Transcripts
1. Gravity, The Basics - Wrapping up!: it's time to up up on review what we have seen together. We started this schools that reminding ourselves how to handle killer Matics problems in one dimension. Remember the five steps to solve a one D motion problem? First step is the acceleration zero constant. Second stead defined the positive access felt Step filling the super data fourth step. Select the motion equation that contains the unknown and the three known valuables and finally lost that solve. After this, we learned and trained on how to use Newton's universal law of gravitation. The force between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. Then we entered the core of the course gravitational fields. First, we defined what is a field. A field is a region of space where each point is associated with a quantifiable property that allowed us to focus on gravitational fields. A gravitational field is a regional space where point mass experiences a force and the quantifiable property here is the gravitational fear strings the force experienced by one kilogram. We realize that the gravitational fear strength is effective quantity dependent on the mass rating the field on the position related lead to that mass. To find the gravitational force exerted on an object place in a gravitational field, you just need to take the mass of the object and supplied by the gravitational field strength at the point where you place for your combining These two equations led us to realize that the universal law of gravitation emerges from describing gravity as a field. After this, we reminded ourselves off the mathematical properties off circular motion like, for example, that angular velocity is two pi divided by the period, or that the linear velocity is equal to the product of the radius. Off the motion on the angular velocity, we've also introduced the concept off centripetal acceleration of centripetal force in a circular motion, acceleration and force always directed towards the centre off the circle and always perpendicular to the powerful the body. In addition, if the net force of a body is causing circle emotion, it opens new perspectives to solve problems. Yes, because of magnitude of the force will be also equal to N B squared over r and and will be get squared are and envy Omega by combining notions of circular motion. With those related to gravity, we were able to dive into orbital motion. This allowed us to play with Stella Systems or planetary System. But we also realize that from this emerges in law the third Law kipler that relates a period of revolution of a planet with the distance to its star. Okay, now it's time to test your knowledge. So prepare some draft paper in the pen and head on to the cuisine.
2. Instructions on how to take the Gravity Quizz: Welcome to the gravity quiz. The Gravity Quays is composed of 12 questions that will test you understanding off gravity and circle emotion. These questions cover classes 234 and five off the course. Gravity The basics. There are two ways you can take this quiz. The first way consists in going through one question at a time by watching the videos. Each video presents one question with the time. Once the time is up, a detailed solution follows. Sometimes a discussion providing multiple routes to solve the question is also presented. The second way to take the gravity quiz is more conventional. Download the pdf file containing the quiz and eventually print it. Place yourself in exam conditions with some paper pencil on the calculator. Make sure you will not be disturbed during the next 30 minutes. Who example. Set your mobile phone to off. Set a timer to 18 minutes. This timing is representative of what is used in International Baccalaureate Multichoice exams. If you wish to take your time doing the test that still wish to feel the pressure, set your timer to 25 minutes. You can check out all answers in the pdf answer. sheet that is provided on the platform. You can also go through the videos one by one, where every answer comes with a detailed collection on the wife. Enjoy the quiz on good luck.
3. Question 1 - Gravity Quiz: picture natural note in the space station, which is orbiting the earth. Well, you can see the astronaut floating around the space station. This question holds full purple issues to try to explain why only one is correct and we have to identify it. So let's go through the four propositions one by one, first of all, on visual. You know, I have to make a little diver. So have here the mass of the Earth and here the location where the national would be at a distance r from the center of the earth. It can help for position A. The gravitational force on the state's cloth on the astronaut are the same, but this they find them right. So the force on the astronaut would be the mass off the astronaut, multiplied by the gravitational fear strengths where they're not educated and I think thing for the space station. Well, the space station and the astronauts are the same location, and the gravitational field strings depend on the mass of the planet on the distance from