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- [Instructor] Say there's a basketball

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heading straight toward a scoop

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of peanut butter chocolate chip ice cream.

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So these are gonna collide.

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There's different ways
you could characterize

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this collision, but one
thing that physicists

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are almost always interested
in is whether this collision

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is going to be elastic or inelastic.

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What does it mean to say
a collision is elastic?

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Elastic collision is one

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where the kinetic energy is conserved.

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And I don't just mean the kinetic energy

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of one of the objects,

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I mean the total kinetic
energy of all the objects.

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So this is where the total kinetic energy

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of all colliding objects is conserved.

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And don't forget, people get confused

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about this word conserved.

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That's really just a fancy way of saying

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the total amount of
kinetic energy is constant,

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i.e. it remains the same value
before and after a collision.

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And we could put this into
a mathematical statement.

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If we're clever we could say alright,

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total kinetic energy conserved,

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so if we just write down the basketball

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has some kinetic energy
before the collision,

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I'm just gonna use the
letter k for kinetic energy,

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so I'm gonna have kinetic
energy of the basketball.

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That's gonna be before the collision

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so we need another subscript.

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This is gonna get a little messy.

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I'm gonna have two subscripts:

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one to denote which
object I'm talking about,

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the b will be for basketball,

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and the second letter is gonna represent

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when I'm talking about it, i.e. this i

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is gonna represent initial,
like before the collision.

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So this is the initial kinetic
energy of the basketball,

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and if we add to that,

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'cause we want the total kinetic energy,

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if we add to that the kinetic energy

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that the scoop of ice cream had,

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I'll use s for scoop of
ice cream and initially,

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this would represent
the total kinetic energy

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before the collision.

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And we could do the same
thing for after the collision,

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we could say that the
basketball's probably

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gonna be moving after the collision,

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so the basketball will have
some final kinetic energy,

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and if we add to that the kinetic energy

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that the scoop of ice cream
had after the collision,

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i.e. finally, this here would
be the total kinetic energy

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after the collision.

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If the collision is elastic,

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that means the total
kinetic energy is conserved,

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that means that this total
initial kinetic energy

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has to equal this total
final kinetic energy.

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I could just say that these two are equal

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if it's an elastic collision.

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And this is what we mean by
a collision being elastic.

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It means that the total
kinetic energy is conserved.

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For an inelastic collision,

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the total kinetic energy is not conserved,

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in other words, this
expression doesn't hold.

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So if I put that over
here, if it's inelastic,

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what you can say is that the
total initial kinetic energy

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does not equal the total
final kinetic energy.

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And for most inelastic collisions

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the initial total kinetic energy

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is greater than the final
total kinetic energy.

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In other words, in an inelastic collision

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you'll lose some kinetic energy,
some of this kinetic energy

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gets transformed into
some other kind of energy

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and that energy is
typically thermal energy.

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'Cause think about it.

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If this ice cream scoop splatters
right into the basketball

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and the atoms and molecules

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that make up the ice cream scoop,

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so this ice cream scoop is made
out of atoms and molecules,

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delicious atoms and molecules,

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and they're not masses
connected with springs,

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but roughly speaking you can think

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of the solid as masses,
little tiny molecules or atoms

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connected by springs.

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It's really electromagnetic forces here

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and chemical bonds going on,

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but that's complicated to
just get a nice visual picture

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of what's happening.

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Imagine this collision happens.

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That's gonna cause this atom or molecule

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to start oscillating more than it was.

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This one's gonna start
oscillating more than it was.

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And since these atoms and molecules

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now have more kinetic energy on their own,

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this random thermal energy,
the total kinetic energy

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that this whole ice cream
scoop's gonna have going forward

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is gonna be less, because
some of that's gonna be

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distributed randomly amongst
the atoms and molecules

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in the ice cream scoop.

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Now, if it's a really
melted ice cream scoop,

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if the ice cream scoop's not very cold,

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these springs are not gonna be very stiff,

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these atoms and molecules
can just slide around

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however they want, there
might be a lot of energy,

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a lot of kinetic energy

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that gets turned into thermal energy.

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But if you freeze this ice cream scoop,

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if you take these things
straight out of the deep freezer,

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then these bonds are
gonna be a lot stiffer

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and these atoms and molecules are gonna be

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much more stuck in place
than they were previously.

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So once this structure becomes more rigid

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it's harder to transfer
that kinetic energy

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into these individual atoms and molecules

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and it'll become more and more elastic.

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You'll waste less and less kinetic energy

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to this thermal energy here.

