I have been working and messing around with Gutenberg since basically, you know, it was in beta stages and it was starting to come out. And I would be really interested to get an idea from the room who here has not yet had a will hands-on play with Gutenberg. Wow, that's a lot of people considering that it's actually in WordPress, you know, it's like it's actually released. And I'd say most of the people here haven't used Gutenberg. Out of the people who have used Gutenberg, on a scale of like one to three, one being you don't like it in three years, you love it, how do you rate it? Can I get, or even if you've messed around with it a little bit, can I get your one's hands up? A couple of twos, okay, and threes, okay. Most people in two, most people right in the middle, okay, and then gosh, all this hands-up stuff. So I also want to know, I want to get an idea of where do you sit in terms of technical ability? Put your hand up if, and we'll keep it up for this one if you've modified your theme before. Okay, and keep it up if you maybe have written your own theme or plugin with PHP, and keep it up if you've got some experience writing JavaScript for Gutenberg with React or something like that. Yeah, there's still some hands up, but a lot of them have gone down. And I wonder if that's partly the reason why maybe this room in general hasn't got such a crash-hot opinion of Gutenberg. And for me, I love it. I use it every day, I blog with it, I'm all over it, and I develop for it, and I have a lot of fun with it. But I absolutely see this need for regular people, for regular agencies, developers who might not have taken the leap to learn JavaScript deeply, that there's this real need to figure out how can we embrace Gutenberg, how can we give our clients the Gutenberg experience? And that's something that's kind of difficult and kind of hard to wrap your head around until now. And that's what my talk's about today. So here's my second slide. So today's talk is for you if you're the kind of person who wants to learn how to build blocks, and you're the kind of person who is familiar and comfortable with HTML and CSS, maybe even comfortable with putting in a little PHP template tag, and that's maybe where your ability stops, or maybe it goes beyond there, but it's always nice to do things a little bit easier when that's possible. So what we're going to do today is a little bit out there and a little bit nerve-wracking, and it's the sort of thing that they tell you when you're a speaker, never do this.  How does that sound? You think we can do it in the space of this talk? You think you can build a Gutenberg block? Yeah. All right. So the first step is we've got to figure out what sort of block we're going to build. Has anybody here had an idea for a block that you wished existed? Maybe keep it on the simple side, given that we're limited in time, but yeah, go for it. A table. It's a good one. There is actually built into Gutenberg a native table block, but we could explore building sort of a custom table. Is anybody else over there? A team member? Oh, yeah. I like that one. That's pretty good. So you'd have a profile picture of them, maybe their title and their name. Oh, yeah. That's great. Yes? Testimonial block. Testimonial block. Also really handy, yeah. Pictures and people. Yeah. Yeah. That makes sense. One other or? No. Well, why don't we take a vote? We could do testimonial block. We could do a table or we could do the team member with the photo and the title and all that sort of thing. So hands up for the first one, the testimonial. Hands up for the table block. Hands up for the team member. Oh, looks like the team member wins. All right. Cool. So when we start thinking about building blocks, the first thing that we really want to do is figure out what the block looks like. So I don't know what design tools you might use. I know, I work with some agencies that like have embraced Figma, Figma's fantastic or maybe you're on Sketch or something like that. But I always just like to start with pen and paper. So let's start thinking about this block. We'll put it in a rectangle. Now, team member, what do we need? Call out to me some of the things that's going to be on this block. Photo. Photo. Photo? What can we do? Photo in a circle. What do we want to put in the middle and the side. Top optional top left middle? Okay. We can make all these fields optional. You know this, I heard someone laughing at my picture. That's not very nice. I heard someone laughing at my picture and that wasn't very nice. I was offended. All right, I think we should feature their name fairly prominent up here. Maybe like, and then below that, their position, yeah, the title, yeah, all right. We'll put that slightly lower, anything else? Contact details, I heard, all right, yeah, that's a good one. I'll put that on, yeah, about a little description. All right, we'll go with that. So let's set aside an area here for, this is gonna be, you know, some text, and then maybe we'll put like, our social buttons at the bottom, like email, Facebook, Twitter, yeah. All right, how's that look to everyone? Good, so let's think about this a little bit more. We're gonna need, from over here, we're gonna need an image. We're gonna need, what's this, this is their name. Now, we might call this like a profile, photo, and that's an image, we're gonna have a name, that's just gonna be a text field. Same here with their position. Over here, this would be, what do we call this? Bio, nice. That's more than just one line of text, we might use a text area for that. And then we're gonna have these three social buttons, and they're all gonna be URLs, yeah. Email, Facebook, and Twitter, URLs. All right, does this seem like a familiar process to you, in terms of design, how you would normally go out about building a website? Cool, let's put it together. This is where we move into the live demo mode. If you don't mind, I'll just drop the lights down a little, because, so that you can see my screen, a little better, how's that? And, all right, well, this is code, but let's switch over to WordPress. All right, so this is a WordPress install I've put together just now. I'm gonna switch to my child theme so that we can make some changes to the theme later on. And to build what we've designed, I'm gonna open up BlockLab. So BlockLab is a plugin that's available for free, that really sort of enables us to get through most of what we need to do here. All right, I got my design, I got BlockLab here. I'm just gonna trash this example block for now, add a new one. So what's it called? What are we gonna call our new block? Team member, that's it, yeah, team member. And before we add our fields, I like to just go in here and choose an icon, that one works nicely, and we'll put it in, ah, common will do, all right. And we'll go ahead and add our fields. So the first one was, we'll put in their name first, and that's just a text area. And BlockLab has these extra fields here for help text and default value, placeholder text, that sort of stuff, but we'll leave that for now. We don't really need that for a name. Can put in here title. Oh, no, we're gonna call it position, when we, we're gonna have their profile photo. Right, and here we change the field type to an image. You can see the options for that changed a little. Close that. And then what have we got next? The bio is gonna be a text area. Close that. And then we have email. We'll put it, we'll ask for the email address. And then, and we can do a mail to link that way. We might put in the Facebook URL and Twitter. Now, if I was doing this for a client, I might choose to fill in a little bit of help text here, like I might put in here a link to the team members Twitter. Because we don't want just the at handle, that's not gonna work for us. Although, you know, we could work around that, but there we go. We could even put in some placeholder text to help with that, okay? And we'll hit publish, and that's done. So, pretty quickly, we've already built out the structure of our block. And now we're just gonna work with familiar languages like PHP, HTML, CSS to build out the block itself. Now I'm not a CSS whiz, so any front-end devs in the crowd might have to give me a hand as we do that. So what we have to do is we're just gonna create inside of our theme a new theme template for our block. And it's in here 2019 child slash blocks slash, I'm gonna copy this block dash team member. So here I am in my editor. I've got a blocks folder already in my theme. Got a new file there. Blocks dash team dash member dot PHP. I'm good to go. I can start writing out my