Basic Physics 3A. Lecture 11.

Let's go right to the example we were going to get to at the end of last class. Right now, we're just very briefly going over the concept of Newton's Three Laws, and we ended with one version of the second law, that F forces or interactions cause accelerations and the magnitude of the acceleration is proportional to the mass. And a standard situation you might have is where you know something about the acceleration and you're curious what net force generated the motion. It is the simplest, most basic of Newton's Second Law problems because to answer it, all you have to do is find A and solve for F net equals ma. So it's pretty straightforward, but I just wanted to remind you, and this is where we start to build and put our ideas together. So in this problem, you are given that you push a book 2 meters, and that time, it goes from a velocity, notice it started at rest, okay, and it goes to a velocity of 1.5 meters per second, so it starts here with v equals 0, it moves 2 meters, and when it gets here, it has v equal 1.5 meters per second. Now how are we going to find, and we are told it's constant acceleration. So how do we find A in this situation? Quickly do that on your piece of paper. This is the kind of problem that should take you less than a minute. And you should be done. Anyone want to give me a number? 0.5 is a good start, 0.56 meters per second squared. Anyone want to tell me how they got it? What? So this is one of those times, it's good to remember the equation we don't use a lot. Now if I make to the right positive, delta x is positive, I'm speeding up, the acceleration is positive, they're in the same direction, so we get a positive number here, and so A, my acceleration, v naught is 0, it's just 1.5 meters per second squared, divided by 2 times 2 meters, and that gives me 0.56 meters per second squared, and I was told the book has a mass of 0.5 kilograms, so the net force is 0.5 kilograms times my 0.56 meters per second squared, which is 0.28 newtons. Any questions on that? What would be another way you might have found acceleration if it was constant acceleration? What are some other ways we find acceleration? Change in velocity over change in time. We use time to do it. v final equals v naught plus A t is another way of writing change in velocity over change in time. So everything we did for the first three weeks will come back in our force problems. Now that's the second law. It tells us what happens, notice the second law, I'll rewrite it here, had two features in it that we have to focus on. It's about the total force and their vectors. So we worry about the total force, we have to add everything up, and their vectors. So we have to add them as vectors, which usually means looking at the components. Now just to confuse you, you will occasionally be asked what would the acceleration be due to one particular force. And that is still given by F for that force equals MA, I'm going to call it particular for P. So if you have a bunch of forces acting on you, and you're not interested in your actual acceleration, you just want to know if only this one force was acting, what is my acceleration? I still use F equals MA. Keep in mind when you talk about the acceleration of the object, that only means really the total acceleration. I mean you only have one actual acceleration, which is your total. You might have lots of forces acting on you to give you that total acceleration. And that's the trick. And how do we find all these different forces? And the answer to that is the third law. And the basic principle, and most of you got this right on the online quiz, is any two objects that interact produce a single force between them, or a single interaction. And that's what you want to keep in mind as we move into force problems. It's two objects making a single force. And the picture we constantly draw is object A, object B, they interact, and that gives us a force on A due to B that is equal in magnitude to the force on B due to A, and the only trick is they're always in opposite directions. So if the two objects are pulling on each other, they move together. If they're pushing on each other, they move apart. And if you want to know what happens to B, you have to ask what are all the things B interacts with. And for everything B is interacting with, because of the third law, you get one force. And then you go to the second law and you add up all those forces. You never use the third law to figure out how an object moves. Notice the third law tells you nothing about acceleration. There is no acceleration mentioned anywhere here in the third law. So if you find yourself saying something like, well, due to the third law, the forces are equal and opposite, so they cancel, so they add to zero, so the acceleration is zero, what mistake did you just make? I used the third law to make an acceleration. You cannot do that. You absolutely never, ever, ever, ever, ever can do that. What you do is you use the third law to find all the forces on an object. And then from there, you use the second law for that object. And you have to keep the two separate. Now, you might end up in the course of a problem finding out all about A so that you can find out what this is, so you can find what that force is on B, and then using the second law to find the motion of B. So you might be multiple steps here, but this connecting force, this third law idea is always just to find all the forces on A and B. So any questions on that? Yes. Oh, that's a good question. That's just a definition. I should have said that when I did it. I meant to and then I forgot. A newton is defined to be a kilogram times a meter divided by a second squared. That's just the definition. Other questions? Yes. This is B due to A. Yeah. So if I was to take off the absolute