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Anderson Video - Momentum and Rocket Propulsion

Professor Anderson
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Let's say you are in outer space and you're working on the International Space Station. Here it is -- solar panels, you're an astronaut. You were working on it. You've got your wrench there that you were working on the International Space Station with and somehow your tether breaks in half. You were tethered to the International Space Station. It breaks. It's gone. It floats away and now you are floating motionless. This is the International Space Station. This is you. And you're too far away to reach it. Your rope is gone. Here's the question. How do you get back to the International Space Station? In the back, what's your name? Alex. Okay, Alex. Somehow you find yourself in this situation floating in space away from the International Space Station. You're motionless but you're not next to it. How do you get back? >> Well, if you use the wrench as the force to throw it away from the space station you can propel yourself -- >> Aha! >> Towards it. >> Take the wrench and throw it in that direction. And what's going to happen if I throw the wrench? >> It propels you backwards. >> It's going to propel you in the other direction. That's exactly right. Why is that, Alex, why is that? >> The force needed to throw the wrench forward is the exact same force that you will use to propel yourself backwards. >> Okay, that's exactly right. And we use that law [inaudible] something called conservational momentum. So let's take a look at this picture as it applies to you. Here you are holding the wrench. This is our before picture. And now in the after picture you've thrown the wrench. The wrench is going this way. You are going that way. This is the after picture, namely before you throw it, after you throw it. If this is the mass of the person and this is the mass of the wrench and you throw this at a speed, VW, then you're going to move at a speed VP. >> Right. >> This is just like an explosion. An explosion is just two things separating. So you throwing it is kind of like an explosion. What is the initial momentum of the system here Alex? >> It's going to be the mass of the person -- >> Okay. >> And that's going to equal the mass of the -- >> Well remember momentum is mass times velocity so the mass of the person times what? >> Times zero. >> Times zero. >> Since velocity -- there's no velocity. >> Okay, what about the wrench? >> And it's going to be the mass of the wrench times at zero. >> So this whole thing is zero. >> Right. >> There is no momentum initially. Everything is stationary. And now in the after picture we're going to have the mass of the wrench times the speed of the wrench, going to the right, we can call that the positive direction, but we have the mass of the person times the velocity of the person in the other direction. We can call that negative. And so now we can set them equal. PI equals PF. Zero equals mass of the wrench, velocity of the wrench, minus mass of the person times velocity of the person and now we can solve for the velocity of the person. I'm going to move this over to the other side. I'm going to divide by M sub p and I get that. This is the velocity of the person. This is how fast you will be moving after you've thrown the wrench. So Alex, looking at this equation, what do you want to do with that wrench? >> Throw it in the positive direction. >> Definitely, throw it in the positive direction so you can go in the other direction back towards the space station. >> Right. >> But what else do you want to do? Do you want to throw the wrench softly or do you want to throw the wrench very fast? >> Very fast. >> Very fast. That's this right here. Speed of the wrench. The faster I throw the wrench the faster I move. If VW goes up VP goes up. What else do I want to do? How can I get back to the space station faster? Look at this equation and tell me what else I could do. >> I'm not sure. >> Okay. If I have mass of the wrench up here -- >> Right. >> That means if I can somehow gather more mass to throw that I'm going to go faster the other way. >> Right. >> So if I not only have a wrench but I had a hammer and I had a screwdriver and I had all sorts of stuff, I should put it all together and throw all of it together because if I increase the mass up there that number is bigger, my velocity is -- ? >> Bigger. >> Likewise, if I can decrease the mass of me then this number is bigger and I'll get there faster. So I could take off my helmet, I could take off my spacesuit, I could take off my boots, toss all that stuff too. It might not be the best approach because it's a little tough to live in outer space without your spacesuit on, right? But this is sort of interesting because we talked about a very simple picture here. A person with an object, throwing an object they go the other way. But this can be any object and it doesn't have to be a person. So guess what? This sort of behavior is exactly the same as a rocket. A rocket works by the same idea. It's going to take some exhaust, it's going to burn it up and spit it out the back and when it does that it's going to fly in the other direction. It's exactly the same problem. Conservation momentum. The only reason the rocket flies away is because it's burning stuff up and spitting it out the back very fast. The faster it does that the faster the rocket's going to go. The more mass it can spit out the back the faster the burn rate, the faster it will go the other way. So when people say oh he's a rocket scientist, she's a rocket scientist -- you should say so what? That's just conservation momentum. It's not that complicated. We wrote it out here in one page. >> Right. >> All right, questions about that one? All right, this experiment you guys should go try. You should definitely go try this. It doesn't have to be in outer space. If you go to an ice rink and you stand in the middle of an ice rink and your buddy is standing next to you, just grab hold of them and push and when you push them away you're going to go the other way and the faster you push them the faster you will go.