Transcripts
1. Introduction: well come to this class. Focused on Blini, Emotion Way will review together and easy and very powerful step by step technique to solve motion problems in one dimension and with constant acceleration. The first video, if the lesson itself. Presenting the technique called the Super Active, the second video proposes a mathematical proof of the motion equations used with this technique. And finally, in order for you to train your newly acquired skills in solving one D motion problems, four exercises are presented in two training videos. This class is part of a larger course named Gravity. The Basics. This is actually the first class off this course, because understanding motion is very useful for the study of gravity. Still, of course, we can gain a lot from this class without having to take the full gravity calls. The level of this class is about end of high school, so it is a great tool for high school students taking physics and preparing exams. It is also suited for any person that wishes to revive the knowledge in the physics of leaning emotion. So now jump to the next video and enjoy the line
2. Solving 1D Motion Problems: In order to fully benefit from this course, you will need to be able to handle motion problems using motion equations. So as a taster to the fund physics that is to come, let's review briefly how to solve motion problems in part one off the school's way. We'll talk a lot about gravitational forces that apply on bodies with mass neutral has taught us that when a body is subjected to a NAM balanced force, this body will also be subjected to an acceleration. So let's consider a body with a mass M. Let's say it's a ball on. Look at the forces on the ball. The ball will have a certain weight on. I could imagine that I am pushing it so there's also in Applied force. Now there are two forces on the ball, so we'll find the result in force, which I will said Cool. The net falls. So you turn tells us that if the net force is not zero, if the net force is unbalanced, then the body will also feel an acceleration which is proportional to the force on the money so we can calculate the acceleration. The acceleration is proportional to the net force has the same direction. Yeah, the two vectors are calling you now that we have the magnitude and the direction of the acceleration. You realize that it is pretty trivial to figure out the motion in the path of the body we will use for this. A simple technique called the silver Technique. Civil technique is a five step technique to solve any motion problems with constant acceleration. To present a technique, we will use an exercise. Imagine that had the ball in my hand and that 1/3 upwards at a speed of 20 meters per second. The question would be what is the height that would reach the board? I illustrated this question by representing myself on board with a ball in the hand that I'm throwing upwards of 20 meters per second. So how can I find out? But high peaceful Reges, First of all, Steph. One Look at the excavation on define if it's constant. If it zero it is not constant. This vaccination equals zero. That means that the velocity does not change with time. So in that case there's only one equation that I can use. Velocity is displacement of a time for speed equals distance of the time if the acceleration is not constant. So the acceleration changes with time. That case, we cannot use the technique. I will show you. Now you have to use Kathryn's. But don't we? In high school level most of the time, 99% of the time, the acceleration is constant. Either zero. Why the constant? In that case, you can use the technique I want to show you now. So here, in our case, the excavation is constant because the exploration is acceleration due to gravity on the surface of the Earth, we consider g being constant. Step number two Define an access on a positive direction. For this actives, I recommend you use a positive direction in the direction of the initial motion. So in our case, I would choose an axis positive upwards. So step number two. Choose an axis. Step number three right down S u V A T. Particularly and finish what is S s is a displacement. So the changing position between the initial moment and the final moment. So the initial moment off this question is at the moment on moving the ball on the final moment of this question it went. The bull reaches a maximum height. So actually s is what I'm looking for. Height. You you is the initial velocity. So in that case, I have my initial velocity upwards at 20 meters per second. So plus 20 three, the is a final velocity. Think about the bowl game puts well intuitively you know, it's going to slow down, right? And to reach a maximum point where here the velocity will be zero. So final velocity is zero. Then acceleration, acceleration The acceleration due to gravity 9.8 meters per second squared. We re round up to 10 meters per second square here. What direction hasn't go downwards? Say the negative direction. This his wife needs to be minus 10. What about time? Well, it's not the question so we don't really care about it on. Besides, we have already three of the data. Yes, When you have three out of five you can solve. You can always solve If you have three other five, imagine we have any exam exercise and you know in this exam exercise you need to use equations of motion on that. You can apply the super technique When you fill up the data, you find only two. That means you know that you've missed something. You missed some hidden data here. For example, there's no indication in the text that at the maximum height of velocity zero that you need to figure out by yourself. It's hidden data. So we filled up the data step full