 So number four Mitchell, I'm going to argue first of all This is almost identical to the car going around a corner question that we did last day in that I think the free body diagram for number four is going to be hey one of the forces gravity down normal force up and Friction pushing this coin in a circle Is that okay? And so it's going to be friction equals FC is that all right? Friction is what times what new times the normal force? I don't know the normal force Oh, but look look look look look another force in size. I'm going to get this Mu M g equals M and 90 to think which expression for acceleration am I going to use and what tells me is This what does rpm stand for? That means it goes around 42 times in 60 seconds, that's a frequency How do I change a frequency into a period now? I did say this on the first day of this unit the first lesson how are period and frequency related you remember? Yeah, thank you The period here has to be 60 over 42 which might be a nice decimal. Let me find out I think it is No, it's going to be a repeating decimal. It's 1.4285 You know what? I'll just care I'll write 1.43, but I'll carry that on my calculator and I'm going to use the 4 high squared r over t squared Conveniently I don't need to know how much the coin weighs which is good What do they want me to find in number four? So to get the mu by itself divide by g It's going to be four do I know the four yeah pie squared. I know did the time of the radius Careful meters Right divided by nine point eight times the period that we just got squared and that should be the coefficient of friction. Let's find out four Hi squared times point one three divided by bracket 9.8 time my previous answers squared Yep to a point two five seven Okay, I think what threw you off was this yes, no. Oh Just it's just like the car going around week where we calculated I think in the car though we calculated it's safe speed here They told me the period so I can calculate the coefficient of friction required. Is that all right any others? I'm getting a sense you guys haven't done the homework and that's going to come back and bite you But I'm going to say then do the homework and ask me questions from here tomorrow or Tuesday because No others that no that was a here number 93 a place. Okay Well, I have for you a take home quiz Lesson for gravitation We're going to change gears just a tiny bit and At first it's going to seem a little unrelated But we're going to tie it all together because we're going to find that actually circular motion when we combine it with gravitation Allows us to do some nearly cool things This is the law of gravity if you've ever heard that phrase if you've heard the fake story about Sir Isaac Newton Getting hit in the head by an apple and having this realization. This is the equation that he came up with We think that story by the way is apocryphal which means fake We're pretty sure he did tell the story in his old age But we think he told the story to make himself sound smarter and better than he was he was a pretty big Gravitation Universal gravity We have said that gravity is a force that exists between the earth and masses on its surface But actually gravity is universal any two masses any two masses in the universe Exert an attractive force on each other. It's just a really really really really really small force You need a huge mass before you notice it example 1 The diagram below shows two masses big M think planet and Little M think moon or satellite Big M is the greater mass Compare the gravity forces on the two masses option a the force exerted by M is greater Option B the force exerted by little M is greater Option C the forces are the same and convince me once again We're gonna vote once again how high you hold your hand up is how sure you are of the answer Once again, if you choose not to vote and I catch you I will damage yourself a scene So we have a planet with a moon or planet a satellite Is the force by the planet greater a two three four five Who says the force exerted by the whole satellite is greater no one Who says they're the same 17 1 2 3 4 5 6 7 8 9 10 11 12 13 18 19 20 21 22 Who's a coward? You didn't vote at all You voted oh you voted coward. Oh, yeah, I know believe me I saw certain people look around at everybody and once more people put their hands up with about a one second delay Their hand when I know these things. I just get more upset with people that can't even have an opinion All right convince me that your right or someone else is wrong Emily You're right Why? So Emily says the forces have to be the same and stable because if one was bigger it wouldn't be in orbit We would never stable orbit. I'm gonna even go more basic than that. What was Newton's third law forces come in if? Object M applies a force on object little M object little M has to apply exactly the same force opposite direction on object big M Really the moon tugs on the earth. Yeah, we call it tides Tech it moves the earth so much that the water around the earth sloshes back and forth. That's what tides are Cavendish a scientist who came after Newton and other symptoms have designed very ingenious experiments to measure this small force of attraction You see the problem is we can certainly measure what the earth does but to try and replicate that in a lab with masses that you can fit into a room The gravitational force of attraction between two masses is extraordinarily small. It's like eight decimal points small How the heck do you measure that and especially 100 and 150 years ago with the instrumentation that they had? They came up with some very ingenious experiments. I'll be talking about one of them a bit later, but here is what they came up with They found that the