 Any questions from the homework? That's going to be a little loud. That's what I kind of implied. Absolutely, Nicole. I would love to. So lesson four. Which one, kiddo? Number eleven. This one here? Good, because I think I like this question. I think I like this question. I think I like this question. It says, draw the force diagrams. Well, I'm going to draw the obvious, easy one first. What are the forces acting on this? Get the obvious ones. Nicole, what are the forces acting on this one? Get the obvious one. Big M, G. What else? Yeah, that's cool. What are the forces here? Well, here I would have little M, G, and I would have a normal force. Do I have friction? The question seems to suggest low friction. I think low friction means no friction. What about this force right here? I know there has to be one, because it's moving in a circle, which means the net force must be towards the middle. Sorry? Absolutely. In fact, that's the force diagram. It says B, find the chord tension. Well, you know what? Tension equals what's moving me in a circle. It has to be. Tension equals M. I'm either going to use V squared over R, or 4 pi squared R over T squared. Let's see, they gave me ah. Wait a minute. I don't know V. Do I? I don't know the period. Do I? Rats. Wait a minute. I have this equation here. I have this mass here. Maybe I can find tension by looking at this mass here. Let's see. Looking at this mass, I'm winning. Wait a minute. It's a tie, isn't it? Looking at this mass here, here's how I can find tension. I'm not going to do this. I'm going to say it turns out tension must be exactly equal to that, because they're in balance. Is that okay? Ooh, I like. Tension equals how big is the big mass? 2.5 kilograms times 9.8 2.5 times 9.8. Turns out the tension is exactly 24.5 newtons. I started out wrong, but I didn't panic when I said, well, they didn't give me the information that I need as a good physics nerd, then I'll ask, what did they give me? Hey, there's a T in my other diagram. Why don't I go look at the other diagram? Now, I bet you I'm going to use this tension to find the V or the period that I couldn't find that I didn't have before. Let's see. Part C says find the speed. Now I'm going to start out by saying tension is also FC 24.5 equals MV squared over R. Is that okay, Nicole? Do I know R? Yeah, do I know the little mass? I think it's 1, as a matter of fact, which is really nice. So I think it's going to be times by R in square root, and that should give me the velocity. Nice little twist. I guess it also means this. Nicole, if this car somehow had a motor and sped up, went faster, it would start lifting this guy up, because it would want to... It's inertia would want to make it go in a straight line, so it would need a greater force to pull it inwards, so tension would get bigger, so tension would now be a winner, and MG would accelerate upwards. Right? If this car slowed down, it wouldn't need as big a tension. This would drop down and accelerate downwards. Makes sense to me now that I think about it. Any others, either from two days ago or last day's homework on orbits? Yeah. From last day? Less than four still? Absolutely. I like number eight. I like number eight. Number eight is a nice question. Now, there's two parts to number eight. The first part drives me crazy because kids keep forgetting it, even though I've tried to emphasize it. When I say gravitational field, they think, oh, that's that. It's not. Gravitational field is symbolized by a lowercase g, which on the earth is how big, by the way, Nicole? 9.8. What about an outer spin? Well, we said you can calculate it, and this is not on your formula sheet. You can derive the equation, Joel, by recognizing that's gravity, yes, the force of gravity, but also that's the universal force of gravity, yes? You may notice, Joel, that the mass is canceled, and you end up with, this is your equation for little g. This is how you can calculate little g. So it's going to be big g, big m over r squared, where big g is 6.67 times 10 to the negative 11, that Newton's universal gravitational constant. M is earth, yes, masses of the earth, 5.98 times 10 to the 24 divided by, and the radius, I got to be careful, they gave me above the earth, oh no, they gave me the distance from the center after all, but what's it measured in? 8, 8, sorry, 8, 3, 8, 0 times 1,000, that now it's into meters squared. I'm going to ask you a gravitational field question. What you need to recognize is gravitational field, Nicole, is as soon as we leave any earth and travel out any distance. And I would, by the way, have no problem, for example, telling you the gravitational field and saying how heavy is the planet that we're on, if you knew the radius of the planet, that would work just fine, or telling you the gravitational field, telling you we're outside the earth, how far from the earth center. We're outside as well. Okay. Any others? Orbits? Okay. Did you get A? Okay. If it's geosynchronous, it stays above the earth, how long to take the earth to go around once? No, not to go around the sun. How long to take the earth to go around once? More specific in time, please. 