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What's a conservative force?

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Conservative forces
are any force

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wherein the work done by
that force on an object

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only depends on the initial and
final positions of the object.

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In other words, the work done by
a conservative force on a mass

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does not depend on the
path taken by that mass.

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If the work done by a
force follows this rule,

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then we call it a
conservative force.

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For instance, the gravitational
force on a 5 kilogram mass

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is 49 newtons.

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If the mass moves downwards
by an amount of 6 meters,

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the work done by gravity
is going to be 294 joules.

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Now let's start over.

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Say the mass again
moves down 6 meters.

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But then it moves up 6 meters,
then down again 6 meters.

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The work done by gravity
for the first downwards trip

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was 294 joules.

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Then for the upwards trip,
since the gravitational force

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is pointing in the opposite
direction of the motion

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of the mass, the
work done by gravity

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is going to be
negative 294 joules.

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Then for the last
trip downwards,

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the work again is
positive 294 joules.

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That means that the total work
done on the mass from gravity

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is still 294
joules, just like it

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was when the mass was
lowered only once.

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In other words, the work done
by the gravitational force

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doesn't depend on the specifics
of the path taken by the mass.

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The work done by
gravity only depends

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on the initial and final
position of the mass.

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In fact, you could
allow the mass

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to take any path from
this initial point

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to the final point, and
the work done by gravity

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is still just going
to be 294 joules.

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Because the work done
by gravity doesn't

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depend on the path
taken, we call

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gravity a conservative force.

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The force exerted by a
spring is another example

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of a conservative force.

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The total work done
on a mass by a spring

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does not depend on the
path taken by the mass.

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It only depends on the
initial and final positions

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of the mass.

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The term conservative
comes from the fact

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that conservative forces
conserve mechanical energy,

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whereas non-conservative
forces do not

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conserve mechanical energy.

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Mechanical energy is kinetic
energy and potential energy.

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An example of a non-conservative
force is friction.

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If I move a mass along a
table from point A to point B,

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friction does a certain
amount of negative work

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on the mass, which creates
some thermal energy.

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If instead of going
straight from A to B,

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I make the block go from A to B
back to A over and over again,

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the work done by friction
will become larger and larger.

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And it'll generate more
and more thermal energy.

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Because the work
done by friction

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depends on the path
taken, friction

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is not a conservative force.

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Similarly, air resistance
is not a conservative force

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since the work done
by air resistance

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depends on the specifics
of the path taken.

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It's useful to note that
if a force is conservative,

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you could define a potential
energy for that force.

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That's why conservative forces
like gravity and spring forces

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have potential energies
associated with them.

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And non-conservative
forces like friction

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do not have potential
energy associated with them.

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This makes sense
because if you do

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work against the
gravitational force

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by lifting a mass
in the air, you

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can get that energy back out
by letting the mass fall down,

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turning potential energy
into kinetic energy.

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Similarly, if you do work
against the spring force

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by compressing a spring,
you can get that energy back

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out by letting the
spring decompress, which

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turns the stored potential
energy into kinetic energy.

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But if you do work against
the force of friction,

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you'll have a hard time trying
to get that energy back out.

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The energy's been dissipated
into the form of thermal energy

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and is now randomly
distributed along the ground

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and into the block.

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