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Suppose we have an
object and we're

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applying a constant force
in the horizontal direction.

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We would now like to
introduce the concept of work.

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Suppose our force
starts at a point xi,

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and goes to a position
x final, and we'll

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call this the i hat direction.

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Then our force as a vector,
we'll write Fx i hat.

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And now what we'd
like to calculate

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is the product of force with
the displacement of the object.

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So our displacement
vector, delta x,

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is equal to delta x i hat,
where delta x is equal to x

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final minus x initial.

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And for our constant
force for the case

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where Fx is a
constant, we would like

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to define the work
done by this force

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in displacing the object
from our initial position,

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and we'll mark it like that.

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To the final position here
is given by the product,

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so we'll call work is
the product of the force

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Fx times the displacement.

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And so that's equal to Fx
times x final minus x initial.

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And this is our definition for
work for the special case where

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the force is constant.

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Now, if we look at this, our
force may-- in our diagram,

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we drew it in the
positive x direction.

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But if our force Fx
were less than 0,

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and our displacement was
in the positive direction,

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positive, then you can see
that the work is negative.

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So if the force is
opposing the displacement,

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and that's what
would happen if Fx

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was pointing in the
negative direction,

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the work would be negative.

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If Fx is positive and the
displacement is positive,

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then the work is positive.

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So we see work is a
scalar that has assigned

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quantity, positive or negative.

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Now, whenever we
introduce a new quantity,

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we always have to be a little
bit careful about the units.

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Since work is the product
of force and distance,

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then our SI units for
work are the units

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of force, which are newtons,
times the units of distance,

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meters.

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And we call this a joule.

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So one joule is equal
to one newton meter.

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Now graphically, we can make
an interpretation of this.

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Let's draw a graph of force,
the x component of the force.

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And here if we had some
origin, we'll have x.

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And our object is starting at
xi and it's going to x final.

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And throughout
this process, we're

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assuming that the
force is constant.

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So what we see in
this diagram here,

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I'll just shade in this
area, that our work, which

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was the product of force
times the displacement,

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corresponds to the area here.

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So we have a geometric
interpretation of work

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as the area under the force
versus position graph.

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And this is our example of
work for a constant force.