24 hours change that to seconds. Okay. All geosynchronous satellites, and any satellite TV dish, any GPS satellite, many satellites are geosynchronous. They have to stay above the same place so that your satellite dish knows exactly where to point always. They have a period of 24 hours. They have a period of 8,600, sorry, 8,6,400 seconds. Okay. Now that you know the period, then you can do B. Let's see. And yeah, they all have the same radius as well, by the way. B is going to be gravity equals circular. Big G, big M, little M over R squared equals M for pi squared R over T squared. I know to use this one because they gave me the period in part A. Does an R cancel? No. Because one's on the top and two are on the bottom. In fact, if I get the R, and they want me to find the radius, if I get the R by itself, I'm going to end up with an R cubed over here. A T squared over here. Hey, the M's cancel and a 4 pi squared. I'm going to end up with this. R cubed equals big G, big M, T squared over 4 pi squared. How do you get rid of a cubed, Vanna? Route 3? Or we like to say cube root. Third root. It's going to be that. I'm assuming. Try that on your calculator. I totally like that question. Absolutely is going to be a question where I give you the period and say find the radius. In this case, you have to derive the period by clueing in it was 24 hours, but I have no problem just giving you a period and saying, okay, if you want the satellite to rotate around the Earth every five hours, figure out how many seconds that is, and okay, how high does the US military have to put it if they want to spy on you every five hours. Would the US military want satellites to go around the Earth in a shorter period or a bigger period? I think it depends. I'm willing to bet they have a bunch of geosynchronous satellites over the Middle East. Probably. But then they probably have a bunch that rotate around the Earth every three or four hours as well, because that would give you, you have them so that they overlap so that when one was vanishing off the horizon, another one was coming into view, hopefully. Because the US likes to spy on people. Although I'm sure we would too if we had the capability and the technology. I don't know if we have any spy satellites though, they're pretty pricey. Is that okay for you? Any others? Yeah. Number ten. Sure. Nicole, this ties in with yours. Here I gave them the gravitational field strength. Okay. I told you that G is equal to this. Yes? I gave you that it was 8.75. You know the mass of the Earth? Could you find your orbital radius at this point in time? Okay. So you find r. And now they want how fast? So now you can say gravity equals fc big g big m little m over r squared, which you just calculated, equals m v squared over r. Conveniently the mass cancels and one of the r's cancels and now you can find v squared. Does that make sense? I'll try it. Or did you try that and not get succeed? Gravitational field. This is one of my big peeps because I keep repeating myself and I'll do the same thing next block as well. Gravitational field strength is that just because it's not on your formula sheet, people are like, I don't need to know. You do need to know that it's that and I've showed you now how you can I don't have it on this page, how you can derive it. It pops out of the gravitational formula by cluing in all the masses cancels and the other big expression must be the acceleration, which is g. Is that okay? Yep. Any others? I would argue that the next two lessons would rank among the top five in terms of difficulty. So pay attention for the whole year. Don't wrinkle your lip. It also means it's nerdily cool. Okay? But because you don't have... How many of you in calculus? Okay. Calculus at the end of this I can give you a way better explanation for what I'm about to tell you but because you don't have calculus, I'm going to those of you that don't have calculus, there's a negative that's going to show up. I'm going to give you a lousy explanation. Calculus the answer would be when you take the derivative you get a negative but I can't really tell them that. So let's start. What we're going to look at today. Last day we looked at the math of what happens once you're in orbit. Maybe I just secretly don't want you to learn. Maybe it's a subconscious like I want to increase your level of difficulty and make it tougher for you. You know what it is really. It's what I'm counting. There's someone that I just miss all the time. I won't mention any names. Okay. I didn't say anything. Why would you assume? People online are going, what's going on? Last day we looked at what's going on once you're in orbit. Once you're up there if you want to achieve a stable orbit, gravity equals a particular motion. Hey, the mass is canceled. Today what we're going to ask is how much energy does it take to get up there? And it's a big issue because first of all you're having to go through a tremendous height that's a lot of potential energy. Where does that potential energy come from? The fuel. Oh, but it's not just like we want to lift you up there and have you stand still once you're up there then Joel we have to give you just the right velocity. We have to give you a bunch of kinetic energy. Where does that kinetic energy come from? The fuel. There's a reason that it's so expensive to put satellites up there. There's a reason that really only countries or multinational corporations can put a satellite up there. There's a reason why we don't say in here in pit meadows, hey let's do a satellite project and put one into orbit. It's not the technology of building the satellite. We could probably build like a little radio beacon for a couple of thousand dollars and it would probably last for a few years. We wouldn't power it through nuclear power the way most of them are. We'd power it through a solar battery. We'd probably do something like that. It's prohibitively expensive to just get them up there. So the problem is, well you'll see in a second recall the area under a force versus distance graph so if we have a force graph versus distance and I tell you that the force is increasing in a nice straight line like that so the force is getting bigger as distance