 Okay, evidently the question about one of the problems, well probably more than just one, but if I explain this one maybe it'll help on some of the other ones because it's actually the sticky part of this problem, the one that Alan asked about, is not really, well hopefully, it's not really setting up for physics, it's solving the problem once you've got the equation set up. So it's the problem where we're given that there's a 50 meter bluff and a ship 12 kilometers away, not to scale, and you're determined given a muzzle velocity of 600 meters per second at what angle should you fire that shot so that you can indeed then hit the USS Hudson Valley Community College. Right, that's the problem, I got all those little pieces right? So this is like any other projectile motion problem in that you've got some horizontal stuff going on and some vertical stuff going on, and you need to put those together to figure out what you've got and what you don't have. So to avoid belaboring it too much, remember that the velocity is constant, you sort of know that, you know that it's 600 meters per second cosine theta, but you don't know what theta is in this problem. In fact, that's what you're supposed to find. Well given that, let's see, you know that this distance it needs to go in the x direction, which are given as 12 kilometers or 12,000 meters, is that x dot times the amount of time it was in the air, which you also don't need. No. Right now there's two things you don't know, really only one equation because we put this equation in there and this becomes one equation with two unknowns. But with horizontal or with a projectile motion you can always go over the other side and see what else you know. The acceleration is that due to gravity. What's the minus sign mean? Of course gravity is downward. What's the minus sign mean? That I chose that direct, I chose positive upward. This is an artificial construct on my part. Whatever g is, well God fixed that whenever he got that. I don't remember which day it was. I kind of been sick that day. Alright, then what else do we know vertically? Well we know it needs to drop 50 meters. So delta y is negative 50, to match that negative. If you don't want to do a negative on those, don't. Just be consistent. Let's see, what else, well we sort of know the initial velocity. Sort of know because it's like the same thing with the velocity over here. We know it's 600 meters per second sine theta but we don't know what theta is. That's what we're still looking for. So this is kind of like the three things you know. Kind of because we don't actually know this initial velocity. We don't actually know that angle. So it's kind of like, but if we use that one equation, delta y equals minus one half g t squared, delta y we know, t we don't plus y dot i t, y dot i we sort of know, t we don't. But if you put everything you know in here and everything you know in here, you get two equations, two unknowns. That's one equation. That will be one equation two and they both have the same unknown, the same unknowns. Both are t and theta unknowns. So you can put those two together and when you do, you get an equation that might look something like this. Maybe your algebra is a little bit different but this is what mine happened to look like. I got an equation that looked like, sorry, I want to put everything together. I had minus 1899 over cosine squared theta. That 1899 is just combinations of the 600 and the g in the 50 and however it shook out your break. Then I had 12,000. Obviously that's the x dimension tan theta minus 50. That's what I did when I put those two equations together, eliminating t. I chose to eliminate t because we weren't asked for it. So I don't want to eliminate theta. That's just going to make more work for myself. So I had that as my one equation, one unknown, once I put these two together to eliminate t. Then the question becomes, well, how do you solve that equation? There's a couple different ways. One of my brighter math students last year pointed out it can be to solve directly. Since I'm not a brighter math student, I had to do something different. What I did with it is I took this side and I graphed it. I graphed theta across there and then this is some function of theta. Now I don't want y. I use an f. This is some function of theta and I just graphed the left-hand side. I put it in a spreadsheet, picked theta and a couple different spots and just graphed it. Actually it comes out like this. It's fairly linear. This happened to be about 9.1. This happened to be about minus 65 or something. That's just where the numbers came out. That's not what I cared about. What I cared about is went to this side that I just graphed equal minus 50. So went to the graph at minus 50, went to my line. That's, remember, the left-hand side of the equation. Just put it in an excel and graphed it. And then that's the theta at which I want to shoot the angle. So setting up to get it here is fairly straightforward. I just found solving this a little bit more difficult. Here's one way to do it. I don't know. I like graphical things on the visual person, I guess. So that was just an easy way for me to solve it. But like I said, somebody else last year solved that directly. Good for me. So, Alan, did you have something like this and then we're just having trouble shaking out the theta? Yeah. Look at this kind of technique where it doesn't matter what, if anytime you have a function with one variable, think about the possibility of graphing it if you can't solve it some other way. It's a