Now that we have an idea
of what the kinetic energy of an object is,
we're going to discuss the potential energy.
Let's first ask ourselves a question,
suppose you have an apple,
again like this one and you throw it up in the air
with the particular velocity, v.
After a little bit of time you might notice
that the apple stops right at the apex
before falling back down.
If you're looking at this, this might seem strange,
we had a kinetic energy and definitely had energy to it
and then it stopped, meaning that it had no more kinetic energy
and we could asked what happened to the energy?
Where did it go?
We know energy is conserve, we hear this all the time
and so if it's certainly initially had some energy
and now it isn't moving so doesn't have any more kinetic energy.
Where did the energy go?
It didn't go nowhere, what we do is we say
that it has a potential energy now by virtue of where it is.
There are many different notations where the potential energy,
so let's just get one lay down right now.
Some people say PE for potential energy or just P for potential.
I'm going to use the letter U
both because it's most common in the literature
and so that we also don't confuse potential energy
with the Momentum which we also symbolize with the letter P
or with PE which looks like it might be two variables.
So U is usually the most common letter
that we use for the potential energy
and it also avoid some confusion so we use the letter U
for potential energy going forward.
So first, let's look one more time at this example,
you have an apple and you toss it in the air
and it goes say some height, h.
And then eventually reaches a velocity of zero
right at the apex of its height,
right at that moment it's not moving anywhere.
If we look at the potential energy
from the ground to this height, h.
We would say that the potential energy
is equal to m times g times h.
So for the gravitational potential energy
which is the potential energy that comes from an object
due to gravity specifically.
The gravitational potential energy for an object
near the earth's surface is m times g times the height
at which it is relative to your coordinate system.
Looking at the energy of the object as it goes into the air.
We could take snapshots of our object at many different times.
We have a particular time when it started,
the time when it ended and a few in between,
we could just give these some names, different energies.
The total energy of an object is conserved
when we have force like this one,
the force of gravity acting on our apple in this case.
The total energy is the sum of the kinetic energy
from the motion and the potential energy
coming from the gravitational potential energy
that we just described.
If we watch this energy, this kinetic changing to potential,
what we would see in other words
is that each one of these energy
that each snapshot is the same in total
but initially the energy is totally composed of kinetic energy
and then finally when it's right at the apex of its height
the energy is entirely in potential energy
and then on its way through its transitioning from
motion to potential energy, from kinetic energy to potential energy.
But again at each point here,
the entire energy that kinetic plus potential is the same.
It's always the same total energy
if I added kinetic plus potential.
What we're going to do
especially in problems is we're going to say that each of these energies
is equivalent, so as far as the problem goes,
what you'll do is take snapshots at two different times
or even more that two different times.
Write down the energy
and each of those times just by examining each scenario
and then finally write that each of these energies
that you've just found are the same as each other
because the total energy is always conserved.
In this case it's important to notice
that we're talking about sort of an idealistic case
where there's no friction or sound
or interaction with the air molecules.
All of which could take energy for themselves.
The total energy of course will still be conserved.
It might just go to different places
but first we're just considering a case
where the energy is staying in our object.
The important thing again just to emphasize,
this is for a problem what you could do is say
I know the energy at any one point in the system
but because the total energy is conserve in an ideal system,
then we also know the energy at all points in the system.
So if I know for example the energy at point one in the system.
I could calculate what the energy is,
maybe the initial kinetic energy.
Then I know what the total energy is throughout the rest of the problem
and I could always use that at each of my snapshots
whichever one I chose to take.