template. So what's it gonna look like? Start with a div. Now we want the profile photo. I could use flexbox or something fancy here, but I might just float it to the left if that's okay with you. I'm even just gonna use a straight image. We'll just leave the source out for now. Then we want the name. We might put that in the H2. I'm just stubbing this out. We're gonna put the position in H3. Any SEO experts here have a problem with that? We'll put the bio in a paragraph. Let's just put a few little comments in here. Make this the name, position, bio. And we'll put in maybe these social things inside of another div. Let's get super fancy actually. Instead of using a div, we'll use a UL. What do we think? Good call. We're gonna have email, Facebook, and Twitter. Obviously this is gonna be blank to start with, but just to test that it works. So that's it. That's my template. Pretty straightforward. We'll have to make sure we fill all this in in a second. I actually put in these values, but let's just see what it looks like so far in WordPress. If we refresh this page, we can see now this is the template that it's using. And in a new tab, I'm just gonna edit my hello world post here. All right, I'll skip these tips. Insert a new block. Here's our team member. All right, none of these actually do anything yet, but why not fill it in? Call out a name to me. I miss that, sorry. Fred, Nirk. Nirk, okay. Silent G, oh, thanks. How's that? And Fred's our resident. Sorry? Techhead, all right. Oh geez, in anticipation of this talk, I did download a couple of example images we might use, but I don't know if I got any of a person. Let's find out. We've got someone pouring coffee. That'll do. We'll drop that in. And all right, any copywriters in the audience? Oh yeah, okay. Oh, dollar. Yeah, and you're okay. Oh yeah. We'll leave out Facebook, because yeah, Facebook. The real Fred Nirk. All right, now if we click away from here, we'll get a preview. Now our preview isn't what we've planned for it to be, but you can see already that we've got that H2 happening in there. We've got our dot points, which is really nice. I've noticed that, I've just noticed this now, is that our 2019 theme includes some predefined styles for the H2 that I kind of don't like. No, I could sort of just counter those in my style sheet, but instead of doing that, I think we'll change to a H3 instead. See if that helps, we'll change this to a H4. It is just a quick work around because I don't like those 2019 things. That's a bit nicer. All right, back to our template. Next step is we're gonna use a couple of really, really simple PHP functions to pull through the data from our block into the template here. So we need to know these field names. That's what we're gonna be using. First one is name, and we can do it really simply here. Just get rid of this. We're gonna use block underscore field and then put in name. So this here, this name is this here, all right? And then we can do the same thing. We just copy paste this. Block field, what do we call this one? Position. All right, and then we can even do the same for bio. Now, the image, let's just see what happens when we put in block field image. What did we use? Profile photo here. Okay, we'll come back to the social in a second. Let's have a look. We can just click in and then click out. It loads it again. We got our image. That's nice, and our name. That's all looking good. Obviously, we need a little bit of style happening, but we'll get there in a second. All right, let's put in our socials now. What I'm gonna do is I'm just gonna add a little bit of a PHP chunk at the top here, and we're gonna pull through into variables, our email. And instead of block field, which outputs the value, I'm just gonna do block value, email. And that returns it so that I can put it into a variable. Hopefully that makes sense to you. We're gonna do the same for Facebook and Twitter. I'm just gonna check that those are the right names. Email address, there we go. And then down here, what we can do is we can just do a simple if block. We're gonna do if not empty email, and then we can do echo email. All right, so we're just checking to see that we've actually got an email address in there. And if there is one, then we'll output it inside of a list item, okay? Now I'm in favor of coding standards as the next guy, but this is a live demo, we wanna get it through it quickly. So don't nitpick on me for that. All right, so if empty email, I'll put the email, empty Facebook, empty Twitter. Anyone see any mistakes here? Looks good. Okay, let's have a look, see what happens now in our block. We just click in here, click out again, there you go. And so you notice we didn't put in a Facebook, so we didn't get that out again. So that's how we use block field and slightly different block value. The next step, you could probably imagine, we're just gonna get a new file here, block, same name, block-team-member, but instead of .php, we'll call it .css. And now we can start doing things like this. Let's see here, we're gonna go our float left, height, well, like 150 pixels with, it's gonna be auto, something like this. It's not gonna work with border radius if I just did an image, so I have to put it image inside of a wrapper here. Span class equals profile photo, border radius, 75 pixels, and then we can do this image with 100%. That's a, like I said, whoop, I'm not a CSS expert or a front-end expert, but I think that should do the trick. Yeah, maybe, no. We might have to refresh to get that CSS. Overflow, really? Oh, yeah, you're right, I need overflow here, nice. All right, let's, sorry, I forgot to save it before I got rid of that, now we have to put Fred back in. Ah, sorry about that, everyone. Okay, well, it's getting there. Slowly, we're gonna need a bit of padding here. Why is that overflow not working? Oh, not padding, margin. Who called out display block, nice work. Oh, no, no, I'm just gonna update this, isn't it? There we go, look at that, hey. That's, we didn't actually need too much more than that. So, of course, all we have to do here is view post, and we'll see it on the front-end, same here. I guess we maybe want to write some CSS because our wrap is not working. I'm guessing there's some styles applied to the header, but you get the basic idea. I won't put you through the ordeal of me trying to get those into circles, but if you're a front-end developer, I'm sure you can do that. But you get the basic principle here. Some of the things you can do with this, though, is it can really go even much further beyond this. Like, you might decide that you wanna build a block for your, we're commerce products, right? And you might wanna put them in a slide show or something like that, and you can put in a repeater and have, you know, populate them with each one with a product or something like that. And you can go nuts. You can use WP query inside of your block to create a query and pull through particular posts and show them that possibilities are as endless as any old theme template, which is what's really exciting to me. It makes building for and developing for Gutenberg a lot more fun and a lot more accessible. So, that's me. That's BlockLab. Hope that you found this talk useful. If you wanna check out BlockLab, you can at getblocklab.com. I would like to take questions. Yes. Hang on, just bringing this. So the million dollar question is, why is WordPress not built this into Gutenberg? Why is WordPress not built this? Well, sometimes I wanna answer people, well, you'll have to ask WordPress, but of course you can't because WordPress isn't any one person. It's a community of people making decisions together. I think part of the reason, speaking honestly, is the earnest of Gutenberg. And if you'll allow me a little side thing here. Okay, so I'm gonna go off track a little bit. This'll be fun. So the best internet ever was the internet in like 2004, right? 