little bit of a brute force technique and sometimes you have to be careful because it didn't happen here. But you can certainly have an equation that has two values and it may not be obvious which is the value that works. Maybe both do. I don't know if everybody noticed that one thing about these projectile motion problems, especially when the angle is of some kind of variable possibility is that there are often two solutions for these. We can shoot at kind of a low angle, get to a there. We can also shoot at a higher angle and get to it in that way, depending upon what that launch velocity is. It doesn't work with this one because this one was already set with a particular magnitude, 600 meters per second. All right. That help? Okay. So, if you want to work on that, if you want to turn in the homework tomorrow, that's fine. You could use a little bit more time. I think there was one other problem that you need to kind of brute force solve like this, too, where setting up the projectile wasn't the hard part. It was then making the solution work from the hard part, or from the projectile part. Also, don't forget, put questions on angel, right? Did that work? Did you get my response? I responded to your question. How was that last night? I practically gave it to you. Do not, do not work on a problem, a single problem for hours. That's a waste of your time. I don't have one single problem I can assign that's worth hours. None of them are that important. All of them together are worth a couple hours, but that's a whole homework assignment. One single problem, not worth it. Work on it for a little bit. If you get to someplace where you're stuck and you're stuck for 15 minutes, stop. It's not worth it. It's not worth your time after that. That's a waste of your time. Now, you're young and dopey and goofy and have all kinds of time to waste. That's why we have spring break and Daytona Beach. But you don't have hours to waste, I don't think, especially in the middle of the term. So, work 15 minutes, put a question on Angel. I check it every couple hours. I'm having trouble connecting from home to the school, but I can't get Angel. So, put a question on there and go on to something else. Spend your time better. Mike, I can maybe say something about it quick, but we've got to go on to new material. We're going to have to spend extra time here. Joe's the expert on that one. Isn't that the one I told you about? All right. I'll help you with this one real quick. This is the one where a plane is flying in a sort of a crosswind. All right. I believe it said the wind is coming from 45 degrees. The wind is blowing 45 degrees south of west, which I took it, I mean, that's where it comes from, because I think that's how they talk about the wind. But it doesn't matter if you get the right idea, that's fine. Oh, blowing from a direction 45 degrees north of west. So, it's doing that. That's the wind speed. The intended trip by the plane is pilot wishes to fly due north. If the pilot flies due north, in that wind, the wind's going to blow him sideways. That's just what wind does to planes, and he's going to really end up doing this. His plane will be facing like that, but the wind will be blowing it sideways as it goes. I don't know if you've ever seen a plane coming into the landing at an airport, and it looks like they're turned sideways. Have you ever seen a video of a plane landing? And he's thinking, my gosh, they're not going straight, they're going sideways. But that's because they're turned into the wind, just so they can keep traveling forwards, because the wind is trying to blow him sideways. So, what you need to do is take that and turn it this way. He needs to actually fly into the wind a little bit, so that he can get an intended trip of due north. And in this case, the plane would be flying in this direction, but its forward motion plus the sideways motion of the plane make it go like this. So, it's those two together. Let's see. This is the true path, and this is the intended path, and this is the wind across there. So, that's how you add those vectors together. VT, the true path, plus the wind will equal the intended path. And you have enough to solve this triangle now, because it is a closed triangle. So, you probably need either law of sines or law of cosines, or both. Okay, Mike? Help some? Joey? Put these things together, imagine what would happen. If you were in a plane, and the wind's blowing on the side, and you're trying to go straight, you're not going to go straight. You're going to be drifted off to the side. So, start putting together with what real experience you might have. Whether it's planes or sailboats, they're all kind of the same. All right. So, turn that in tomorrow if that'll help. Also, Lynn, you had a question, and probably others do, because I can't remember if it showed it on the schedule. The lab report business, I'm changing a little bit. So, no lab reports do tomorrow. Bring with you your projectile motion study stuff. Also, make sure you have access to the previous report, the tape drop report, because we're going to start putting these reports together. So, we'll talk a little bit about the specifics from the projectile motion problem. We did a little bit already in class, but we'll talk more about it. Then I'll talk some about the specifics of how to start putting a report together that's made up of related but separate parts. Most of us have access to computers in there that start doing some of this writing. So, four weeks have gone by. We've got three weeks till spring break. Time