force of gravity depended on two things if you multiply the two masses together and you divided by The square of the distance between them We're gonna use a radius because you'll see why in a bit now that gives you an answer But that doesn't give you an answer in Newton's unfortunately And so we have to add a little conversion factor a constant a number to put in front the same way For example as when you go from let me think of a good example because you guys all grew up metric well when you go from meters to centimeters you have to multiply the meters by a hundred right when you go from Celsius to Fahrenheit. It's like double it and add 30 if you're traveling in the US The constant is capital big G Which is called the universal constant the gravitational constant The first mass in kilograms the second mass in kilograms How far apart the center of each mass is? Squared times this number now this number is on your formula sheet Don't get it confused with a little G little G views 9.8 big G is it's also right here 6.67 times 10 to the negative 11 and this was the tough number to find Because is it times 10 to the negative 11 a very small number That would be point zero zero zero zero zero zero zero zero zero six six seven It was really tough to measure But we knew that the numbers that we were crunching weren't working out exact how the heck there's the conversion factor This formula is on your formula sheet although you probably end up memorizing it because you're gonna be using it so often so Calculate the force between two one kilogram masses separated by one meter It's gonna be small Because if you're holding two one kilogram masses like this, which is about one meter apart Do you feel them tugging towards each other? Are you having to work to hold your arms apart as though they were somehow magnetic pulling towards each other? In fact gravity is the smallest force in the universe We think it's the biggest because it dominates our life, but again K that's because the earth is so huge Really gravity is a really small force What would the force between two one kilogram masses one meter apart beat? Well, let's write down the equation for practice This section here for the next few days is where you also want to practice using your calculator From previous experience the kids that don't try punching these in now Almost always have all the right numbers on the test and all the wrong answers on the test. I've seen it before Big G is 6.67 times 10 to the negative of 11. It's on your formula sheet. You might want to find where that is on your formula sheet It's right on the same page where the mass of the earth and the mass of the Sun and all that You know what you might want your formula sheet out for the remainder of this lesson. Just be thinking Mass one is one mass two is one divided by one meter squared By the way, do I really need a calculator for this question? Because Emily when I times by one times by one and divide by one square does that kind of make a difference at all Can you tell me what the answer is? It's going to be 6.67 times 10 10 negative 11. What no equal sign names negative 11 Newtons really small But it's there Any objects that have mass are attracted to each other Trevor and Joel. I'd like you to look at each other Gaze at each other in the eyes and Joel. Here's what I'd like you to say to Trevor Trevor I'm attracted to you Trevor, I'd like you to look back at Joel and say Joel. I'm attracted to you too But Joel I'm attracted to you by But Joel I'm attracted to you by The product of our masses and The reciprocal of the square of the distance between us But there is no denying we've seen the attraction all year long But any objects with mass are attracted to each other now It is true that there is a force of gravity between Trevor and Joel But at the same time Joel to your left there's another human being of roughly the same mass That's pulling you in the opposite direction. Most of all these attractive forces cancel out. We ignore them a they're really really small And they almost all cancel out because there's masses all around you We don't we don't even include them in our calculations. The net force is zero Joel looks relieved example three So Let's talk a little bit about how the force of gravity works What will be the if the force of gravity between two equal masses m? Separated by distance D is f then what will be the force of gravity if so right now we have this our force of gravity is big G if Both masses are the same. I think I can write it like that mass times mass over The distance squared okay, a asks What if we double the distance? What if we Put a two there. Let's write it over here. So for part a I would have this still big G Still m squared all Over Matt what's gonna happen to that two when I take it out of the brackets. What's it really gonna become in? Fact we get that Joel could you stand up, please? Could you roughly double the distance between you and Trevor so step backwards stop right there? It's four times weaker Their force of attraction is four times weaker go back to where you were at the beginning Could you roughly triple the distance between you and Trevor? Yeah, how many times weaker it is now nine times weaker because that three is gonna get squared go back to where you were Could you roughly quadruple the distance between you and Trevor? How many times weaker is the force of attraction between you guys now? 16 times 16 times Joel Inverse square relationship we call it. Okay, so four times smaller Nine times smaller 16 times smaller D. What if I leave the distance back to the original but I double one of the masses so for D. I would have this big G One mass would stay the same, but I'd have a second mass doubled