 Okay, well let's go with lesson seven since there was no questions from the homework Orbital mechanics and what we're going to do is basically try and crystallize The last two lessons that looked at orbits and energy in orbits So example one a mass little M To have how about a rocket ship is moved from the surface of a planet To a distance big R from the center of the planet Which of the following is true about the work done a the work is given by Fg times R The work is given by fg times big R minus R The work is given by that the work is given by that or the work is given by that and it says explain your answer Well, let's see if we can derive what the answer is supposed to be Now way back when in physics 11 and the beginning in physics 12 we said this Which if I had a writing utensil in my hand, I might be tempted to scribe down problem is We can't use this here because Fg is changing This only works for a constant force Now the second definition of work that I gave you Jacob was the area under a force versus distance graph See if thou a graph here anywhere then What was the third definition well the third definition was We called this the work energy theorem It said look if you want to know how much work you've done on an object Figure out how much potential energy is gained or lost and how much kinetic energy is gained or lost And that's how much work you did If we ignore friction and we outer space I think yeah, so Let's assume looking at this picture that we're starting from rest and if We're lifted to here. It doesn't look like the rocket ship is pointed sideways as though it was in some kind of orbit I think I can assume that the change in kinetic is zero What's changing anything Nicole so the change in potential is going to be Potential energy final minus potential energy initial Can I use mgh for potential energy? Why not? G's changing we're cosmic here, so I got to use that ugly expression for potential energy, which was Negative big G big M little M over and the final would be our final which they've symbolized Mitsui with a capital R minus Because change anything is final minus initial and then I think Emily initial would be negative big G big M little M all over and I think the initial radius was given by a lowercase R Mitch I do notice a minus minus here, which is a what yeah negative big G big M little M over R big R plus There we derived it says explain your answer There's my explanation I Derived it. I don't memorize this Brett. I do I I do know that when we're talking cosmic This is true, and I decide if I'm an orbit then I have kinetic energy But if I'm just being lifted up, which is what this diagram looks like then I have no kinetic energy And I derive it from there Too much to memorize and keep straight To escape from a planet's gravity means in theory to travel in infinite distance from the planet Realistically in real life Emily it means to travel far enough away from the planet that the pull of gravity has become barely very small near zero We can't get to infinity to barely escape Means to escape from a planet with no extra kinetic energy left at the end so you end up at rest and at an infinite Distance we called this escape velocity. We looked at it actually last lesson Of course, you can also reach infinity and still be moving Which means you've gone faster than escape velocity You had enough to leave the planet and you had some left over Example to a 12,500 kilogram rocket blasts off from the earth and barely escapes the earth gravity with no additional engine use So it fires its engines once and shuts them off and coasts the rest of the way and again John we're going to ignore air resistance in our magic physics world where we have nice numbers and all that stuff How fast was the rocket moving at lunch? This question mentioned work at all. No, what's it want us to find Jacob? Are we in orbit? So I'm not gonna write this don't write this down Joel Don't need to tell me to write not not write something down. That's a given. Okay. Um, Don't write that. That's if we were in orbit Right fg equals fc and they haven't mentioned work have they Then here's my third approach. I'm gonna solve this one saying you know what we must have had some kinetic energy at the beginning And some potential energy at the beginning and we must have some Potential energy at the end and some kinetic energy at the end but Conor if we barely escape earth's gravity What can you tell me about my final speed if we barely escape? What did that imply? Oh? And how did we define? Potential energy out of infinity. We said how much gravitational potential energy do you have we get this a Half m the initial squared Minus or sorry plus negative big g big m little m all over our initial Equals zero This is how we derive to the escape velocity equation. It's good review Remember then Emily we said you know what let's take this negative and since there's a zero over there Why not plus it over we quickly rewrote it as a half Little m the initial squared equals positive big g big m little m all over our initial Then we smiled Brianna we smiled Then we smiled to smile Why did we smile Brianna because we noticed something on this line? Didn't need to tell me the twelve thousand five hundred nice try I Did one more thing because they want to know how fast they want me to get this by itself I said you know what times by two times by two and Katie how to get rid of a squared Square root we said this Your initial or your escape velocity is equal to big square root of two G m over r and I said don't bother memorizing this I derive it. It's a couple of lines Not on your formula sheet, but we do need some of these numbers from our formula sheet Brett I see you have the formula sheet out to I know big g is six point six seven times ten to the negative eleven I've memorized that one. What's the mass of the earth again Brett five point nine eight And if we're starting out on the earth's surface, I think it's reasonable to assume that The initial radius is the radius of the earth six point three eight Times ten to the sixth. We