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And if you take this idea to the extreme,

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if you instead try to take a steel ball

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where these bonds between atoms

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are extremely stiff and
rigid, you start to approach

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a collision that might
be considered elastic

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because your final kinetic
energy might be almost the same

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as your initial kinetic energy.

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Now, if I were you, I might
be like "hold on a minute."

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Total kinetic energy is not conserved,

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but we just said that kinetic
energy in the collision

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goes into kinetic energy
of these molecules.

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That's still kinetic energy, right?

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Thermal energy is still
mostly kinetic energy.

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And yeah, it's true.

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Thermal energy is mostly kinetic energy.

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I mean there could be a
little potential energy

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and different kinds of
energy in there as well,

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when you're dealing with thermal energies.

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But it is mostly kinetic energy.

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So we should make a distinction.

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When we say total kinetic
energy is conserved,

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we mean the total kinetic energy
of that macroscopic object

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moving in a certain direction.

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So the speeds, in other words,
that we're talking about

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and these kinetic energies

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are the speeds of the
macroscopic objects, right,

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of the ice cream scoop itself,

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not of the individual atoms and molecules.

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In other words, we're not gonna include

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the random jiggling kinetic energy

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that these atoms and molecules have

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in this calculation over here.

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Otherwise basically every
collision would be elastic

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'cause yeah, that
macroscopic kinetic energy

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turns into microscopic kinetic energy.

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But up here we're talking
about the macroscopic

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kinetic energy of that entire object

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moving in a certain direction.

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So to make this clear
let's show an example

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with some numbers here.

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Let's just say this basketball
and this scoop of ice cream

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had a certain speed before the collision.

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So let's say this basketball was going

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10 meters per second before the collision

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and the ice cream scoop
was going, let's say,

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eight meters per second.

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And let's say after they collide

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this basketball's still
moving to the right

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but it's only moving at
about one meter per second,

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let's say, and the scoop of ice cream,

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let's say, gets to backward

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and it's now going five meters
per second to the right.

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And I looked up the mass of a basketball,

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the mass of a basketball
is about 0.65 kilograms.

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And now with that mass of the basketball

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I have to pick the right mass over here

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for my mass of the ice cream

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'cause I picked these velocities
just kind of randomly.

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So, in order to conserve
momentum for this collision,

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and almost all collisions
should be conserving momentum,

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the mass of the scoop of ice cream

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should be about 0.45 kilograms.

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Now with these numbers in here we can ask:

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was this collision elastic or inelastic?

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And one mistake people make is they say,

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oh well, they bounced
off of each other, right?

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Because this basketball
is going to the right

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at only one meter per second

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and the scoop of ice cream
is going to the right

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at five meters per second.

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They must have bounced off of
each other, they separated,

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doesn't that mean elastic?

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And no, that doesn't mean elastic.

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Just because they bounce off of each other

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does not imply that it's elastic.

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It works the other way.

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If it's elastic they do have
to bounce off of each other,

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but just because it bounces
does not mean it's elastic.

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So be careful there.

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Just 'cause they bounce here
does not mean it's elastic.

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What do we do to check
whether it's elastic?

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What we do is we check whether
the total kinetic energy

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was conserved or not.

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So let's just check.

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We've got enough numbers
here to figure that out.

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So I can use the formula
for kinetic energy,

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which is one half m v squared.

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And I can find what is
the initial kinetic energy

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of the basketball, it'd be one
half mass of the basketball

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times the initial speed of
the basketball, which was 10.

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So I'm using initial speeds here

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'cause I want to find the
initial kinetic energy.

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And I'm gonna have to add to that,

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because I want the total kinetic energy

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I have to add to that the
initial kinetic energy

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of the scoop of ice cream.

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So it's gonna be plus another one half

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times the mass of the scoop of ice cream

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times its initial speed, which
was eight meters per second.

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You might say, isn't it negative v?

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We're gonna square this
anyway so it doesn't matter,

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so don't forget the square.

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And if we add all those
up, we get 46.9 Jules

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of total initial kinetic energy.

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So is this equal to the final now?

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Let's just find out the final
amount of kinetic energy.

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If I take the final
speed of the basketball

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and use that to find
the final kinetic energy

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of the basketball, I'd have
one half mass of the basketball

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times the final speed, is
only one meter per second,

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and I still square it, and
then I have to add to that

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the final kinetic energy
of the scoop of ice cream,

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which is gonna be one half the mass

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of the scoop of ice
cream times five squared

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'cause five was the final speed
of the scoop of ice cream.

