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I'm going to show you
some examples of how

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to solve problems
involving work.

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Imagine a 4 kilogram trashcan.

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The trashcan is disgusting.

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So someone ties a
string to it and pulls

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on the string with a
force of 50 newtons.

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The force of kinetic friction
on the trashcan while it slides

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is 30 newtons.

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The trash can slides
across the ground

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for a distance of 10 meters.

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Let's try to find the work done
by each force on the trash can

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as it slides across the ground.

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To find the work
done by each force,

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we should recall the
formula definition of work.

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Work equals Fd
cosine theta, where

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theta is the angle
between the force doing

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the work and the direction
the trashcan is moving.

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There are four forces
involved here-- tension,

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the normal force, the
gravitational force,

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and the force of
kinetic friction.

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In finding the work done
for all of these forces,

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the displacement is
going to be 10 meters.

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But the value of the
force and the angle

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between that force
and the displacement

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is going to differ for
each of the forces.

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For instance, to find the work
done by the force of tension,

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we'll plug in the size of the
tension, which is 50 newtons.

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The displacement is 10 meters.

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And since the tension
force is pointed

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in the same direction
as the displacement,

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the angle between the force of
tension and the displacement

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is 0 degrees.

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And since cosine of 0 is 1, the
work done by the tension force

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is 500 joules.

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To find the work
done by friction,

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we'll plug in the size
of the force of friction,

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which is 30 newtons.

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The displacement
is still 10 meters.

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And since the force
of friction points

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in the opposite direction
as the displacement,

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the angle between the force of
friction and the displacement

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is 180 degrees.

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Since cosine of
180 is negative 1,

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the work done by the
force of friction

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is negative 300 joules.

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Now let's figure
out the work done

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by the gravitational force.

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The force of gravity is mg.

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So the force of
gravity is 4 kilograms

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times 9.8 meters per second
squared, which is 39.2 newtons.

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The displacement
is again 10 meters.

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But the angle between
the gravitational force

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and the direction
of the displacement

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is 90 degrees in this case.

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And since cosine of 90 is
0, the gravitational force

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does no work on this trashcan.

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Similarly, if we were
to find the work done

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by the normal force, the
angle between the direction

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of the displacement and the
normal force is 90 degrees.

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So the normal force also
does no work on the trashcan.

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This makes sense
because forces that

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are perpendicular to
the motion can never

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do any work on that object.

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So that's how you can find the
work done by individual forces.

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And if we wanted to know the
net work done on this trashcan,

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we could just add up the work
done by each individual force.

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So the net work is
going to be 200 joules.

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Now that we know the net
work done on the trashcan,

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we can use the
work-energy principle

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to figure out the
speed of the trashcan

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after it's slid the 10 meters.

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The work-energy principle
says that the net work done

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on an object is
equal to the change

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in kinetic energy
of that object.

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So 200 joules is going
to equal the difference

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in kinetic energy.

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If we assume the
trashcan started

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at rest, which seems reasonable,
the initial velocity is 0.

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So we can solve for the final
speed of the trashcan, which

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comes out to be 10
meters per second.

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This time, let's say
you take the trashcan

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and lift it upwards
with a constant velocity

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for a distance of 2 meters.

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In order to lift the trashcan
up with a constant velocity,

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you need to push with a
force equal to the weight

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of the trashcan, which means
you have to push upwards

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with a force of 39.2 newtons.

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So to find the work done by
the force that you exert,

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the force is going
to be 39.2 newtons.

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The displacement is
going to be 2 meters.

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And the angle between the
force and the displacement

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is going to be 0 degrees because
the direction of the force

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that you exert is in the same
direction as the displacement

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of the trashcan.

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So the work that you've done
in lifting up this 4 kilogram

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trashcan is 78.4 joules.

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To find the work done
by the force of gravity,

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we can use the force of gravity,
which is again 39.2 newtons.

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The displacement
is again 2 meters.

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But the angle
between the direction

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of the displacement and
the gravitational force

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is 180 degrees because
the displacement points up

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and the gravitational
force points down.

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So the work done by
the gravitational force

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is negative 78.4
joules, which means

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the net work done on
the trashcan is 0.

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And that makes sense.

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Because since the trashcan moved
upwards with constant velocity,

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there was no change in the
kinetic energy of this object.

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