All over D squared. I think Brett. I'll still end up with an M squared. Yes But you know what I have in front of everything I think To I think it's gonna be twice as big In fact if we doubled Joe's mass He'll be twice as a Trevor would find Joel twice as attractive if he was twice as bad. I Don't know what that says about Trevor's mind, but still okay Doubling the mass Trevor Two times but larger because the ems are on the top of the fraction. What if we doubled both of the masses? How many times bigger would their force of attraction be now? four times bigger Joel stand up again, please Okay, so starting right there Move your chair forwards push it in Half the distance between you and Trevor so move closer to him What would happen to the force of attraction between them now? How many times it's gonna be bigger how many times bigger think square? four times bigger four times bigger Joel go back to where you originally were Okay, one-third the distance so divide it by three nine times bigger Okay This is how gravity works. Thanks Joel. So if you have the distance Because when this number gets smaller Andrew when this number gets smaller The overall answer gets bigger because this number is squared the overall number gets bigger by the square of how many times smaller You made the number it's called you're learning something called the inverse square law This applies to anything that radiates out So for example right now between me and Connor and John is sound John are you twice as far away from me as Connor is roughly? I'm four times quieter compared to what Connor hears Okay, and if I think Kara is about three times further away from me than Connor You hear me nine times quieter than Connor does the inverse square low That's why when you go right up close to somebody put your ear right by their mouth You can hear them whisper so quietly because there you've really dramatically shortened the distance It's probably several hundred times stronger because it's a square relationship Okay, hey, what if you double both the masses and the distance? Let's see that for G Let's see if I double one mass by double another mass and I Double the distance What oh? You mean they can't everything cancels isn't I got a four on top see it And I'm going to get a four on the bottom when I pull the four out of the brackets no change And having said that we're almost never going to be looking at masses of a human being type size Gravity is usually minuscule negligible. Oh unless one of the masses is huge for instance a planet or a star or a moon That's what we're going to be looking at and that's why you probably want your formula sheet out because we're looking at masses Of the moon in the earth and the Sun and you don't have to memorize them But you want to look at them so specifically you want the back page of your formula sheet that has all the data on it okay example for Assume the mass of the earth is 5.98 times 10 to the 24th kilograms Which it is how do they figure that out? I'll show you will actually calculate the mass of the earth in just a few minutes because it's not like they Could throw the earth on a scale or anything and it's not even like we could assume that the earth was Uniform all the way through and maybe measure You know 10 tons of dirt and multiply that by how much dirt there was because there's an iron core Which is a different density in a different way. How do they figure out how heavy the earth was fairly easy cross multiplying questions But for now I'm telling you Andrew it's 5.98 times 10 to 24 And it's radius is 6.38 times 10 to the 6th That's fairly easy to calculate just simply by watching a ship vanish over the horizon if you know how high the ship's mass was It's fairly simple trig to figure out what the curvature was and then just extent It's the arc length formula for those of their math well by the way It's a very easy calculation the arc line could be the entire circumference Find the force the earth exerts on a 50 kilogram person on its surface. This is Newton's law of gravity What's big G you might want to take a check a chance right now to find it on your formula sheet so you know where to look There's the data stuff. That's the page. Yeah, we're on the you're on the back page That's photocopied to do a page with all the data on it, right? There's a whole bunch of stuff and somewhere in there. I think you'll see a capital letter G. Yes How big was big G? Okay Every year there's some kid who right now is completely out to lunch and starts putting 9.8 in there on the test And I give them zero because this is not little G 9 This is big G completely different and I've tried to walk you through right now where it is on your sheet But I also see there's two or three kids that didn't bother getting up their formula sheet haven't bothered walking it through fine But you're taking a big risk. What's the big M the mass of the earth? Find where it is on your formula sheet even though I gave it to you you should be able to spot where it is Do you see it 5.98 times 10 to the 24th? Yes What's the little mass the mass of the person 50 the question says? Divided by the radius of the earth squared You might want to find where the radius of the earth is on your formula sheet So you know where it is even though I gave it to you in this question 6.38 times 10 to the 6th squared This is complicated enough with enough scientific Notation I strongly encourage every one of you right now to try this on your calculator So that you know for example how to type in a scientific notation squared See what you get you should get this think I don't get it bang on I cheated and did a shortcut in my head You for my bang on or is it like 489.9999 something 499.95? okay So if you