 Questions from the homework number six eight point five hours. I want to change that to seconds How do I go from hours to seconds? Well, it's eight point five times sixty minutes in one hour Times sixty seconds in one minute. That's my period. I'm gonna write that down up here t equals 37,000 Sorry uppercase t. Can you guys stop talking whoever that is? Thank you Appreciate that T equals what did I say it was thirty thousand six hundred Okay, what do you want me to find Brandon? So I'm gonna start out by going gravity equals circular Gravity is always going to be big g big m a little m over r squared And then don't write this next bit down circular is always going to be m ac But I need to figure out which ac I want to use So I'm going to erase that there are two one, which one do I want to use? Sorry This is the key to doing this question, which is why I'm asking so you probably want your formula sheet out I suggested you guys all have it out because we're going to be using a game today Mass of the earth mass of the moon, you know who wants to memorize all that so there are two equations Taylor How do you know I want to use that one and not the v squared over r period right, so I'm going to be using the Erase that erase that I'm going to be using the four pi squared r over t squared But just don't forget you got to put the mass in front Although conveniently brandon mass cancels come on pen Conveniently mass cancels What do they want me to find? I move both of these to the top. I'll have three of them there That will move there those will move down. I'll get this r cubed equals big Come on pen big g big m t squared All over four squared Sorry Yeah, it feels like I'm running out of ink. Is that okay? How do you rid of a cubed? So here's the answer it's going to be that now we just got to type it into our calculator correctly Where g big g is 6.67 times 10 to negative 11 m is are we on the earth? Yes The mass of the planet. So by the way, could I have you orbiting the moon? Yes Could I give you the mass of let's say mars and orbit that just to be different? Yes Uh period is 30 000. So let's see. I'm running out of room to write brandon. So I'm just going to go straight to my calculator Sorry You're fine from here. Okay number nine Brandon you got to written down because I got to erase this because I need to do number nine right here too. Okay. Good. Good. Good. Good. Good. Good. Good. Okay Okay, I am running out of ink. It seems There we go Who asked number nine? Okay, astronaut sally stands on a bathroom scale when in orbit Are they floating in orbit? What did we say at the beginning of class? What? Sorry? Okay, free fall. What is a scale read? It doesn't read weight Doesn't read mass Jacob, what is a scale read? Normal force it can't possibly read your weight or your mass because I did a demo at the beginning of the year showing that Even though your weight and mass weren't changing the scale was changing. So here's the real question What's the normal force when you're in orbit? You can prove it by going winner minus loser. We would have oh mg down normal force up And you would say well, this is going to be mg minus normal force because he's in free fall equals m Except the acceleration in free fall is also g and you're going to find in that equation there for that to be true Normal force does have to be zero or you could have gone like this And noticed that normal force is zero in orbit But what you really had to remember it was a good review is what does the scale measure doesn't measure mass So we're in outer space. Let's suppose and let's suppose we have uh Alyssa and Jacob in the space shuttle And Alyssa you have a 1000 kilogram satellite big satellite and you and Jacob are both in the cargo hold It's shut. So there's air But you gently push the satellite across the cargo hold you give it a shove and you let it go And it majestically glides across the cargo hold because it's in free fall And Jacob decides that rather than stop this 1000 kilogram satellite with his hands He's going to stop it with his face because he thinks to himself. Well, it has no weight. So it won't hurt Is that correct? It's still going to break his nose because the mass hasn't vanished and newton's first law talked about inertia It still has inertia It still is going to require a force to bring it to a stop So it would be easy to keep it moving And you could apply a very small force to get it moving as opposed to here on earth Where with friction you'd have to really really push the thing 1000 kilograms. That's a fair chunk But to bring it to a stop you'd have to give yourself plenty of time to be able to slowly slowly slowly Apply a force to bring it to a stop right 10 is that what somebody asked? okay I sort of like this question Not this specific question, but this key concept of gravitational field That's going to be on your test Because this is not talking. This is not talking about gravitational force This is talking about gravitational field and what you need to realize is gravitational field symbol lowercase g is calculated by going big g big m over r squared Where'd that come from we did it in the lesson It comes from the idea that if big g big m little m over r squared also equals m g And if we cancel out both masses We're ending up with gravitational field is big g big m over r squared. That's how we calculate it We know the answer on earth. What's the gravitational field strength on earth? 