value, then yeah, one is the negative value of the other because they're in opposite directions. But I really like to keep it separate. The magnitude is the same, the directions are opposite instead of using a minus sign in there. I just find for me conceptually that helps keep it separate because you don't know which one is going to be negative because you don't know which direction you're going to pick as positive or minus. Now we're going to do some demos today, but what we're going to be looking for the next two weeks or so, we're going to be doing problems that use F equals MA. Now we did the first three weeks on problems involving A. So a lot of the ones we do will connect back to problems from the first three weeks. So if there's two steps in the problem, you're either going to be starting with forces to find A so you can do your kinematics or you're going to be doing kinematics to find A so you can find your forces. And A will be the connection between the two problems. Now how does that work out? What are some of the questions you want to be looking for that tell you you're doing forces? Well, one is the trivial one where, and we already did this one, you know A or you find it from kinematics or some other way and you're asked for the total force. That's just a plug-in to F equals MA. What makes that one hard maybe is you might have an object moving somewhere and you know how long it took to go some distance and because it was being pulled and pushed and there was gravity and all this stuff and friction and you need to put all that together to find A and then you get the total force. Now a slightly more subtle one is you'll know A or you'll have to find it and you'll be asked for a missing force. This type of problem is one where an object's interacting with multiple things and you really want to know what the force between it and another object is. So an example might be two football players colliding on a football field and you want to know the force between them and you know the friction with the ground. And what you want to do, and you know the acceleration, but you want to find that missing force. If I have just one missing force and I know the acceleration, I will be using F equals MA to find that missing force. So I'll have a bunch of forces summed up on the left, one will be missing, I will know A and I can solve for it. So it's a variation on the first problem. Now and we're going to do this as our first demo in a moment. You might know A or find it, you see a theme here, and you'll be asked if something breaks. Most objects, when subjected to enough force, they break. This piece of paper, instead of accelerating, broke. And you'd like to know when that happens. And so how does that happen? It happens when you try to make an acceleration that is too big. So again, what you do is you plug in F equals MA, you find out the force that's required. If the force required to make that acceleration is too big for the object trying to generate it, the object breaks. So it's another type of problem we would be doing. This would also be very common if you were building stuff. I learned the other day, 25% of our bridges in California are not considered safe structurally. So you've got a three-fourths chance of getting home safely if you have to cross a bridge. The other way I heard it was our dean of engineering described it as just every time you go over a bridge, count. And on the fourth one, hold your breath. And then occasionally, you end up knowing the net force or you found it for some reason and you're being asked to find the acceleration. Often in that case, you're being asked to find the acceleration because the forces are constant and you're actually wanting to know something about the motion. You want to know where it lands, how far it went, how high it went, what speed it was landing at, what angle it hit with. And you're going to use kinematics to solve some problem. But to do the kinematics, you need A. So it won't actually ask you for A. It'll ask you for a kinematics type question knowing you need A, you can get A from the forces and plug it into F equals MA. Any questions on those things? So that's what you want to be looking for for the next few weeks. Yes? Yeah. Well, you're usually given the minimum force required to break it. So yeah, that's what will have to be one of the given. That's how you know you're in that breaking problem. People say something like, a rope can only support a hundred newtons. Spider-Man swings on the rope, does it break or not? That's like a classic one. Usually it's either Tarzan or Spider-Man swinging and the rope breaking. They're the ones we make suffer. And it usually happens when they have to catch someone. Like they're swinging fine and then they have to hold someone else and now does it break? You know, because we don't like to put kids on swings and ask if it breaks. Spider-Man or Tarzan, if it breaks and they land, not such a big deal. They bounce. Okay. So, we're going to do our first clicker question. I'll start it, but I'm going to come over here and explain it. So what we have going on, I have a large mass here and I'm going to have two strings and so it's hanging from the top string and what I'm going to be doing is using the bottom string to pull on it. So I'm going to put my bar in and I'm going to pull on the string. And the question is, I want to pull it in such a way that the top wire breaks and not the bottom wire. That's my goal. So I'm going to be pulling on it. If I pull, eventually one of the two wires will break. Right? If I want to make the top wire break, my choices are quickly would break the top wire, slowly would break it. My other choice is either it's always going to break or it's never going to break, it doesn't matter how fast I pull. So does that make sense? I'm either