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Anderson Video - Is Momentum Conserved for a Tossed Object

Professor Anderson
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>> Hello class. Professor Anderson here. Let's talk in general terms about conservation of momentum. What we said last time was Newton's third tells us that there are equal and opposite forces between objects. No isolated force exists. You always have equal and opposite forces. This is the action/reaction law. For every action there is a reaction. And what that led to is conservation of momentum. Momentum we're writing with a P. For some reason we've run out of letters again. M got used up by mass so momentum we're using P. It's a direct result from Newton's third law. [Inaudible] Newton's third you can get to conservation momentum. But what do we mean by momentum? Well, momentum is MV. That's the definition of momentum. It's the mass times the velocity. It is a vector -- Which means it has components, P sub x is M, V sub x, P sub y is M, v sub Y. It has vector components. Now, anybody have any problem with what I just wrote? I'll give you a hint, you probably should have a problem with what I just wrote. Kevin? Joseph can you hand it back to Kevin? >> You wrote components on the mass term. >> Yeah, why would I write components on the mass term? Is the mass a vector or is the mass a scaler? >> It's a scaler. >> It's a scaler so there should be no components on the mass term because it's just a number. It's 5 kilograms, it's 10 kilograms. It's just a number. No components on the mass term. Components go on the velocity. The velocity has components to it. So what does conservation of momentum tell us? It tells us that P initial equals P final. And this is really important to understand everything that's in this equation. There's kind of a lot that's in this equation. This is the system's momentum initially. And that is equal to the system's momentum -- Finally. Okay you have to be able to identify the system. So in the example that we just talked about with a rocket exploding into three pieces you could put a dash line around that rocket and that will define the system. But let's ask a question of you guys. Here's Newton's apple. Newton's apple fell from the tree and supposedly hit Newton on the head and he went "what's going on" right? And he thought about it. We know what's going to happen if I drop this. It's going to fall. Gravity is pulling it down. Is the momentum of this apple conserved here? As soon as it leaves my hand and when it comes back to my hand is the momentum conserved? Let me ask you guys? Raise your hand if you think the momentum is conserved in that simple experiment that I just did? Okay, about half of you. Raise your hand if you think it is not conserved. Okay, one of you? A half plus one equals -- all right, the answer is it's not conserved. The momentum of the apple is not conserved. Why? Because when I threw the apple up -- It was going in the positive Y direction but when it came back down it was going the opposite direction. There was a minus sign. The momentum of the apple was not conserved and yet this whole section is about conservation momentum. So what are we missing here? What are we missing in this experiment? Megan, do you want to pass the mic over to Megan? Okay, while you're getting ready for your question I'll do the demonstration again. I know it's very complicated. >> Okay, I'm not 100% positive but I think it's because when the apple leaves the hand you are no longer factoring in the entire system. >> Okay? >> Because isn't your hand part of the system? >> Well my hand is maybe part of the system but as soon as I let go of the apple I can just keep my hands stationary, right? And now I'll catch it again. So the hand could be basically velocity zero so maybe that's not really part of the system but is something else part of the system? >> Gravity? >> Gravity due to what? >> Due to -- I don't know [laughing]. I'm not sure. >> Okay, well there's something that's pulling this apple down. It's the same thing that's pulling you down. >> Weight and gravity. >> Right. And what is gravity on this planet due to? >> Weight, mass -- >> It's due to the mass of what? >> Of the object. >> Of the object, but it's being pulled on by the mass of -- >> The earth. >> The earth. The earth is part of the system -- >> Oh. >> The apple is not the system. The system is the earth/apple combination. So that's kind of weird to think about, right? But the idea is you have to identify the system and you can't have any forces that are crossing across your dashed line. So let's draw the picture. Here's the earth. And here's the apple. Okay, it got a little mangled. The apple is falling. If I draw a dashed line around this to identify the apple as my system, are there any forced lines that are crossing across that dashed line? Yes. Gravity, FG, is crossing that system line and so that cannot be our system. If there is any forced lines that are crossing, your dashed line that you just drew, that's not the system. You have to draw a dashed line such that no forces are crossing that line and therefore the system is really that. >> So hypothetically if you threw the apple far enough that it left our atmosphere would you then be breaking the rules because you're taking it out of its system? >> Okay. >> As far as conservation of momentum goes? >> All right, that's an excellent question. Let's say I throw that apple up so high that it's sitting way up here, here's my apple and it's outside the earth's atmosphere. Are there forces that are acting on the apple? >> Yes. >> What? >> A little bit of gravity. >> A little bit of gravity, right? It's may be smaller. We'll put a prime on it. It's something less but there's still a force acting on it so now your system envelops everything again, the earth/apple system. It's around the whole thing. I mean just because you get out of the atmosphere doesn't mean gravity turns off. It just means there's no more air but gravity is still acting on it. That's why the moon stays in its orbit or the International Space Station stays in its orbit. So you still have to include