Introduction to work and energy

Welcome back.

I'm now going to introduce
you to the

concepts of work and energy.

And these are two words that
are-- I'm sure you use in your

everyday life already and
you have some notion

of what they mean.

But maybe just not in the
physics context, although

they're not completely
unrelated.

So work, you know
what work is.

Work is when you do something.

You go to work, you
make a living.

In physics, work is-- and I'm
going to use a lot of words

and they actually end up being
kind of circular in their

definitions.

But I think when we start doing
the math, you'll start

to get at least a slightly more
intuitive notion of what

they all are.

So work is energy transferred
by a force.

So I'll write that down, energy
transferred-- and I got

this from Wikipedia because
I wanted a good, I guess,

relatively intuitive
definition.

Energy transferred by a force.

And that makes reasonable
sense to me.

But then you're wondering, well,
I know what a force is,

you know, force is mass
times acceleration.

But what is energy?

And then I looked up energy on
Wikipedia and I found this,

well, entertaining.

But it also I think tells you
something that these are just

concepts that we use to, I
guess, work with what we

perceive as motion and force
and work and all of these

types of things.

But they really aren't
independent notions.

They're related.

So Wikipedia defines energy
as the ability to do work.

So they kind of use each other
to define each other.

Ability to do work.

Which is frankly, as good of a
definition as I could find.

And so, with just the words,
these kind of don't give you

much information.

So what I'm going to do is move
onto the equations, and

this'll give you a more
quantitative feel of what

these words mean.

So the definition of work in
mechanics, work is equal to

force times distance.

So let's say that I have a block
and-- let me do it in a

different color just
because this yellow

might be getting tedious.

And I apply a force of--
let's say I apply

a force of 10 Newtons.

And I move that block
by applying

a force of 10 Newtons.

I move that block, let's
say I move it-- I

don't know-- 7 meters.

So the work that I applied to
that block, or the energy that

I've transferred to that block,
the work is equal to

the force, which is 10 Newtons,
times the distance,

times 7 meters.

And that would equal 70-- 10
times 7-- Newton meters.

So Newton meters is one, I
guess, way of describing work.

And this is also defined
as one joule.

And I'll do another presentation
on all of the

things that soon.

Joule did.

But joule is the unit
of work and it's

also the unit of energy.

And they're kind of
transferrable.

Because if you look at the
definitions that Wikipedia

gave us, work is energy
transferred by a force and

energy is the ability to work.

So I'll leave this relatively
circular definition alone now.

But we'll use this definition,
which I think helps us a

little bit more to understand
the types of work we can do.

And then, what kind of energy
we actually are transferring

to an object when we do
that type of work.

So let me do some examples.

Let's say I have a block.

I have a block of mass m.

I have a block of mass m and it
starts at rest. And then I

apply force.

Let's say I apply a force, F,
for a distance of, I think,

you can guess what the distance
I'm going to apply it

is, for a distance of d.

So I'm pushing on this block
with a force of F for a

distance of d.

And what I want to figure
out is-- well, we know

what the work is.

I mean, by definition, work is
equal to this force times this

distance that I'm applying
the block-- that

I'm pushing the block.

But what is the velocity going
to be of this block over here?

Right?

It's going to be something
somewhat faster.

Because force isn't-- and I'm
assuming that this is

frictionless on here.

So force isn't just moving
the block with a constant

velocity, force is equal to
mass times acceleration.

So I'm actually going to be
accelerating the block.

So even though it's stationary
here, by the time we get to

this point over here,
that block is going

to have some velocity.

We don't know what it is
because we're using all

variables, we're not
using numbers.

But let's figure out what
it is in terms of v.

So if you remember your
kinematics equations, and if

you don't, you might
want to go back.

Or if you've never seen the
videos, there's a whole set of

videos on projectile motion
and kinematics.

But we figured out that when
we're accelerating an object

over a distance, that the final
velocity-- let me change

colors just for variety-- the
final velocity squared is

equal to the initial velocity
squared plus 2 times the

acceleration times
the distance.

And we proved this back then,
so I won't redo it now.

But in this situation, what's
the initial velocity?

Well the initial
velocity was 0.

Right?

So the equation becomes vf
squared is equal to 2 times

the acceleration times
the distance.

And then, we could rewrite
the acceleration

in terms of, what?

The force and the mass, right?

So what is the acceleration?

Well F equals ma.

Or, acceleration is equal to
force divided by you mass.

So we get vf squared is equal
to 2 times the force divided

by the mass times
the distance.

And then we could take the
square root of both sides if

we want, and we get the final
velocity of this block, at

this point, is going to be equal
to the square root of 2

times force times distance
divided by mass.

And so that's how we could
figure it out.

And there's something
interesting going on here.

There's something interesting
in what we did just now.

Do you see something that looks
a little bit like work?

Well sure.

You have this force
times distance

expression right here.

Force times distance
right here.

So let's write another
equation.

If we know the given amount of
velocity something has, if we

can figure out how much work
needed to be put into the

system to get to
that velocity.

Well we can just replace force
times distance with work.

Right?

Because work is equal to
force times distance.

So let's go straight from this
equation because we don't have

to re-square it.

So we get vf squared
is equal to 2

times force times distance.

That's work.

Took that definition
right here.

2 times work divided
by the mass.

Let's multiply both sides of
this equation times the mass.

So you get mass times
the velocity.

And we don't have to write-- I'm
going to get rid of this f

because we know that we started
at rest and that the

velocity is going to be--
let's just call it v.

So m times V squared is equal
to 2 times the work.

Divide both sides by 2.

Or that the work is equal
to mv squared over 2.

Just divided both sides by 2.

And of course, the unit
here is joules.

So this is interesting.

Now if I know the velocity of
an object, I can figure out,

using this formula, which
hopefully wasn't too

complicated to derive.

I can figure out how much work
was imputed into that object

to get it to that velocity.

And this, by definition, is
called kinetic energy.

This is kinetic energy.

And once again, the definition
that Wikipedia gives us is the

energy due to motion, or the
work needed to accelerate from

an object from being stationary

to its current velocity.

And I'm actually almost out of
time, but what I will do is I

will leave you with this
formula, that kinetic energy

is mass times velocity
squared divided by

2, or 1/2 mv squared.

It's a very common formula.

And I'll leave you with
that and that

is one form of energy.

And I'll leave you
with that idea.

And in the next video,
I will show you

another form of energy.

And then, I will introduce
you to the law of

conservation of energy.

And that's where things become
useful, because you can see

how one form of energy can be
converted to another to figure

out what happens to an object.

I'll see