9.8. What it's saying is if it's 8.75 how higher? Oh, sorry, uh, how fast are you moving? Well, I can use this to figure out how high I am r is going to be the square root of big g big m over g And once I know what my radius is then I can go f g equals f c I can go big g big m little m over r squared Equals m v squared over r using v squared because they want to find the orbital speed Hey, one of my rs cancels Mass cancels. Yay, and I can tell you uh once I square root how fast the space station must be moving I'm I don't really have enough room. I guess I can do it right here. Do I'm gonna do it? I can do it if you want Sure Okay, let's are you okay with this little line of reasoning here and the key idea is and the part I do like is Giving you the gravitational field somewhere in space and asking you to do something with it Because the most common mistake aired is kids right away put I think This is the force. It's not newtons. It's newtons per kilogram So let's see What orbital radius does the space station orbit at if it has a gravitational field strength of 8.75? Now that doesn't mean that they feel that Because they're in free fall But it does mean that if you wanted to measure it That's what it's going to calculate it. Let's see Uh, no, I want r mr. Doock Their orbital radius is going to be the square root of 6.67 times 10 to the negative 11 5.98 times 10 to the 24th All over compare it with the earth's of 9.8. No not 9.8 mr. Doock That's just going to give me the radius of the earth. Come on I want to use 8.75 Crumps the numbers Really what the problem is is I have way too many programs open at once here There let's try that. Come on computer 6.67 Scientific notation button negative 11 times 5.98 Scientific notation button 24 divided by 8.75 Square root So that's the orbital radius. That's not its altitude. That's its distance from the center of the earth If I wanted its altitude, I would subtract whatever the radius of the earth is 6.75 times 10 to the 1 2 3 4 5 6 Now I'd like to find its speed So I would say gravity equals circular Gravity equals circular with the v in it and I think I'll end up with v being the square root of Big g big m over r Which is going to be oh, you know what I noticed right here two lines ago I have big g times big m divided by something. I'm going to go like this And instead of 8.75, what do I want to divide by in this question here? There that's going to save me some time and square root that Speed should be 7 6 86. Is that what it says? I hope there you go By the way international space station not very high Most of our orbital stuff not very high anymore Yuck yuck yuck yuck yuck you got you notice the 80 blah, right So first thing I would do is go 80 divided by 3.6 22.22 meters per second 22.22 meters per second Okay, erin what path is this car tracing out? Where is my net force then towards the what force is pushing it in the center? Gravity straight down Uh, that's why we can't turn on ice So the key idea here is to recognize friction equals fc And I'm going to use mv squared over r because they told me it's speed Friction is what times what? Mu times the normal force. I don't know the normal force It's going to be mu times gravity because this looks like a flat curve So far so good conveniently yay That cancels and they want me to find the radius So I would have gone. Okay r equals V squared over mu g do I know v 22.22 Do I know g? Yep, oh What don't I know? What information haven't I used anything of yet? That whole beginning of the track like why the heck did they give me that I haven't used it yet Oh, um Hey, when the car is accelerating What force is pushing it forwards? friction Do you think maybe I might be able to solve for what coefficient of friction that I need based on the information that they gave me here? Oh, cool. Let's see. Let's see. So, uh, the car is accelerating forwards. It's really Friction that's pushing the car forwards friction is what times what? I don't know the normal force. Oh, but you know what we're on a flat ground I'm pretty sure the normal force is mg. I think we really have this mu mg is equal to m A and conveniently erin the masses cancel and I get this Mu equals the acceleration divided by g now. I know g That's good um Oh What acceleration look what they told me Look what they've told me they've told me that vi is zero see it And v final Is 120 no not 120 22.22 22 22 222 And they told me the distance is 120 Could I figure out what a has to be? So this is a nice question. I I'm not going to say I like this question I like this question in in that I think to me this would be a little bit tricky for the test, but Look at this unit one unit two Unit five. Ooh, that's that that's not bad at all You see we're going now by the way see and you could find the acceleration once you get mu Plug mu into there and it's going to be b squared. Yeah, you'll use vi squared equals vi squared plus 280. Yep, and you should get 240 Someone was saying to me by the way on some of these questions on the geosynchronous one If you use a different period of the earth or something like that you get slightly different answers Who was asking me about that? Okay, um, I'd probably take both on a test then so The earth is 24 hours times 60 minutes times 60 seconds 86,400 what does it say on the sheet? 