is flying by. When time flies by, it's really easy to get behind. It's very tempting right now, I'm sure, to say, oh, I'll catch up at spring break. You won't. I never did. Stay caught up. It's very hard. Catching up is virtually impossible. So, time is flying by. Stay on top of it. All right. Any other questions before we get going to new material? All right. What we've been looking at so far is particle kinematics. That's what we've spent four weeks. I mean, by particle. We didn't look at a part. We looked at cars and planes and crates and projectiles. What do I mean by particle? Why was that an important designation to us? It made it a little bit easier because we didn't care about what direction it was facing. It didn't matter if the car was facing forward but driving backwards or any of those type of things. It also made it so we didn't care what size the thing was. We talked a lot about, especially in the first week, an object going a certain distance. And we didn't have to say, yeah, what do you mean when a car goes a certain distance? Here's my car. What do you mean when a car goes a certain distance when the bumper gets there first? The front bumper gets there before the back bumper gets there. We didn't have to have that kind of argument. We just took it as a particle. We didn't even say what particle of that car represented the car. We just kind of understood that it meant something. If you want to, you can say it's the center of mass of that car. Where the center of mass goes, let that represent the car. Let's not worry about the bumpers. Let's not worry about which way it's facing. Let's not worry about any of that kind of stuff. And it does make the problems more straightforward, a little bit easier. They get more complex and more realistic they get. That shouldn't be any great surprise. That's part of why it takes at least four years to become an engineer because we need to take you through steps of increasing realism as your background in both physics and mathematics gets better. That's what we're doing here for four years. I'm going to charge two of it. You'll go somewhere else for the other two. Hopefully only two, maybe more. You can also imagine that we're just back so far that the car just looks like a little dot and then that's all we're concerned with is how fast is it and all those kind of things. So it just makes things so we can get going quickly and we'll add realism to it as we go. Later in the term, we will be very concerned with how big things are, what their size and shape and orientation are, which way are they facing. That'll be very important next term. And if you take the follow on course, if you continue on engineering and take a course we call dynamics, we're very concerned with that kind of stuff. So it's a little bit of a simplification, but it gets us going here so we can really start doing some work and then we'll increasingly make it more realistic as we go. What do kinematics mean? That's what we spent four weeks doing. We've learned enough now to go on beyond kinematics now, but what was kinematics? We've been doing it for four weeks. We only learned four things. One thing a week is all I've asked you to learn so far. One thing a week, that's not so much as it. I bet you have other teachers after you learn seven or eight things by now. I only asked for four things. What are they? What are the four things we've learned so far? Well, oops. Yeah, it takes a while for things to do something. Yeah, well velocity, how fast are things moving? And it can take some time for that velocity to change. And we were concerned with that. That position, that's what we started with. Where are these things? And then once we knew they were there, then we saw a little bit later they'd moved, so that's when we brought in velocity. There's three things. What was the fourth thing we learned this term so far? Acceleration, of course. That's all we've learned. We learned how to do nothing else but work with those four things. One thing a week. See, now you look back and you think, oh, now I understand why this four has been so relaxed and carefree. Now we're going to continue with particle. We're still going to be working with particles. Now we're going to work, though, on what's called particle kinetics. That's going to be our concern. Well, both of them are a concern. But we're going to add to it our concern with particle kinetics. Basically, the kinetics is mostly focused on that acceleration piece. It doesn't mean we're not going to do with the other ones, because they have a lot to do with the acceleration. So the fact that we're going to focus mostly on the acceleration doesn't mean those other three are gone. They're still there. It's just our main focus is going to be on A. Questions like, how do we get A? If I need something to move with a certain acceleration, how do I get that? And I don't care if it's a piston and a car engine that I need to accelerate or the car itself or the space shuttle or anything. If I need to get something to accelerate at A, what do I do to get that A? I don't want to just guess and hope it accelerates like that and then find out it doesn't and whatever it was, I was looking at it as I lost. It was accelerated wrong and I lost it. We might also ask, how do we prevent? How do I prevent things from accelerating? That's a pretty important concern. You worry about this. You probably worry, well, you boys, you live for acceleration, but for women and adults, we're much more concerned with things not accelerating, because that's what you want bridges