2005, something like that. When there was no sort of centralized place for everything, everything was messy, everything was kind of ugly, and it was hard to find stuff that you needed, but gosh, it was fun and you could discover and you could explore, right? And the essential idea of the internet is that it's a distributed system, right? So web distributed around the world and you can end up anywhere. These days it's getting less and less distributed, right? Like we have Facebook, lots of people think Facebook is the internet and you can find almost anything there. Google is now not letting its visitors see your site, it'll pull through the content of your site onto the search results, right? It's becoming less and less distributed all the time. I think that's a real problem because I believe in this vision of the internet. I believe in this idea that the way it should be distributed, that content creators like you, it should be easy for you to put what you want out there. But the reason why it's becoming more and more or less and less distributed, more and more centralized is because consuming content on those platforms is a lot funner. It's a lot more user-friendly. It's a better user experience, right? And so it's sort of hard for us as publishers, as content creators to put content out there that competes with that. So how do we find a solution? Well, to me, that's what Gutenberg is about. Gutenberg is about making it easy for content creators to put stuff out there easy for people like us to create these highly engaging, interactive, like high quality content all over the internet, not just in one place. But in order to do that, we need to build a product at Gutenberg which isn't only working with this major driver of the internet WordPress, but also works with a lot of other platforms. Did you know lots of people don't realize but the latest version of Drupal has Gutenberg built into it. Gutenberg was originally created for the current version of Drupal, works with Gutenberg. And Gutenberg was created for WordPress, but the big picture of Gutenberg, at least to me, is to get these tools to create these engaging experiences into the hands of everybody who wants to create content on the web, not just WordPressers, but anyone in the distributed web. So in order to do that, we can't be platform-specific, we can't be just tied down to PHP. We have to build something that uses some of the more difficult modern technologies. Sorry, it was a bit of a rant, but hopefully that answers your question. We have time for more questions. There is also a bit of a change in tact. Our speaker for the next presentation has not showed, so we're gonna do an alternate session. So while we're organizing that, let's just keep the questions going. Yeah, I have a question over here to your right. It's Pat, I have a question about that block. So would it be easy enough to then create a block called Team List that you could drop onto other pages using that content that you just created? Yeah, absolutely. The only change that I would make in that case is that I would create a repeater field as my first field in BlockLab, and then put all of those fields that we did create as sub-fields of the repeater. Hopefully that makes sense, but that would just then allow us to go new team member, new team member, new team member, new team member, and fill out all of those fields. Okay, yeah, cheers, thank you. Given what you said about Gutenberg being used in Drupal and there's a Laravel plugin for it too now, how easy is it to export from BlockLab into a format that you can use standalone without having to install BlockLab? Yeah, it's a great question. It's something that we get asked a lot, which is wouldn't it be good if I could take my blocks that I've created and export them to put them on my client sites, maybe without needing BlockLab installed? And the answer is that in shipping in WordPress 5.3 in November is a new block directory. And I'm still coming up, like still learning about what it does, but my understanding is we're gonna have, in WordPress we're gonna have plugins, gonna have themes, we're gonna have blocks, right, as a separate thing for the first time where you can install these custom blocks. And this is a new thing coming to WordPress and we've been waiting to see what that looks like and see what the format for that is before figuring out how to export. Does that make sense? So long term vision is maybe if we can, BlockLab would love to be able to export blocks, but we're waiting to see what that looks like in core. Big round of applause for Luke.


For enjoying the first International Conference on Rice for the Future in Bangkok, organized by Beltic, National Genetic Engineering and Belt Technology Center of Thailand, to celebrate the International Year of Rice 2004. In this conference, the Golden Zinkle Awards were conferred to outstanding rice researchers from all over the world who have contributed to the advancement of rice research promoting RLD on rice for mankind. Thank you.


Classmates, questions, comments, concerns. We're sailing through this term. So for some of you that have missing grades, remember everything is on angel. So you can't say how I didn't know I was missing something that's right there if you aren't. So catch up quickly so you can have a relaxed spring break. You need at least the second half of it to sober up from the first half of it anyway. So it's not the way you want to spend your spring break, I don't think. So get caught up, stay caught up, do all right. Any questions before we get going? All right, yesterday we had a problem. We'll take it up again here in a slightly different form. We had one of my personal rocket ships. I had a certain mass, also had a certain thrust to it. I think I called that T, is that right? I think it's kind of 10 to the fifth. Now as we go through this stuff, now the things are changing a little bit. We only have four things, the whole four weeks coming up there. Now we're adding more stuff as we go along. One of the things I'm going to expect you to do as we go along is recognize what we're talking about, what the quantity is in terms of what the units are. I won't always make it so obvious as to say M equals so that you know that's the mass. I might just say a 20,000 kilogram rocket ship. You have to know from that wording that that's the mass you were given, not the weight. What's the difference between mass and weight? Weight is the gravitational force on an object. That object being of mass, M, whatever that is, in a gravitational field, which we designate with G. Now we typically take G to be 9.81 meters per second squared. It does not mean the object's actually moving at that acceleration. You are subject to this very same relationship. You have a weight because you have mass in a gravitational field, but you're not accelerating right now. Some of you in certain ways are decelerating right now. Feeling it, Joey? Yeah, yeah, because we're past noon on Wednesday. So we're heading downhill, decelerating. So don't take it means that that is your acceleration. It is, it's the gravitational field of strength giving us an idea of what the gravitational force is on you in that gravitational field. If you go to some other planet, which some of you seem to do frequently, that G will change because it depends upon, it also depends upon, if you remember what we were looking at in some of the earlier chapters, where you are on the earth and even the altitude above the earth, the higher altitude you go, in general, the less the gravitational field strength. So we use that to calculate weight, but this will have units of meters per second. That will have units of kilograms. And that will have units of newtons, which we, because we're lazy, we're not efficient just right hand. We don't write out the word newtons. Too much right, they hate the right, so we don't do it if they don't have it. So starting up here, yeah, I'll put M equals for you, so you know that means mass. T, I don't know, maybe you have to think about what that might stand for. I could have put F because it is a force. I might have put F sub T, meaning it's a thrust force. Those kind of things you can do, like the origin, it's optional, what you use for these variable designations. I try to do something that's both simple and clear. So instead of putting F sub T, it makes sense to me to just put T, paying attention to that being a force, even so, it's gotta be a force, because it's got units of force. So start gathering this stuff, start becoming more conversant with it. In some ways, part of what you're doing here is learning a little bit of a language you may not have spoken before. You're, I'm trying to teach you some of the language that we use in science, whether it's written, or verbal, or arithmetic, algebraic, and calculus, hey, right, that should take notes. Write down what I say. So we had that problem yesterday. What do we have to, oh, we had to find the acceleration, and we did so. How do we do so? How did we find the, oh, is that the acceleration right there? That would be the acceleration of an object in free fall, an object where the only force is gravity. And we're gonna talk in a little bit about why there's another force on you right now that's preventing you from being in free fall. What do we use? What do