86 one earth is 24. We we we determined that time The days of the year we're stuck with not being equal, but the earth I'm pretty sure is exactly 24 hours. I thought Yeah, like we we divided the length of one day into 24 chunks one earth rotation Hmm We'll come back to that I I'm gonna do some emailing and googling and find out if that's a typo or not or what the deal is with that Is that it says the earth's period of rotation. Is that what it says on the sheet? 8.61 Okay, I will take both for now, but Let's move on This seems to be Where kids start to get stuff mixed up a little bit. So Turn your brains on lesson six orbital potential energy Lesson six so last day Lesson five we looked at orbits Being up in space Today, we're going to be looking at orbital potential energy Getting up into space. So last day was once you're there. How does it work? How high do you have to be? How fast do you have to be traveling? How long does it have to take you to go around? What we're going to be looking at today is Getting yourself up there and this is where you're going to start to see some really big numbers This is where you're going to start to see why it's so expensive to get stuff there keeping stuff in outer space cheap Basically, it stays up there long as you want to now Probably some of the lower satellites aren't completely out of the earth's atmosphere because the earth's atmosphere doesn't just stop It goes for quite a while, but it's so thin there. They're almost near zero But there's probably a tiny bit of friction tailor. They probably have to occasionally accelerate to keep themselves going but getting up there big bucks Okay, by the way, what was the equation for potential energy? Do you guys remember? Now this is what we've been doing so far. Don't write this down The problem is g is only 9.8 where? On the earth's surface. We're going to have to derive a cosmic potential energy equation So let's do it recall The area under a force versus distance graph. So if we have a force versus distance graph And we'll draw a nice line kind of like that. What was this area here? Do you remember? Okay, now I'm going to be a bit fussier Erwin said work I'm going to be a bit fussier It was if I call this location a and I call this location b it's the work required To move from a To b because we want to talk about how much work is required to move from the earth's surface to an orbit the problem is For a graph of gravitational force Fg Versus separation distance r What would that look like? Well put your pencils down for a second math 12s Don't write all this down. I'm just going to show you a quick argument here As it turns out gravity is proportional to 1 over r squared math 12s Really that's similar in terms of a graph To the reciprocal of a parabola And so for those of you that are math 12 you've done the reciprocal transformation Bigger becomes smaller smaller becomes bigger zeros become asymptotes asymptotes become zeros the reciprocal of a parabola It looks an awful lot like this Never quite gets to zero and shoots off to infinity over here And this is where the system kind of breaks down because you're saying oh does that mean there's an infinite gravitational field at the center of the earth No, it Don't work. It looks like this though That's what the gravitational field force graph looks like now that this makes sense as you move further away from the planet What happens to the force of gravity gets bigger or gets smaller gets smaller Okay, does it ever truly reach zero? Well, no, you could argue at the edge of the universe for all intents and purposes It is calculus students. Yes, it's a limit But you can see we're getting closer and closer and closer to zero but never quite touching So let's consider a specific example Once again, we're going to draw fg and r Here's our little curvy graph But we're going to add a specific location right about Here and we're going to call this point right here The radius of the earth and we're going to add another location. How about Right here I'm going to call this point right here Our orbit how much energy will it require for us to move from the surface of the earth To just lift an object in orbit now. We're only talking about potential energy here Once you're in orbit if you want to stay there. Can you stand still? No, what do we have to do? We said we have to give you a sideways velocity that matches the curvature of the earth So you also need some kinetic energy all we're looking at right now Evan is just lifting it up to you know, however many hundred miles But if you let it go it will fall because it's not an orbit We haven't given it a sideways velocity, but how much work would it take? this much This area Is How much work read how much energy to lift surface But i'm going to put brackets standing still so How are you staying up there? We'll just kind of imagine little bit more angels are holding you or something like that Because as soon as as soon as in other words, we're going to freeze time negan, right? We've done this a lot We're going to freeze time as soon as time actually did start this thing would come crashing back down Oh, unless we give it enough sideways kinetic energy and you're going to start to see why again It's so expensive to put stuff in orbit not only are the potential energy numbers huge But then Did we calculate orbital speed last day? So think a half m v squared of those things and they were big numbers You have to get that much potential Or sorry kinetic energy as well to keep it up there That's all got to come from the fuel cells from the rockets from the