to do, is not accelerate. It's pretty spooky, I would bet, if you're on a bridge and it accelerates. A couple years ago, that bridge in Minnesota, remember accelerated? A couple school buses on it and they dropped into the river and, I don't know, 30, 40 people died because the bridge accelerated. We sometimes, we very often want to prevent acceleration. You're not worried about it specifically right now, but I bet you hope this building doesn't accelerate. Yeah, now you're going to start losing some sleep, lying in bed. What if my house accelerates? Just get on Angel and put it on the discussion board. We'll talk you down. These are the things that we're concerned with. All right, so we'll take that first one there. How do we prevent A? Well, the whole business that we deal with here are called Newton's Laws. Newton's first law deals with exactly this. How do we prevent A? Well, what he kind of does, it's sort of an around about way. We're going to be more direct when we get there. This is the one. An object at rest. Sound familiar? Almost anybody out on the street could come up with something to the rest of that. An object at rest tends to stay at rest. That's what almost anybody out there could give you. So we'll give them three dots there to show our respect for them. Those people out on the streets. There's more to it than just that. Do you know what the rest of it is? An object at rest tends to stay at rest. An object in motion tends to stay in motion. So we can say an object in motion. Now this is where an object in motion tends to stay in motion. That's what you'd get from 75% of the people out there on the street. And it's just, yeah, it's right. It's not a specific enough for us. When we say an object in motion, what we're saying is an object with a certain velocity. Notice that's a velocity vector. I hope that's important to all of us. An object in motion, an object moving with velocity v, tends to continue to move with that velocity v. And I don't want to write the whole thing down and go something like that. Tends to, we'll just say tends to keep v. Just any sort of a shorthand here without being imprecise. Alright, let's see. Let's see if we can be a little more concrete with what this means to us. Moving with a velocity vector like that tends to keep that velocity vector. In other words, I could say the velocity vector is constant. Wouldn't that work? Because that means preserve, that to us means preserve both magnitude and direction. We talked about that with uniform circular motion. Magnitude was always the same, but the vector was always changing. And so that wouldn't be one of these cases. V is a constant. Velocity vector is a constant. If velocity is constant, then what do I know about the acceleration vector then? Acceleration vector. See, acceleration vector is the time-rated change in the velocity vector. Time-rated change of a constant is, is zero. If you said zero, then I said, you know, it's a vector and you backed off a zero. I wish I could play poker with you guys. Here are easy marks. So Newton's first law is in a situation of zero acceleration. Well, we've already had that. We've had non-accelerating problems. The issue becomes for us now with the use of Newton's first law, how to ascertain, either make sure the acceleration is zero or determine if it will be zero. Either way is the same, same basic same idea for us. And I think at least one of you already sort of hinted at this where we were at this. What we do is we look at an object represented by some mass m. So as we talk about objects, we're going to care how massive they are, what their mass is. We haven't worried about that before. We were shooting projectiles and we were spinning things and we were, we were accelerating here and there and putting on the brakes. But I never once said, how much is that thing way? How massive is it? We never once brought that up. We didn't bring that up with objects falling through, from, from a height or being shot through the air or any of those things. We didn't look at that. It never came up. Now it will. Now we're going to be concerned with how massive these things weigh. To accelerate things like masses, you've got to push on it. You've got to exert some kind of force on them. And we're going to add up all of those forces. That's why we looked at chapter two how to add vectors. Here's the number one reason we're going to add vectors. We have to add force vectors. Any problem that has more forces in it than one, we've got to add those forces up. So we haven't talked about forces. Well, we, we did a little bit. Remember what I said was the definition of a freefall problem? What do I tell you that? Because our, how to determine problems of freefall problem, what did I say? Yeah, the only force is gravity. I just said that. I didn't define force. I didn't talk more about, well, what if there are other forces? Didn't look at any of that stuff. Just simply said that the only force is gravity and everybody was comfortable with it. It's not that huge a concept. So it was easy to kind of say and sort of toss out there and, and you guys went with it and you did great with it. So what we're going to do is push on with force some object and that object will accelerate. However, for Newton's first law, I want the acceleration to be zero. So it doesn't even matter what the mass is, but it does tell me how to get zero acceleration. If I want zero acceleration, all of the forces have to sum to zero. For every left going force, I need as much right going force to cancel it. For every up