- [Instructor] Our world is extraordinarily complicated.
So in physics we're going to have to make simplifications.
Even things in our world that seems simple
are extraordinarily complicated.
So consider a basketball seems simple enough,
but it's composed of an extraordinarily large number
of air molecules bouncing around inside, colliding
with the outside leather and rubber membrane,
which itself is composed of an extraordinarily large number
of atoms and molecules all bonded together
holding on tight, trying to prevent themselves
from being ripped apart and exploded by the pressure inside.
So do we have to keep track of every atom and molecule
in this ball to include it in a physics problem?
Typically not, nor would we ever really want to.
I mean, we can't keep track of all that info, not yet,
nor would you want to for most scenarios.
So for instance, if you were an astronaut,
you went to the moon,
you took your basketball and you were going to drop it.
If all you wanted to know was how long it's gonna take
for this ball to strike the lunar surface below,
you don't need to know about the ideal gas law,
you don't need to know about the structural integrity
of the rubber leather membrane.
You could solve this by treating the basketball
as if there was no internal structure whatsoever.
Like you were dropping a rock that had
no interesting internal structure whatsoever.
So in physics, the good news is we can typically get
away with making a lot of simplifications
and ignoring the internal structure
if it isn't relevant to the problem that we're asking.
Sometimes it will be relevant though.
So here was a case where it wasn't relevant.
The internal structure wasn't relevant.
So we could ignore that internal structure,
but other questions like if you were an astronaut,
I mean if I was an astronaut, and I was bringing
my basketball to the moon, I'd be like, wait a minute,
there's no atmosphere on the moon.
That means there is no pressure pushing in from the outside.
That means all this air pressure's still pushing
out from the inside is my basketball just gonna explode?
I'd want to know this before I brought it out there.
I don't wanna carry a little bomb out
that's going to like blow up in my face
and I don't want to lose a basketball.
If you wanted to know if your basketball
was going to explode, okay now it does depend.
That question does depend on the internal structure.
It depends on the pressure inside
which is fundamentally related
to the force of the collisions between these air molecules
and the rubber membrane and then it depends also on,
well, how strong are the bonds between these rubber membrane
and leather molecules?
How much force can they withstand before they burst?
For that question you would have to consider
the internal structure.
So, in some questions you get to ignore
the internal structure and other questions you don't.
It's just context and question-dependent
and in physics, we have terminology to sort of
sort this out and the terminology we use is the idea
of a system or the idea of an object.
So the idea of a system is just a collection
of objects, that's the definition of a system in physics.
But that begs the question,
well what do we mean by an object?
By an object, we mean anything that you could treat
as if it had no internal structure.
We don't mean that objects have no internal structure.
They typically do, the only things that don't truly
have an internal structures as far as we know
are truly fundamental particles like electrons or neutrinos,
these fundamental particles in particle physics
that as far as we know, have no internal structure.
So unless you're doing particle physics,
you're probably don't have a true object,
but you can treat things like an object.
We can treat this basketball like an object.
That is to say, we can act as if it has
no internal structure if that internal structure
isn't relevant to the problem.
So to make this a little more meaningful
just imagine another example.
Say you collide two objects so you collide a putty here.
Let's say this is three kilogram object
and it comes in with a certain speed
and it collides with a five kilogram object.
If all you want to know is when they stick together,
say these stick together and move off
with some common speed.
If all you want to know is what is that common speed
that they move off with after they stick together?
Notice what you don't need to know.
I don't need to tell you that this was made
out of gold here or that this one was made out of copper
as long as you know, the masses and that
they stick together, physics will let you solve
for how fast they'll move off with a common speed afterward
if you tell me that they stick together.
So if that's all you want to know
doesn't matter what the internal structure is.
However, for other questions, if you wanted to know
if this was going to set off some nuclear explosion, okay
well then it really is going to matter if these are made
out of gold, made out of copper, made out of clay
or if they're made out of uranium, so to speak.
So for that question, you do need to know
about the internal structure.
So the idea of a system and the idea
of an object is an important one in physics
and it's not just important conceptually or abstractly
it can actually help you in problem solving.
So let me show you a more like, tangible example
of where this might help you
in solving a problem you might encounter
in your physics courses.
So let's say they're two boxes
and they're just too big and unwieldy to handle.
So you're going to push them across the floor.