choose emotion equation. So have to choose the motion in question. Let's first list. Um, you have for them s equals new plants. V over to tea equals year plus 18. These glad equals use. Grabbed Just two. Yes. And s equals beauty. Plus 1/2 a t square. I don't use science. So which one should I use? Well, look at your data. You should use in question where you have the three known kilometers on the one you're looking for. Alternatively, you can also look at the question which does not have the one you do not have on you do not care about. So here time. That would be this one. That leads us to step five. I put step five here. Okay, so I write down this equation b squared equals C squared. Plus two A s. I ve zero so I can just observe. I'm looking for s so adjusting to rearrange this for s s equals minus you squared divided by two a And now I plug in the numbers that's minus 20 squared Divide about two times I understand s is minus 400 divided by minus 20 which is 20 meters. Do you go step by step? You can solve an emotion Problems with the exhibition is constant Your turn now from the moment I send a ball upwards to the moment the ball comes back into my hand How much time has passed? Theo? Bull goes from my hand, reach a maximum height on, then falls back into my hat. The initial velocity was 20 meters per second. Step one, Look at the acceleration. Is it constant? Yes. So stick to to find a positive access. Already done. Step three right down soon. But what is it? This basement between the initial moment on my problem and the final moment of my property . Well, it's my hand in my hand. Whatever the path of the ball, it could have gone the other side of the universe and come back into behind the displacement is still zero. Initial velocity is 20. The final velocity we don't really can actually, because we know the acceleration, which is minus 10. And the time is what we're looking for. So which equation should I use When one wish that have the That makes this one the women and I can write it down s equals. UT plus 1/2 a squared should be careful with my eyes and then they need to rearrange this. I see that s equals zero, but so I can actually factor wise t out. This expression is zero If t equals zero where that's not the case. That means a ball would have stayed in the hand. All this is even. So go you Plus 1/2 80 equals. So just we range 40 t equals minus two view of a minus. Two times you was 20 divided by minus 10. The tea is I give it off the negatives 40 on 10 4 seconds. If you master this technique, it will really simplify things when you are actually solving more complex problems
3. Deriving Motion Equations: I'm pretty sure that many of you are quite stubborn like me. I don't like to be fed on equation and just told. Believe it. Any proof? So these motion equations, I will for bows here a proof too. Let's start with the 1st 1 s equals U plus V two by two teeth. Now, you know that if you draw a velocity time graph so you would have here you the initial velocity and here V the final velocity. And here the time If you draw a velocity time laugh, you know that the area under the graph is actually the displacement A She's written like this s equals the DT where vida belong t So it means the area under the graph is this meaning this area of this rectangle plus the area of this trying. So let's calculate this s so for this with Tang was reviewed by t beauty. That's this triangle is going to be the man issues. So this height v minus you, my t divide by two I didn't like this one minus 1/2 is 1/2 so s equals ut to minus sweetie to go placidly. Theo too. But that's it and then I just Specter iced tea out u plus V two t straightforward. Let's look at the other one. The equals u plus This one is directly linked to the definition of acceleration. Acceleration is the rate of change of velocity that the minus you divide by the final minus t initial t finalist t and t ensure zero. So we mine issued by my team. They found justly radiate a bit. I get 80 equals demand issue O V equals plus 18. You can see this. That velocity of the final time will be the velocity initial plastic contribution to the acceleration during the time I like to read questions like this like a little like English , you know? Okay, well, you got these two? Well, two others, actually. Just the live from these two, for example, I can consider that's I'm going to put V inside this one forget s equals U plus U plus 80 or to t. And then I develop yet ut of a two plus few team of two plus 80 squared over two. So that gives me you t plus 1/2 it is quit. So we go 3rd 1 beauty class 1/2 a T squared Now let's find 1/4 1 which is B squared equals U squared plus two a s I dont t So what should I do? I should get try to get rid of on example. Could be actually to trust for this. Well, in t equals two s over You bless V right? An example. Oh, I could actually plug in t equals V minus you a and plug it in him Do many different things A Les Waas one I never done before. I never like this one into there, so maybe this is just worthless. See the equals u plus eight times two s on you. Place deep. Send a little bit femaleness. You're decidedly man is you equals a to A s on nuclear t. Oh, that's a nice one. Because when I pluck this here yet v minus you on the plus, you equals two a s. On this is the squared minus. He squared, Justin Identity B squared minus. You squared because too. Yes. So I end up with the square equals u squared. That's too well, that's a very pretty way to do it. I never did it. This way. It's the first time improvise on this camera, so I probably will use this technique when I teach it to my students. I hope this was useful. Now let's go to the next deal where you can train.