reactor and whatever you're powering your object It's all got to come from somewhere This energy is concerned Yep, oh, they've talked about the space elevator Um theoretically we could build one that'd be a cheaper way to put stuff in orbit because you could do it using electric currents And you'd already have something up there and probably in a couple of days I might go up on the tangent and talk about it But for now in terms of our current level of technology because we are finding it is useful to have stuff up there It's rockets. It's rockets It is rocket science Um, they're not hugely inefficient. Otherwise we wouldn't have done so many It's it's more that They're dangerous. They're risky stuff goes wrong fairly often It's much harder than you realize. It would be nice to have a simple reliable Again, we built six space shuttles two of them exploded. That's not a great That's a 33% failure rate From nasa the best in the planet Not really that good. It's got to be a better way Here's our problem Zach We don't have an equation for finding the area under a curve Calculus was invented to do that and those who are in calculus when you start doing something called integration You'll learn shortcuts for doing it, but right now we're gonna have to cheat So Work equals force times distance work equals which force big g big m little m over r squared times The distance that we're moving it from the center of the earth is r This is sort of a fake work times distance equation Technically, I can't do this mathematically because this force is changing to really derive this equation I would love to be able to integrate it and show you where it comes from in calculus. I can't here is our Cosmic potential energy equation big g big m little m All over r because can you see one of the r's cancels? Unfortunately, what does that look an awful lot like force don't get them mixed up What's the difference r squared versus r? Oh Wait a minute one more thing. Look at your formula sheet find gravitation find potential energy and you notice we're not quite right Negative negative Why negative? Suppose we went to the edge of the universe And the phrase that we use is relative to zero at infinity. Suppose we went out to infinity If you were far away from any planet If we let you go would you fall anymore? No, so if you won't fall how much potential energy do you have? Zero none as a number zero So if you're not at the edge of the universe You must have less potential energy because we'd have to do work to get you to the edge of the universe What's the number that's less than none? Negative okay as soon as we start talking about potential energy on the cosmic scale We refer everything relative to zero at infinity out of infinity. You have no potential energy So that must mean you have less than that negative Who's my calculus students? Okay, it's negative because if you take the derivative of this with respect to r you need to get the gravitational equation And you need a negative to cancel Take the derivative of that with respect to r and you'll get f equals big g big m little m over r squared okay So What numbers are less than zero potential energy? Negative numbers now Don't worry. You'll get positive answers because often we'll be doing Change in and what's change in anything? Final minus initial and that minus initial because it's going to be a minus minus is often going to give you a positive answer So don't freak out just be really careful with your signs So we use the phrase Relative to zero at infinity Example one then how much work is done in lifting A 1200 kilogram satellite from the surface of the earth to a height Of 1.2 times 10 to the seventh meters So what we're talking about here is Come on Come on Uh circle Geez Not cooperating with me right now Okay, we're gonna try this mr. Dewick Is that roughly circular? A little bit further this way mr. D Okay, there's the earth They've told us the height H is 1.2 times 10 to the seventh But remember in our equations, we don't use h we use r for radius And that's going to be the distance from the center of the earth So what am I going to have to do to this number? I'm going to have to add The radius of the earth r e let's try that again mr. D The radius of the earth So let's make a little note here then the orbital radius is going to be 1.2 times 10 to the seventh Plus what was the radius of the earth six point something? Six point three eight times 10 to the What is my orbital radius? I always if they say height or altitude I always take care of that first because I'm worried I'll forget later on 1.838 times 10 to the seventh and I'll carry the extra sig figs because I'm going to be using this answer So my orbital radius is 1.838 Times 10 to the seventh meters you guys see why we had to add the radius of the earth to this one because instead of saying Radius they said height All right Kyle what's this question want me to find? What's this question want me to find kyle now that you're back with me? How much work Now We have a bunch of definitions for work. We have work is force times distance. We can't use that Because the force changes the higher you go gravity changes We could use area under a curve except we can't find the area under a curve So we're going to have to use our third one which is work is equal to the change in potential Plus the change in kinetic So here's our satellite on the earth's surface. What's its kinetic energy right now? Zero and