Physics 12 Final Exam Review of Circular Motion and Gravitation

We're now I I told you for work and energy I didn't put a separate section for work and energy on your test, but you need to know the law law of conservation of energy g g I snuck it in in other locations. And this took us to after Christmas. We started circular motion I think maybe one lesson before Christmas, but it's primarily after Christmas. So, what were some key concepts? If we're moving in a circle, we always asked ourselves what path are we tracing out? What was the response? Starts with letter c. A circle. If that's the case, which way are we accelerating? That was the key idea towards the center. Oh, which way is the winning direction in my free body diagram then? Same answer. Of course it's the same answer because that's what Newton's law says, the unbalanced force is the direction you're accelerating toward the center. You might recall I showed you a motorcycle merry-go-round video. I can't find it on YouTube anymore. Okay, I got to pause for a second here. Give me a second. Those of you on YouTube, I got interrupted my chain of thought, so it's going to seem weird. I think Oh, I think I was talking about the motorcycle merry-go-round video. Y'all remember that one? Where the guy went flying out and we had to say first of all, he was accelerating towards the center. He would have thought he was getting pushed outwards, but that's because he was having to apply a force with his arms and because he's not used to doing that, he would think, "Oh, I'm accelerating outwards." He's not. When he flew out, what direction was the velocity? Something to the something. Tangent. To the radius, at right angles to the radius. You're accelerating towards the center, then that force is towards the center, the velocity is at right angles tangent to the radius of the center. And that's what we saw him fly out. I showed you a few other ones as well, but that was the most dramatic one cuz I know I can pause that at just the right moment and freeze him in midair as he's about to experience some bad physics. Note, on your formula sheet, there is not a single equation that says FC equals. I gave you the acceleration. How do I turn an acceleration into a force? F equals what times A? Don't forget to multiply by the mass because the circular motion equations were so complicated, it was easy to think, oh, that's the force. No, no, no, no, it's MA. So, remember that FC equals MAC, where AC was which two equations? V squared over R or 4 pi squared R over T squared? WHICH ONE DO I USE? Depends on what they gave me. I've got You'll have two different circular motion questions, and it'll be between a Ferris wheel, a Gravitron, and a roller coaster. So, you'll see two of those. Geo has a mass of 67 kg. He's riding a Ferris wheel of radius 11.2 m. At the top, he experiences a normal force of 542 N. Part one says, how fast is the Ferris wheel moving? Canaan, any suggestions on how I might want to start? Is he ready? I'll give you your hint. What path are we tracing out? What path are we tracing out? The line you're looking for is a circle. Which way are we accelerating? What might this be a good job for? Okay. Where are we in this question? Top or bottom? Where are we in this question? Top or bottom? Okay, read the question. Don't look at Read the question. Where are we? What are the forces acting on him? Get the obvious one. Why did I draw mg so long? Which way are we accelerating? Toward the Which way is mg pointing? Toward the It's the winning. Okay? What else? Which way? Whichever way your head is pointing, which in a Ferris wheel will always be up. On a roller coaster, it depends where you are in the loop. Why did I draw the normal force smaller? Which way are we accelerating? Toward the Cuz what path are we tracing out? A circle. Okay, there's my start step one. Those are the two forces right there. Who's winning? Losing. Equals MAC. Winner minus loser equals MAC. Now, here's the question from my formula sheet, which version of AC am I going to use? What are they asking me to find? So, which version of it Go look at your formula sheet. Which version of AC am I going to use? You're going to use an acceleration. You have two ACs. Go look in the circular motion. I I know I sound harsh. I'm pushing you. See Can you look in the right place? It says AC equals There's two Which Now you're seeing it. You're going I should have had that 5 minutes ago. Which version am I going to use? The one with the V in it or the one with the T in it? Yes. So, I can say this. mg minus the normal force equals mv squared over r. Now, technically, if I wanted to get the V by itself in one step, don't write this down, but you can. It would be times this whole thing in brackets by