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In order to transfer
energy to an object,

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you've got to exert a
force on that object.

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The amount of energy
transferred by a force

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is called the work
done by that force.

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The formula to
find the work done

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by a particular
force on an object

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is W equals F d cosine theta.

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W refers to the work done by
the force F. In other words,

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W is telling you
the amount of energy

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that the force F is
giving to the object.

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F refers to the size of
the particular force doing

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the work.

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d is the displacement of
the object, how far it moved

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while the force
was exerted on it.

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And the theta and
cosine theta refers

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to the angle between
the force doing

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the work and the
displacement of the object.

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You might be wondering what this
cosine theta is doing in here.

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This cosine theta
is in this formula

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because the only part of
the force that does work

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is the component that
lies along the direction

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of the displacement.

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The component of the force
that lies perpendicular

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to the direction of motion
doesn't actually do any work.

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We notice a few things
about this formula.

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The units for work are
Newton's times meters,

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which we called joules.

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Joules are the same unit
that we measure energy in,

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which makes sense because
work is telling you

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the amount of joules
given to or taken away

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from an object or a system.

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If the value of the
work done comes out

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to be positive for
a particular force,

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it means that that
force is trying

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to give the object energy.

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The work done by a
force will be positive

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if that force or a
component of that force

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points in the same direction
as the displacement.

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And if the value of the work
done comes out to be negative,

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it means that that force is
trying to take away energy

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from the object.

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The work done by a
force will be negative

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if that force or a
component of that force

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points in the opposite
direction as the displacement.

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If a force points in
a direction that's

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perpendicular to
the displacement,

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the work done by
that force is 0,

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which means it's neither
giving nor taking away energy

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from that object.

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Another way that the work
done by a force could be 0

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is if the object doesn't
move, since the displacement

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would be 0.

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So the force you exert by
holding a very heavy weight

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above your head does not
do any work on the weight

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since the weight is not moving.

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So this formula
represents the definition

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of the work done by
a particular force.

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But what if we wanted to
know the net work or total

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work done on an object?

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We could just find
the individual amounts

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of work done by each particular
force and add them up.

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But there's actually a
trick to figuring out

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the net work done on an object.

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To keep things simple, let's
assume that all the forces

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already lie along the
direction of the displacement.

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That way we can get rid
of the cosine theta term.

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Since we're talking about the
net work done on an object,

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I'm going to replace F with
the net force on that object.

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Now, we know that the
net force is always

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equal to the mass
times the acceleration.

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So we replace F
net with m times a.

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So we find that the net
work is equal to the mass

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times the acceleration
times the displacement.

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I want to write this equation
in terms of the velocities

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and not the acceleration
times the displacement.

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So I'm going to ask you
recall a 1-D kinematics

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equation that looked like this.

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The final velocity squared
equals the initial velocity

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squared plus 2 times
the acceleration

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times the displacement.

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In order to use this
kinematic formula,

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we've got to assume that the
acceleration is constant,

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which means we're assuming that
the net force on this object

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is constant.

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Even though it seems like we're
making a lot of assumptions

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here, getting rid
of the cosine theta

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and assuming the
forces are constant,

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none of those
assumptions are actually

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required to derive the
result we're going to attain.

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They just make this
derivation a lot simpler.

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So looking at this
kinematic formula,

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we see that it also
has acceleration times

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displacement.

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So I'm just going to
isolate the acceleration

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times the displacement on
one side of the equation

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and I get that a times
d equals v final squared

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minus v initial
squared divided by 2.

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Since this is what
a times d equals,

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I can replace the a times
d in my net work formula.

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And I find that the net
work is equal to the mass

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times the quantity v
final squared minus v

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initial squared divided by 2.

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If I multiply the terms
in this expression,

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I get that the net work
is equal to 1/2 mass times

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the final velocity
squared minus 1/2

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mass times the initial
velocity squared.

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In other words, the
net work or total work

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is equal to the
difference between

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the final and initial
values of 1/2 mv squared.

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This quantity 1/2
m times v squared

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is what we call the kinetic
energy of the object.

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So you'll often hear that the
net work done on an object

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is equal to the change in the
kinetic energy of that object.

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And this expression is
often called the work energy

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principle, since it relates
the net work done on an object

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to the kinetic energy gained
or lost by that object.

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If the net work
done is positive,

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the kinetic energy
is going to increase

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and the object's
going to speed up.

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If the net work done on
an object is negative,

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the kinetic energy
of that object

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is going to decrease, which
means it's going to slow down.

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And if the net work
done on an object is 0,

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it means the kinetic
energy of that object

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is going to stay the same,
which means the object maintains

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a constant speed.

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