moves further. You'll remember this is good review. What was that area? What was the area under a force distance versus distance graph? It remembers. And I'm going to add a phrase now Emily the work done on the object. Let's instead of just saying abstract the work let's say it's how much work you did on the object that you're applying the force to the object gained this much energy and usually it was in the form of kinetic energy. Usually it was speeding up. This time it's going to be gaining potential energy because we're going to be pushing it up higher and higher and higher. The problem is this we have to look at the graph of the force of gravity. The force of gravity unfortunately is not a nice linear graph. It's got exponents in it. If you graph FG versus R so you're moving further and further and further and further away from the Earth. When you're close to the Earth it's at its maximum but as you move further and further and further away what happens to the force of gravity? Does it get bigger or does it get smaller? In fact it looks like this. Those of you in Math 12 look up for one second when you're done copying that. It's the reciprocal of a parabola. It's the reciprocal of R squared. So remember Math 12, those of you that are in Math 12, the reciprocal graph. Zeros become asymptotes. Bigger becomes smaller. So as the parabola graph gets bigger and bigger the reciprocal graph is going to get smaller and smaller. As the parabola graph gets closer to zero the reciprocal graph shoots off to infinity. Those of you that are not in Math 12, whatever. It looks like that. We actually experience that big a force of gravity right there on the surface of the Earth. And then as you move further and further and further away essentially gravity gets weaker and weaker. What would the force of gravity be out here at infinity? And yeah, calculus students I'm sort of taking the limit but you're wondering about that. What would this eventually get closer and closer and closer to? Zero. We would say out of infinity you're so far away from any planets there you can float forever. There you have nothing talking on you. And it's kind of an abstract concept I realize but those of you that are in calculus get the limit. Consider the following. So here's the force of gravity. Here's your separation distance R. Here's our little sketch. Let's suppose we wanted to lift off from some planet and reach a certain height and say a significant height not like 30 meters where G hasn't changed. Not even like Mount Everest height where G has changed maybe on the tenth decimal place but nothing that we can really measure. But let's say several thousand kilometers of height. Several hundred thousand meters of height. Let's suppose we'll call this right here zero. Your initial radius that's the planet's surface. And you'll notice now I'm trying to generalize from the Earth. This could be the moon be Mars. I just have to change the numbers forever but the concept would be the same. And I want to end up way over here at our final. How much work will it take? How much fuel will I need to burn to get the energy to get that high? Joel the answer is this much here. This is compared to lift object from the surface R zero to a big height. Our final. Got a bit of a problem here though. All of the math that you've done in high school nothing has taught you to find the area of a curvy shape. Unless it's a circle and it's not. So we're going to have to cheat just a little bit here. I'm going to do some math that a math prof would kind of scream at me about but that's okay. It'll get us to the right place. Work equals force times distance. So we can say this then the work done against gravity is equal to the force of gravity times and we've been calling the distance the radius because we've been moving in circles. Now this work here because it's a change in height because we're lifting you up and up and up Brett I'm going to argue that it's really the potential energy. It's change in but Katie potential energy. Gravity is big G big M little M over R squared times R. Oh R is on top. One. How many on the bottom? R cancels. Here's what I get. Big G big M little M over R. On Earth potential energy equals MGH and the reason we can use that shortcut is because G doesn't change. The gravitational field is 9.8 and even on top of Mount Everest Breanna it's probably like 9.7999998 close enough. But as soon as you start really going cosmic distances except this isn't quite right. We have to add one more thing. We're going to add it to both of these. Negative and this one here negative and this leads to the obvious question. Connor what's the obvious question? Calculus students it's negative because if you take the derivative of this with respect to R you get the force equation and you get another negative appearing and you want the force equation to be positive. If you're bored Calculus students take DR, DT or whatever. Take the derivative with respect to R. It's R the negative one, the negative one moves to the front, the exponent moves down by one, you get an R the negative two. It's an R squared! Calculus students. Those of us that are in Calculus here's also why it's negative. Here's a physical explanation Brett what did you say earlier? What will the force be out at infinity? Zero. Which means I won't fall. If I can somehow go out to infinity I won't fall because there's no gravity on me. If I can't fall if I can't fall how much potential energy do I have if I can't fall? Think about it. If I can't fall how much potential energy do I have? Zero. Out at infinity you have no zero potential energy. Now here's the question. Do I have to get to infinity to do work? Do I