we use when there's more than one force, more than the gravitational force acting on something to figure out what its acceleration is? We've gotten mass, we've got something about the force that we wanted to figure out what the acceleration is. What do we use, Phil? Yeah? We use F net. All right, he said F net equals who? Times the acceleration. This is a complete, good start. You get the rest of the day off because you gave us a real good start, but it's incomplete. You should be sitting there going, uh, fix it, quick. If you're gonna be good engineers, with someone you wanna be, you've gotta have this anal retentive thing, this compulsive disorder dwelling up in you that you can't stand to see something on the board that's not right. Billy would've given him more if I'd given you more time. That's why your skin's not crawling right now. Do you have that, that, that oaky feeling? It's just not right. Don't leave it like that. Something you don't look like you're feeling oaky. Oh, Billy, you do. You just kind of an ookiness about you. An aura of oaky. Lem's doing his best to suppress it, but he feels it. What's wrong? This is a vector equation. Force is a vector, and acceleration is a vector. We can't have an equal sign if we don't have equal things on either side of it. So we gotta have both sides being a vector, if it is and it is in this case. If you don't believe force is a vector, well, of course it is. You push left on something. It's very different than if you pushed down on something. Even with the same amount of force, you push in different directions, different things are going to happen. Phil gave me this F net. It's a little bit different than I personally choose to write. This is perfectly fine. It's just not what I choose to write. So what's another option for writing instead of F net? The summation. I'd like to do that just as a reminder that we've got Anna all the forces in the problem. So we've got this thrust driving this rocket ship up. That's a force. If we divide it by the mass which we've got, we should get the acceleration, didn't we? Is that what we did yesterday? Or on Monday? I don't think that's what we did on Monday.  We did, there it is. What forces do we have to put in this summation? Every single possible little force there is. Well there's lots of forces acting on the odds.  And all those atoms are working on each other and all the nuclei are working on all the electrons and the nuclei, the neutrons are working on the protons and there's all kinds of happy stuff going on in there. Do we need all those forces? Well when we drive ourselves crazy, if we had to take into account the forces, all the atomic and nuclear forces, we can't. Those in fact are all forces inside the thing. None of those forces are coming from outside acting on the object. None of those forces are going out in any way acting on, those are all internal forces. And in fact, those all cancel each other. Remember we talked about Newton's third law? A little bit on Monday, the action-reaction pair. This is an object, of course, from one object on another gets an equal and opposite force back on itself. Remember that? We talked about it a little bit. We'll hit it some more in a second. Well that's what's going on with all the electrons and the neutrons and all that stuff. As a nucleus pulls on an electron, the electron pulls on the nucleus with an equal and opposite force and those two forces cancel out each other. So that's why we don't have to worry about those. They're internal, they have always come in an equal and opposite pair, they always cancel each other out, so let's not mess with them. But this thrust isn't that way. This is a force on the rocket that isn't canceled by anything directly. So we have to account for it. But, do the math real quick. Take this force, divide it by m, and we don't get the acceleration we got on Monday. It was 5.1, wasn't it? 5.2. You divide this force by that mass, just like we could do here, we don't get this acceleration. Did we goof up on Monday? It happens, so it's pretty easy to goof up at the board. Are you checking it? Check it for us, Joey. Three times 10 to the fifth, divide it by 20,000? You don't get that. You can just do it in your head. 300,000 divided by 20,000 is about what? So how can we don't get the same numbers now that we got on Monday? Yeah, check your notes. I don't have all the forces on this picture that were in this problem. And we can't do this till we have all the forces in the problem. All the, what did I call? What did I say? I said something about what forces to use. Huh? I said something, I think. Check your notes, did you write it down? Who's my favorite student who takes good notes? No? In this case, we could call that the why I called. But I said something else. Oh, there's no forces. Huh? Of course, they gotta be real. You guys have so many imaginary forces going on in your head, we've never finished a problem.  That's a force on your life. That doesn't count here. That's not the kind of stuff we're at. Yeah, it'd accelerate you in a certain way, but that's not what we're talking about. We're talking about real forces. All the forces on the object. Yeah, all the forces on the object because we don't want forces on something else. To help us figure out how the rocket's gonna accelerate, that wouldn't make any sense. It's gonna be with forces on the rocket, but I did use a word. Excuse me. All the forces. Did I say external? I think I said something else. Yeah, they gotta be external because I just talked about the fact that all the internal forces cancel each other out in pairs, all the molecular, all the nuclear forces we don't care about. The force is a vector anyway, so that's absolutely vital, but I wouldn't have said it a step. I'm looking for, I did say something else here. Holy. No. Maybe I didn't. I'm pretty sure. I thought I said it. In dynamics, we're doing kind of the same thing in parallel that we do in here as we go along. It's just in dynamics, we do it in much greater depth. So I may have said it there and I didn't say it here. All the pertinent forces. Did I not use that term for it? Okay, there you go. All the pertinent forces. All the ones that matter. There might be other forces in a problem. They just don't matter. Getting, judging whether a force is pertinent or not may take a little practice as we go along.  That makes that slippery. If we push on something like that, its weight is not necessarily a pertinent force. Because it's that way, the object can only move that way. So the weight may not be a pertinent force. We might need the weight to figure out what the mass is and then figure out how it's accelerating, but the weight does nothing in terms of the acceleration directly itself. So there are times when certain forces are in a problem, certain values may be part of the problem, but they might be in pertinent to the acceleration to the summation that we're doing here. So what's missing here, Alan? I think you said it a long time ago. The weight. We also have weight in this problem, acting down. We know the mass, we know G, we can figure out what the weight is. Once we have the weight, it kind of makes sense, I think, that the thrust is working against the weight, and so we have to use the two of them together to find out the acceleration. All right, so that's what we did on Monday, right? All right, we're gonna add to this problem a little bit, a little bit later in the flight. Same thrust, same engine, still squirting along at the same amount, but now the acceleration is six meters per second. What was 5.2? Now it's six, neglecting air resistance, which we will do in almost all of our problems. So I'll say that right now, neglecting air resistance. Why would the acceleration change, huh? What do you mean a decrease in weight? Did they open the door, kick my brother-in-law out? I would, tried to do it in the car once, grabbed on, held on, and they took me in the eye. That ain't fair. Why, Tyler? Yeah, it's burning up fuel. The ship is getting lighter, so if they're still the same thrust, but it's losing mass, because it's burning fuel and squirting it out the tail, its mass is going to be less. How much less? In fact, you figure out for me, what's the change in mass?  