going to pull real slowly or I'm going to jerk it quickly. And will a quick jerk break the top wire? Will a slow pull break the top wire? Or does the time not matter, no matter which way I do it, either the top wire will break or the bottom wire? We are split. A couple of people refusing to answer, no. So, let me do this. I'm going to do the quick version first before I show you the answer. So this is pulling it really quick, ready? So I pulled it really quickly and the top wire did not break. So clearly quickly does not break the top wire. So let's vote again, we've eliminated one answer. Will slowly break the top wire or does the time not matter? Interesting. So it looks like, what this looks like is how many of you who thought quickly have now decided time does not matter? So everybody who thought quickly went to slow and everybody who thought slow has gone to time does not matter, is that what it is? Because we've lost all the quicks and the only thing we gained was time does not matter. Interesting. So let's do slowly. So the top wire breaks first, yes, it's not a no, it does. And trust me, it's not magic. So why does this happen? And at the heart, by the way, you want to talk about practical applications of physics. Really the most dramatic application in my mind of Newton's laws and forces is almost everything in martial arts or karate is actually related and works because of Newton's second law and third law. And what's happening here is a standard kind of situation where we're going to want to look at the ball in the center and all the interactions on it. So if I look at the ball in the center and I'm drawing what we will call a free body diagram, I draw all the interactions. There's one for me pulling down, there's one for gravity, and then there's this string attached to it that's pulling up. So it has three interactions and that's one of the things you've got to get used to, you know, for instance, there's gravity there, you'll learn to identify that. But you want to identify pretty much anything touching an object interacts with it. Two strings were touching it, so there's at least those two interactions, and then gravity because we're not floating in space. Now I can write these as an F sub P for pull, an F sub G for gravity, and we'll do an F sub U for up. And I can add these two together and just call it an F sub D for down. So I can kind of simplify my picture. I have a down force and an up force. And so my total force, now let's take up to be positive, so my total force is whatever the size of the up is minus the size of the down, and that'll equal mass times acceleration. Now everything is moving in just one direction here, so I don't have to worry about the vectors anymore. I can just call this all in the Y direction, and I don't have to label that. If I plug in my up minus my weight plus what I'm pulling with, or gravity, sorry I called it gravity here, minus gravity plus what I'm pulling with is equal to MA. So putting those together, let's look at the different things that can happen. What is the definition of acceleration again? Change in velocity over two days to the test, good job. Notice, if I have a very short time, which means I pull quickly, then I have a large acceleration for a given change in velocity. So given some change in the velocity that I'm going to try and create, if I try and do it really quickly, my acceleration is large and it's down. So if we look at putting these two things together, I take a large acceleration, I put it in here, that means this, FG plus F pull, has to be much bigger than my force up. Given that the strings were the same, they're going to break with the same force, which string experiences the much bigger force in this case? The bottom string or the top string? The bottom, because even though the weight's there, it's so much bigger, the weight's some constant value, the bottom string will break first if I do it quickly enough. Now on the other side, if I do it slowly, then delta T is big, A is small, and now my up force, if I take this equation, is equal to whatever that acceleration is plus whatever gravity is plus what I'm pulling with. And if this is pretty small, now this starts to matter and this, my up force, is bigger than my pulling force. And now which one breaks first? Which one's the bigger force? Top or bottom? Top. So that breaks first. These kind of arguments are a bit tricky and they will show up in the course of a problem that you're doing to get numbers. So you do want to pay attention to this kind of thinking and you'll see it come up and you'll want to watch for it when we do problems. Any questions on that? Now I want to do a fairly similar thing with this book, oh yes, yes? Well it's a two-step process, right? What happens is, and this is why it makes the arguments a little tricky, I'm attempting to accelerate the ball with a large force. And this is kind of the weird thing about physics. So you're mostly right, but the logic is you first need that first step of I'm trying to make an acceleration here. To achieve that, the force pulling down has to be bigger than the force in the top. Otherwise it won't accelerate big. However, as I'm trying to generate all that force, the first thing that happens is the string breaks. And yes, once it breaks, then the ball just hangs there and this string doesn't get any bigger forces in it and it stays the same. A little bit of the force is, but not all of it, because, and it's not all translated because this is starting to accelerate. If this wasn't accelerating at all, if I was like holding the ball with my hand to make sure it never accelerated, then whether I pulled fast or slow, the bottom string would always break. So that's kind of the subtle difference. It's starting to translate the force, but the bottom one is getting bigger