Newton's third law states that forces always come
in equal and opposite pairs.
One way we can write that is if you imagine two objects,
object one and object two, the force exerted by object one
on object two is equal and opposite to the force exerted
by object two on object one.
This makes explicit that real forces always arise
from a physical interaction.
For any force in a problem, you should always
be able to identify the other member of the interaction pair.
Newton's third law is the most subtle
and sometimes the most confusing of his three laws of motion
so I'd like to do an example that will help
clarify how to think about it.
So I'm going to pick a very extreme example.
Let's imagine the collision between a marble moving
this way and a train moving that way.
And so we'll say that the mass of the train--
I'll write that as "m sub train"--
and the mass of the marble is m sub marble.
And obviously, the mass of the train
is much larger-- I'm going to write that
as several greater-than signs-- much, much larger
than the mass of the marble.
And so the question I want to consider is, at the instant
that these two objects collide, which experiences the greater
force?
So think about that yourself for a moment.
In terms of outcomes, clearly, the marble
will be smashed by the train whereas the train will not
be noticeably affected by the marble.
So your intuition might therefore
suggest that it's the marble that feels the greater force.
But that's incorrect because Newton's third law tells us
that forces come in equal and opposite pairs.
And what that tells us is that each object
will exert an equal but oppositely directed
force on the other.
Now I chose a very extreme example
to capture your attention.
But that might seem like a surprising result
but Newton's third law tells us that the forces on each object
are going to be equal and opposite.
But just because the forces are equal
doesn't mean that the motion will be equal.
The accelerations of the two objects
are vastly different because of their different masses.
And the accelerations and the forces
are related by Newton's second law, F equals m a.
So if I write that in terms of the acceleration,
the acceleration of the marble, "a marble,"
is equal to the force divided by the mass of the marble
whereas the acceleration of the train
is equal to-- so since I wrote "F" for the force acting
on a marble, I'm going to write minus F for the force acting
on the train.
So that's minus F divided by the mass of the train.
And so if I want to look at the ratio, how big is
the acceleration of the marble divided
by the acceleration of the train?
And let's take the absolute value so we're just
talking about magnitudes here.
That's going to be equal to the mass of the train divided
by the mass of the marble.
But the mass of the train is much, much,
much larger than the mass of the marble
so the right-hand side here is a very, very big number.
And that tells us that relative to the acceleration
of the train, the acceleration of the marble
is going to be enormous.
Even though the force experienced by each object
is identical, because of their different masses,
their accelerations will be very different.
So that gives us an example of what
we mean by Newton's third law, in terms of the interaction
pair and equal and opposite forces acting.
I want to reiterate that for any force in a problem,
you should always be able to identify the other member
of the interaction pair.
So forces always come in pairs.
It's important to keep in mind that these force pairs don't
both act on the same object.
They never act on the same object.
The interaction pair always involves
a pair of objects, two different objects.
And let me just make that explicit with an example.
The example I'll consider is, imagine a person standing
on the ground.
What are the forces acting on this person?
I'll draw the force diagram here, say.
There's gravity, mg, acting downwards
and there's a normal force upward exerted by the ground.
And those two balance to give a net force of zero, which
is why the person is standing on the ground
and not sinking down into the ground, for example.
Now, you might look at gravity and the normal force
and wonder if those are an interaction pair.
And they're not because notice that these two forces are both
acting on the same object, the person.
The interaction pair always comes
from realizing what is exerting the force on the object.
So let's look at each of these in turn.
Gravity is exerted by the Earth.
So if the Earth-- and this means really the entire Earth--
exerts a force mg on the person, Newton's third law
tells us that the person exerts a gravitational force
on the entire Earth of mg upwards.
Now, that might seem remarkable to you
if you're just standing around on the floor
that you are exerting a gravitational force
on the planet but you are.
However, this is like the example we just
talked about a moment ago.
The masses are extremely different
even though the forces are the same.
So the acceleration of the Earth due to this person's mass
is negligible because the Earth is so much more
massive than the person.
But Newton's third law tells us that there
is a tiny acceleration on the Earth due to the person.
That is the third law pair for gravity.
mg downward exerted by the Earth on the person
is paired with mg upward on the Earth exerted by the person.
Now, for the normal force acting on the person,
that force is exerted by the ground.
So the ground exerts an upward force N on the person.
Newton's third law tells us that that
means that the person must exert a downward force
N on the ground.
That is the interaction pair for Newton's third law
for the normal force.