center. It's the same for for the astronauts on the space station. Therefore, G is the same for both by the masses are different, so the forces will be different. So Proposition A is incorrect. Proposition B. The national is located at the position where the gravitational field strength is. You were obviously not because the national earth is not zero. The universal gravitational constant is not. The low on the distance from the planet is not infinite. Therefore, G is not Proposition me isn't great for position. See, the accelerations experienced by the astronauts and spacecraft are the same. I'm to TV. This kind off makes sense to me. Let's see why. Imagine that I haven't object subjected to have gravitational force F vehicles and Jean. It's the only force on it, therefore, to net four so I can apply the second law mutant. It's also equal to M A. On I can cancel the ends and I see that the gravity's for fear strengths will provide the acceleration off the subject. Now let's do the same thing on the forces of the national and on the space station. So here we have massive yesterday ought to play by the acceleration of yester note masses of space station with God about the exploration of the state station. Good. I'm going to remove this and I see that that can cancel the masses. G is the same for both. That implies that the acceleration of the astronaut is the acceleration of the space station. Those quantities are equal. Surfer position, See is correct. What about Proposition D, the gravitational force experienced by the ash Note zero. Well, obviously this is ridiculous because force here on the afternoon would be and I should note g the mass of the astronaut is my zero on. We have seen also that he's not zero therefore, the force on the afternoon. It's not proposition decent collect yet I can understand the problem. Some students have been figuring out a national floating around like flying. Why, there's a gravitational force on him. Let me try to explain it to you another way. The elevator to draw here on the elevator, which is actually accelerating downwards in the elevator place a block off mass. I want to do everybody like I want to analyze what's going on. So I have here a force of gravity and G and here the normal force. I also they find a positive access. Don't. Okay, So what's the normal force here? Well, you know, when you're in the elevator and it goes up, you feel suddenly heavy. This is, you know, feeling your weight. Your feeling. The reaction off the ground to your weight when you feel heavy is testing reaction of the ground that you're feeling. If you're feeling very light, it's because your weight is not pushy as much on the ground, and therefore the normal force is less and you feel lighter. That's normal force that you feel when you're measuring yourself in the balance on a new bathroom. Well, we're not measuring your way to actually measuring the reaction to your weight normal force . So let's determine this normal force. For that, I will write down the Net Falls, which is here n g planets, and apply the second or neuter. This is equal to and pay unless we arrange this and equals M g minus may, which I can also relight and equals and G minus a no. If I replace the acceleration here baggy, meaning that the acceleration is a gravitational field strength that I am in a free for, then becomes a hero, there's no compact force anymore. That means if there's no contact rules that new compact. This is why the astronaut appears like floating around in the state station. There's no reaction force because he's not pushing.
4. Question 2 - Gravity Quiz: the average density off the material forming Planet X is twice that off Planet. Why? So let's write down this relationship. Mathematically, four X equals twice whole wife on they have the same age is also like O X equals what would be the ratio GX of a G y off the gravitational fierce place. So when I have a ratio like this with a choice, I like to write down the ratio as a ratio. The formulas. It's very useful because usually I can see things that will cancel immediately, like gravity for fear, strength, but also the radius that simplifies drastically these expression into a mix of m y. But I do not have an X when y I only have the densities of the planet. Yet I know that density is mass divided by volume, so I can rely. G excellent you Why? Because ho x, the x of Hawaii. Why? But there's a volume dependent on the under radius. 4/3 pi acute. The agencies are the same for the planet, so I can kill the bowling's, too. I'm done ho exit hole. Why is to we'll also be
5. Question 3 - Gravity Quiz: this question was an easy one. You only need to recognize that the object in orbit isn't Soglo motion. Therefore, the acceleration of this object will be centripetal with expression B squared off. If you want to find the minimal acceleration, you should have a minimal velocity because it's on a waiter on the maximum radius because it's all the denominator. So the minimum be lost years for being D on the neck and radius out of BND will be for B, so the answer is that's where you will have minimal.