did crunch this number once before but for practice since I was away for a day What velocity would get you out of the earth? What's escape velocity if we ignore air resistance? two times six point six seven scientific notation button negative eleven times five point nine eight scientific notation button twenty four divided by six point three eight scientific notation button six Square root of this. Oh, yeah, we said it was just over eleven thousand. I remember this now is one point one two Well eleven thousand two hundred eleven thousand two hundred meters per second or eleven point two kilometers per second Front page. I like this question. I like this question. I like this question. I like this question says this a Stationary twelve thousand five hundred kilogram rock same rocket as the last question Blasts off from earth. Ah, but this time it enters into a circular orbit. That means there's going to be some kinetic energy to two thousand well twenty five thousand five hundred kilometers from the center of the planet okay First thing I'm going to make a little note here is our orb equals Two five five zero zero that's kilometers. I add three zeros to make it meters per second I start to make it meters, right? One two three four five six seven Two point five five times ten to the seventh. So there's my orbital radius They're not going to get me on kilometers Part a says write a work energy equation. Well the amount of work is Equal to its change in potential Plus its change in kinetic Connor can I cross this one off this time? No Can I cross this up? No What change anything final minus initial we'll tackle that in a second be part one I guess be part one Nicole what is be part one want me to find did you say orbital and fg is always the same thing Big g big m little m over r squared equals fc is always mass times acceleration because forces always mass times acceleration Ah, which acceleration equation will I use? Which one will I use? The v squared over r. Yeah, because it said orbital speed now in this one conveniently The little mass canceled Brianna Smile oh and even better Brianna One of the ours canceled because I got two on the bottom and one on the bottom That's the same as having one on the bottom fact Katie how would I get rid of a square and We're I would normally not do all of this this compressed But I know from experience we're gonna run out of room almost So I'm gonna go like that and even add that to the same line instead of rewriting it V is gonna be the square root of big g big m over r Which is one of the equations that we wrote in a box a while ago mitzvah I said don't memorize it. I know this and I can derive whatever I need to derive we're gonna get v equals the square root of 6.67 times 10 to the negative 11 Mass of the earth it is the earth. Yes. Yes What's my orbital speed? Don't all rush by the way. I'm gonna say it again Some me need to practice with your calculators not mention any names or do that for swapping power this off because you're not that important You get one here. No, I know ignore it. It'll be fine Come on swap you have a graphing calculator or a regular one You lost yours probably want to get one iPhone I wonder if you password for Texas what will happen if I put a password on it? setting general passcode lock Turn passcode on cool Neato, what do we get? Matt would you get? 3,900 3 3 9 5 5 anybody else? Yeah so 396 0 meters per second. Is that right to three sig figs? Is that rounded off properly? No, oh three nine five four so three nine five zero Meters per second, but keep that number on your calculator Because what does part two want me to find it's kinetic energy. How do I find kinetic energy? That hasn't changed kinetic energy is equal to what? What's kinetic energy equal to a half? M V which be oh V orbital squared Which M the M? That's moving not massive the earth the M. That's moving which is the rocket 0.5 times 12,500 times Three nine fifty, but use the exact value that's on your calculator squared How many joules of kinetic energy doesn't this rocket ship have? It's gonna be big like a 10 to the 9th or a 10 to the 10th or something like that I think if my math is correct Emily, what'd you get? You're looking a little befuddled, but what'd you get? 2.5 times 10 to the 7th anybody else? Nope shaking heads. Yo 9.78 times 10 to the 10th units oh jewels Where'd that energy come from Trevor the fuel? Okay, so that again You need to realize how prohibitive it's really expensive to get these things up there. We're not talking small distances here. Oh And that doesn't even count That's only Trevor how much energy you need to get it moving to the speed in orbit That doesn't count the energy to get it up there to the right altitude so that it can stay in orbit What's the third thing they want me to find its potential energy when an orbit? Okay, it didn't say it's change in did it just said potential energy in orbit That's going to be negative big G big M little M all over our orbit Not our initial because you said potential energy in orbit the potential energy in orbit is going to be negative 6.67 times 10 to the negative 11 5.98 times 10 to the 24th 12,500 Divided by what did I say the orbital radius was 2.55 times 10 to the 7th now this answer bugs some kids because you get a negative answer You do I got negative 1.95 5 2 2 5 4 9 times 10 to the 11th. Yeah So I'll go with negative 1.95 times 10 to the 11th But I expected a negative answer Really? Yeah If I wanted to reach the edge of the universe Would I have to burn more fuel? If I wanted to go further away from the earth what I have to burn more fuel Yeah, so I'd have to do more work I'd have to add more energy. Oh But how much energy do I have once I reach the edge of the universe? Connor Zero so if I have to add energy and at the end of the universe it's zero But I got to add energy to get there I better start out negative so that when I add energy I End up at a zero that should be negative Okay, this makes sense little What's the fourth thing that wants me to find say? Total energy in orbit. What