have to burn some energy to get out to infinity? That means Zay that to get there I must have less energy because out there I used up all my energy. What numbers are less than zero? Negative. Let's read this out. It says out at infinity at the end of the universe an object would have zero potential energy since it's not being affected by any gravitational field. Can't fall anywhere. If our height is less than infinity we have less potential energy. What numbers are less than zero? Negative. This is the equation that's on your formula sheet underneath Fg then you'll see pe equals negative big g big m little m over r. I think it's the last equation in this unit so here is our trigger phrase. We often will use the phrase relative to zero at infinity that says use the cosmic potential energy equation with a negative in front. Or it'll just be very clear that we're in outer space. Example one. How much work is done in lifting a 1200 kilogram satellite from the surface of the surface to a height of 1.2 times 10 to the 7th meters. By the way this is where you want to get your calculators out. This is the question I think I mentioned this the other day where I don't bother trying to get stuff by itself. This is the question where you'll be doing the most calculator typing all year. Connor what does this question ask me to find? Now look up I'm going to start out wrong. Normally I would say this wrong. Why is this wrong? Because this assumes the force is never changing as you go further from the planet. What happens to the force of gravity? It changes. Can't use this. If they'd given me a graph and I could find the area I could use the area under a graph have they given me a graph? No. Let me remember what was our third definition of work? Yes it was force times distance, yes it was the area underneath the graph but there was a third definition. It was called the work energy theorem. We've got some change ins. Now read this question carefully. Does it say that we're putting the satellite in a stable orbit or does it say we're just lifting it up there and letting it sit there? I think the fact that it says lifting says we can imagine little visible angels or something they're lifting it up there and they're hanging on to it but it's standing still. You know what that means? It's not moving. It's not a stable orbit. If you let this thing go Katie it's going to come crashing back down to earth like a meteor. By the way we wouldn't. We would then also add some kinetic to put into a stable orbit that's going to be coming down later but I'm starting out with a simplified case. How much would it take just to get it to the right height? Katie what's changing anything? Oh don't let me down here. What's changing anything Katie? Nicole help her out and now look at Katie and just smile sadly. Katie what's changing anything? So when I want to find the change in potential can I use MGH or are we cosmic here? We're cosmic we're in outer space so can I use MGH? No no this is where I'm going to use the brand new equation for potential energy which is negative big G big M yeah I made a mistake for a second there little m over r final minus negative big G big M little m over r initial. Change in I'm assuming it's not the masses that are changing the planet's not changing oh it's the radius it's the distance that's changing. By the way what do you notice right here? I got a minus minus which is a plus just keep an eye out that will happen very often anytime you need to change in. Alright let's plug in our numbers here. Work is equal to negative 6.67 times 10 to the negative 11 Andrew that's the Newton's gravitational constant. Big M what planet are we talking about in this question? Earth? 5.98 times 10 to the 24th. You'll notice the little masses don't cancel here that's because although once you're up there it's easy to keep you up there to get you up there the heavier you are the more fuel we have to burn sticks around divided by what's my final radius? Did they give me the orbital radius in this question? Ah no they gave me the height. So I think my final radius is going to be 1.2 times 10 to the 7 plus the radius of the earth. Yes is that okay so far Emily? What's a minus minus the same as? 6.67 times 10 to the negative 11. 5.98 times 10 to the 24th. 1200 and my initial radius it says from the surface of the earth is just going to be 6.38 times 10 to the 6th. I do not try and type this in Matt in one fell swoop but this is where those of you that would have graphing calculators I'll show you a great trick. Those of you that don't if you're able to back edit that's also very useful here's what I'm going to do I'm going to type in the first expression very carefully 6.67 times 10 to the negative 11 times 5.98 times 10 to the 24th times 1200 divided by bracket 1.2 times 10 to the 7th plus 6.38 times 10 to the 6th. I'll double check to make sure I typed this incorrectly. Did I put the negative in? I'll put a negative in in front of my answer because it is negative. That first expression works out to 2.60413 times 10 to the 10th. I'll carry some extra sig figs negative Mr. Dewick 6.60413 times 10 to the 10th plus question here's where if you can bring back the previous line on your calculator on the graphing calculators at section function enter you can save yourself a lot of typing because is that the same in the second question? Yeah. Is that the same in the second question? Yeah. Is that the same in the second question? In fact you know what the only difference is I want to get rid of delete, delete, delete, delete delete that 1.2 times 10 to the 7th enter plus 7.50218 type 7.50218 times 10 to the 10th this is how many joules of energy is taking me