when I lift it up and just leave it hanging there. What's its kinetic energy at the end? Zero so I'm going to cross this out But I'm always going to remind myself that that's there because as soon as they start saying Oh and put it in orbit well then there's going to be some kinetic energy to move What's changing anything? So work is equal to Potential energy final Minus potential energy initial and in unit three we would have gone mgh final minus mgh initial But now we have to use cosmic potential energy because we're talking about big distances and we're getting away from the planet Work is going to be equal to What was potential energy on the cosmic scale negative big g big m little m all over our final Minus negative big g big m little m all over our initial This thing right there. Oh, but final minus initial. It's the radius that's changing Do the masses cancel this time? No because there's no mass in work Which makes sense because a heavier object should be more expensive to lift into orbit In fact now it's straight plug-and-chug and this is one of the few times I do not try and do this all in one step. I'm going to get this number I'm going to get this number and then I'm going to Well, wait a minute. What's the minus minus the same as? Okay, the work is going to be Negative 6.67 times 10 to the negative 11 5.98 times 10 to the 24th What was the mass of the satellite? What did I say a thousand? 1200 all over My final radius is 1.838 times 10 to the seventh Or when I have a minus minus I'm just going to do a plus 6.67 times 10 to the negative 11 5.98 times 10 to the 24 1200 All divided by What's my initial radius? Oh radius of the earth. Good. I'm starting off on the earth's surface. Oh, except instead of writing re What is it everyone six point? 6.38 times 10 to the sixth who has the good graphing calculators Here's the nice thing here's how I handle these the other reason I type this all in at once is can you see only one number Is different before and after which means if I go second function enter I can have the second thing appear and just change the bottom number first number first term It's going to go like this negative 6.67 Scientific notation button negative 11 times 5.98 Scientific notation button 24 times 1200 divided by 1.838 scientific notation button 7 And I get negative 2.604 times 10 to the 10th plus And the nice thing here Erwin is if I go second function enter I need to delete the negative which I can do pretty quickly Well, and I change the bottom number to 6.38 Times 10 6.38 Times 10 to the sixth. I think that's a way easier way to do this. You make sure you're very careful on your first one And I get 7.502 times 10 to the 10. Is that right? That's what that times 10 to the 10th means Okay The block for you Put it face down and block D for me today And my final answer is that I'm going to do this number which I already have stored conveniently minus because that's a negative minus 2.604 Times 10 to the 10th How much energy now you'll notice I get a positive answer Which I should because it does take work to move it up there. It should require energy 4.89 in fact, you know what to 2 sig figs 4.90 isn't it? Times 10 to the 10th Units for work jewels Is that a fair number of jewels? Yeah It's expensive. Uh, it would depend but uh do do some googling you'll find out. I there is a site I used to know it roughly. It was how much per meter it cost It was how much per meter per kilogram I think or something like that because of course the bigger the mass the more expensive it is too Okay Now that's just lifting it up and then having invisible angels holding it there That's not what happens in real life. We lift it up and then once we're up there We give it a tangent velocity. We give it some kinetic energy now Technically, you don't lift it up and then head straight sideways. You go up and kind of a curvy For kind of a sort of a Per parabolic trajectory, but not quite but it's kind of a curvy shape But you know what since energy is a scalar Who cares what path you trace out all we want to know is before and after this is like those roller coaster questions Where we didn't care about what was happening with the hills We just want to know how high at the beginning how high at the end here We want to know how high at the end how fast at the end example two How much work is done placing a 925 kilogram? satellite I forgot the word satellite. Whoops In orbit, I am going to underline the word In orbit that means it's not standing still in other words, we have this Work equals I like this question. I like this question. I like this question. I like this question work equals change in potential plus Change in kinetic It has kinetic energy too. What's changing anything? What's changing anything? I'm going to treat these separately Let's do the change in kinetic first A half mv in orbit squared minus a half mv initial. Oh, wait a minute Before we launch how fast are we traveling? But that velocity is orbital velocity How do I find that we did it last lesson? How did we find orbital velocity or orbital speed? Ah, this is where we said gravity equals circular Big g big m little m all over r squared equals m Which circular am I going to use v squared over r or 4 pi squared r over t squared? First one because they're talking about velocity Brandon Don't need to be whistling But Brandon you will notice The only is a mass cancel One of my r's cancels And you know what what do I have