r, divide this whole thing by m, mass of square root. And if you want to do it that way, that's fine. This was around where my love of formula manipulation started to hit a wall. This was around where I would have said to you, "Just turn this into a number." I would have said, "You know what? Let's go 67 * 9.8 542 that equals MV squared over R. Also, notice the mass doesn't cancel here because all of you experience rides differently. What you're experiencing is the normal force and your normal force depends on how big you are. You may find as you get older and you put on your middle-age weight, you may age out of rides that you used to like when you were a kid. You may suddenly go, "I'm feeling crazy now." It's because you're experiencing a bigger normal force. Uh let's get out our calculators. 67 * 9.8 542 and I get 114.6. I'm not going to round that off at all. That equals MV squared over R. Now, I can use formula manipulation jet. Now, I can go divide by M times by R square root. V is going to be R * 114.6 / the mass square root. And to cut down on time, I'm going to go straight to my answer. On the test, I'd certainly write out the numbers so that I could if I made a mistake, still get part marks. What was R? 11.2 * answer button divided by the mass square root of that. I get double check me 4.38 m/s. Not very fast. Is the Ferris wheel considered a scary ride or a tame ride? Is the Ferris wheel considered a scary ride or a tame ride? Yeah. Roller coaster, I'd be looking at something in the teens or maybe even in the 20s. Ferris wheel, single digits. Yes. Pause. 4.38, is that right? m/s What else could I have done? Oh, instead of asking you to find the speed, I could have asked you to find the period of rotation. Uh it would be the same except Kanan right here you would have written m 4 pi squared r over t squared. You get the t by itself. What's Geo's normal force at the bottom of the Ferris wheel? Alexis, you know who this is a good job for? Okay, now we're at the bottom. What are the forces acting at the bottom? Get the obvious one. What else? Which way? Bigger, smaller, or the same size as mg and how do I know? What path are we tracing out? So, where is my bigger unbalanced force going to be pointing? Winning. Losing. And I guess because I have the speed from part A, I'm going to use mv squared over r. I can do use the speed for a Ferris wheel because the Ferris wheel is rigid. Everyone's traveling the same speed. Not on a roller coaster loop. You're slowing down at the top and you're speeding up at the bottom. So, I couldn't clone this for a roller coaster loop. I'd have to ask something different. Um what do you want me to Oh, get the normal force by itself. The normal force is going to be mv squared over r plus mg. What's your normal normal? What are all of you feeling right now is your normal force? Oh, but look look look look at the normal force. So, the normal normal is mg. We're adding you feel heavier at the bottom, which you do. What's your normal normal? mg. At the top, you're feeling lighter because the normal force is less than gravity. See it? So, we can explain the physiological feelings of that ride. The normal force is going to be What was m? 67? times answer button squared since it's stored on my calculator divided by the radius. What was the radius? 11.2? plus 67 67 shut up times 9.8 Uh YouTube, if you're watching this like 5 or 6 years from now in the year 2016 middle school and teenagers middle school students had a stupid 67 meme thing going on right I whatever. No one really understood it. Uh answer button squared divided by 11.2 plus 67 times 9.8 Of course, by now you're typing this into your calculator and getting an answer. Do we got an answer? What you get? You did more typing to be less accurate and introduce the possibility of a typo? 771.2 if you use the answer button all the way through? So, I'll go 771. Uh what else could I do with this as follow-up questions? Ooh, if he's sitting on a kilogram scale, what would the kilogram scale measure? How would I convert that to kilograms? Okay, just for kicks. divided by 9.8 Not feeling much heavier and again, that's because the roller coaster Ferris wheel's a tame ride. It you're not going on there for the stomachy you're going on there for the view and a breeze on your face and maybe the swing the car is a little bit, but it's not one necessarily unless you're afraid of heights. Most people are going to go on the the Ferris wheel, okay. Gravitron Oh, what a great ride. You'll notice it wasn't running at Playland. Why? Cuz the PNE owns the Gravitron, not Playland. So, it only comes out in the summertime at the PNE. Gravitron has a radius of 8.35 m. It spins once every 4.65 seconds. A rider of mass 76 kg on the ride, what's