Systems and Objects | Dynamics | AP Physics I | Khan Academy

Our world is extraordinarily complicated, so in physics, we're going to have to make simplifications. Even things in our world that seem simple are extraordinarily complicated. So consider a basketball. It 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 going to 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 could 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're 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's no pressure pushing in from the outside. That means all this air pressure still pushing out from the inside— is my basketball just going to explode?"

I'd want to know this before I brought it out there. I wouldn't want to carry a little bomb out that's going to blow up in my face, and I don't want to lose a basketball. If you wanted to know if your basketball was gonna 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; in other questions, you don't. It's just context- and question-dependent.

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. 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: 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 structure, 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 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.

To make this a little more meaningful, just imagine another example. Say you collide two objects. Say you collide a putty here—let's say this is a 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 that's all you want to know; it 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.

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 tangible example of where this might help you in solving a problem you might encounter in your physics courses.

So let's say there are 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 going to 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 gonna go push these over here, and you're gonna 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. They're gonna move together.

As I keep pushing with nine newtons, the velocity of both of these boxes is gonna be the same to the right, and the acceleration of the boxes is gonna be the same to the right. They're never gonna 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 because 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 3 here, and this is legal; this is allowed. The properties of this total mass of my system are 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 3. I could ignore the fact that this was a one and a two, and the total mass of my system is going to be three kilograms. 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 this system as a single object. What question would I not be able to treat this 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?" 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 this 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 is gonna 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 on two 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 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.