NASA does this on launches. They check the measured acceleration against the expected rate at which fuel is burning, make sure they've got the all the right values as things are going along, and find the change in mass. How much fuel was burned? Did you say yes or no? Huh? Yes. You think so? Did you stop working? Yeah. What was the thing you got? First acceleration that we had on money, right at takeoff, full fuel tanks was 5.2. Do you need that number? I don't think you need that number. Plus we're doing the same problem, so if you get an answer, find somebody else who has an answer, see if you got the same thing. Good engineering expectation. For a second opinion when you can't. You can't on tests. Anybody's name? Anybody? What's his name? You're wrong, he's not. What's his name? Okay, good. You can ask John. Or you can introduce yourself. No, he doesn't look at me. He didn't want to play, does he? Yeah. So you're trying to be friendly, but Chris won't let you. Thing to do, we've got acceleration. We've got thrust. You can find out the weight now, find out the mass now, find out what the change in mass was. So you don't need the original acceleration. You do need the original mass because you want to find out the mass changed. Did you get something? Is your name Chris? Somebody's name is Chris? Joey? I don't know. Is it he? You don't even like to be Chris? All your folks get your name changed? Now you got something left? You just know he's back there or somewhere. Cause I keep looking over your head when I talk to Len. Maybe there's no one there and I'm just faking you out. Do you know who Len is? Check with Len. No, that's better. Oh, that's good. I know. I made a wrong turn. I think you're in your car. Find delta M. You see delta means two minus one. We have mass one. That was mass take off 20,000 kilograms. Need to find mass two now. Anybody agree yet? Len, did he agree with you? Was he wrong? Is that something that we're talking about? Then check with Len. Everybody, does anybody not know Joey's name? Joey. Joey, everybody knows your name. And class with me. That's a bit difficult. Actually, it's third, cause you're in IED as well. We did know that. Check with John now. There's a one name you know. Anybody who checked, did you and Alan agree? Evidently, it didn't agree, cause otherwise we'd just start over. Tyler's not playing with anybody. He's not being anything fun. Come on, Tyler. Calc's our name is the boot of this Calculator.  Here's a big idea. We're doing the same problem. Should get the same answer. You guys agree? Joey's going, Cal, all these names, people. There's an Andrew, and a Mark, and Tyler, and I don't even know how these people are. Nobody agreed yet? All right, let's see, let's do it here together, see if we can agree. We need to find M2. M1 we were given, that's the way to take off, or the massive take off, that we already had the 20,000 kilograms. If we can find M2 now, the mass now, that goes with this acceleration, under the same thrust as before, we could find delta M, so we need to find M2 to find delta M. Let's see, we need to, we have some of the forces to get the acceleration. We have a new acceleration because we're accelerating a new mass. Is the sum of the forces the same as it was on Monday? And that's the only thing that's changed. I said that thrust is the same, is the sum of the forces the same. Why not? The weights change because the mass has changed. It could even be that this rocket's high enough, now G has even changed, but I'm not pushing my luck here in terms of what we can do on hand. So let's see, I think we picked up as positive because we got the forces in different directions. So we've got T, which remains the same, minus W2, because they're in opposite directions. My recommendation to you is, do these directions algebraically as you go. So I put this minus sign in here, indicating that the weight is down. That way, every time I put in weight, I have a positive weight, which makes more sense. Have you ever gotten on the scale and had negative weight? You may have lost some weight, but your reading was never negative, so it just makes sense to leave the values positive and do the minus signs algebraically. It's gonna cause whatever mass it is we're looking for to go the acceleration that I gave you. That's what this is here, this A2, we can call it now. M2 appears in two places. It's already here, because that's the mass we're accelerating, but it's in here because the thrust has to push against the weight. So we've got all of those numbers in, except M2, should have come up with an M2 of what? You're gonna have it? Is that a hand up? Samantha, you have it? Okay. Oops, that's not what I had. Phil, what'd you have? A $19,000. Yeah, that's what I had. Check your numbers, maybe a minus sign or something. M2, remember in here? Well, let's see. W2 is M2G, so we can make this T equals M2 times A2 plus G. Is that the right algebra? The thrust we're given, taking the thrust to be the same. The same engine, running the full power divided by A2 plus G. Is that what worked? That's what you did? Samantha, did you catch? Similar, would you have maybe a minus sign? A lot of students think the accelerations in the opposite direction of G, how come there's a plus sign here? There's a plus sign, because this worked out, these are not vectors here that we're adding. This is just quantities that we're adding right there, algebraically. So don't put in a minus sign when one isn't there. You should get just under 19 kilograms. So the change in mass, and burn about 1,000 kilograms of fuel so far. About as simple as they're gonna get, because they're gonna get more complicated from here. Because you're smarter now. You're smarter now than you were Monday. So let's keep going. All right, I can erase this, start clean. Are you okay? And I hope you believe me, whether you may have put it to use yet, that one of the most useful tools in doing these problems, and it will be so for the rest of the term. For those of you continuing on in engineering, who will have statics in the fall, and dynamics and mechanics materials in the spring, this will continue to be true. So let's get a handle on this now while we can. That's this business of drawing free body diagrams. There are very few problems you should do for me for the next year and a half that don't have a free body diagram with them. That's part of why I even started doing that course. We have the technical pre-hand sketching course, is to help with this. It's that important, free body diagram. Simple and large. If they're too small, they're not gonna be helpful after this. Once you've drawn it, and then have to do something with it. If you've done it too small, it's not gonna be helpful. So why do it? You've gotta make them big enough because there's more stuff we gotta get in there once we've drawn the basic free body diagram. We need to use it to help us solve the problems. And if you make it too small, it's not gonna help. Make it simple because you don't wanna waste your time on the drawing, don't put in windows and bumpers and decals and paint jobs and the like. Just make it nice and simple so you can get to the physics stuff, finish that early, catch an earlier flight to Daytona Beach. So make them large and simple. Just the object undergoing the forces. So if we're talking about a simple problem like a crate on some greasy ice, which we are pushing across the ice, very simple problem. When I go to draw the free body diagram, I draw the object we're pushing with the forces free of anything else, free even of the ground. It's just, I'm not pushing, I'm not accelerating the ground. I'm trying to accelerate the object itself. So just the object, that's the free part. Just the object, free of anything else. There's a rope attached to it and somebody's pulling on the rope. I don't draw the rope, the object. Free of everything else. To put down on it as accurately as possible. The more accurate you do this, the more helpful this drawing's gonna be. If you're sloppy about it, that's the kind of help you're gonna get from it. Sloppy help. All who might not know yet if a force is pertinent or not, but that's fine. As you go through the calculation, it just won't be used and then you'll know, okay, that one was an impertinent force. But there's no harm if it's on the diagram and you just don't have them to use it later. What you can't do is be missing any forces. If you're missing any forces, you're not doing the right problem. You're doing a different problem. You gotta have all the pertinent forces. So let's talk about the types of forces we're gonna see in here. So you'll recognize them in the problem and know how to apply them to the free body diagram so they're useful to you. You mess these up at all and it's just gonna mess up the problem for you. You're gonna get frustrated, obligated by law to take points away, get the red pen out and starts flashing it and slashing it all in place. Red because it looks like blood, like I'm drawing blood. So we gotta get all the pertinent forces out. Don't forget, when we're looking for forces, whether we're solving for them or we're applying them in a problem, these are vectors. So you've got to have all of the parts of a vector to do these problems right. What are the parts of a vector? The characteristics of a vector. There's three of them. Direction, the free body diagram, the direction and the magnitude are the most crucial. It's in the calculation itself where the units really come into play but pay attention to all of them. So as we go through these forces, remember at any time we're looking for as much as we possibly can about the direction and the magnitude of the forces. The more we can figure out ahead of time, the less we have to figure out later in the problem. The less work for you to do.  