When a car drives along the road, it moves forward because the tires push against the road, and due to the friction force, the road pushes back. So a car can move because of friction. Even when you walk. When you walk, you're pushing against the sidewalk, you're pulling back against the sidewalk, which you move forward really, due to the friction force pushing you back. Sometimes when I walk, I like to try to imagine it. I'm not pushing against the road, the sidewalk, the sidewalk is pulling me. See if you can imagine the sidewalk pulling you. It will lead to some strange contemplate of walking. Rocket engines. So now, say we want to go into space. They can't really do this. There is no friction, there is nothing to push against in space. So if we want to move in space, what you're going to do is use the conservation of momentum. So let's think about a rocket. So you know it's giant structure and it's got a nose on it, it's got some fins to make it fly straight, but the important thing is on the inside. Inside here is the fuel or the propellant. When the fuel is inside the rocket, before you light the fuel, before you do anything, the whole thing is a system and its momentum is zero because it's sitting on the launch pad, or in this case, let's imagine it's just in space and not moving. Well, what you do, you light the fuel, big chemical explosion happens and the fuel shoots out the back. Here's the fuel, and it's moving very fast. V_fuel, and therefore, the rocket ends up going this way with its fins and everything, and it's going at some speed, V rocket, due to conservation of momentum. The final momentum of the system in this case is zero for two reasons. One, momentum has to be conserved, and two, if you look at how it can be zero, remember it's a vector quantity. They both pick up a speed, they both pick up a momentum, but since momentum is a vector, they can still cancel. So if you read about the analysis of rocket thrust, and motion, and the speed of the exhaust that you need, all these things, it gets very complicated because here's what's really happening in a rocket. The rocket needs a lot of fuel, you want as much fuel as you can get. This whole thing is fuel. As it starts to burn, you send some of the fuel out, but as it burns, as it comes out, a lot of the fuel is solid and it's still on the rocket. So in the early stages of the burn, a lot of the mass of the fuel is part of the rocket that was accelerated or that was pushed or given momentum this way, and then as it burns, then it comes out. So that makes it more complicated. Basically, the issue is that you have a change in mass per unit time. You have a dmdt as we would say in calculus. That just leads to more complicated analysis and something we aren't going to do. But in the end, what you need to make a fast rocket is a large mass of fuel and you needed to come out really fast. So the result is not too surprising, it's just getting there is pretty complicated because of this issue of the significant mass of the fuel. But I have another rocket over here. Well, that won't be an issue. So this is an empty water jug and it's got a little bit of fuel inside, and I'm not going to tell you what the fuel is because I do not want you to try this at home. But trust me, the mass of the fuel inside the jug is very small compared to the mass of the jug. The jug is suspended from the high ceiling on thin strings and it's like a very long pendulum. So it's sort of an approximation of free one-dimensional motion. So I'm going to light the fuel. But first, I'm going to turn the lights out so you can see a little better. Here we go. Let's see. That was a good one. Well, that was a little more exciting than I intended. Let's see. So lets just analyze our rocket a little bit. It was a water bottle and it had a nozzle where normally, water comes out. Let's see. I can tell you a few things about it. The mass of the rocket is about 0.69 kilograms, and it's just the mass of the water bottle. At first, the momentum was zero. Then after we lit it, the rocket goes this way with some velocity, V_r, and the fuel goes this way with some velocity, V_f. We can calculate the change of momentum, we can calculate basically the impulse that these applied to each other. I analyze the video and measured V rocket to be about 7.2 meters per second. So we can get the final momentum of the rocket, it's just mass times velocity. It's 0.69 kilograms times 7.2 meters per second, which is about five kilogram meters per second. So if you want to think in terms of impulse, even though it's internal, we can think of the impulse each applied to the other, and still conserve momentum, then the impulse is also five kilogram meters per second because the impulse is equal to the change in momentum. This really is the change from 0-5. Since we have the impulse, we could say I equals 5 kilogram meters per second, which equals the average force times Delta t. So also from the video, I was able to get approximately what Delta t was just by watching the frames, and it was about 5. We're going to divide five kilogram meters per second by the Delta t, it was about 0.375, while the fuel is coming out and really pushing. So from that, we can get the average force of the thrust on the rocket, it was about 13 Newtons. So not huge, but enough to really get it going. This is all ignoring air resistance and the little strings pulling back and everything. But as an approximate situation, when you have the case that your fuel is very light and doesn't really contribute to the mass. This is how you can just solve a simple problem.