the minimum coefficient of friction needed between the mass of the rider and the wall of the ride? Okay. Arnica, you know what this is a good job for? Let's represent this person with a dot. I'll do it in red. What are the forces acting on this person? Get the obvious one. Which way? Down. Is this person accelerating downwards? Are they accelerating upwards? That means forces must be I'm looking for one that starts with letter B. I know there's an arrow the same size as mg pointing up. I'm not sure I know what it is, but I know it's there. Mine looks a little too long. About there. Oh, what path is this person tracing out? Where must there be an unbalanced force pointing toward the So, I also know there's a force here. That's the one I think I can figure out. What force is that? What's pushing this person inwards? Well, it's the wall. What do we call the force from a surface like a table or a wall? Ha. And that gives me a hint as to what that vertical force might be. Who remembers, what's that vertical force? Friction. This one was interesting because you had two equations. One equation is gravity is the same size as friction. And the other equation is normal force is what's pushing me in a circle. Over here, Canon coming back at you, which version of AC am I going to use? The one with the V or the one with the T in it? How do I know? Why? They gave me the period. Or they could have given me the speed. Or they could have asked for the period, then I would have used the one with the V. OR THEY COULD HAVE ASKED FOR the speed, I would have used the one with the V. But I can certainly say this, the normal force is equal to M 4 pi squared R over T squared. Mr. Dweck, it just says 4 pi squared R, there's no M. That's because I told you the acceleration. F equals M A. On the left-hand side, I would drop the mg down, and I would probably do physics 11. Friction is what times what, Arnica? And then you might recall I would often say something like, I don't know the normal Wait a minute. Okay? Now, I'm going to pause. Or I could have given you the coefficient of friction and asked you to get the T by itself. You could still plug this whole thing in there and get the T by itself. Or I could have given you the coefficient of friction and asked you to get the V by itself. You'd have an M V squared over R, and you get the V by itself. Basically, for this particular Oh, or I could ask you to find R. For this, I can spin off four different questions from the gravitron. I can give you one piece of information, either mu, R, V, or T, and you can find any of the other ones that I ask you to find. In this case, this is probably the easiest case version because I can say, "Hey, mg equals the mu drops down and then it's m 4 pi squared r over t squared." Arnica, can little kids and grown-ups go on this ride together? Why? So, even though they gave me the mass, and I guess they want me to get the mu by itself. I guess I'm going to divide the four and the pi squared and the r and I guess I'm going to times the t squared. That'll get the mu by itself. So, the g is going to drop down like a domino. I'm going to times the t squared. I'm going to divide the four, the pi squared, and the r. That's apparently the minimum coefficient of friction. Why did I say minimum? Shaz, there it could be way stickier and give you a lot of breathing room, but you have to have at least that. It's going to be 9.8 times Arnica, I've scrolled down. What was the period? Don't forget the squared divided by 4 pi squared. What was the radius? Gerry, I thought for a minute I forgot to give it to you. It's good. Did I give them an impossible question? I hope not. What's mu? I don't know. What's mu with you? You'll miss that joke. Trust me. It's funnier than you all let on. It was them at the physics conferences. 9.8 * 4.65. Don't forget the Oh, not the square root, Mr. Squared. Divided by bracket 4 pi squared * 8.35 No squared. Close off the top. I hope I made up good numbers. Oh, sure. 0.643 Has anybody been on the Gravitron? Okay. If you're on it, feel what's behind you. It's fairly gripy. They They didn't put you on like something slick. Some kind of a fabric usually some kind of a rubber where you can Oh, yeah, I can feel if I try and slide down doesn't want to let. Oh, units. Good. Okay? So, you've seen how I can mix and match the Gravitron. I think all of you might Well, again, Ferris wheel, Gravitron, or roller coaster. I've got several different versions of my final exam. I got four different versions, five different Maybe five, I can't remember. Um So, probably two out of Well, I got three blocks. Yeah, two out of three blocks will probably see the Gravitron statistically. Or we could do a roller coaster. At the top of the circular roller