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And if I add all that up,
I get that this equals

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5.95 Jules of total final kinetic energy.

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So is this collision elastic?

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No way, it's not even close.

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This initial total kinetic
energy was 46.9 Jules,

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this final total kinetic
energy was 5.95 Jules,

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the kinetic energy here was not conserved

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and because it was not conserved

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we would consider this
an inelastic collision.

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But if you're clever, you can
just look at the numbers here.

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You didn't actually have to
go through all this work.

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You could just say, hey,
the basketball started

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with 10 meters per second,

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it ends with one meter per second.

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It's definitely got less kinetic
energy than it did before.

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And this ice cream scoop started

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with eight meters per second

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and it ends with five meters per second,

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it also ends with less kinetic
energy than it did before.

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So this final kinetic
energy has to be smaller

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than the total initial kinetic energy.

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And you can ask: where did that energy go?

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00:10:22,679 --> 00:10:26,684
It goes into the thermal energy
of these molecules and atoms

256
00:10:26,684 --> 00:10:29,601
in the objects vibrating
thermally a little more

257
00:10:29,601 --> 00:10:32,465
than they did before,
including in the basketball.

258
00:10:32,465 --> 00:10:34,883
As well as sound waves
that can get created

259
00:10:34,883 --> 00:10:36,481
that also takes away energy,

260
00:10:36,481 --> 00:10:38,824
there's lots of places for energy leaks,

261
00:10:38,824 --> 00:10:41,222
and in this particular collision
there were a lot of leaks

262
00:10:41,222 --> 00:10:43,376
because we lost a good majority

263
00:10:43,376 --> 00:10:45,438
of the kinetic energy
that we started with,

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00:10:45,438 --> 00:10:48,117
which made this an inelastic collision.

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00:10:48,117 --> 00:10:50,352
So recapping, for a
collision to be elastic

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00:10:50,352 --> 00:10:52,255
it's not enough to just know it bounces.

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00:10:52,255 --> 00:10:54,641
You have to see if the
total initial kinetic energy

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00:10:54,641 --> 00:10:57,540
is the same as the total
final kinetic energy.

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If that's the case, it's
an elastic collision,

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00:10:59,718 --> 00:11:02,908
and if that's not the case,
it's an inelastic collision.

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One last note.

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Sometimes you'll hear the word
perfectly elastic collision.

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Well that's redundant.

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00:11:07,990 --> 00:11:10,659
That's just another way to
say an elastic collision.

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In other words, a collision
where the initial kinetic energy

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00:11:13,820 --> 00:11:16,400
really is equal to the
final kinetic energy.

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00:11:16,400 --> 00:11:18,196
But you'll also sometimes hear

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00:11:18,196 --> 00:11:21,317
about a perfectly inelastic collision.

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00:11:21,317 --> 00:11:22,731
And this is meaningful.

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00:11:22,731 --> 00:11:25,921
This means that the two objects
that collide stick together

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00:11:25,921 --> 00:11:28,753
so if it's perfectly inelastic, this means

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00:11:28,753 --> 00:11:32,888
that they must stick together
and move off as a single unit.

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00:11:32,888 --> 00:11:34,474
In other words, if the scoop of ice cream

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00:11:34,474 --> 00:11:37,958
splattered into the basketball
and then stuck to it,

285
00:11:37,958 --> 00:11:41,124
and the two moved off to
the right at some speed,

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00:11:41,124 --> 00:11:44,382
that would be a perfectly
inelastic collision.

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00:11:44,382 --> 00:11:47,656
Now, whether it's elastic or inelastic,

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00:11:47,656 --> 00:11:50,509
momentum is still gonna be
conserved for these collisions.

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00:11:50,509 --> 00:11:53,471
If that collision happens
over a short time interval,

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00:11:53,471 --> 00:11:56,008
there's not enough time
for an external force

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00:11:56,008 --> 00:11:59,323
to cause enough impulse to
impact the momentum greatly.

292
00:11:59,323 --> 00:12:02,118
So if it's one of these
instantaneous impacts

293
00:12:02,118 --> 00:12:04,675
that happen in collisions,
then the momentum

294
00:12:04,675 --> 00:12:08,026
will be conserved for
both elastic collisions

295
00:12:08,026 --> 00:12:10,436
and inelastic collisions.

296
00:12:10,436 --> 00:12:12,744
Sometimes people get
confused, they're like,

297
00:12:12,744 --> 00:12:15,503
wait, I know that energy is only conserved

298
00:12:15,503 --> 00:12:17,710
for elastic collisions.