force, I need just as much down force to cancel it. I don't care what directions are involved. After I've added up all of the forces acting on an object, if nothing's left, there'll be no acceleration. If I want to guarantee there's no acceleration, I've got to put on forces such that they all cancel each other. Some people, I like to write that as the sum of the force vectors. Is everybody familiar with the summation sign? That just means you add up everything that's there. So that means we add up all the force vectors. We add up all the force vectors. We add up, we take into account their direction and their magnitude when we add them together. Some books, and maybe you as well would rather write F net, the net force. Kind of a business term like net profits and net worth and all that time. It just means after you've summed up everything what's left, some books like to put an R on it says resultant. We use that term I think in chapter two. It's what you have when you've added some vectors together. In this case, we want the resultant to be zero. So any of those you write are fine. Just some kind of indication that it's several, could be several vectors added together. Sometimes it'll be just one. You can imagine that might give you a good place to start, but you can also imagine fairly quickly we'll be working with multiple vectors that will be doing problems with more than one force vector in it. So Newton's first law. An object in motion remains in that motion. And by that motion, I could mean it's just sitting there. An object in motion remains in that motion unless acted on by unbalanced forces. Well, these are balanced forces because they all sum to zero. Newton's second law. Well, we've already screwed it around in here, kind of got it there. It's what if the forces don't balance? Or what if I do need some acceleration? You want to come to the line in a drag race and say I don't want any acceleration? Well, maybe you do because if you just sit right there, you can wink at the girls in the stands where the other guy's down the track and he's way down there. Who knows what he even looks like. He might be dreaming that nobody knows. So this is the case. What if we do want some acceleration? How do we get it? What do I do with all of the forces acting on an object such that there's enough left over in the right direction to give me the right acceleration? In fact, it's this form that is used actually to define mass. That's where we exert a force on an object, look at its acceleration. The ratio of those two, actually it's not a vector because we can't divide vectors. So let me do this. I'll put magnitude signs on it. That'll be better. Then you don't have to erase. We exert a force on something of known size, measure its acceleration. From that, we can figure out its mass. That's actually how they weigh astronauts in outer space. That's how they could determine how fat my brother always get. Because they drink way too much beer, John. They knock that off. They get on a sled that wiggles back and forth like a spring does. They know the force that's exerting. They can see what accelerate, what period it's accelerating. They can figure out what the mass is from that. That's how they weigh astronauts in outer space. Figure out what their mass is. We broke about six of those. We're going to spend some time here putting forces on objects, making them accelerate. This works, of course, again in lots of different ways. If I have a particular acceleration and I have known forces, what should my mass be to make sure that all works? All of those kind of things we're going to do. Then Newton's third law will get you in a second. Well, no, I don't have that. Most of you know it. I bet. Yeah, Tyler, you got it? For every action, there's an equal and opposite reaction. It's not really one that has an equation that goes with it other than one thing equals another, because it's real straightforward. Well, we'll get to it in a second. I'll just put down action and reaction period. If you push on something, it pushes back on you with an equal and opposite force. If I punch you in the nose, you're going to feel that most of you wouldn't live through that, not my punch, but even so, me punching the face is going to hurt my hands because your face is going to punch back in retaliation. All of my fights in my life have been one punch fights every time I always fall down before they can hit me again. That's why there's only one punch. All right, so we need to look at forces. We need to figure out what kinds of forces there are and how to deal with them. All right, let's see. A couple ground rules with forces. These aren't things I made up. This is the way it is out there in the real world, the natural world. Changes in motion. That just sounds kind of like Newton's second law, but there's a real important underlying point here. Forces cause changes in motion. It's not the other way around. Changes in motion do not cause forces. Objects undergoing changes in motion might cause some forces such as when I punch in the nose with my fist. I'm not going to really do that. Administration told me, stop hitting the students. It used to be a great demonstration. I'd bring everybody up here and punch them in the nose and they'd say, okay, I get it. I get it. And then they'd sit down and they'd tell me, stop doing that. Forces cause changes in motion. The fact that my fist is changing in motion, it's my fist changing in motion that can cause forces or have forces caused on it. We'll come across that again in more specific ways in a