coaster of radius 9.8 m, I'm already regretting using the 9.8 cuz you'll mix it up with gravity. I'll change that number next year. Don't like me using the same number twice and causing confusion. A 76-kg rider experiences a normal force of 4.2 times their weight. How fast is the coaster traveling at the top of the loop? Oh, that's it. Matt, what might this be a good job for? Hey, what are the forces acting on this rider? Get the obvious one. What are the forces acting on this rider? Matt, get the obvious one. Yes. What else? Normal force. Which way? Which way is the head pointing? So, for a roller coaster, if you're in a loop, unlike the Ferris wheel where at the top the normal force was pointing up, here the normal force is pointing down. I'll put it beside. Oh, at the bottom, it would be mg down, normal force up, and normal force would be bigger. Who's winning? They both are. Cuz what path are we tracing out? Which way we accelerating? Toward the Okay, so I could say winner plus winner equals m a c. Canon, back to you. Which version of a c am I going to use here? How do I know how fast? And Honestly, for a roller coaster, I can't ask you to find the period because it depends on the speed of the loop. I'll ask you to find the speed at the top and a different speed at the bottom if I do anything. Or ask you to find the normal force. Uh here they gave me the normal force. They said 4.2 times their weight. No, now, when I say weight, what do I really mean? Two letters. So really, this is going to be 4.2 m g's plus m g. That equals m v squared over r. What number is in front of the m g right here? It's invisible. What number is sitting right there technically always? So what's 4.2 m g's plus 1 m g? Yeah, they're like terms. I get 5.2 m g's equals m v squared over r. Will little kids and grown-ups all feel 4.2 times their weight? Carly, is there an m in the left-hand term? Is there an m in the right-hand term? Is there an m in everything? Will little kids and grown-ups all feel 4.2 times their weight? Yes, but because little kids have less mass to begin with, they're not going to feel it as much as an obese heavy person like me. Right? I'll feel it more than you guys will. Um Oh, get the v by itself. How do I move the R over. And we see our old friend. Hello, old friend. I see the square square root of gir and other stuff, but that was kind of my If that showed up, I've probably done it right little mental checklist. I'm going to get V equals the square root of 5.2 * gir. If I give you a roller coaster loop, I probably won't make it survivable. Who remembers we actually looked at roller coaster loops? What was the minimum Gs that you were pulling at the bottom? Minimum. It was six, minimum. It was six. And that's that's barely making it over, so close that you almost fell off the top of the loop. Of course, in real life, you would want a big safety margin. Please don't try and calculate the number of Gs they're pulling at the top or at the bottom. Well, here, they're pulling 5.2 Gs at the top. They're probably pulling seven or eight at the bottom. This is not a safe ride, but I wanted to make up a roller coaster. Uh it's going to be the square root of 5.2 * 9.8 * also 9.8. You see why I said I felt bad using R as 9.8? CUZ YOU WHY ARE THERE TWO GS IN THERE when you're looking at it later? It's a preventable dumb error that I should have thought of as a veteran teacher, Annie. Uh oh, well. Although the bonus is, Annie, I can just go 9.8 squared and save myself some typing, I guess, even though that's not really what I mean. Uh 22.3 m/s. We did do a car going around the corner. I'm not putting that on your test. That was where friction is what's pushing us around the corner. It was too basic. I'm going to give you two amusement park rides. Ferris wheel, roller coaster, gravitron. Two of those. I think that's the end of the circular motion section. Yeah, yeah. So, then gravitation overlapped a lot with circular motion because in orbits you're moving in a circle. First of all, you need to know the difference between a gravitational force and a gravitational field. What was our equation for gravitational force? That was big G, big M, little M over R squared. What was our equation I lifted that right from the formula sheet, yes. What was our equation for gravitational field? Tucker, here's what I wrote on your formula sheet. Gravitational field, little G, is the force of gravity divided by little M. It's this e k this this thing cross out the little M. It's big G, big M over R squared. A number of us lost marks on the test. There was one question on your unit test where I said find the gravitational field around a black hole and some of you found me the gravitational force. Not what I asked for, you got a zero. I