299
00:12:17,710 --> 00:12:20,146
Maybe that means that
momentum's only conserved

300
00:12:20,146 --> 00:12:21,733
for elastic collisions?

301
00:12:21,733 --> 00:12:22,583
But that's not true.

302
00:12:22,583 --> 00:12:25,519
Momentum will be conserved
for both inelastic

303
00:12:25,519 --> 00:12:27,930
and elastic collisions

304
00:12:27,930 --> 00:12:30,945
You might object, you might
be like, wait wait wait.

305
00:12:30,945 --> 00:12:33,241
If you're clever, you
might be like, hold on.

306
00:12:33,241 --> 00:12:35,456
In these inelastic collisions we're losing

307
00:12:35,456 --> 00:12:39,854
all kinds of energy to the
random thermal oscillations

308
00:12:39,854 --> 00:12:41,056
in this material.

309
00:12:41,056 --> 00:12:45,220
Aren't we also losing momentum
to those random oscillations?

310
00:12:45,220 --> 00:12:49,005
I mean movement implies both
kinetic energy and momentum,

311
00:12:49,005 --> 00:12:50,796
so why aren't we losing momentum

312
00:12:50,796 --> 00:12:52,679
in these inelastic collisions?

313
00:12:52,679 --> 00:12:54,795
And the reason is the oscillations

314
00:12:54,795 --> 00:12:57,503
of the atoms and molecules
in this material,

315
00:12:57,503 --> 00:13:00,844
they're oscillating randomly,
in random directions.

316
00:13:00,844 --> 00:13:03,738
This thermal energy gets
distributed in a random way

317
00:13:03,738 --> 00:13:06,451
so that the momentum of
the atoms and molecules

318
00:13:06,451 --> 00:13:08,940
in that structure cancel out

319
00:13:08,940 --> 00:13:11,296
because if you've got momentum
in every single direction,

320
00:13:11,296 --> 00:13:15,272
and momentum is a vector,
that equals no momentum,

321
00:13:15,272 --> 00:13:17,046
at least no net momentum,

322
00:13:17,046 --> 00:13:19,069
because these are all gonna cancel out.

323
00:13:19,069 --> 00:13:20,576
This one cancels with this one,

324
00:13:20,576 --> 00:13:22,157
this one cancels with that one,

325
00:13:22,157 --> 00:13:23,913
that one cancels with that one.

326
00:13:23,913 --> 00:13:25,751
So that's why in an inelastic collision

327
00:13:25,751 --> 00:13:28,333
there's no loss of total momentum

328
00:13:28,333 --> 00:13:31,239
to the microscopic atoms
and molecules of the object,

329
00:13:31,239 --> 00:13:33,839
but there is a loss of kinetic energy

330
00:13:33,839 --> 00:13:35,758
because kinetic energy is a scaler,

331
00:13:35,758 --> 00:13:37,851
kinetic energy has no direction.

332
00:13:37,851 --> 00:13:40,144
Kinetic energy can't cancel in this way

333
00:13:40,144 --> 00:13:41,560
because it's not a vector.

334
00:13:41,560 --> 00:13:43,976
So even though in an inelastic collision

335
00:13:43,976 --> 00:13:45,682
you lose kinetic energy

336
00:13:45,682 --> 00:13:48,257
to the microscopic atoms and molecules,

337
00:13:48,257 --> 00:13:50,610
you don't lose any net momentum to them

338
00:13:50,610 --> 00:13:52,925
because all that momentum
just cancels out.

339
00:13:52,925 --> 00:13:55,904
And the bulk motion of
these macroscopic objects

340
00:13:55,904 --> 00:13:58,249
must maintain the total momentum.

341
00:13:58,249 --> 00:14:00,271
And this is wonderful news actually

342
00:14:00,271 --> 00:14:02,902
because that means
momentum's gonna be conserved

343
00:14:02,902 --> 00:14:06,777
for both elastic and inelastic collisions.

344
00:14:06,777 --> 00:14:09,761
It doesn't matter what
kind of collision it is,

345
00:14:09,761 --> 00:14:12,756
momentum is gonna be conserved
as long as there is no time

346
00:14:12,756 --> 00:14:16,808
for any net external impulse
to act during that collision.

347
00:14:16,808 --> 00:14:18,573
So even though energy is only conserved

348
00:14:18,573 --> 00:14:22,025
for elastic collisions,
momentum will be conserved

349
00:14:22,025 --> 00:00:00,000
for every collision.