bit as we start going through these problems. All forces. How many? I didn't say some or a few or most. I said all. All forces are caused by something real, something tangible, something that you can put your hand on as we go through these problems and we start lining up all the forces in the problem. We're not going to know all of them without thinking about it some. And so every time we put a force up there, I can say to you, really, what causes that force? And if you don't tell me something real, like the earth or a rope or a jet engine, if you can't tell me something real, I'm not going to accept that as a force that we can put up on this problem. Forces are not caused by motion. Motion exists, but it's not something you can put your hand on. It's not something tangible. We can study motion and we can cause motion with forces, but you can't go put your hand on velocity. You can't go put your hand on acceleration. So that's what I mean when I say forces are caused by something real. I'm going to ask you when you say put that force up there and say what causes it. If you can't give me a good answer, it's not going up in the drawing. Not going in the problem. That's not my picky rule. That's God. He did that. As we go through this, we are concerned with forces we know from action-reaction pair that if there's a force on the object, the object is causing a force back on something else. We're not concerned with that force. It's not part of the problem doing the accelerating. We will need this at time to find certain forces, but when we're accelerating a mass, we're concerned with the forces acting on that mass. All right. All of this will become more apparent as we work through it some. I want to leave those up. Need a little space here. Hope everybody got those. If not, videos are on sale on the lobby. All right. We'll do a simple problem there. This is my rocket ship. Oh, when you drive? When nobody else is around to hear them? See, I think they should use that as the gender test at the Olympics. You know, they have to determine if women really are women in the Olympics. Yeah, they do that. They used to do it by DNA, but then the South African woman had some odd results or something in the DNA, so even that wasn't working. And then gender transfer people were trying to get in the Olympics now. I think they just asked them to make a gun notice. Can't do it, you're a woman. That's what I say. And that's on tape. In case you want to press charges in there. Now's your chance. All right, so here we go. My rocket has a mass of 20,000 kilograms. It's not uncommon in physics and engineering like to leave a space where a comma would be because in a lot of European countries, a comma is a decimal and a decimal is a comma. And so they might think it's 20 kilograms, which is really a tiny rocket. It's just not worth it. Thrust is three times 10 to the fifth newtons. Hey, that's going to need defining right there equals MA. If I accelerate a one kilogram mass, that's about a liter bottle of water, I think. If I accelerate a one kilogram mass at the rate of one meter per second squared, one kilogram mass and I want to accelerate at one meter per second squared, to do so would require a force of such a size that we'll call that force a newton. So there's our definition, that's what three bars means. We define one newton as one kilogram. It's purely artificial. We could have picked any other numbers there. Remember what I told you the first day in the SI system, the kilogram, the meter and the second are all predefined. So we take those, fundamental one each and we'll call that a newton. It's an honorary artificial convenience. That's the only purpose in it. So instead of riding one kilogram meter per second squared, we save a little bit of trouble and ride a newton one in. Just convenience. Internationally recognized, but nearly a convenience. That actually does a couple things for us. One is it's convenient, it's easier to ride n instead of all that stuff. It also allows us to honor a dead white male German physicist because we like to do that. So if you're not dead, white, male, or German, we'll never name anything after you. You have to be a dead white male German physicist. So that's one newton. Oh, by the way, if units are ever written out, which they almost never are, but if for some silly reason you wanted to write the newton, the units out, it's no longer capitalized. It's not his name there. It's a unit and we don't capitalize units. We might capitalize up here because then it's in honor of someone. So as you write your report, get the units written in the right way, almost never would be spelled them out. So don't even bother. Again, save some trouble. All right, so that's a newton. So I've given you the mass. We want to find out how fast this rocket's going to accelerate. Now, here's what we need to do. We need to make what is called a three-body diagram. The better you get at drawing these, the easier these problems will be for you. If you're lazy and sloppy with them, they're not only going to not help you, they'll probably hurt you in certain instances. I've seen it happen. I've had it happen to me when I was lazy with it. Take the object of interest, which in this case is a rocket ship. We're trying to accelerate it. We want to figure out what that acceleration is. We take the object of interest, the body, draw it free of anything else in the problem. No exhaust cloud. No, I didn't even bother with the fins, though they got to be accelerated, too, but I want to make it real simple and real useful. Free