mean, you may have done it right, not what I asked for. So, make sure you understand the difference between force in Newtons and field, which is that. Newtons per kilogram if you want to be nitpicky because Newtons per kilogram. That also means it's technically meters per second squared cuz that's got to be an acceleration. If we're in orbit, what's pulling us in a circle? So, gravity, I'll write FG, is what's pulling us in a circle. If we are in an orbit, we would say gravity is what's pulling us in a circle. Big G, big M, little M over R squared equals MAC. Which version of A can it depend on on whether they asked for or gave me the period or the speed? >> know any one of orbital speed, orbital period, orbital radius, or orbital altitude, if you know the radius, subtract the radius of the planet, now you've got the altitude, we can find the other three. You need to know the difference between altitude and radius. A lot of us got those mixed up. Radius is measured from the center of the planet, altitude is measured from the surface of the planet. Um I might even have space to do a diagram there. If I can, I will. Then we said that potential energy, we couldn't use mgh. Why couldn't we use mgh for gravitational potential energy anymore? Be nice. Why can't I use mgh? Cuz as you move further away from the planet, g gets smaller and smaller. So, we had negative big G, big M, little m over r, not r squared. Why was it negative? We had to define zero somewhere. The phrase I introduced to you was relative to zero at infinity. We said that you had no energy out at the edge of the universe. Why? Cuz if we let you go, you wouldn't fall. No gravity. Anywhere closer, there'd be a tiny pull of gravity, you would fall, you must have some energy. So, you have less than zero. What numbers are less than zero? Negatives. Who's in calculus? It's negative because it's the integral of the force equation. You have an r squared on the bottom, that's an r to the -2. If you take the integral, you will get a negative one in front of everything. Oh, I've been That's the correct answer, not the garbage I gave you before. Oh, there will be an escape velocity question, even though it should be called escape speed. I'd be crazy. Planet Pit has a mass of that and a radius of that. A satellite of mass that is in a stable orbit above the planet surface. What is its orbital period? Okay. What word is this right here, folks? It's a trigger word. What word is this right here? Orbit. If I see the word orbit, I can't say gravity is pulling me in a circle. But, let's visualize what's going on. So, here is planet pit. Here's the satellite. That's the altitude. This is 1 .2s * 10 ^ 6 m. Is that the radius from the center of the planet? We're going to have to add the radius of the planet. In other words, before I start this, because they gave me a little altitude, not attitude, I get that from you guys, little altitude, I'm going to have to make a little note that the orbital radius is going to be the planet and let's write this out, so when you're studying we know what we did. Plus the altitude. Now, if they give you the orbital radius, you're home free. Take it. But, if they give you an altitude, you've got to add the radius of the planet. So, the orbital radius is going to be What was the planet? 7.74 * 10 ^ 6. And again, the reason I know it's an altitude above the planet's surface. If they had said from the center of the planet, div, that's a radius. I'm home free. Uh uh plus the altitude, 1.2 * 10 ^ 6. So, let's get the orbital radius. We had to remember how to do scientific notation. >> [snorts] >> At an altitude above this planet pit, our radius is 8.94 * 10 ^ 6 m. Now I'm good to go. Peyton, can you read to me the last sentence of this question? Did you say orbital? Gravity is what's pulling me in a circle. Which gravity? Now we got to use the cosmic Newton's law of gravity. That was the one that said big G, big M, little m over r squared equals m a c. Peyton, not Canaan. Peyton, which version of a c do they want me to use? What are they asking me to find? I've scrolled down. You'll have to read. Oh, which is the version of a c that has the period in it? Go look at your formula sheet. It's on there. By the way, folks, look up. Apparently, I don't need the mass of the satellite even if they gave it to me. Which is true. Yeah. Good. Okay, let me write that down on the next line. It's the big G the big G big M over r squared drops down and here it's got four pi squared r Keep going. Is it over t squared? Is that right? Okay. From this equation, if they give me the radius, I can find the period. If they give me the period, I can find the radius. Let's get the t by itself. Peyton, where's the t squared right now? On the I would multiply