Which means the less points you're gonna lose. All the better. All the better. All I'm trying to do here is keep you on your dot given points. All right, so some of the forces, not in any particular order, but some of the forces that we're gonna come across in our class here. Things like pushes. Well, that's what the thrust was doing. It was pushing on the rocket. Lots of problems we're gonna see in here where somebody you can pretend it's you if you want is pushing on an object to move it. Whether it's a crate or a girlfriend or anything else. There's pushes. Generally, we don't know anything about the direction of magnitude other than what's given. And it may be nothing is given, but it may say somebody's pushing on a crate with a 30 degree angle. Great, now you know the direction. Now you know the angle, you just may not know the magnitude depends on how the problem's written. A lot of times though, we will know the direction. If you have a push on a problem and it says it's at 30 degrees, it usually means something like that. That's good. Half of the part of that force vector is taken care of. You know the direction. It's acting on directly towards the object because that's how pushes work. And if they give you the angle, put it in. Look at the drawing if one comes with it. Look at the wording carefully. We'll have some forces like this. We'll have some that are levels, some that are vertically. There's lots of possibilities. This is just one example. Cables, anything you might find in your bedroom. Anything that you wanna throw on that list?  No, okay, you're all right. The thing that's good about anything in a problem that pulls is you do know the direction of it because, well, rope, strings, cables, chains can only pull. You can't push with a cable. I guess you could get a rope, wet it, freeze it and then push with it. But in general, any of these things attached to an object, it can only be a pull force. It can only be directed away from the object. So if we have some object and somebody's pulling on it with a rope, it's got to be a force away from the object. That's how pulls work. The force is directed right along where the rope itself is pointing. You can't push with a rope sideways. You can't put a rope on something, be pulling on it and direct the object sideways. If you move sideways, will the rope move sideways with you too and you're still pulling only in the direction the rope points, direction. So if you've got a rope, a string, a cable, a chain in a problem, you know that the force is away from the object in exactly that direction of the rope itself. It can't do anything else. That's great. That's all of the direction is already known. It's one less thing for you to have to figure out. If they tell you to find what's the force in the rope required to give it a certain acceleration, you already know the direction. You just have to work on the magnitude in that problem. Half of it's done. If you recognize ropes only pull and they only pull in their own direction. Those kind of, these are sort of what we might call maybe a better word is applied forces. Because these are forces we have to come in and do something. We have to come in and push it. We have to come in and pull it. There's other forces we're gonna have that just kind of happen because they're there. See some other forces. Let's see. All right. Oh, here, here's something you're doing right now. Let's figure out why. Here's you to a simple free body diagram. This is how I see all of you. When I look at it because this is what I see. Bunch of blocks. Oops, dead of that, I don't know. Mike's already quick dialing his lawyer. Any forces on you right now? Well, of course, you're sitting here, you have some mass and you're in a gravitational field so you have weight. An object, forces on a mass will cause that mass to accelerate. Why aren't you accelerating right now? That must be some force pushing back up against the weight that cancels it. That's the only way the sum of forces acting on a mass, in this case you, to have no acceleration. If that's zero, then that must be zero. There's no other two ways about it. This, F equals MA, this is not a simplification, an estimation. This is the way it works. This equation has never been proven wrong. It's the way of the universe. This side is zero, which it is. Not one of you is accelerating right now. The forces must sum to zero. So something's gotta be missing here. There must be something pushing back up on you with exactly the same amount as your weight. There's just gotta be. It's the chair. Actually what it is is the molecular forces of the chair. You're on the chair being pulled down by the earth. The earth is trying to pull you through the chair. The chair is fighting back with its own molecular forces. Materials in general don't like being torn apart. All of those little forces in the chair are pushing back on you, hold themselves together.  It's pretty funny when it happens. And I'm thinking sometimes it might be fun to bring in some trick chairs just to watch y'all accelerate. Look how he accelerated. But the administration asked me to stop doing that. So these chairs are stout enough to push back on you with enough force that they maintain their integrity and they counteract the weight. This is also an example of Newton's third law. You're pushing down on the chair. The chair's pushing back up on you with an equal and opposite force. That's an action reaction chair. Sorry, force. Action reactions parent. Your weight is pulling down on the chair. The chair's pushing back with the same amount. Not more, otherwise you'd take off. Not less, otherwise you'd go down. Just the right amount to leave you where you are. We call this the normal force. Typically give it the letter big N. Be careful because we also have big N for Newton. This is the normal force. Physics and engineering, this word normal has a particular meaning. It's not the meaning, it's not the normal meaning of what you're thinking where ordinary, it doesn't mean that at all to us in physics and engineering. It means one thing and one thing only. It means perpendicular. But I need to explain it more carefully. Perpendicular to what is the question? The normal force, it only occurs when one thing is in contact with another. Your butt is in contact with the chair. If you stand up and you're off of the chair, there's no longer a normal force between you and the chair. It's gone. Contact force between two objects, between two surfaces. If those two surfaces aren't in contact, there's no normal force. Now, careful with that. I have students in problems, a lot of times we'll try to put a normal force in a problem just because they think there should be one there. But then they can't tell me what's the object that's causing it. Where's that normal force coming from? The object we're talking about is not in contact with anything. If it's not in contact with anything, there's no normal force. That rocket problem we did, there was no normal force. That rocket wasn't in contact with anything. Not the way it laid out the problem. It's a contact force. Object causing the normal force can only push. So that's what I drew here. Here's you. Here's the normal force coming from the chair because it acts on you, it's only pushing. So it's always directed towards the object. Only perpendicular to the two surfaces in contact. So if you know where those two surfaces are, you know the full direction of the normal force. Only perpendicular to surfaces in contact. Just look at a problem, see what surfaces are in contact. If any, you know the normal force is acting towards the object because normal forces can only push. And you know it's perpendicular to the two surfaces in contact. Completely important because we gotta get this normal force right in these just like we got any other force right. We're gonna get the problem wrong. Here's an object on an incline. Two surfaces in contact? Of course, the box, whatever it might be.  