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Conservative forces

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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.
Title:
Conservative forces
Description:

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Video Language:
English
Duration:
04:02
dhbot edited English subtitles for Conservative forces
רועי חרמוני edited English subtitles for Conservative forces

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