then I drop it down. Let me show you how these are conservative. And
so I am going to show you those same values. What is the only difference in this equation?
I lifted it to 3 meters remember to begin with. So that is going to be -59 joules. But
then when I dropped it that last meter, that is is going to be a -1 meter, and so I got
20 of those joules back. And so if I take -59 and add 20 to it I get that same -39 that
I had before. It does not matter the path by which we take, it still has the same amount
of gravitational potential energy. This also applies to a mass spring oscillator. And so
I have a baseball here attached to a spring and I am going to push it in like that. Now
is that a conservative force? If I let it go am I going to get some of that energy back?
For sure. And there is a different equation for that. It is 1/2 k x squared. What is k?
That is going to be the spring constant. We will say that is 125 newtons per meter. What
is going to be our x value? It is the displacement, how far we move it. So that is 22 centimeters
or we could say that is 0.22 meters. And so if I plug that in my equation and figure out
significant digits I have done -3.0 joules on that baseball. So when I let it go we are
going to get that work back. We are going to get that energy back out of the system.
Now we also have conservative forces when we are looking at charges. So if I put a charge
inside an electric field and move it in that direction, if I do work on it, am I going
to get that energy back? For sure. And so a good example of this would be charges inside
a circuit. And so if you think about it we have positive charges on this end of the battery.
And so as I move a charge like that I am doing work on it. And so am I going to get that
energy back? Well we have a different equation. That equation, or the amount of potential
electric energy, is going to be equal to the charge, what charge we have, times the change
in voltage, change in potential. And so if it is a 1 coulomb charge and we have a 1.5
volt battery, we are going to get negative 1.5 joules of energy just on that one charge.
And so did you learn how objects in a system can store potential energy due to their position?
And then finally as long as those are conservative forces, could you quantitatively figure out
how much potential energy there is in a system? I hope so. And I hope that was helpful.