to lift this satellite from the earth to orbit oh actually this is ignoring air resistance so this is the minimum amount of energy oh and I said into orbit actually I'm not in orbit yet I'm just lifted there and if I let it go it's going to come crashing back down to the earth minus 2.6043 413 Mr. Dewick times 10 to the 10th here's my final answer now I'll do sig figs 4.90 times 10 to the 10th that's a fair bit of energy that's not a real heavy satellite you can try typing this whole thing in in one fell swoop I never do Matt I always type in the first one write it down to like 5 or 6 sig figs and then almost always most numbers are the same anyways so I just delete and edit and change what I need to and there's my second one just be careful minus minus minus plus that was just lifting it up but Kara if you lifted it up and let it go it would fall back down number 2 says how much work is done now we're going to place it in orbit we're going to lift it up that's potential energy but then we're also going to give it just the right kinetic energy so that it can continuously fall towards the earth but at the same time match the curvature of the earth what's this question asking me to find how much what can I go force times distance no can I find the area under a graph it didn't give me one it's going to be that it's lifting it up and holding it there into an orbit oh so you know what I can't assume the kinetics going to be zero fact it can't be zero it's going to be also having some kinetic energy this question is going to have two parts find the change potential find the change in kinetic I like this question I like this question I like this question I like this question John what do you want to find first change potential or change in kinetic I don't care which change potential okay Katie what's changing can I just go MGH final minus MGH initial no because G is changing I have to use my cosmic potential energy equation let's see the change in potential is going to be negative Trevor what's big G 6.67 times 10 to the negative 11 yes that's big M it's mass of the planet and that's my way of saying I see your formula sheet tucked inside the inside cover if I see a little blue sheet there do I not that's not it I want to have it in front yeah there we go what's the mass of the earth okay what's little M Andrew that's the mass of the satellite minus did they give me my final orbital radius or did they give me my final altitude oh they give me the radius I don't need to add the radius of the earth that's nice minus minus which is a plus all right Mr. Duke Mr. Duke do you mind if we do this because the top is identical and we just use ditto marks yeah sure I probably wouldn't on a test but in your homework or on a quiz yeah sure because the only difference here is going to be the bottom oh what's my initial radius why that's the radius of the earth surface which you from your formula sheet is what I think you read that wrong radius of the earth is I don't think it's 6.13 that makes more sense by the way there's a reason I left you a whole page to do this question we're almost halfway done but not quite all right boys and girls try typing this into your calculator my suggestion is do the first one to five sig figs do the second one to five sig figs and then add them up see if you get what I got yeah yeah and I said we're barely halfway done because all we found is the change in potential but what do we say work was equal to at the very very top line change potential Katie plus what kinetic Katie what's changing anything now I've done so much writing by the way usually what I do at this stage is I put a box around this to remind well I need your box in that slightly neater to remind myself I'm going to be using this there's my change potential that's this part Katie now my change in kinetic which is going to be final minus initial on the earth before the rocket launches how fast are we going Mr. Duck yeah technically that's not right okay why technically is that not right are you guys moving right now yes you are really yeah why the earth is spinning okay so you could make and in fact what NASA has found out is the further south you launch closer to the equator you actually get a boost from the earth spin that's why Cape Canaver was built in Florida and not in New York that's why Russia's space program they have to burn way more fuel they don't get that boost because they're further north in fact the best place to build a space launching platform would be on the equator somewhere and they're looking at I've seen a couple of models of building a ship based one that would launch from the ocean on the equator and you could use then the spinning momentum of the earth as some extra kinetic energy boost but since that changes depending on what latitude we're on once again we're going to say in our idealized physics world it's a super standing still okay what is kinetic energy equal to a half little m v squared do I know little m the mass of the satellite yeah do I know v how fast we're traveling in orbit ooh why did I suddenly get my aha and almost caused Kara to wake up can anybody see the guy what is this question really asking me to find v how can I find the orbital speed I'll give you a hint you did it in the homework last day do this big g big m little m over r squared equals m v squared over r yes z mass cancels one of the r's cancels how to get rid of a squared hey wait wait hang on hang on wait a minute wait a minute wait a minute I just saw something Jacob what did I write here I'm going to actually say you know what I don't need v I need that don't I so why don't I just leave the v squared by itself and save myself some square