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Systems and Objects

Systems are collections of objects. Objects can be treated as if they have no internal structure. You can treat a system as an object if the internal structure is not relevant to the question. Created by David SantoPietro.

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  • blobby green style avatar for user Shae S
    Am I missing something because the practice for this is giving us equations that were not covered? Did I miss something?
    (58 votes)
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  • blobby green style avatar for user brunobarbosaaustin
    I am very confused about how this course works. So far, I've watched the videos, then when we get to the questions, they require knowledge/equations that were not in the videos. Is there something else I'm supposed to be reading or watching as we go through the course? Every other KhanAcademy class I've done, the videos have all the information you need to solve the problems. For example, the problems after this video deal with sum of forces and tension, which hasn't been discussed anywhere up until this point.
    (41 votes)
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  • winston baby style avatar for user Mason Smith
    What is Newton's law?
    (3 votes)
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    • female robot ada style avatar for user wendi <3
      Newton has 3 laws, so you can't refer to a specific 'Newton's Law'.

      The first of Newton's Laws states that an object at rest will stay at rest unless some external force acts on it.

      The second states that Force = (mass)(acceleration).

      The third states that when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

      Hope this helps!
      (6 votes)
  • blobby green style avatar for user Jillian Zhu
    So in the last example that he gave, why is the mass that he plugged in 2 kg? Wouldn't it be 1 kg since the box 1 is exerting the force on box 2? Confused.
    (1 vote)
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  • blobby green style avatar for user Soham Deshpande
    The One thing that I don't understand with this whole problem is when David uses the acceleration equation to find the acceleration of the system as 3m/s^2 and then uses the same acceleration to find the internal force of the 2kg box. Wouldn't the acceleration be different for the 2kg box when the "internal" force is being taken than that of a "system "being the collection of objects as mentioned in the video?
    (1 vote)
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    • blobby green style avatar for user koksarem
      Both boxes are in contact, and the applied force is transferred through the 1 kg box to the 2 kg box. Because they are connected, they must move together with the same acceleration. If they had different accelerations, they would separate or compress, which contradicts the problem's conditions.
      The force applied to the 1 kg box results in an acceleration that is transmitted through the 1 kg box to the 2 kg box. The interaction force between the two boxes ensures that the 2 kg box experiences the same acceleration.

      Hope this helps.
      (2 votes)
  • male robot hal style avatar for user Vanduss
    Im confused because I thought calculating it is 9/ 2 = 4.5
    How did he get 6 m/s^2
    (1 vote)
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  • blobby green style avatar for user rod132
    The video on Systems does only one practical example of how to do calculations within a system. However, the practice problems reference material that doesn't come until the next unit. As a teacher I am trying to brush up on material I learned years ago but this is not a particularly good way to present material. If I presented this to students they would be very confused and get frustrated very easily.
    (1 vote)
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  • leaf blue style avatar for user 3010998
    What exactly is center of mass, and how is it affected by forces?
    (1 vote)
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    • duskpin ultimate style avatar for user jasonmoses05
      The center of mass of an object is the average position of all its mass. Its position is dependent on how the mass is distributed around an object. The center of gravity of an object is the average position of all its weight. In a uniform gravitational field, like on Earth, the center of mass coincides with the center of gravity.
      (1 vote)

Video transcript

- [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.