by itself here? v squared now normally I'd square root except what do I have kind of right here v squared Why don't I just leave it as v squared save myself some unks In fact, I get this When we're talking about putting something in orbit The change in kinetic is equal to one half little m What's v squared the same as big g big m over r? I don't really memorize that one As I've said to you I fall back to here and I can figure out whatever I need to figure out This is going to be A half little satellite 6.67 times 10 to the negative 11 5.98 times 10 to the 24th All divided by Oh, and they didn't give me a height or an altitude. They gave me the radius I don't need to worry about adding in the earth's radius all divided by 2.6 Times 10 to the 7th How much kinetic energy will my satellite have to have once it's up there? Otherwise it's falling back down to the earth 0.5 times 9 25 times 6.67 negative 11 Times 5.98 24 divided by 2.6 to the 7th See if you get that Can you put it block the face down on top? 7.1 Times 10 to the 1 2 3 4 5 6 7 8 9 That's how much kinetic energy Our fuel has to supply We haven't even looked at getting it up there. We haven't even looked at the potential energy Sorry, did I say block B block H right you put it in the right block? Yeah, sorry So there's the change in kinetic That's that and megan you're okay why we use that because they said orbital radius which is the I like that better But sometimes they'll give you an altitude or a height like the last question So I want to make sure you notice sometimes you got to add the radius of the earth this one though We didn't have to you. That's the change in kinetic What else I need to find melanie Change the potential what's changing anything Okay, so I'm going to go now Change in potential Which is potential final minus potential initial and I wish I could go mgh mgh But we're talking the cosmic equation. So sadly I've got to go negative big g m m Over our final minus negative big g big m little m all over our Initial Brandon. Do I have a minus minus not be a plus on the next line? Let's start plugging in numbers negative Big g 6.67 times 10 to the negative 11 Big m mass of the earth 5.98 times 10 to the 24th little m 925 all over 2.6 times 10 to the 7th minus No, plus mr. Do it. You got a minus minus which is a plus 6.67 times 10 to the negative 11 5.98 times 10 to the 24th 925 all over What's our initial? Oh ready to the earth uh 6.38 Times 10 to the 6th the change in potential energy is equal to Did I go on a big rant about how it's important to practice with your calculator? You guys getting the hint These are these are pretty lengthy expressions. This is as long as it'll get There'll be a couple that else later on in the year that are this long but nothing much bigger than this negative 6.67 negative 11 times 5.98 Times 10 to the 24th times 925 divided by divided by 2.6 times 10 to the 7th negative 1.419 times 10 to the 10th plus Second function enter or backspace if you got a scientific one lose the negative 6.38 Times 10 to the sixth 5.783 times 10 to the 10th take away 1.419 times 10 to the 10th oh 4.364 times 4 point 364 Times 10 to the 10th Joules that's how much energy it's going to take to get it up there kinetic energy is less but depends on the height that you're at The lower you are the faster you have to be going so the less potential and the more kinetic There is an equilibrium point somewhere. I don't know what it is figured out if I was bored I guess We're not done This question wanted us to find The work Darn right Taylor says we're going to add them absolutely 7.1 Times 10 to the 9th plus 4.364 times 10 to the 10th Thankfully, I got that number in my calculator still plus 7.1 Times 10 to the 9th equals 5.07 times 10 to the 10th joules So what is that five one two three four five six seven eight nine 10 50 billion 700 million joules of energy and I got to be honest a 925 kilogram satellite That's a pretty small one But doable and still profitable Oh, yes, we can go Chuck Norris joke if we want to but in terms of in terms of the technology Very nice back to reality though in terms of the technology despite the fact that's a lot of fuel Companies are doing that and making a profit It's certainly far cheaper to do that with our telecommunications Then to lay the cables across the oceans like we used to we used to lay dozens of cables along the bottom of the ocean And they had to be maintained and replaced and you know bottom The ocean is not exactly a hospitable place And then they would get snagged on other cables or snagged on trawlers or whatever yo Hustle back, please So let's do some conceptual stuff And then we'll talk about Then we'll talk about how you calculate escape velocity. You may have heard the term So A missile is launched from the surface of the earth Its fuel is used in an initial burst. So they fire all their fuel for like 60 seconds And then they turn off the engines so that as it rises the only force that experiences is gravity We're going to ignore air resistance. Who's really realistic? Well, it would be on the moon As it rises what happens to the kinetic energy and the orbital potential energy? Let's see As it rises. So we fire the engines. Let's say for 60 seconds and then we shut them off As it rises what happens to its kinetic energy? Well really what it's asking is what happens to its speed Okay, it's gonna Gravity is constantly pulling it down slowing it down It's going