So we draw a free body diagram. I make it big. I try to give it the same amount of slant so the drawing helps me. It's got some weight. I figure, I didn't say where it was, but let's figure it's on the earth or somewhere or some planet. Normal force, let's see, it's a contact force. We do have two forces, surfaces in contact. It's only a push so it's only gonna act towards the object and it's only perpendicular to the surfaces that were in contact. There's the surfaces, there's the perpendicular, and I can draw the normal force. I don't know how big it is, but I know it's direction. That's great, that's half the problem. You know it's direction. It's not the magnitude of the normal force. There's only one thing you can do and I don't know any other way to come up with the normal force than to do this. I'm actually on a free body diagram and then sum the forces on the object, but normal force will be one of those forces and that's how you can figure out its magnitude. There's no other way. Occasionally, occasionally the force will be equal in magnitude to the weight of the object, but only occasionally. Do not assume that right into a problem or you'll screw up. Occasionally it happens, but not always. Let's see, let's do a little bit more with this problem. There's gotta be something keeping the box from actually sliding down the plane. You put a block on a slippery, greasy, icy, Adirondack hillside, it's gonna slide down. So there's gotta be something keeping it from sliding down. So let's say that is some force parallel to the, let's say that's u, so that's f u. Do that because it would hurt your wrist. Let's figure out then. Let's say that's, let's put some numbers on here. Let's say the weight is, make it something nice and round. We'll say 200 newts. Let's say this slope here, this incline, just to give it a nice fat round number is 30 degrees. You need to exert because we need to know is Mike strong enough to do this? Or does he have to call in reinforcements? So let's figure out how big a force must you exert to hold the box there? Too much force, you'll push it up the hill. Not enough force, it'll go ahead and come down the whole hill. Remember this is a greasy, icy, frictionless surface. Who frictions a force, we just haven't talked about it yet. It's coming up. Is that a problem we could solve? How many unknowns are in this problem? How many things do we not know? Well, we don't know the mass, but we're gonna say if you know the mass, you know the weight, if you know the weight, you know the mass. We're not gonna consider that an unknown. It's always w equals mg, so if you know one, you know the other. We'll take it as that. Make things a little simpler for our discussion. What do we not know in this problem? Because we need as many equations as we have unknowns that we couldn't solve it anyway. Mike, one thing we don't know. We don't know the magnitude of this force. So there's one thing. We don't know the magnitude of that force. Do we know the direction of that force? Yeah, I said it's parallel to the slope, so we already know its direction. Remember, all forces are vectors. You've got no direction of magnitude, or you don't know the force. So there's one thing we don't know. We need the magnitude. Let's do it. Question mark, just to remind us we don't know it. So we need at least one equation. What else don't we know? You could say, well, I don't know what we don't know, and that way, I guess you answered the question. No, no, no, it's perpendicular to the surface. So don't we know it? Yeah, we don't know the magnitude. Again, on this one, we know the direction because we know the surface, the angle of the surface. We don't know the magnitude here either. Things we don't know. We need at least two equations to solve this problem. Anything else we don't know? Anything else we don't know? We know the direction, not the magnitude. Direction, not the magnitude. We know the... There isn't anything else we don't know. There's only two things we don't know. We only need two equations. I'll give you one, just to help. So here's one equation. What's the acceleration? Yeah, zero. We don't want it to accelerate the problem. I said exert enough force so it stays put. So we know the acceleration here. We must know the sum of the forces, but to do that we need some of the magnitude of the business, too, so there's one equation. That the sum of the forces equals zero. Substitute into what? We need a second equation. In terms of what other one? There's only one equation there. It's the same equation here. What do you have, weight? Your job as undergraduates is to get as many equations as you have unknowns. That's your job. We have two unknowns. Maybe it helped. I numbered them. There's two unknowns. We only have one equation. I gave you that. What's the other equation? That's a force, sum's right in there. We don't need the mass because it's not accelerating. So w equals mg is not an extra equation we need. We already got it and we don't need it anyway. We already got the weight. We don't need the mass, so w equals mg won't help us. Let's see other equation. This is your job as undergraduates. You're failing at the one thing I need you to do is just come up with as many equations as you have unknown. That's all the homework's ever been. Joe, what do you mean an equation for magnitude? This is the only force equation we've got. We don't have an equation for magnitude. Do we? We don't be nice if we did. Equation of magnitude. It's kind of like pulling out a great sword. Well, okay, so I can do trigonometry on this 30 degree angle. So what? I still don't have two equations. That's just mechanics. That's just algebra. That's why we let the math teachers teach basketball. Where's the second equation? Give up. Do you surrender? You cry uncle? Do I have you in a headlock? Simply speaking, that's true. They're perpendicular, but again, that's just mechanics. All right, you give up. You want the second equation? Patrick does. Patrick did about 20 minutes ago. Here's the second equation. We have two things, magnitude and direction. So that equation can handle two things at once. Here's how we do it. We break it into the cosine and the trigon, the dot product if you want. Those are all the mechanics to actually do this. Remember when I told you in projectile motion that the two directions, the x, y directions are kept separate. Same thing here. We keep the x and the y directions separate. There's things going on in both. There's intertwining between the two. Then you know it's the same mass in each of these. But this is actually two equations so we can always handle two unknowns in our problem. We have two equations. What is the x direction? What is the y direction? Whatever you say. Remember the origin and the coordinate system, that's arbitrary. You can set any one. That's not gonna change to physics. That's you. That's a human invention. So put x and y wherever you want. Here's my advice. Take it or leave it. My advice is if possible, put the x and y directions in the direction of the unknowns you're looking for, the unknown parts. We don't know the magnitude of either of those. If we could put the x and y in those directions, that's just less complication. The answer's gonna pop right out because each force then is entirely in one of the directions. It's just easier. But you don't have to. You can put x and y anywhere you want. You don't even have to make them perpendicular if you don't want it. I think it'd be a fool if you didn't. But so my advice, if possible, look at the problem. Put the component directions in the direction of the unknowns. Well, we know the directions. We don't know the magnitude. So let's go ahead and line them up like that. That would work. That's okay. Another thing that does for us, only one of the forces is off angle. The other two are right on angle. They don't even have any angle to go into them. Cosine of 90 is one. The cosine of 90 is zero and everything's easier. Do not take this problem and retilt it so that there is no incline. Don't you dare do this. It's hot to do that in high school. Do simple. Some of, I guess nobody here, I'm glad. Some well-meaning high school teachers will teach students to do this. It hasn't changed the problem any. Except it's made it physically unrealistic. Because now where's the earth? Not where I last thought, which is right down there. It's now over there somewhere. And you now have a physically unrealistic problem. So