6. Question 4 - Gravity Quiz: this question is so typical. It is so typical off certain exams, like the I B or the A levels, where you have a mutual section. This type of question is a case. One case to question going to the quantity the defense upsets and valuables. Well, that would be case one. Now change the valuables. The quantity that depends on this valuables is going to change to now. You are in case, too. Usually the question would be find a new value. We'll find the ratio off the value of the quantity between case, too. In case what things like these. For example, here we have a Planet X was radius twice that of the earth and four times its mass. So these variables that change on the quantity that they required to beautify its gravitational fear strengths That depends on these valuables. So how do you solve this? Well, first of all, you extract the data, so we've got the Planet X. It has a radius twice that of the earth. You write it down mathematically and the masses four times. Now you have the data. It's a good idea to write a mathematically to have it available for you when you need it. And now they ask you to find the gravitational field strength of Planet X as function off that of the earth. So something like this G X equals about a number here, G g for the Earth. There are two ways to solve this a slow way. But you're sure to get it right and a faster way. Let's do the slow way first. So in the slow way, right down Govs case Well, the formula and in case do I get there for the same formula. And now a place the valuables in the second case by the valuables off the first case, That's two boys quit. Don't forget to put the two times. And now you put all the numbers on the side because I want something like this. I want to be able to extract the formula for G E from this formula. So I do four times by two squared I g and e of his quid. That gives me one time. He actually g reverential fear. Strengths are the same for both. So it's on to be that is a slow way We caught it. A case one right on the forming of a case to then you plug in the relationships in the equation off case to in order to extract the equation of case one out off case to and here you should have a number which is oration. The foster way is a bit more dangerous because you drink in your head. Basically, you just write down the formula on. Do you look at it if I double the mass well at that both of gravitational field. If I double the distance, I divide my gravitates for fear strikes by four they found two by by four because of the mass and divided by four because of the distance. Well, my gravitational field strength stays the same. You see what I mean? For example, you could imagine this time I'm going to apply the distant by three years of mass back to If I multiply the mass by two by gravitational field strength. It's been troubling to so by. But if I would try my distance by three gravitational field strengths would be divided by nine so divided by night they're full G case to will be to ninth off What she wants makes sense. Okay, good to this next question
7. Question 5 - Gravity Quiz: - in this question, we have a mass nine in on the Mass. 69 which are separated by one meter between them we have on us and which is located at the position where the residential force on would be zero. Yes, there's a gravitational full, some M due to dining, miss. That's call it F and there's a gravitational force or AM due to 16. It's write it down like this F 16. What is that? I define a positive access on the Net force to be zero. If that is equal to F 16 then honest after him. Cool. Zero. That means he's to force his article. So let's lie down Expressions G Mass and by 60 name over the distance between the two D squared fools Dream mess on by nine AM between them, one minus the It's quit Now can cancel a few things all the G's and the ends and I end up with this expression. 16 Over the square equals nine of ah, while this squared, unless we may just a bit get 16 1 minus t squared because 90 squared and I recognized immediately a squared equals B squared C continues Cuevas from the science. Giving me full by one man's day equals three D elegance. So 40 four minus 40 equals three d. So 70 equals 4 30 equals four seventh. He also to this question is on so
8. Question 6 - Gravity Quiz: in this question. We have two moons A and B which are all between the same planet off. We learned from the text of the radius off be triple that moon so we can write it down mathematically. So that is available to us when we need it. They want to question what is the ratio off the acceleration of moon be to that of moon A. So when I have this I like to write down Were they asking me right here to ratio of accelerations on that would be my stuff. First I need to know how can I express the exploration of the moon? Well, a moon will be subjected to the gravitational force, right? So mg when m is the mass of the move on G the gravitational fear strength at the location of the movie. But because it is also the Net force I can write down, I may give me ankles so I can write this G b of a J and then plug in the formula for the gravitational field Strengths G. And I'll be squared divided by g m of a squared. You see that many things cancels the G on the mass creating the field. So I got a B over a a is equal to r a squared of r B squared. This is a racial squares. So also the square of the ratio, this ratio I know it from the data we got from the text. Oh, a B is good. Therefore, if I like it in 1/3 squared, that is one night, the answer is also
9. Question 7 - Gravity Quiz: in this question. We have a car traveling on the bridge. Spv the bridge can be assimilated at a knockoff circle of Radius R. We have requested to find out what his reaction falls off the bridge on car. When the car is on the top of the fish, passion falls. Maybe it's a good idea to everybody diagram to find out what are the forces acting on the car. So for that first defined Maxus and then look at the forces on the car, well, I have to wait OMG and I'll have the normal falls. It could be a good idea to express the net falls. The net force on the car will be plus M G minus. The bridge can be assimilated as a circle, so when the cars on the bridge it is in circular motion. Therefore, the net force will also be a centripetal force which we can express and the squared off on . By rearranging this equation, we can find an expression for any Andi minus B squared of from the propositions in the question, we realize that this expression for the normal force is answer deep
10. Question 8 - Gravity Quiz: - Let's write down mathematically the data which is provided to us. But first we've got this mass a place that the distance D from a small physical body on this past experiences a force gravitational force off 60 new terms. Then we replace it by a mass B which has a mass three times larger and which is position that the district's twice from that off a DB equals two Depay. We want to find the gravitational force experience by a point mass be so let's express it. F b. It cools gravitational constant guard by the knights of the body attracting attracting it by the mask be divided by the square of the distance. Between these two masses on industries are one nation so three times the mass A here on two times a nasty that square, including the tooth. Now I would put all the numbers on left to be able to express the force on last check This out feels there. The two squared Is there second wife G and a of a deer squid, which is F A, which is 60 new terms on 1 82 by my Foy's truths of 45 you dopes, which is answer
11. Question 9 - Gravity Quiz: - in this exercise, we had an object X off mass and X distance from a distance. The two mass of an object? A last a on We know the force that exerts awnings. Let's call it F A. It's 20 new terms that the first act off this question. The second act is at the at last be yeah, at the same distance D. But the other side and we know that denies B is twice a mass. We're requested to find the net force due to the two masses on the object X. Okay, let's look at the FAA Well. It would change right that we can find an expression of it if it would be cool to the mast X multiplied by the gravitational field strength. At that point due to object A. J, we need to find the net falls. So it's a good idea to define an axis because forces victors so the net force will be equal to F B minus. A FV would be the mass off object eggs with a plan by the gravitational few strengths at the point where X is due to be and same thing for a what is the relationship between the gravitational featuring would be on that of a well, we have the massive. So let's expressing gravitational fear strings at location off the object X due to be t V equals G and B D squared. We know that NBC's twice so we get to time stream on a squared with Chase G A. So we got vehicles to J. It's a good idea to taste G B here, my GS. Let's do that. The Net force will be Amec's Multiply to J Matters. Next, The plan by J. Well, that's just an extra, which is 28 times. So the answer to this question is also see.