to slow down down down down down down down down down down in fact eventually it's going to reach its maximum height It's perihedron perihelium. I can't remember what the word fancy. There's a fancy trajectory word for it It's going to reach its maximum height, but until then it's slowing down until then It's decreasing its kinetic energy Now what about its orbital potential energy? As it gets further and further away from the earth what happens to its orbital potential energy? Well there It's increasing because the higher it gets The more energy it'll have when it falls back down to the earth And this is the idea that we're going to use for escape velocity. Here's we're going to ask ourselves Let's suppose instead of firing the jets for 60 seconds We're not going to fire them for 30 seconds. We're not going to fire them for one second or a tenth of a second Zach, let's suppose we fire the jets just for a split instant Boom so that we're at max speed instantly How fast would we need to be going if we ignore air resistance? To get away from the earth and get to the edge of the universe. That's what we call escape velocity Except because we said the edge of the universe has a potential energy of zero What it's really asking is how much work is necessary to bring potential energy to zero We can solve for an escape velocity by using conservation of energy. We can say this kinetic energy initial Plus potential energy initial equals kinetic energy final plus Potential energy final good old conservation of energy Where initial is on the earth surface And final is at the very very edge of the universe If you're at the very very edge of the universe, how much potential energy do you have? Okay, so i'm going to say equals zero because we're at the edge of the universe And if we want to do this as efficiently as possible So we're coasting we're coasting we're coasting when we get to the edge of the universe How fast would we like to be traveling if we've done the math just right? We would like to come to a stop at the edge of the universe If we do the math just right, that's what we want. In fact, if we do the math just right Here's really what we're saying The amount of kinetic energy that we need our engines is equal to negative The amount of potential energy on the earth The amount of kinetic energy that we need to impart to our engines that we need to impart to our spacecraft Initially is going to be negative The amount of potential energy What was kinetic energy what was the equation? A half m we're on outer space from the earth's surface now so we can take the shortcut Yes, it is a half big g big. We got the shortcut here half m b squared And potential energy was negative big g big m little m all over R Oh, are you saying there's another negative because it's already negative. Are you saying the two negatives would cancel? Yes, they would We'd get a minus minus was a plus and not only would the negatives cancel. What else would cancel? It turns out it doesn't matter how much mass you have your escape velocity is the same Now the more mass the more kinetic energy the more fuel you have to burn to get to that escape velocity But once you're there, it doesn't matter how big you are Let's get the v by itself. How would I get the v by itself? First of all, I'd move the one half over how I think times by two is the nicer nicer. Yes, it's divide by point five times by two and then how are they get rid of a squared We have this That's the escape velocity of any planet The moons is fairly small If you watch the old Apollo moon missions, you'll see on the very very last one They had a remote control camera and because there's a six second delay between the camera signal Getting to the earth and sending the signal back to the moon What the guy on the camera had to do when they were counting down to leave the moon is on six He started to pan the camera up and he was hoping that by the time the signal would get there He was panning up at just the right time for the Apollo moon Module to launch from the moon and the first two times they screwed it up on the very last one If you google you'll find a youtube image of them able to follow it up just wonderfully And it's fairly any escape velocity. It looks like they're just basically above the propeller plane Doesn't look like they're going fast at all. Well Does the moon have a big mass or a small mass? Smaller compared to the earth and what's its radius compared to the earth bigger or smaller smaller in fact Let's calculate the escape velocity for the earth and for the moon escape velocity we said was equal to two big g big m over r So the escape velocity for the earth is going to be two six point six seven times ten to the negative eleven five point nine eight times ten to the twenty fourth All over six point three eight times ten to the sixth and then square root that puppy If we ignore air resistance how fast you have to be traveling On the earth's surface to lift off and reach the edge of the universe to get away from the earth's Gravitational field to break out of the earth's pole square root One point one two Times ten to the fourth. Is that right? I got eleven thousand one hundred and eighty one so one point one two Times ten to the fourth meters per second What about on the moon? Well the mass and the Radius are going to be different. I don't have those ones memorized. You'll have to give them to me from the sheet What are they? two Six point six