faster than the top one, and so it breaks first and then no more force gets transmitted. There are lots of different ways to kind of say it and think about it. You could believe that, and if I had more strings, which I think I'm out of, unfortunately, because they only gave me four, oh wait, no, I can do it. Here's a brand new string. Now you just want to see the demo again. So here's a brand new string on the top. Here's a string that's already been used, so in principle, if your theory is true, it's much weaker now. I pull slowly and the top string still breaks. Luckily, I had a string left. So it still works. So it really does work, and it's really why an expert in karate can break bricks and break wood. It all has to do, even though there's the same hand hitting the same object and there's the same force between them, it has to do with the relative attempted accelerations, the time involved, the time of contact, lots of other things like that. So the question I have for you now, I have a book and I have a piece of paper under it. Imagine, if you please, that the piece of paper is a tablecloth and the book is all the china on the table. And I'm a magician and I have any skill whatsoever. So I pull quickly, ta-da, and none of the china falls over. Isn't that exciting? I pull slowly and all the china falls over. You all imagine that, right? We're going to put that in post-production. So why does that happen? Talk to the person next to you. You've seen my argument for the breaking of the string. Why when I pull slowly does the book slide, but when I pull quickly the paper comes out? So any thoughts on why the quickly pulled paper comes out and the slowly pulled paper, everything stays behind? Yes. I think you basically got it. If we want to be really careful, and here's what I was saying, we've got to be careful of doing second law and third law. Notice if I'm the book, I have one interaction. That's with the paper or the china with the tablecloth. Now we learned in kinematics that X and Y directions are independent. So I'm only worried right now about X interactions. There is an interaction with gravity, and we'll come back to that later next week. I don't have to worry about that now because I'm only worried about the book moving in the X direction. So I just ask for those interactions. If I'm the paper, how many interactions do I have? Be careful. How many interactions do I have? Three. What are they? No, ignore gravity, just the X direction. It was not a trick question. hand, the table and the book. You got to remember the table for the paper. It is interacting with it. Now what does this mean? Notice the interaction between the paper and the book is of the exact same magnitude. It is some force between the paper and the book that's the same as the book on the paper. This happens to be the force due to friction, which we will learn has a maximum value. It can't exceed some number. So when delta T is small and A is big, and this is in a case of what I will call the attempted A, is too big, it actually cannot occur. I did this all in red because it is really very hard, I think, to think about. But what is going on is the paper is going to accelerate no matter what because I am pulling on it. So the paper is stuck with these three interactions. So it has F pull, and then the interaction with the book will be in the opposite direction. The interaction with the table will be in the opposite direction. And there will be some MA. And I can make that as big as I want, and any A that I want I can achieve. Now I have to take into account the friction and pull a little harder than I would if there was no friction, but I can do it. For the book, the only force is the force on the book due to the paper. And the question is, is it big enough to give the same acceleration as the paper? If it can't accelerate it as fast as the paper, then the book can't be moving with the paper because it will have a different velocity and it gets left behind. The bigger I make the acceleration of the paper, so that it's that much bigger than the book, you don't even notice the book accelerating. Before the paper is gone, and then the force on the book is zero, and it stops moving. Well, there's a little friction that stops it, then it stops moving. I have to say that carefully because it does hit the table. And that is one of those conceptual types of thinking you're going to have to do when you face F equals MA problems, is think about an attempted acceleration and ask the question, does it or does it not occur? And that's where these problems get, I think, the most challenging as we go forward with F equals MA. Because you're not used to thinking of, let's see if this A would happen, and then does it happen or not? That's kind of the challenge. So we have a clicker question related to that, if there's any other questions on the book. Notice the answer here was slowly. What is the ultimate limit on a car's acceleration? Engine torque, engine power? So keep in mind, for those of you not expert in cars, the engine torque is basically the force the engine generates. It's a torque because the engine rotates, and rotational forces are torques. The engine power, power is energy per unit time, we haven't done energy yet, but power is how much energy you can generate in a certain amount of time. Tire friction with the road, or how fast you can push down the gas pedal. And good. Let's see what we got. Excellent. Most people went with the friction on the road. And again, this comes from thinking about the interactions. I have a car. The only thing the car is interacting with is the ground, right here. This is the only interaction. Everything else is inside the car. It's parts of the car interacting with itself. So the only thing that can generate a force that moves the car forward is the