didn't get that you want to start to figure out what you did on your calculator Because for the next five days, this is the easiest calculator calculation. They're gonna be longer and uglier By the way, we could also have calculated this by going mg What is 50 times 9.8? What is 50 times 9.8? See we actually knew the force of gravity able to do it So why did we do it this long way? Well as you move away from earth. What happens to the force of gravity? It's weaker So what we're trying to develop is how the heck can we calculate what the force of gravity is saved by the space shuttle by the space station up in orbit? also well This result should not be surprising since we could if we calculate the force of gravity use it using mg then we get 490 this is going to give us something else neat until now We've been aware of two ways to determine the gravity field now the gravity field of the earth is 9.8 and you can either call it meters per second squared although it's also Newtons per kilogram because it's an acceleration and an acceleration is a force divided by a mass right We found that fact you found it in physics 11 you all put a weight near the ceiling you dropped it and you timed it and Although you got a lousy value for g in physics 11 because we're using craft equipment You can imagine if we did it in a lab with electronic photo gates and instant timers We can calculate that 9.8 really easy. This is not the neat thing, but the fact that we know this Allows us to be Fairly clever so the gravity field at a point can be determined by measuring the weight of a small mass m and the ratio of the weight gravity divided by the mass gives us g or We did it by calculating the acceleration and free fall last year. There's a third way this means this if this is gravity and This is gravity and these two m's are the same That means that the equation for calculating this on Jupiter where we can't go and drop something in free fall or On Saturn where we can't go and drop something in free fall or on the moon before we went there Is well Emily that m's the same as that m that must mean the gravitational field is If you know the mass of the planet and you know the radius of the planet you can calculate its gravitational field ahead of time without going there That's how you can find Connor g on the moon or G on the Sun You can make it because you're looking really out of it Okay, in fact if I go like this 6.67 times 10 to negative 11 times the mass of the earth Desperate didn't go mr. Doek Divided by the radius of the earth squared mr. Doek squared Mr. Doek Do I get 9.8? Now we know the 9.8 ahead of time. Yes This is what allows us to go backwards and figure out what the mass of the earth has to be in order to get the 9.8 this is how they figured out how much the earth weight it was finally we know The hard part was calculating this so Cavendish did an experiment where he was actually able to measure something to the 11th decimal place And one of the first things he did once he had that value accurate as he was So we call this the gravitational field The gravitational field strength of a planet now this equation is not on your formula sheet is that Well, it is on your formula sheet. Can you see it's tucked away in this and that's what I've tried to show you I? Guarantee you on your test on a question multiple choice. I'm gonna give you some mystery planet planet do it I'll tell you it's math and it's mass and it's radius, and I'll say what's the gravitational field strength there What I'm really saying is can you go big g times the mass of the planet divided by the radius squared of the planet? And tell me what it would be there this last property is useful because it provides us with a means to calculate the mass of the earth Let's repeat what Cavendish did about 120 years ago, and let's see if we can get the same dumb smile that he did when he finally knew He said well, I know this He said Get the m by itself How would I get the mass of the earth by itself? R squared goes on the top right Kara, and the big G goes on the bottom He said I guess it's gonna be The 9.8 had been measured for quite a while Not that hard to measure the 9.8 you can figure it in all sorts of ways, so he happily put that in Radius of the earth you can measure that's been measured actually for about 2,000 years pretty actually another way you can measure it is looking at the shadow of the Sun and comparing how that changes as the Season is all sorts of ways to measure the curvature of the earth So they knew that it was 6.38 times 10 to the 6th squared and then he smiled as he plugged in his just Determined in the lab value for the universal constant of gravity type thing that in How heavy is the earth? You get something very close to 5.98 sorry 5 point what is it 5 point times 10 to 24th Right, and this is a mass of kilograms And he smiled one of the next things he almost instantly did was he said hey now that I know this Now that I know this and I know the force of gravity that the moon pulls on us from the tides I can find the mass in the moon. I know the radius of the distance I know the distance between the earth and the moon. Ah, it was a bunch of dominoes down to close So gravitational field strength. This is how strong G is on anywhere This also is going to let us calculate what G will be in orbit somewhere Because gravity isn't zero in orbit But it's smaller how much smaller depends how far away you are from the earth We can figure it out. What's your homework number three number six? Please notice they gave you the radius of the moon in kilometers. You'll have to change that to meters This is what cabin. This is how you can find the mass of the moon seven eight Also in kilometers Yeah, I'm good 11