4. Exercises 1 & 2: and exercise appears on the screen. Also video and work on the question. When you're ready, please use the video on view. The collection the first exercise says that the car, which is a speed of 100 kilometers per hour, in just 2.2 seconds and we need to find its acceleration well, we assume here that the acceleration only constant because they ask you for this value. So that's step number one. Step number two. We could cause it up and access, which is in the direction of motion of the car which is positive step number sleeve down super s. We don't really need it. You that the initial velocity zero v The final velocity is 100 kilometers are now up that we need to put it in meters per second to stay in a science Celtics Your little trick when you have kilometers Palau and you want to go two meters per second. Just divide by people in sex. If you need to go for meters per 2nd 2 kilometers flower, just multiply by 3.6. So here V is 100 divided by 3.6, giving me 27.8 meters per second. A That's what we're looking for. And t well, we know that the car goes from 0 to 27.8 meters per second in 2.2 seconds. Step four, which equation should I use? Well, one which doesnt have s this one. So have I. Did down equals u plus 80 on the range for what I'm looking for, which is the acceleration A equals V minus you divide by t I plug in the numbers and I get 27.8 minus zero. Do I like to point to? So excuse me. 12.6 meters percent limbs, quit In this exercise we have a car driving at 100 kilometers. And now on a motorway The driver Cesaire, 80 kilometers an hour speed limit sign 30 meters away. So in order not to exceed the speed limit, the car needs to slow down. The question is what should be the deceleration of the car. Oh, if you prefer the acceleration knowing that it will be negative. So Step one is the acceleration constant? Well, this is a question. So we can assume that it is step number two, The final axis So we choose positive direction in the motion of the car Step number three Fill in the super table s 30 meters You 100 kilometers now, but we divided by 3.6 to get different meters per second. You mean 27.8 meters for second V? Well, at the final point of the exercise after 30 meters, we need to make sure that we have 80 kilometers or now a speed. So in meters per second, this gives me 22.2 the acceleration. That's what we looking for. The time we don't really care because we already have the data. So which equation from we use one which doesn't have the time, This one. So I write it down and then I just revenge it to find a plug in the numbers. 27.8 squared minus 22.2 squared, divided by two times 30. I found 4.6 meters per second squared
5. Exercises 3 & 4: and exercise appears on the screen. Also video and work on the question. When you're ready, please use the video on view the collection. In the third exercise, someone drops and metallic bowl whatever from the top of the Eiffel Tower, which is 300 meters high. The question is, how long will it take before it reaches the ground? Is the acceleration constant? Yes, it's gravity, so we can use seven second step. Choose a nexus. So this time are true. The nexus downwards for the positive direction downwards. Step number three, Fill in the suit. That table, the displacement covered If 300 meters, What is the initial velocity? Zoom? What is the final velocity? We don't care because we have the acceleration, which is 10. And now we're looking for the time. So which equation should we use? This one seems good because there's no final velocity in it. So let's write it down and your engine. So you're a zero s equals 1/2 a T squared. And now we waited for team for T equals quote off two s of A, which is two times 100 divided by 10. So this is 600 on my tents or 60 and I found this close of 60 7.7 seconds. In the final exercise, we have a sniper rifle which is shooting straight up. We know their initial speed of the bullet 1000 meters per second. The question is what is the higher that bullet will reach stepped in a while? Is the acceleration constant? Well In the exercise, we saw that we can elect a resistance. So the only force which is acting the bullet is the force of gravity. Therefore, yeah, the acceleration will be constant. We can use a super technique to solve this question. Stepped on the to define a positive access positive direction. It's a good idea to define it in the direction of initial motion. So upwards stepped on the three filling the data. The displacement will be the difference between the initial and final position. Initial position is when the bullet just comes out of the gun right on. The final position will be added maximum height. So this is actually what we are looking for. The initial velocity is given in the text. 1000 meters per second on the final velocity will be the velocity of the bullet when it it is at its maximum height. So you yes, the bullet goes up says down we to my from height and then the velocity change sign. So at this maximum position it issue the acceleration is the acceleration due to gravity. But this time is that I think downwards. Therefore, it is my understand and forget the miners on finally time. Well, we already have UV and a so we don't really need it to find s the full choose a light equation which went for that years which doesn't have time. This one's good. So let's write it down and then we wage it to find s. I know that I can get rid of the V because it's equal to zero. So I have minus two squared because to a S O s equals minus two squared over two a. Now it's time to plug in the numbers as it was minus 10 to 3 squared 1000 if I did by two times minus 10. So that's actually a millions of minus 10 to 6, divided by minus 20 and fined 50,000 meters. Note that in the exercise they ask you to comment on the result Well 50,000 meters, 50 kilometers. It seems highly unlikely that you can have a bullet going so high. This is because we have neglected our resistance. Resistance at a speed of 1000 meters per second will be very, very strong. So we can expect the bullet to sell down much quicker then minus 10 meters per second squared. I should actually put unit. This exercise closes our view of motion. Now we can start the study off gravity.