Potential energy | Middle school physics | Khan Academy

- [Presenter] Energy is a quantity

that is measured in joules,

and one kind of energy is kinetic energy

that is associated with moving things

or motion of an object,

but there's another kind of
energy called potential energy.

What exactly is that?

That's what we wanna
talk about in this video.

Okay, so what exactly is potential energy?

Well, if you take any
fundamental interaction,

like gravitational
force or electric forces

or magnetic forces,

you probably know that
they're mediated by fields:

gravitational fields, electric
fields, and magnetic fields.

Now, whenever there's another
object that enters the field,

like another mass or another charge

or another magnet, for example,

we say that there is energy
stored in these fields,

and that energy stored
is the potential energy.

So what's interesting is that
potential energy is an energy

that is assigned to a group of objects,

not just one object.

For example, kinetic energy is an energy

that can be assigned to a moving object.

But potential energy is not assigned

to a particular object.

You can't say, you know,

"Earth has that much potential energy,"

or, "This charge has that
much potential energy."

No, you can always talk
about potential energy

for a group of objects
or a system of objects.

You can say, this system of earth and moon

has a specific amount of potential energy.

Or this system of magnets has some amount

of magnetic potential energy, for example.

So the important characteristic
of potential energy

is that it's an energy that is associated

with a system of objects,
not a single object.

But now comes a big question.

Well, what does this energy depend on?

Well, it depends on the
specific arrangement.

So potential energy depends

on the arrangement of the system.

But how exactly?

Well, let's see.

Let's look at gravitational
potential energy first.

So consider a system of an earth and ball.

This particular arrangement
will have some potential energy,

but what do you think will happen

if I were to raise this ball higher?

Will the potential energy
increase, decrease, stay the same?

Well, let's see.

If you have to raise that ball higher,

you have to push it and then move it.

In doing so,

you would have transferred
some energy into the system.

Ooh, because you're adding
some energy into the system,

the gravitational
potential energy increases.

And so when the ball moves higher up,

then the distance between the
ball on the earth increases,

the gravitational
potential energy increases.

See, this is how the gravitational
potential energy depends

on the arrangement.

The more the distance between
the ball and the earth,

the more the gravitational
potential energy.

Similarly, if the distance were to reduce,

the gravitational
potential energy reduces.

But how do we know exactly

how much is the gravitational
potential energy?

How do we assign a number to it?

Well, the first step is to assign

the gravitational potential energy

of some arrangement to be zero.

That's the first step.

So for example, we could say,

"Hey, when the ball is on the ground,

let's assign this arrangement

to be zero gravitational
potential energy."

It's completely your choice.

We are completely free to
choose what arrangement we want

to have zero gravitational
potential energy.

But once we do that, now, take
this ball and raise it up.

In doing so, we would've transferred

some amount of energy into it.

Let's say we transfer 15 joules of energy.

Now, as a result,

the gravitational potential energy

has increased the 15 joules.

So it goes from zero to 15.

And so now we know that this
arrangement of the earth

and ball system should have a
potential at your 15 joules.

Isn't it amazing?

This is how we assign numbers to it. Okay?

But wait a second.

Is it always necessary

to choose the ground to be zero potential?

Not necessarily.

For example, if you are
doing some experiment

in an apartment, for example,

now, if you were to
choose the zero potential

to be when the ball is on the ground,

that would be so inconvenient.

Instead, this time,

what we'll do is we'll
choose the zero potential

to be, you know, when
the ball is on the floor.

That's more convenient.

So now, we'll say when
the ball is on the floor,

that arrangement of the earth and ball,

that, let's call it zero potential energy.

And then we can do it just like before,

figure out how much energy we transferred

in moving it from here to here,

and figure out the potential energy

of this particular arrangement.

So you see, we choose
whichever arrangement

is convenient for us to assign zero,

and then from there,

we assign values for
every other arrangement.

Now, what's cool is that
the same thing applies

to other forms of
potential energy as well.

For example, consider
electric potential energy.

If you have two unlike charges like this,

separate by some distance,

this particular arrangement
will have some potential energy.

Now, what do you think will happen

if we were to move the
charges farther apart?

What do you think will happen
to the potential energy?

Why don't you pause and think about it.

Same way we did gravitational
potential energy,

think in the same way.

All right?

I know light charges attract
each other naturally,

and therefore, to pull them apart,

I have to put a force and move them.

In doing so, I would transfer
energy into the system

and therefore, the electric
potential energy increases.

Similarly, if the charges were
to come closer to each other,

the electric potential
energy would reduce.

And again, just like before,

we can choose a particular arrangement

to have zero electric potential energy.

And then from there,

every other arrangement can
be assigned a particular value

for electric potential energy.

Okay, let's consider one last example.

What if you have light charges?

What do you think will happen

if I were to move light
charges farther apart?

Do you think electric potential energy

would increase or decrease?

Again, pause and think about this.

All right, this time I know light charges

naturally tend to go further apart.

Ooh, which means if I have
to push them together closer,

now, you know, I'll end
up transferring energy

into the system.

And so this time,

pushing them closer increases
the potential energy,

and therefore, when they go farther apart,

the potential energy this time reduces.

And we can actually see
electric potential energy

in action in many places.

For example, during a thunderstorm,

we have massive electric potential energy

due to separated charges,

and as a result, we get lightning strikes.

But we can see them in
other places as well.

You probably know that
matter contains lots

and lots of charges,

which can attract or repel each other.

And some arrangements of these charges

can actually make materials deform.

For example, consider a spring.

You can easily compress a spring,

and while compressing,
look, you're pushing on it

and you're making it move.

You're transferring
energy into that spring.

And so when you let go,

that energy is released

and the spring relaxes back and exact.

This is exactly how, for example,
a pogo stick works, right?

You compress it, store energy into it,

and the energy gets released.

We call this elastic potential energy.

But guess where this
elastic potential energy

fundamentally comes from?

Well, it comes from the
distribution of charges,

arrangement of charges.

I mean, it's really complicated,

but here's how we can think about it.

If you zoom in, we can
model that there are,

let's say for example,

a couple of positive
charge particles over here,

there at some distance.

And you know, when you
have the relaxed length,

there is some potential energy.

Now, when you compress it,

look at what happens to these charges.

The charges come closer,

and so the electric potential energy

of the system increases.

That's what's really happening

when, you know, a spring is compressed,

and so when you let go of it,

that energy is released.

So elastic potential
energy is fundamentally

just electric potential energy.

Similarly, chemical potential energy

is also fundamentally
electric potential energy.

For example, we say that food
has chemical potential energy.

What we really mean

is that certain arrangement of charges

will have certain
electric potential energy.

And after eating it,
that arrangement changes.

As a result,

the electric potential
energy reduces, for example.

And in doing so, some energy is released

and the body can use
it to do useful things,

like, for example, move
from one place to another.

That's pretty amazing, isn't it?

So long story short,

potential energy is the energy associated

with the system of objects.

Remember, it's always
defined for a system,

meaning a group of two or more objects.

And what does it depend on?

Well, the potential energy purely depends

on their arrangement.