They're not heavy, they're just like shaped weird, let's say
and let's say the floor has been newly waxed.
So it's real slick against these boxes
which are also slick and there's negligible friction.
You could ignore the friction between the boxes
and the floor, so let's say you come up
and you're gonna push on these things.
Push them into the corner of some warehouse,
you're working in the warehouse here, earning
your pay for the day and you're going to go
push these over here and you're going to exert,
let's just say nine newtons of force
on this one kilogram box and then that pushes
into the two kilogram box
and they move off to the right.
So can we treat this system
of boxes as if it were a single object?
Well, like we said, it's question-dependent.
If the question we want to ask is, what's the acceleration
of these boxes as they slide to the right?
Well, they're going to move at the same rate
because as you push on this one kilogram box
that one kilogram box pushes on the two kilogram box
and they're going to move together.
As I keep pushing with nine newtons, the velocity of both
of these boxes are going to be the same to the right
and the acceleration of the boxes
are going to be the same to the right.
They're never going to become separated.
What that means is the fact that there were two boxes
didn't matter, I can treat this system of two boxes
as if it were a single three kilogram box.
I don't even need to know that they were actually
a division here, 'cause they're never going to become
separated for this question that I'm asking here.
So I could treat this whole system
as if it were just one big three kilogram object
and this is an important idea.
The properties of a system,
like the mass of the system, are determined
by the properties of the objects in that system.
So I put a three here and this is legal, this is allowed.
The properties of this total mass of my system is determined
by the mass of the individual objects in my system.
So you really can just add up these masses
to determine the total mass of the system
that you're going to be treating as a single object.
And now that I get to treat this as a single object
I'm in luck, I can use Newton's second law.
The acceleration is going to equal the net force
over the mass, we'll do this for the horizontal direction.
I'm just going to put a mass of three.
I could ignore the fact that this was a one and two
and the total mass of my system is going to be
three kilograms and the only force on my system
that I'm treating as an object here
is the nine Newton force.
I could ignore, in other words,
I can ignore the internal forces between these boxes.
I don't care about the one pushing on the two
or the two pushing on the one I'm treating the system
like an object and I'm ignoring that internal structure
that makes this problem really easy
when I solve for the acceleration
I just get three meters per second squared.
So for this question I could treat the system
as a single object.
What question would I not be able to treat the system
as a single object for?
Well, if I wanted to know, let's say the question was
with how much force does the one kilogram box exert
on the two kilogram box?
And you might think, oh, it's just nine, but it isn't.
So stay tuned, hold on.
It's counterintuitive. I know,
but the main idea I'm trying to stress here
is that this force on two by one is fundamentally
a question about an internal force.
So if the question you're asking is about
the internal structure, clearly you're not allowed
to ignore the internal structure.
So for this question we cannot treat the system
of two boxes as if it were a single mass.
We'll have to focus on the internal structure.
So again, consider this a one and a two separate boxes
and we'll do the same formula.
Acceleration's going to equal the net force over the mass,
but this time we do have to focus on a single mass.
So we'll focus just on the two kilogram mass
the only horizontal force on this two kilogram mass
if this really is frictionless
is this force that we want to find the force onto by one.
And that's the only force that's exerted
on the two kilogram mass.
This nine newtons is exerted directly on the one.
So it's not directly exerted on the two.
We don't draw that up here.
We don't include that here.
These are only forces directly on the two, and then
we'd have to put the acceleration of the two kilogram mass,
but we already found that this three was the acceleration
of the one, the two and the entire system.
Everything was accelerating at the same rate.
So I can put my three meters per second squared here
and I find out that the force exerted
on the two by the one is six newtons.
So it's not as big and this isn't surprising.
It takes more newtons from the left here
this nine newtons to accelerate the entire system
of three kilograms than it does to just
accelerate the two kilogram mass over here.
So the fact that this force is accelerating less mass
means it doesn't have to be as big.
But the key idea is that to find that,
we could not treat, to find this force here,
we could not treat this entire system as a single mass.
So recapping, if the question being asked does not depend
on the internal structure, you can simplify your life
by treating that structure and that system
as if it were a single object, in which case,
the properties of that will be determined
by the properties of the objects in that system.
But if the question being asked does depend on
the internal structure, then you cannot treat
that system as a single object.
You will have to focus on the internal structure.