WEBVTT

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We previously
discussed the concept

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of conservation of momentum.

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We will soon see that there
is another very powerful

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conservation principle
in physics called

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the conservation of energy.

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It states that there is a
certain quantity called energy

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that remains unchanged
in the system

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except for any that flows
in or out of the system.

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It's hard to say
exactly what energy is.

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It's an abstract quantity that
we count up in a certain way.

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When calculating the
energy of a system,

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we must keep careful
track of any energy that

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enters or leaves the system.

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There are also a number
of different forms

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of energy-- kinetic energy,
gravitational energy,

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elastic energy, electrical
energy, heat energy,

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and others.

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Each of these has its own
formula for calculation.

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If you sum all these
energies up for a system,

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the total will remain
unchanged except for what

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goes in and comes out.

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It turns out that using
energy rather than force,

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one can construct a
complete system of mechanics

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that is fully equivalent
to the Newtonian system.

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This was done by
Lagrange and Hamilton.

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And you may encounter
their system in the future,

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if you take more advanced
courses in physics.

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However, even in the
Newtonian system,

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energy remains a useful concept.

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This week, we will
discuss kinetic energy,

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the energy associated
with the motion of a mass,

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and also the concept
of work, which

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allows us to calculate
how the action of a force

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changes the kinetic energy.

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We will see that the
work done by a force

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is calculated by
evaluating an integral that

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in general depends upon the
specific trajectory or path

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taken by the object or system.

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However, we will also
see that there [? is ?]

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a special class of forces called
conservative forces for which

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the work integral
is path independent

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and instead depends only on
the starting and ending points.

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Finally, we will
discuss examples

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of both conservative and
non-conservative forces.