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Newton's third law states
that forces always come

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in equal and opposite pairs.

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One way we can write that is
if you imagine two objects,

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object one and object two, the
force exerted by object one

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on object two is equal and
opposite to the force exerted

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by object two on object one.

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This makes explicit that
real forces always arise

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from a physical interaction.

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For any force in a
problem, you should always

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be able to identify the other
member of the interaction pair.

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Newton's third law
is the most subtle

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and sometimes the most confusing
of his three laws of motion

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so I'd like to do an
example that will help

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clarify how to think about it.

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So I'm going to pick a
very extreme example.

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Let's imagine the collision
between a marble moving

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this way and a train
moving that way.

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And so we'll say that
the mass of the train--

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I'll write that
as "m sub train"--

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and the mass of the
marble is m sub marble.

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And obviously, the
mass of the train

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is much larger-- I'm
going to write that

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as several greater-than
signs-- much, much larger

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than the mass of the marble.

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And so the question I want to
consider is, at the instant

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that these two objects collide,
which experiences the greater

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force?

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So think about that
yourself for a moment.

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In terms of outcomes,
clearly, the marble

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will be smashed by the train
whereas the train will not

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be noticeably affected
by the marble.

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So your intuition
might therefore

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suggest that it's the marble
that feels the greater force.

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But that's incorrect because
Newton's third law tells us

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that forces come in
equal and opposite pairs.

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And what that tells
us is that each object

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will exert an equal
but oppositely directed

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force on the other.

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Now I chose a very
extreme example

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to capture your attention.

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But that might seem
like a surprising result

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but Newton's third law tells us
that the forces on each object

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are going to be
equal and opposite.

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But just because
the forces are equal

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doesn't mean that the
motion will be equal.

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The accelerations
of the two objects

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are vastly different because
of their different masses.

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And the accelerations
and the forces

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are related by Newton's
second law, F equals m a.

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So if I write that in
terms of the acceleration,

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the acceleration of
the marble, "a marble,"

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is equal to the force divided
by the mass of the marble

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whereas the acceleration
of the train

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is equal to-- so since I
wrote "F" for the force acting

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on a marble, I'm going to write
minus F for the force acting

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on the train.

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So that's minus F divided
by the mass of the train.

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And so if I want to look
at the ratio, how big is

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the acceleration of
the marble divided

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by the acceleration
of the train?

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And let's take the absolute
value so we're just

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talking about magnitudes here.

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That's going to be equal to
the mass of the train divided

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by the mass of the marble.

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But the mass of the
train is much, much,

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much larger than the
mass of the marble

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so the right-hand side here
is a very, very big number.

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And that tells us that
relative to the acceleration

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of the train, the
acceleration of the marble

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is going to be enormous.

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Even though the force
experienced by each object

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is identical, because of
their different masses,

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their accelerations
will be very different.

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So that gives us
an example of what

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we mean by Newton's third law,
in terms of the interaction

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pair and equal and
opposite forces acting.

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I want to reiterate that
for any force in a problem,

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you should always be able
to identify the other member

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of the interaction pair.

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So forces always come in pairs.

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It's important to keep in mind
that these force pairs don't

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both act on the same object.

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They never act on
the same object.

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The interaction
pair always involves

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a pair of objects,
two different objects.

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And let me just make that
explicit with an example.

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The example I'll consider
is, imagine a person standing

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on the ground.

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What are the forces
acting on this person?

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I'll draw the force
diagram here, say.

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There's gravity,
mg, acting downwards

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and there's a normal force
upward exerted by the ground.

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And those two balance to give
a net force of zero, which

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is why the person is
standing on the ground

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and not sinking down into
the ground, for example.

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Now, you might look at
gravity and the normal force

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and wonder if those are
an interaction pair.

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And they're not because notice
that these two forces are both

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acting on the same
object, the person.

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The interaction
pair always comes

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from realizing what is exerting
the force on the object.

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So let's look at each
of these in turn.

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Gravity is exerted by the Earth.

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So if the Earth-- and this
means really the entire Earth--

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exerts a force mg on the
person, Newton's third law

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tells us that the person
exerts a gravitational force

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on the entire Earth
of mg upwards.

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Now, that might seem
remarkable to you

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if you're just standing
around on the floor

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that you are exerting
a gravitational force

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on the planet but you are.

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However, this is like
the example we just

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talked about a moment ago.

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The masses are
extremely different

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even though the
forces are the same.

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So the acceleration of the
Earth due to this person's mass

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is negligible because
the Earth is so much more

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massive than the person.

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But Newton's third law
tells us that there

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is a tiny acceleration on
the Earth due to the person.

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That is the third
law pair for gravity.

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mg downward exerted by
the Earth on the person

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is paired with mg upward on the
Earth exerted by the person.

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Now, for the normal force
acting on the person,

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that force is exerted
by the ground.

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So the ground exerts an
upward force N on the person.

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Newton's third law
tells us that that

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means that the person must
exert a downward force

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N on the ground.

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That is the interaction
pair for Newton's third law

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for the normal force.