it to the top. I'll drop my equal sign. I already have a 4 pi squared. That would stay behind. How would I move this r squared over? It would multiply up to here. I would have an r cubed. How would I move the big G and the big M over? Okay? Tucker, is that okay? This would end up right here. The big G and the big M would end up getting divided down to the right-hand side. That would give me a t squared. A t what? A t squared. Talk to me, Tucker. How do I get rid of a squared? And you may recall, hint, hint, hint, one of the ones I loved was getting the r by itself because how would you get rid of an r cubed? This was where you had to do a cube root. I had that on your test. That's going to be on some of the versions of the final, as well. Okay? So, you would start off with this equation, but you would get the r by itself. Times the r cubed here. Times the t squared. Divide the 4 pi squared. Cube root. Here, we're getting this by itself. You're going to have to read me the numbers, Payton, because I've scrolled down. It's going to be 4 pi squared. What was r? We calculated it. It should be up there. If you wrote it down. Uh-oh. Did someone not write it down? Yes. What? Sorry, what was it? 8. Times 10 to the? Yes. And cubed. I'll have to find my to the power of and cube button. All divided by Hey, everybody, what was big G? Shut up. 6 7. Okay, 6.67 times 10 to the -11. And I made up a mass, Payton. What was the mass of this mystery planet? I missed that. 6. 2 5. Times 10 to the? Earth-like. Earth, I think, is 5.98 times 10 to the the 24th. And Earth's radius is 6.38. This This is an Earth-ish planet. What do you get? I would probably, for something this complicated, I'm going to type what's inside the square root first, and then I'll go square root answer button. 4 pi squared times 8.94 scientific notation button 6 to the third power divided by bracket 6.67 scientific notation -11 times 6.25 scientific notation 24th close off the bottom. Let's wait Oh, oh, square root, square root. Almost forgot. Y'all get 8,225? 800 6 actually. I'll just I'll go 8,230. Yes? 8,230 m/s. I'm going to add a part Is that right? Oh, that's the period. That's good. I was thinking that seems way too fast for me. That's almost approaching Earth's escape velocity. It's the period, Mr. Dewitt. It's seconds. By the way then, just for giggles, that's seconds divide by 60. You'd be orbiting every 137 minutes divide by 60. You're orbiting every basically 2 and 1/2 hours. Okay. Um I'm going to add a part B. Find the gravitational field strength on the planet surface. That's Oh, I did add a part Jeez, thank you, Shaz. I was going, "How did I miss that?" Is it the same numbers or did I change them? I used them again cuz I was thinking this seems fairly Earthish. I'm going to guess we're going to get something not hideous to live in. So, how do I find the gravitational field strength? Thanks, Shaz. Uh little g equals the force of gravity divided by little mass. The force of gravity is big G big M little mass over r squared divided by little mass. Your gravitational field strength is big G big M over r squared. If you plug in Earth's numbers, you'll get 9.8. I get 9.799 as it it 9.8. Mystery planet, I don't know. 6.67 * 10 ^ -11 6.25 * 10 ^ 24th all divided by don't forget the squared mystery doohickey. 7.74 * 10 ^ 6th squared. This should be close to Earth, I think. We're a little larger in mass, which would increase it, but we're a little larger in radius, which would decrease it cuz you're further from the planet center. So, I'm not quite sure which one's going to win out here. >> [sighs] >> You get 6.96? Basically about 2/3 of Earth's gravity. Fairly livable. You'd have to adjust cuz everything your timing would be off for everything. If you dropped something, it just wouldn't quite fall right to your eyes. But probably you'd be able to stay in this for a few months without major damage. Your heart muscle would be the bigger challenge. It would weaken a little bit cuz it's not having to pump as hard. 6.96. And you could say meters per second squared because the acceleration due to gravity on this planet, but I usually go Newtons per kilogram because Annie I went force divided by mass in my original definition, but I would take either. So, that was a quick review of orbits. Gravity's what's pulling us in a circle. I can give you one thing, you can find lots of other things. Uh gravitational field strength. Oh, escape velocity. So, let's suppose we were on this planet and you wanted to get off of this planet and head back home to Earth. And again, we're assuming that we end at rest. What we're saying is we're going to fire our engines in one mighty blast and then coast the rest of the way. And we're ignoring air resistance. Who remembers