would the word total suggest if they say total things up what mathematical operation does that imply? You know what now by the way, I think what I'm gonna do is I'm gonna draw the line down the middle of page and I'm gonna do Move my page over a tiny bit part four right here. How about Te for total energy? There's my abbreviation in orbit is Gonna be potential energy in orbit Plus kinetic energy in Orbit, I haven't taught you total, but I'm going to assume that when you see the word total you clue in Katie I think I'm up there It's gonna be add your potential in your kinetic, please. I got my potential still in my calculator Plus the kinetic was nine point seven eight And I get negative nine point seven seven Times ten to the tenth Is that right? It's actually not I'm gonna I'm gonna tweak my answer a tiny bit look up because I know what the answer is supposed to be Actually, the answer is negative nine point seven eight Times ten to the tenth jewels Mr. Dewick Yeah, Brett That's the exact same number as the answer that we got for but positive We're going to show you in a little bit that as it turns out your total energy is always Half of the potential but positive which happens to be the kinetic energy and you're gonna see why we'll show you some Neat stuff that cancels out in a second. I Don't really have that memorized It's a built-in error check that I have as soon as I got that answer of negative nine point seven seven times ten to the tenth I went yeah, I'm right even though. I know it's really supposed to be that we've rounded off Kayla, what's the fifth thing it wants me to find? Okay, P. E launch I'll use a capital L because a lowercase L looks like a one to me and that confuses me Well, can we use MGH? No, we're going cosmic here Negative big G big M little M all over But this will be our initial or our launch. Oh What is my initial our radius of the earth isn't it Emily? Okay, you might be able to on your graphing calculators if you have them go second function enter a few times Until you get to the line where you typed in the potential energy and just change the radius in other words I know the answer is going to be this negative six point six seven times ten to the negative eleven Excuse me, you know what I need to move this down just a bit so I can fit this in I know that potential energy is going to be negative six point six seven times ten to the negative eleven five point nine eight times ten to the twenty-four twelve thousand five hundred Divided by but this time it's my initial so radius of the earth six point three eight times ten to the six And I noticed that on my calculator I Have everything typed in I just got to change my radius six point three eight Times ten to the six get good at your calculators, especially those you have the graphing ones It's worth the short cut and I find that on the earth the potential energy We have and it should be negative because do I have to add energy to get out to the edge of the universe? Yes, and at the edge of the universe is zero So if I have to add energy I better be starting below zero negative seven point eight one times ten to the eleven Is that right someone else get that too? Nicole. Yeah, Kara. What's the last thing they want me to find? Ah Don't write this down Joel Can I do that? Why can't I do that? The force is changing the further you go from the earth is there a graph that I can find the area underneath of? No, oh Change in potential plus change in kinetic say what's changing anything? Minus minus a no, yeah You know what I think it's going to be the potential energy in orbit Minus the potential energy at launch which we've already calculated both of there in which is kind of nice plus the kinetic energy in orbit minus What did I put a zero there? What is my initial kinetic energy? I think I'm starting from rest And this is where Mitchell we said we have to ignore the rotation of the earth. Otherwise the math gets yucky It is true that technically none of us are at rest right now. We're on an earth that's spinning Yeah, I don't forget it. Okay, let's see here. I got all these numbers somewhere See if I can get them all on the same page. Yeah, I can So potential energy in orbit was negative one point nine five scientific notation button eleven minus my last answer which was the potential energy on the ground plus nine point seven eight Times ten to the tenth. I think that's right Final minus initial plus final and minus initial. Yeah, I think I think I think I Think the total work done is six point eight two times ten to the eleven and you'll notice our final answer Joel is positive Because all these minus-minuses do work nicely Emily they let us know at the end you have to add energy To get to where you're going. I do get a positive answer even though I had all these negatives kicking around at the beginning The math and the universe take care itself. Is that okay? So on your test you can expect a question now the odds are I'm gonna go like this I'm not gonna do a or B part 1 B part 2 B part 3 B part 4 B part I'm gonna get jumped straight to tell me the work required to get into orbit, please and You can combine some of these into one step instead of all these separate steps Matt. It's up to you You're gonna make it. You're not looking good Brett example for using the expression for orbital speed show that in a circular orbit the kinetic energy is half the magnitude of the potential energy Well, we already said this That's the potential energy in orbit Mitchell apparently I can prove that the kinetic is half the potential. Let's see What was the equation for kinetic energy? We've known that for a while a half Kara Have him be squared. Okay a half little M Be squared, but they just told me Kara that I have an expression for V What's the expression for V in orbit this? Oh, what if I square this because it is a V squared What would happen to my square root Caitlin? So, you know what they're saying you can just go like this and if I tidy this up I get a half Big G big M little M over R. Yeah, brand and I want look Does that have