tire with the road. The only thing that generates a force that moves me forward is the ground pushing on me. If I try and do this on ice, unless I'm very careful, I slip, I don't go forward, because the ice can't push on me. It's not me pushing on the ground, it's the ground pushing on me. When I push on the ground, I move the ground backwards. Because my pushing on the ground does something to the ground, not to me. Any questions? Excellent. Now, we had some volunteers earlier for demos, if they would please come down. Our demo volunteers. Yeah. Excellent, excellent. So, I'm going to have you take, whoops, we don't need those papers. Look at these lovely volunteers. Oh, make sure a friend has your clicker. This is the one place I'll let a friend click your clicker for you, just so you don't get messed up. Okay, you take the rope and go stand on that. Very safe device, with wheels. And I'm going to have, right now, just, can two of you stand on this, do you think? Yeah, see if, I only want one on that one for now. You guys hold this rope. Okay, excellent. So the question we have, they're just going to stand here and pose for a moment. Now we're going to have the person, the single person here, that's person A. I wanted to make a massive group here and a less massive group here. So you're going to pull, you guys are just going to hold. Is he going to go flying towards them? Are they going to go flying towards him? Or are both going to move? That's what you're voting on. So remember, you guys are just balancing, just hold the rope, and you're going to pull on the rope. And I'm really hoping the wheels work. This will fail miserably if the wheels don't work, so keep your fingers crossed. If they work too well, somebody will fall over, but that's a separate issue. Five, four, three, two, and one. Good. So the prediction is, okay, either only he's going to move, where'd my prediction go? Oh, there it is. Either only he's going to move, or they'll both move. Okay, go ahead, pull on the rope, let's see what happens. Step off, please. Go back. Let's see if this would happen. With the carpet, the wheels generate a lot of friction if I put too many people on it. Go. Now try again. Oh, you're standing, stand in the middle more, so you're not, oh, and there's a bump in the floor. There's a bump in the floor. Trust me, that's the problem. Let's try it one more time. Pull. There we go. You can see he's moving. Try it again, since we've moved him off. Oh, actually, I know what we're going to do. Okay, put your cart on the wood. Let's get rid of all bumps in the carpet. Yeah, now we've got it. Okay, now stand on it. Now pull. Now they both move. Notice what happened. Once I put him on the wood, he moved less. So, we're actually finding out about friction. I know it didn't quite work as well as we expected, but we're finding out about friction. That worked well. We're going to give them a hand. We're going to do one more thing. We'll use you and we'll use you for this one. You guys can go back and sit down. So, do you want to catch or throw? You want to throw? Then you get to catch. So, why don't you come over here. You go ahead and stand on the lovely cart. On the wood? Yeah, on the wood. You got good balance? This is why I've got to volunteer. Okay, he's going to throw him the ball. He's going to catch it. Wait, before you do it, what do you think is going to happen when he catches the ball? Let's see. Ready? Throw him the ball. Okay, that was like a very wimpy throw. Here, watch. Not to make fun of you. Sorry. You got to throw him the ball. Ready? See? And he moves backwards. Let's give him a hand. Thank you. Sorry, I didn't mean to insult you there. I did not give him good directions. It was not his wimpy throw that was the problem. It was my directions. So, what we were looking at there, it's very important to take home the following two messages from that. We were focused on two different things. The interaction between the two people when they pulled on the rope. This is Newton's third law. There is an equal and opposite force here. And I'll actually do it this way this one time. Once I focus on a single person, I now have to ask about all possible interactions. And I also have to ask about the mass. Because the impact or the effect of the force depends on the mass and it depends on adding them all up. So notice when there was a lot of friction here, when the one cart was on the carpet, it caused us a lot of problems. You didn't notice that there was a force pulling them forward. As soon as we put them on the wood and got rid of the friction, the force on this person was obvious. What's amazing, and this is something we often forget about, is this person was pulling on the rope. And the first thing we saw when there was a lot of friction was their cart moved this way. There was no obvious sense in which there was a force this way. We were having him pull that way. As soon as he pulled, as soon as this person A pulled this way on the rope, there was an equal and opposite force on him due to the rope. And that is why A moved. And so you really have to be careful using Newton's Third Law. It's going to set up these interactions between people. And the other big thing, same thing happened with the ball. When we threw the ball, there is now an interaction. There was a force backwards on the person that only really showed up when we got rid of friction or we made the force big enough. Now, the final point of all this, in physics with ropes, they're going to be special for us. You're going to have to watch for that. They're going to be massless and they simply connect objects. So the rope itself is like two objects we're touching. So these two lectures taken together will give you that real conceptual groundwork for all the detailed problems we're going to do next week.