how do we do escape velocity? And your hint is it should be called escape speed. The reason we use a scalar approach. You may have memorized the formula and as long as you have it in your cuz I won't let you put it on your yellow sheet. As long as you have it in your brain, you can jump straight to it. But let's re-derive it. We derived it from the law law of conservation of energy. We said this. KE initial plus PE initial equals KE final plus PE That part is Faith Physics 11. But then it got a bit weird. We wanted to escape the planet, which means we want to make it to the edge of the universe. What's our gravitational potential energy exactly as a number at the edge of our universe? So, strangely, this became a zero. And we wanted to do it so perfectly that we're coasting, slowing down, coasting, slowing down, coasting, slowing down cuz gravity's still pulling on us. The second the split second we're actually out of all gravity, we come to a stop. And so, we wanted that to be zero as well. It was a little weird. KE is still what it is from Physics 11. Faith, what's kinetic energy? A half little m v initial squared plus potential energy I've got to use the cosmic one from my gravitation section. Negative big G big M little m over r initial. That equals zero. First thing that I always did is I said, "Well, let's get rid of the negative. Let's just plus that over since there's a zero there." And I rewrote it as a half m v initial squared equals positive big G big M little m over r initial. Thank you. Did they need to give me the mass of the spaceship? Did they give me the mass of the spaceship? Nope. All the spaceships will have the same escape velocity because there's a little m over here and a little m over here. In fact, I could have crossed it out on the previous line, but it's a little easier to spot there. Get the V by itself. I'm going to go times by two. You could also divide by 0.5, but that looks cleaner. That's a squared Escape speed is the square root of two big G big M over R initial the surface. And what we notice, I don't know if you remember this, I think Owen does cuz I think he was remembering this equation. Don't write this down, but look up. That was orbital speed without the two. That was escape speed with the two. We said to get I went on a big rant. I said the big challenge for space travel is getting off the planet. Once you're off the planet, getting further out Alexis way less energy. To get off the planet takes us all that whoop, sorry. Let's go forward. To get off the planet takes all of that. To leave the solar system only takes the square root of two as much, which is 1.41 times as much. So much more of your energy is getting off the planet. I think I probably mentioned to you Earth's gravitational field of 9.8 is so big we can barely make it to orbit. If Earth was much bigger, about 15% larger, you can run the equation for E equals MC squared, which is the most energy you can get and you can show yeah, not getting off the planet. And I think I mentioned there may be intelligent life out there that is involved evolved on larger planets somewhere in the universe, they'll never have a space program. They can't. It's impossible. Which is sad. But cool. Let's crunch the number. Faith, you're going to have to read the numbers to me. Square root of two. I'm just going to write big G instead of writing out the numbers. Uh what was the mass of the planet? And the radius of the planet? Louder, please. Sorry. >> This is Earth-ish, Earth-like. I think Earth's gravitational Sorry, Earth's escape velocity was 11,200 m/s. I'll bet you we're going to be in around the 10,000-ish, but I don't know. 2 * 6. Okay, I thought thought that's what I heard. It's going It doesn't seem 6.25? I think she read it as 7.35, did she not? And what's the radius? Tucker, you have an answer? Yeah. Good. What's your answer? I I said I think it's going to be close to the Earth, and I know the Earth is 11,200, so that seems ballpark. I'm wait Oh, square root, Mr. Dewitt. 10,400? Yeah. m/s. I can't remember if on your final I put you on a planet or near a black hole, but I could ask you all of this near a black hole just for giggles as well. That is a really quick review. Hold the toy, please, Brett. That's a very quick review of circular motion and gravitation. Are you feeling up to trying to dive into some circuitry. Let me check my schedule, Mr. Dewitt. Um, I got one, two, three more classes. I have to go over the test. How many do I have? One. Oh, only two? Oh, you know what? I'll bet you I have one that we have to rewrite. Yeah, here I don't have a pair at all. Ugh. Oh, no, I do have a pair. This one's going to fall apart. I don't need to rewrite this one. This one I'll have to rewrite. I think Pause.