rooting wouldn't that be clever v squared is big g big m over r yay we're halfway done almost the change in kinetic energy is going to be a half m big g big m over r there's a half m v squared by the way Sean that was me being very clever and very lazy to say wait a minute actually technically I don't need v I it's v squared that I want there's a v squared there why square root if I'm just going to square it again on my next line say let's be clever because now it's plug and chug ugly plug and chug lots of calculator work but plug and chug it's going to be a half 6.67 times 10 to the negative 11 massive the earth oh wait a minute I missed the little m didn't I be more careful come on I actually missed the little m first of all that one half suddenly became a little wonky let's try this again make that a two what was the mass of the satellite 975 925 big g big m all over a single solitary r what was the orbital radius 2.6 times 10 to the 7th what's my change in kinetic okay I'm going second function calculator a few times because I just realized I have big g big m little m and r typed in except with the negative in front of them so I can just go delete and then multiply this whole thing by point five so you can save yourself a lot of typing if you know how to use your calculator there's a half little m big g big m over r I get 70952 2500 so 7.0952 times 10 to the 1 2 3 4 5 6 7 8 9 7.0952 times 10 to the 9th 7.0952 times 10 to the 9th joules yo yo I did let's see I did instead of 6.38 good gosh Mr. Duke how much is that going to change things 5.7829 what did I say it was holy smokes 5.8725 this is going to change stuff going to point this out a little sooner there mr 5.7829 it's been going so well I told you though this is as much calculator work as you'll do for one question all year long so 4.3099 Brandon is that better you got a candy for catching the mistake meanwhile there's our change in potential only took us 1 2 3 4 5 lines there's our change in kinetic only took us 1 2 3 4 5 6 lines so none of this was what I wanted to find what was I asked to find Emily at the very very beginning oh the work which we said was change in potential plus change in kinetic change in potential 4.3099 times 10 to the 10th plus change in kinetic 7.0952 times 10 to the 9th alright here it is how much energy to put this satellite into a stable orbit 5.02 now I'll go to 3 sig figs times 10 to the 10th joules I guarantee this question is going to be on your test I'm going to say hey here's the orbital radius how much work you got to find the change in potential Katie was change in anything yeah very good then you got to find the change in kinetic Katie was change in anything oh if you find the change in kinetic you have to go fc equals fg conveniently there's a little shortcut there next page a missile is launched from the surface of the earth but this is a strange missile counter we're going to use all of its fuel on an initial burst and then shut off the engine and coast and we're going to ignore air resistance so that the only force is experiencing is gravity so here's my question as this missile rises what happens to its kinetic energy what happens to its orbital potential energy well what happens to its kinetic energy if you fire the engine then shut it off and you start coasting what's going to happen to your kinetic energy what's going to happen to your potential energy what's the correct answer see escape velocity escape velocity asks a simple question how much work do you need to do to get the potential energy to zero how much work do you need to do to get the potential energy your final potential energy to zero we can solve for escape velocity using conservation of energy conservation of energy said this ignoring heat if we want to escape the earth's gravity in such a mighty burst that we can shut our engine off and coast to the edge of the universe when we reach the edge of the universe what will our final potential energy be what did we say that our final potential energy was out at infinity and what we would like to do Kayla is reach infinity coasting but slowing down coasting but slowing down because gravity is still plugging at you we'd like to time it so well Matt that right when we get to infinity we come to a stop if we come to a stop what will our final kinetic energy be in fact the right hand side of this equation is going to be zero left hand side is going to be a half m v initial squared plus can I use mgh or are we going cosmic space in this question negative big g big m little m over r you know what Brianna since this is negative why don't I plus it over to the zero side and get a nicer equation I'll get this a half m v initial squared equals big g big m little m over r what turns out the escape velocity for a tiny rocket is the same as the escape velocity for the space shuttle and since I'm asking for the escape velocity why don't I get the v by itself how would I move this one half over well having a one half here the same as time zing by what over on this side two and then how do you get rid of a squared turns out the escape velocity needed if we ignore air resistance Caitlyn and on the earth we couldn't but certainly on the moon or most other planets we could because they don't have an atmosphere the escape velocity to leave those planets is equal to two big g big m over r sorry kind of a cool question kind of a neat question I mean one second I'm just trying to plan my attack here I think we're going to pause here I'll finish this part of the lesson next class but for now your homework number one number two number three number eight right now I've assigned one two three and eight nine and ten eleven we'll pause there