a G? Does this have a G? Does that have an M? Does that have an M? Is that these are identical except this one is negative and This one's half as big. Oh The kinetic energy is half of the magnitude of the potential energy as a shortcut once I found the kinetic right here I could have gone times by two and make it negative to get that answer Do I memorize that Caitlin? No, it's a nice built-in error check for me though I kind of have it in the back pocket Mitsu what's the second thing it wants me to prove? Okay well that's potential Plus kinetic because total means add right bit see Potential is negative big G big M little M all over R Plus and we just said that kinetic was a half big G big M little M all over R vendor Aren't these actually like terms look GG MM MM are? What number is in front of the G? It's invisible This is negative one plus a half. It is negative a half big G big M little M over R Turns out the total energy is Half of the potential Kind of nerdly neat That's how I knew by the way that this answer was supposed to be 9.78 not 9.77 because I knew that this was supposed to be half of that John what's the third thing they want me to prove? Te apparently is The opposite of ke question mark. Let's see John what's the expression I have for total energy read it to me What's the expression I have for kinetic energy read it to me and we said apparently these are the same if I put a negative in front of them Are they oh? Yeah, I think Kind of cool Someone back there example 5 says write work energy equations a Rocket at West well, let's try that again a Rocket at rest on the surface of the earth blasts off to and rises to a maximum altitude height We would say here Work equals change in potential Plus change in kinetic Look at this diagram. Is this rocket ship in orbit then it hasn't got me kinetic energy What's changing anything? final minus initial negative big g big m little m all over Minus negative big g big m little m all over now my our initial is going to be the radius of the earth What's the final radius here? R plus h Little r plus h now. They called it big R that would tell you how much work was done B a rocket moving at speed v at liftoff. Oh your initial kinetic is not zero Rises to a height h with no engine use We're still going to start off with this but here. I think we're going to have work equals potential energy final minus potential energy initial plus Zero minus kinetic energy initial You know what? I lost a few of you instead of a zero what I'll do is I'll put a ke final But if it just barely gets to that height, let's assume it comes to a stop at the very very top That okay Sean Initial would be radius of the earth initial would be a half mb squared they need to tell me v and And then I could find out how much work was done oh Final would be radius of the earth plus height or big R They give you the orbital rate the not the orbital radius the distance from the center of the planet see a Rocket rest at rest on the earth blasts off and barely escapes to infinity here. I would use Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy Final I wouldn't use a work approach because they didn't mention work at all And Emily I would remember that out at the edge of the universe Potential energy final is zero and if I just barely make it there. I think that suggests that we just came to a stop This is escape velocity. What's our initial speed? Here the amount of work done would just be your potential energy Initial here. We have a speed be it lift off and we barely escape. I would go with Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final Here I would say those are zero, but your initial speed is not zero This is one we would use to find out what you needed to be traveling at. I'm not going to really be emphasizing too much C&D escape velocity. It's part of the old curriculum and it's nerdily cool. I will ask you how much work to get to a certain height and E definitely a rocket blasts off and enters a circular orbit. You have your final potential minus your initial potential plus Your final kinetic minus your initial kinetic We're going to assume you start out at rest. This is going to be a half m orbital speed squared and to find that we went Gravity equals circular. This is going to be negative big g big m little m all over our orbit minus negative big g big m little m all over a Rocket moving at speed v at lift off rises with no further engine use and enters a circular orbit of radius r same as e But ke initial is not equal to zero. They'd have to tell you the speed. I don't think I'm going to give you one like f but g a Satellite moving at speed v a distance r from the earth's center Falls to the earth's surface. I think I'll give you something falling out of the sky and here because there's a change in height and Speed is mentioned. I would use my initial kinetic and my initial potential equals my final kinetic and My final potential but make sure you use the cosmic equations here and here number one homework Number one now there's a little typo. I'm pretty sure this is Initial initial and final the subscripts in your answer for part a where it says write a work energy equation Rocket blasts off from the earth and reaches infinity moving at 250 meter second write a work energy equation fine I'm just going to assign to be Three is good Or is good? Five is good But I need to talk about this phrase here RT Z AI Can anybody think what RT Z AI stands for when it says find the potential energy RT Z AI of the satellite on the sir said abbreviation first word is relative to Zero at Okay, that's the phrase I've used relative to zero out of pity other words He's saying make sure you use the cosmic potential energy the negative one Okay seven 1314 We're nearly done the unit Basically technically right now you can do every question on the reviews. You can start those two I just have to fine tune a few examples the roller coaster loop and a few other things So we'll have to take home quiz right now. I'm looking at your unit test being today's Not next week but the week after Okay