WEBVTT
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Let's consider our
one-dimensional collision
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again, object 1 moving
with velocity V1 initial,
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and object 2 moving
with V2 initial.
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Let's call this or
i hat direction.
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And this is our initial state.
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And our final state after the
collision, we have object 1.
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We'll say it's moving this,
V1 final, and object 2 moving
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that way, V2 final.
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Now recall our principle
of impulse and momentum.
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We said that if there
is an external force
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during the time of a collision
delta t, then physically that
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will cause the momentum
of the system final
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minus the momentum of
the system initial.
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Now when we do this analysis,
this side was a description
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and this side is physics.
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Now for our
one-dimensional collision,
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we need to look
at this collision
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and ask ourselves are
there any external forces
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acting on the system, which
is consisting of particle 1
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and particle 2?
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So what we're going
to identify here
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is that the surface
is frictionless.
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And we'll ignore
all air resistance.
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And so by our assumptions that
there are no f external is 0.
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And therefore, the momentum of
the system remains constant.
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So here our statement is-- many
people call this conservation
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of momentum, but we're
saying in this example based
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on our assumptions that
the momentum of the system
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is constant.
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Now how do we actually
write that down?
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Well, let's now write it
first as vector expressions.
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So we have the initial momentum,
V1 of the system, m1 m2 V2
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initial is equal to the
final momentum of the system,
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V1 final plus m2 V2 final.
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Now, how do we represent
these equations?
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Well, you could treat them
as vectors if you wanted.
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But what we're going to do is
express them as components.
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So if we wrote
this as components,
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we would have m1 Vx initial i
hat plus m2 V2 x initial i hat
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equals m1 V1 s final i hat
plus m2 V2 x final i hat.
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So that's the vector
expression expressed
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in terms of components.
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The advantage of this
is that we really
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don't know the signs of
these two final components.
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That's our target quantities.
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But we could just
write this equation--
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instead of writing it
as a vector equation,
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let's just now write this
as a component equation.
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And when we write this equation
in terms of components,
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we have m1 V1 x initial plus
m2 V2 x initial equals m1 V1 x
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final plus m2 V2 x final.
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And this equation
here is the equation
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that we use to
express the constancy
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of the momentum of the system.
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We'll call this equation 1.
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Now our next approach
is to ask are there
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any other quantities in the
system which are constant?