seven times ten to the negative eleven. What's the mass of the moon? Ten to the what sorry 22 And what's the radius of the moon dam? Now I'm going to be kind of lazy and go second function enter a second function enter And let's see if I can just change these numbers to seven point three five times ten to the 22 and one point seven four times ten to the Sixth square root of that considerably slower smaller two point three Seven times ten to the third And as well the moon doesn't have no atmosphere so the whole ignoring air resistance there is mathematically valid here Clearly not Well, this would be if you wanted to fire it all at once. Okay What they really do of course is they leave the engines burning for quite some time And in fact the most efficient way they played around with two stage three stage four stage Most efficient way is the three stage rocket Where you because most of the fuel is burned for the first chunk when you're done with that You don't need those big engines anymore. They're dead weight And in terms of potential energy, you know if the masses don't cancel so then you Toss those you burn another set of smaller engines burn some more fuel And it's the third stage then you've gotten rid of I think it's 90 percent of your mass And you've achieved 90 percent of your velocity So you're in a much better shape the three stage rocket is the way to do it That's why they did it for the moon landings and the space shuttle is somewhat similar has the booster rockets And then the space shuttle's main engines burn the tank still and then the tank itself falls off And then the shuttle is using its onboard fuel and its main engines. So it's similar Last one for me Like a one. Yeah, I had to transformers one when I was a kid Hello, we're back. I know it's been a long lesson, but key concepts here last one A 3400 kilogram mass is so here what we're talking about This is the physics or the maths the math of an asteroid hitting us except rather than an asteroid I'm going to have a satellite something's gone wrong I'm keeping the math simple. I'm ignoring any kinetic energy that it has So let's suppose somehow invisible angels brought a satellite to the to a stop And then let it go To the fall to the earth How fast will be going when it hits the ground? If we ignore air resistance and all that stuff Uh Mass will matter because we're talking. Oh, sorry for the speed. No for the energy. Yes So we're falling we're dropping something. This is going to be the same as when we drop an object here on earth. It's going to be Potential energy initial plus kinetic energy initial equals potential energy final plus kinetic energy final Since it says released We're going to assume that our initial speed was zero Will its initial potential energy be zero? No What about its final? Well, we're not using mgh anymore. We're using the cosmic one It would only be zero if it fell to the center of the earth It's not going to be doing that Well, it's final kinetic energy be zero. No, it's going to be hauling In fact, we're going to get this Negative big g big m little m all over our initial Equals negative big g big m little m all over our earth because that's the final radius plus a half mv Final squared dan was right the little masses cancel. That's kind of nice And I think I would do this first of all I'll move this over by plusing it And I don't like this one half. How can I get rid of this one half? Okay, I'm going to go times by two times by two times by two they'll cancel right there But that gives me a nicer expression. In fact, I think I get this v final squared is equal to negative two big g big m all over our initial Plus two big g big m all over our Final, which is our earth Or the plus come from this was a minus and I plused it over so it became a plus Or the twos come from I didn't like the one half over there Oh, and how do they get rid of a squared? squared So it would be two times Mass of the earth Times now the initial radius it does say above So the initial radius is going to be 6,300 Plus 6.38 times 10 to the sixth meters might be Yeah, you are probably I should have made this a much bigger number. I think so. Yeah, I think you're right 6,300 meters. That's not even a very high mountain. It means above the earth's surface Really, I should have added a couple of zeros here. I think I think what I was thinking initially was kilometers, but that's okay Pardon me 6,300 They measure from sea level. Yeah, depending on how you want to call it Mount Everest is not the highest mountain on earth It's not the closest mountain to the stars Because the earth bulges at the equator There's a mountain in Ecuador because the earth bulges out at the equator that is technically Further away from the center of the earth when you measure. It's very very tip. It's closer to the stars But they measure them from sea level Folks this class lesson's gone on quite a bit and the tone's going to go I'm going to pause. I'm going to give you a couple of questions to try though one two three By the way in the homework rather than writing relative to zero at infinity He uses the abbreviation r t z e i but that's relative to zero at infinity. In other words He's saying use the cosmic potential energy Seven And I'm going to be assigning more from this lesson I'm going to probably next class temporarily press pause Okay, if you haven't handed in last lesson, please do Tone's going to go in about 15 seconds or well 45 seconds