of anything else in the problem. I don't have the ground. I don't have the gantry tower. I don't have mission control. I don't have any of that. Just the object, the body we're trying to work with. Two key words drawing free-body diagrams. Make them big. If they're too small, again, not only will they not help, they might hurt. You're not working for the post office here. You're trying to get as much stuff right as you can, so make them big. Also, make them simple. I didn't need the fins on here. I don't need the windows. I don't need the USA flag on the side of it. Make them simple. We have a lot more stuff we need to do with these diagrams and anything else is going to get in the way of making those diagrams useful for us. This is one of the number one tools to help us solve kinetics problems. It's going to be especially true for those of you going into engineering that will be with me next year in statics and following that in strength of materials and or dynamics. Big and simple. Thank football player. Big and simple. You're a football player? I was. Yeah? Were you big and simple then? Yeah, I see you were. Yeah, kind of. Yeah? Mike, football player. Big and simple. Samantha, do you mean any football players that weren't big and simple? Pretty much all of them, isn't it? Very much. That's the key. Yeah, but he's not a simple player. He's really a soccer player who's sold out. All right. Make them big. Simple. Beautiful. And some people need to take technical free-in sketching. Not too big because we might need to put some stuff below it. Sometimes you've got to be a parent ahead of time. Go ahead and flip the page. Make them big. Simple. Now, what we put on that diagram is nothing more than all of the forces in the problem. To accelerate that mass, we need to know what forces are on it. Let's see. Well, you help me. Any forces on that? Gravity. Or what we call the weight. The weight is going to be pretty easy for us to figure out. Always do it in just the same way. In fact, it's a form of f equals ma. The force due to gravity, which we call weight, is equal to the mass of the object times the gravitational field strength or what we often call the acceleration due to gravity. But an object has weight even if it's not accelerating. So just because we're using G there doesn't mean it's moving with acceleration G. It just means that's how strong the earth is pulling on it. If you take physics 3, you'll learn about field strength and you'll see how that's known more precisely as a field strength rather than as an acceleration. Because things that aren't, you're not accelerating right now, but you all have weight. Well Samantha doesn't, but the rest of you do. So we've got this. We've got 20,000 kilograms. What's G? Oh, we've got two labs on it. Okay, 9.81 meters per second square. Wait, wait, wait, wait, wait, wait, wait, wait. Shouldn't there be a minus sign in here? Why aren't some nodes? I heard some yeses. I have some blank stares. Gravity. Look, it's acting down. Doesn't this have a negative sign in? Nope. It's not up to you. Nope. Sorry? G is always positive. Yeah, it has direction and we may need to assign the negative to that direction. But there's no direction in here. This is just calculating if I had a negative sign in there, there'd be a negative weight. Who's ever gone to the doctor and asked you what your weight is and you said, oh, my weight's a negative, negative 240. But Len, is that what you're about? You're guessing for me? Yeah. Maybe a little less. Little bit. Is the strength of the Earth's pole on us. It always is down. We may need to assign a negative to it when we get to the rest of the problem, but as it is here, there is no negative sign in it. G itself never has a negative sign built in. We may have to put one on, but that's our official and that's personal choice, and we haven't even made any choice like that yet. Any other forces on this rocket ship, this M? Well, you can look at this problem and tell there's got to be, because right now with only a force pulling it down, that's all it's going to do is go down. There's got to be something pushing it up for it to accelerate up. What? I thought it was, wow, he's a ventriloquist. I didn't even see his mouth move twice, he said. Yeah, there's got to be, well, that's what thrust does, is it pushes up on rockets. So I'll just draw it there and I'll call it T for thrust. Isn't all this stuff shooting out the back? Isn't that thrust? Now that's exhaust shooting out the back. That's not the rocket itself being thrown forward. We'll see why a rocket engine has to shoot some stuff out of the back later. We'll talk specifically about that. Any other forces on this problem? Because until we've got all the forces in a problem, there's no sense summing them together. If we're summing together the wrong number, we're not doing the right problem. Any other forces? There could be air resistance. Of course, for something like the space shuttle, that's a huge factor, a huge factor. However, air resistance, well, one, we often neglect it. Remember all those projectile problems, what was always said, neglecting air resistance. It's a problem that you're not ready to tackle yet. You'll need a course called differential equations. Actually, later in the term for the third part of the big report, we'll do an estimate of air resistance, the effective air resistance. But we can only estimate it. When you take differential equations, you'll be able to solve this problem. It's because the force of air resistance depends upon the speed of the object. But