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Welcome back.

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When I left off, I was hurrying
a little bit.

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But we'd hopefully come to the
conclusion that if I have a

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simple lever, like I have here,
and I know the distances

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from where I'm applying
the force, to the

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fulcrum, to the pivot.

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And I know the distance from the
pivot to where the machine

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is essentially applying the
force, the machine being the

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lever in this situation, I know
the relationship between

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the two forces I'm applying.

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The input force-- so actually I
shouldn't call this a force

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too, I should call this an
input force-- anyway, the

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input force times the distance
from the input force to the

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fulcrum is equal to the output
force times the distance from

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the output force
to the fulcrum.

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And that all fell out of what
we did in the last video.

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The conservation of energy and
that the work in has to equal

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the work out.

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And all work is, is a transfer
of energy, so the transfer of

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energy in has to be the transfer
of energy out,

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assuming we have no friction
and none of the energy is

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lost.

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And how is this useful?

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Well we could do a bunch
of problems with this.

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Let's say that I have
a 100 newton object

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right here, 100 newtons.

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And let's say that I know, no
matter what I do, my maximum

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strength that I could push--
well let me draw this a little

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different-- let's say it's like
this, cause of my goal is

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to lift the 100 newton object.

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So the 100 newton object
is right here.

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That's a 100 newtons.

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And let's say I know that the
maximum downward force that

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I'm capable of applying is
only 10 newtons, right?

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So I want my force to
be multiplied by 10

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to lift this force.

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So let's figure out
what would happen.

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My input force is 10.

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And I want to figure
out the distance.

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So let's say my input
force is 10.

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And let's call this the
input distance.

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And I want the output force
to be 100, right?

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And let's call this the
output distance.

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So if I have a fulcrum here,
this is the input distance and

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this is the output distance.

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Let me switch colors.

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This is getting monotonous.

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This is the output distance,
from here to here.

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And let's figure out what the
ratio has to be, for the ratio

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of the input distance to
the output distance.

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Well, if we just divide both
sides by 10, we get the

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distance input.

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It has to be 10 times the
distance output, right?

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100 divided by 10.

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So if the distance from the
fulcrum to the weight is, I

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don't know, 5 meters, then the
distance from where I'm

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applying the force to
the fulcrum has

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to be 10 times that.

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It has to be 50 meters.

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So no matter what, the ratio of
this length to this length

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has to be 10.

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And now what would happen?

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If I design this machine this
way, I will be able to apply

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10 newtons here, which is my
maximum strength, 10 newtons

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downwards, and I will lift
a 100 newton object.

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And now what's the
trade off though?

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Nothing just pops
out of thin air.

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The trade off is, is that I am
going to have to push down for

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a much longer distance, for
actually 10 times the distance

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as this object is going
to move up.

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And once again I know that
because the work in has to

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equal the work out.

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I can't through some magical
machine-- and if you were able

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to invent one, you shouldn't
watch this video and you

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should go build it and become a
trillionaire-- but a machine

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can never generate work
out of thin air.

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Or it can never generate
energy out of thin air.

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That energy has to come
from some place.

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Most machines actually you lose
energy to friction or

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whatever else.

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But in this situation, if I'm
putting in 10 newtons of force

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times some distance, whatever
that quantity is of work, the

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work cannot change.

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The total work.

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It can go down if there is some
friction in the system.

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So let's do another problem.

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And really they're all kind
of the same formula.

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And then I'll move into a few
other types of simple systems.

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I should use the line tool.

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We'll make this up on the fly.

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And you could always create
problems where you can

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compound it further and et
cetera, et cetera, using some

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of the other concepts
we've learned.

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But I won't worry about
that right now.

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So let's say that I'm going
to push up here.

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Well no let me see what
I want to do.

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I want to push down here with
a force of-- let's say that

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this distance right here is 35
meters, this distance is 5

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meters-- and let's say I'm going
to push down with the

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force of 7 newtons, and what
I want to figure out is how

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heavy of an object
can I lift here.

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How heavy of an object.

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Well, all we have to do is
use the same formula.

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But the moments-- and I know I
used that word once before, so

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you might not know what it is--
but the moments on both

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sides of the fulcrum have
to be the same.

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Or the input moment has to
be the output moment.

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So what's the moment again?

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Well, the moment is just the
force times the distance from

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the force to the fulcrum.

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So the input moment is 7 newtons
times 35 meters.

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And realize that that does not
work, because the distance

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this force is traveling
is not 35 meters.

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The distance this force
is traveling is

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something like, here.

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But this 35 meters is going
to be proportional to the

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distance that this is traveling
when you compare it

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to this other side.

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So this quantity, 7
newtons times 35

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meters, is the moment.

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And that is going to be equal
to the moment on this side,

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the output moment.

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So that is equal to 5 meters
times the force that I'm

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lifting, or the lifting force
of the machine, times let's

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say the force out.

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So we can figure out the force
out by just dividing both

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sides by 5.

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So let's see, 35 divided by 5
is 7, so you get 7 times 7

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equals the force out,
or 49 newtons.

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And you can see that, because
you can see that the length of

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this side of the lever is 7
times the length of this side

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of the lever.

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So when you input a force of
7, you output a force of 7

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times that.

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And of course, in order to move
the block 1 meter up in

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this direction, you're
going to have to

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push down for 7 meters.

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And that's where we know that
the input work is equal to the

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output work.

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Well anyway hopefully I didn't
confuse you and you have a

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reasonable sense of
how levers work.

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In the next couple of videos,
I'll introduce you to other

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machines, simple machines like
a wedge-- I've always had

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trouble calling a wedge
a machine, but it

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is one-- and pulleys.

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I'll see you in the next video.

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