I don't want to see that. And it doesn't sound like I'm going to if nobody learned that from their physics teachers. There's a reason that some teachers only teach high school. All right, so let's do this problem here. Some of the forces in the x direction will determine x acceleration except we don't expect there to be any. Right, so I like to write this down and then actually do the summing of the forces below. So I put this kind of as a header. It just organizes things for me better. And generally we'll do so for you too. So let's see. Any x forces, let's see. And isn't, it's a y force. It's perpendicular to the x direction so it doesn't have any influence on the x direction. F u's there, but it's in the minus x direction. So I'll put minus F u, Charlie. Is that it? If that was the only force in the x direction, we'd have x direction acceleration. Something must be opposing it, huh? No, the normal vector is perpendicular to the x direction. Remember, these two directions don't mix. So if I have a force entirely in the y direction, it's not even gonna show up here. So there's got to be some force opposing you. What is it? Notice that the weight is pushing a little bit in the x direction. Maybe I'll call that wx there. And the y direction, maybe I'll call that wy. So I've taken the weight out and I've replaced it with its two component directions. That's just trigonometry. Now bring in your Sokotoa, Krakatoa, East of Java or whatever that thing is, I don't even remember. So wx is opposing your force. If you weren't there, that's the force that's gonna pull it down the plane. It's directed down the plane. We know those forces will sum to zero because there is no x acceleration. We know that. You can look at the problem and tell there's no, I told you, I don't want the box to go anywhere. So the magnitude of f u, let's see.  That's just algebra. You can look and see, yeah, that follows out of the picture as well. Nice big free body diagram because we need to do this kind of stuff. We need to have room in there to break forces and do their component directions. Isn't that the opposite direction? I already got the negative in here. So if I do that algebra, yeah, now we're okay. See, remember, that was the directional stuff. What we're looking for now is the magnitudes. And so that'll take care of itself now if we keep our algebra just right. Do we know how big this is? Well, yeah, we would if we, we know the magnitude of w, if we knew these angles, one of these angles, we'd be okay. Here's a little helper for you. I invented this myself, this beautiful thing. This helps us, this represents any incline I want. Notice the weight always points straight down. See the magic of that? Fies are getting heavy, good feeling on a straight line. That's why I didn't make that shine because you would have just conked right out. We could have made you bark like a dog and stuff would be very funny. Notice that any time I put an incline in, the normal force is always perpendicular to that incline. Remember, this represents an incline. So let's see here, here's horizontal. That's about 15 degrees, isn't it? Notice that's the very same angle between the weight and the normal direction. So if you remember that, the incline angle is the same as the angle between the weight and the normal direction, you won't have to worry about it anymore. That's all you have to remember. And if you can't remember, just visualize it or make a little sketch. So that 30 degrees is the angle between the weight and the normal direction. There's the normal, there's the normal direction, there's the 30 degrees. The weight is always the same angle as the slope from the normal direction. The normal is always perpendicular to the slope. So WX is the hypotenuse W times, well you only have two choices, sine or cosine, 30 degrees. We're looking for this side here, but that's the same as this side here, which is the side opposite to 30 degrees. Again, this is why you need a big picture. Otherwise you're not gonna be able to see that well.  There, I'm working for the post office, you're working for me. Nice big picture, because there's a lot of stuff to get in here. This problem only has three forces and then what if we had four or five? So be careful, so it's W, sine, 30. You need help seeing that right triangle that we do our trigonometry on. Feel free then to turn your paper a little bit. You don't actually move the earth when you do that. You move the earth when you do this, that's what happened in New Zealand yesterday. Somebody did this in a physics class somewhere. New Zealand wasn't ready. We've got W, it's 200 Newton, sine, 30. Look it up, this is sine of 30. I went numbers, five, didn't even do it right. Why did I think of the 300? Oh, 30, I made it 300 in my head. Now I'm doing it again, three, I'm stealing all of it. 100. Trouble is I'm in three different time zones up here. I just said something, I'm right in something and I'm thinking of what I'm gonna say next. So I'm in three time periods at once. That's how you screw up at the border. There we go. The magnitude of the force you need to apply. We need somebody, maybe it's Mike, maybe it's not, it can push with 100 Newton force. That's about the weight of 100 apples. Could you hold 100 apples? What? There's quite a few apples. Road apples? You have to have had a horse to know what road apples are. Now you got it. He said seven. All right, and then, sum the forces in the y direction, which we can do because we know the y acceleration is also zero. It's not going anywhere, y or x. And we can look at it, we're all done. N, w, ask for that, we're asked for this. But that wasn't unknown. We got other forces to talk about. We'll do it real quick on Monday. Good free body diagrams.  I'd bring in a little ruler or use a, your student ID or something, a straight edge can help with these pictures a lot. Allow you to make bigger pictures accurate. Well done, my friend. You leaving any dirt this time?


Hi friends, I am Purva and today we will work out the following question. If a line has the direction ratios minus 8 comma 12 comma minus 4, then what are its direction cosines? If a directed line L passing through the origin makes angles alpha, beta and gamma with x, y and z axis respectively, then cosines of these angles namely cos alpha, cos beta and cos gamma are called direction cosines of the directed line L. Now, let a comma b comma c be the direction ratios of the line. L comma m comma n be the direction cosines. Then we get L is equal to plus minus a upon under root of a square plus b square plus c square m is equal to plus minus b upon under root of a square plus b square plus c square and n is equal to plus minus c upon under root of a square plus b square plus c square. So, this is the key idea behind the question. Let us now begin with the solution. Now, we are given that direction ratios are minus 18 comma 12 comma minus 4. Now, by key idea, let a comma b comma c be the direction ratios, then we get thus a is equal to minus 18, b is equal to 12 and c is equal to minus 4. Now, we have to find the direction cosines. Now, by key idea, we know that L, m, n are the direction cosines and they are given by L is equal to plus minus a upon under root of a square plus b square plus c square and this is equal to now a is equal to minus 18. So, we have minus 18 upon under root of minus 18 square plus 12 square plus minus 4 square and this is further equal to minus 18 upon under root of now minus 18 square is 324 plus 12 square is equal to 144 plus minus 4 square is equal to 16. This is equal to minus 18 upon under root of 484 which is further equal to minus 18 upon 22 and cancelling common factor 2, we get this implies L is equal to minus 9 upon 11. Now, m is given by m is equal to plus minus b upon under root of a square plus b square plus c square and this is equal to 12 upon under root of minus 18 square plus 12 square plus minus 4 square. This is equal to 12 upon under root 484 which is equal to 12 upon 22. Now, cancelling common factor 2, we get this implies m is equal to 6 upon 11. Now finally, n is given by n is equal to plus minus c upon under root of a square plus b square plus c square and we get this is equal to minus 4 upon under root of minus 18 square plus 12 square plus minus 4 square and this is equal to minus 4 upon under root of 484 which is further equal to minus 4 upon 22. Now, cancelling the common factor 2, we get this implies n is equal to minus 2 upon 11. Thus, the direction cosines are minus 9 upon 11, 6 upon 11 and minus 2 upon 11. This is our answer. Hope you have understood the solution. Bye and take care.