12. Question 10 - Gravity Quiz: - this question is a typical case. One case. Two questions in case when we have a satellite which is orbiting the earth at a distance, D one equals 20 The speed of the satellite would be good of GM to, in case to the engineers wish to bring a satellite down so that the height is Haft, meaning they reduce the distance from the center of mass by off to, so the new height becomes final. New distance Excuse me, becomes three are over too. Therefore, we have this Tuesday. He, too, is three horse, and the two will be quoted scrabbled off GM over three halfs. I don't like having fractions the denominator, so just you ranges of numbers to G. M over three. Now it's a typical case one case to question, because what I can do now is trying to extract an expression for B one from this one. One thing I could do this with Apply that to all the new Mary turned denominator and see what I get to equal squaring off two times two GM over three times to oh, on. You recognize this, Then I actually can dispute the square root square it off for with me But the blood by square root off GM of a two hour to extract V one from the expression Skoda four is too Dr Unscripted three by a few one. The answer is they're full. No.
13. Question 11 - Gravity Quiz: - in this question were requested to find the distance between Venus and the Sun. The data were given. It's the length of the year. Venus. 225 days birthdays. Well, the year on the planet is also its period of revolution. I think I'm going to call the third Law of Key Player to the rescue. Yes, because this whole states that if I have an object in circular motion around another one, I eat a bit. The distance between this object on sort of mass, divided by the period of revolution of the subject, is a constant. So if I take this ratio for Venus, I know it would be the same ratio for the earth also, or four miles for computer off any planet or object in circle orbital. Understand? Well, I have everything I need because I'm looking for this. I know this different this less for your injured. I'll be good. Who's t squared? V P. Oscar E. Let me rewrite it a little bit sweeter to my eyes. The ratio of the periods power 2/3 by the distance between the sun and it's breaking numbers, So that's turning 25 by 3 65 power 2/3 by 150 million kilometers. So I also will be in 1,000,000 kilometers. And if I plug this in my calculator, I find 108 million kilometers. The answer is answer be
14. Question 12 - Gravity Quiz: I'm sure when you saw the question the 1st 2nd that looks like a complicated one. Because of the big formulas, which I proposed as answers. Don't get fooled by this. This is one of the easiest question of the test. Look, we're requested to find the difference in gravitational force off one kilo here on one killed there. So let's get creative Force F one and forced to on just makes a difference and see what we get at this location. Both the Earth and the moon. I'm going to act gravitationally on this one. So if one be cool to G one kilogram by the mass of the Earth If I did by, I was quick. And here Well, here's gonna be negative because, you see, I've got a force Garrity Dutilleux like this on a force of gravity to move that way, it will be negative. G times one by mass of the moon divided votes the distance between the handle scent of the moon D minus R squared. Good. Let's do this one now. Same thing in terms off the action of the Earth. But this time the moon is going to pull it in the same direction. The two forces which contribute to have to are the ones to the earth and the one due to the moon. Plus, he plus G one mass of the moon divided by Was the distance between the two d plus are so de guess Square. Now let's find out F two minutes if one which is a difference, that's that's a question like, I don't think the difference. I see these two expressions of the same. They'll cancel. So leaving me only with these the G mass of the moon of a D plus squared and minus one of minus minus This So it's gonna be a plus. G mass of the moon, the minus square. I can factor life G and massive move. Well, uh, so what expressions? Course from two. Well, the expression proposed in answer be The answer is