everything. So let's go back to this simple problem for a second. If this is the system and now I'm holding the apple like this and you're looking at the apple/earth system, what is the momentum of that system right now? What's your name? Emilio, okay. Emilio, what's the momentum of the apple/earth system right now? >> Zero. >> Zero, because the earth isn't moving, the apple's not moving, everything's stationary, right? Velocity, zero. So now when I throw it up and it's on its way up what is the momentum of the apple/earth system? What do you think Emilio? I'll give you a hint. Conservation of momentum. If you started with zero, what does it have to be from there on out? >> Zero. >> Zero. The apple on the way up, the momentum of the system is still zero but it doesn't make sense, right? The apple's going up. Shouldn't that be like some sort -- oh I bruised my apple. Shouldn't that be some sort of positive momentum? What does that mean is happening to the earth Emilio? If the apple is going up, if this is our apple and its heading up right after I throw it what does the earth have to be doing? >> Pulling it down? >> It has to be going down. The earth itself is actually going down and now when the apple is coming back down what is the earth doing Emilio? >> Exerting a force on the apple basically -- pulling it. >> We just flipped the directions of the arrows. If the apple is coming back down, the earth is going back up. And so this is really weird to think about, right? But if my fist is the earth and here's the apple what they do when I toss it is this -- and then I catch it again. That's what happens, which is kind of weird to think about. It goes like this and then it comes back together and then I catch it and everything comes to a stop and the momentum of that whole system is zero the whole time. Now the earth is pretty massive so it doesn't move very far. It doesn't have a lot of velocity but it has the exact same momentum as the apple. M times V since M for the earth is huge the velocity can be small. So inherent in this thing that we just talked about is the notion of an isolated system. You have to draw a dashed line around your system such that no forces cross that dashed line in that sort of step one in identifying these problems. Yes, Joseph? Can you hand the mic to Joseph real quick? >> If that's the case where if you have any forces on it it has to be included within the system, would that mean that -- what about forces like you were saying before like the moon or the sun's gravitational force on this? Would that be included in the system whenever you're using any physics properties? >> Okay, technically yes, right? Technically if we said this is our isolated system, that's not quite right because you still have the moon out there. The moon is pulling on the apple. The moon is pulling on the earth. You've got the sun over here, the sun is pulling on the earth, the sun is pulling on the apple though specifically you're right. We don't really have an isolated system. This is an approximation to an isolated system because the moon's poll is pretty weak compared to the pull of the earth. The sun's pull on the apple is pretty weak compared to the pull of the earth. >> So does that mean when we do do something there's an opposite force to those gravities that's just not really recognizable? >> So when I throw this thing up in the air I'm applying a force to get it going which pushes me and the earth down and when it comes back down that is gravity acting on it, that's pulling the earth back up and it down and when it comes back into my hand there's a force that my hand applies on the apple and everything comes back to rest. So the system sort of goes like this and then comes back to rest and during that interaction Newton's third tells us that all forces are equal and opposite. If there is gravity on the apple, the apple is exerting gravity on the earth. If there's a force of my hand on the apple, there's a force of the apple on my hand which is pushing me down. So simple concept, very confusing ramifications of it which I think is kind of cool. >> What if you blew up the apple? >> What if we blew up the apple? >> Yeah, while it's in the system with the earth? How would that affect the earth? >> Okay, I like that question. I think any sort of questions where we get to blow stuff up, those are good questions. >> A demonstration would be cooler though. >> [Laughing] anybody bring a firecracker [laughter]? Yeah so if you have an explosion, momentum is conserved so it doesn't really matter when that explosion happens. If I put a firecracker in this apple and I throw it up in the air and exploded in mid-air and let's say it goes into two pieces, one that goes up and one that goes down, the momentum of the entire system still has to be conserved. The apple parts combined with the earth, that whole system, the momentum still has to be conserved. So there's some fantastic videos on YouTube, one by a group called The Slo-Mo Guys. You guys seen any of their stuff? So they have these high-speed cameras and they like to blow things up a lot. So one of the videos is them blowing up a watermelon and they put -- I mean it looked like a half stick of dynamite in this thing. It was probably like and an M80 but this thing just obliterates and what's interesting about that is -- well what I thought was interesting was one, the guy sitting there without wearing safety goggles which I thought was a little ridiculous, but two, the shrapnel basically goes in every direction nearly uniformly. So if I think about a sphere and I put an explosive device right in the center of the sphere and it's going to blow apart into a whole bunch of little fragments, all of those fragments are going to go equally spaced in every direction. They're all going to go out radially and it's basically like you've blown up the entire watermelon in some uniform distribution. So as you get to more and more parts that you're exploding, everything is going to go out with essentially the same direction, radial, and similar velocities. It's going to conserve momentum of the whole system of course but it's going to go out uniformly.