the speed of the object depends upon the forces on it, because that term is the acceleration. But the forces depends upon the speed, and the speed depends upon the forces, and the sport isn't around and around. So that's why you can't solve it yet. That's why you need a course called differential equations, when you can solve those things that are intertwined like that. So we'll do either one of two things. We'll just say neglecting air resistance, or we'll assume we're right at launch and it's not moving yet. Things can have acceleration, but no velocity yet. Isn't that right? The thrust is turned on, it's starting to accelerate, but it hasn't accelerated long enough to actually have any velocity yet. So that means the air resistance is essentially zero. So we've got all the forces in this problem. Now we can do something like, let's say up is positive. If you don't want to, don't. Say it's negative. That's entirely up to you. And now we sum all of the forces acting on the mass. We can determine its acceleration. So sum the forces. It's a vector, but we're only moving in the y direction. So let's only sum the y direction business. There's nothing going on in the x direction. It's almost zero. All of the forces in the y direction. T is positive. I happen to choose that. You might want to choose something else. I don't care. W is down. It's negative. Notice I didn't do that back here. I did that here, and that was my choice. I didn't even ask if we didn't even consult on that. Sum all the forces in the y direction. Well, that's all there is. That's going to cause that mass to accelerate. And it's that acceleration we're looking for. What is its weight? Did anybody come up with that? $196,200. All right. So we've got everything. Now we need a equals t minus w over m. And now you just fill the pieces in and you got them all. You're laughing. It's that easy. So let's see. t, best of the thrust, remember, is 3 times 10 to the 5th newtons minus 1, 2, 3, 4, 5, 1.96 times 10 to the 5th 20,000 kilograms. Does that give us units of acceleration? If not, we screwed up no way we sense even going on the calculator if we screwed up. Check your units. Does that give us units of acceleration? A newton is a kilogram meter per second squared. We're dividing my kilograms so we have meters per second squared left. So we're okay. What's it equal? Who's got there? 5.19 per second. Straight forward. Be careful with this. Problems are going to get a little more complicated. We'll be moving to two-dimensional problems shortly. One other thing that is kind of subtle and students forget it that I want to point out, oh, actually two things we'll do. Oh, we got some time. We're okay. Whether or not there's acceleration, whether or not the problem forces some to zero, that's our working equation from now. One thing I want you to notice about it, mass is always positive. There's no such thing as negative mass, at least not in this class. There is any matter in some other things we could consider in physics 4, but in our class, mass is always a positive quantity. Therefore, because it's a positive quantity, and this is important, it's subtle and important. Therefore, the sum of the forces, after we add all the forces of whatever's left over might be a single, something we could represent with a single force. Remember, one of the things we could do is write it like that. Therefore, the sum of the forces is, and I'm going to leave a little space because I don't know what to put in there. What could I put in there? Therefore, the sum of the resultant force is something to the acceleration, equal and opposite, parallel to, perpendicular to, what other possible, oblique to, that's such a great word. Any other possible, huh? Equal to, just simply equal to, greater than, less than, not equal to, the inverse of, what do I put here? Well, we know it's proportional to, because there's a proportionality constant right there, but I want to be more complete. These are two different vectors. This will help us get the magnitude of the vectors. I'm asking really, what's the deal with the direction of those two vectors by sum up all the forces and have a net force left over in what direction will the acceleration be? Same. Since this is positive, it's not going to do anything to the direction is, sum of forces is, what would I say? I guess parallel to, but not only parallel to, parallel and collinear. Even that's not enough, because you go south on the north way, the people going north on the north way are going parallel to you and collinear, well not collinear, then they'd be in your lane. That'd be terrible. In the same direction, that's very useful. Obvious in a simple problem like this, it'll be very useful in problems that aren't so simple, aren't so obvious. We had 300,000 nukems pushing up, 200,000 pushing down, so our net force is about 3,000 up, 2,000 up, about 100,000, because I had an up force and a down force and the down force was less, the weight was trying to hold it down, so I know the direction of the resultant force. I also know the acceleration. They're parallel in the same direction. Actually, it'd be collinear. Technically, I'd write them over each other, but then you couldn't see them. Alright, questions. Wednesday, we'll talk about what kind of forces there are in these problems and how they act, because we need to get them all on this drawing in just the right way. They won't all be as easy as this one is, so you can bring your homework tomorrow if you wish. Wait a minute, not bring it tomorrow if you wish. Your choice.