 So here's my forces tutorial. I've started the recording. I think we'll jump on in. I'm not going to zip through the entire unit from stem to stern because I think we've been reviewing the fundamentals every time. Free body diagrams. Now I showed those to you on the first lesson, but have we been using those every single lesson since? Yes. Normal force we talked about I think in lesson two. Have we been using that ever since? Yes. Friction the same way. So I'm going to do specific questions, but first if you look at the big review, the ultimate vector review dynamics assignment, I would love to give you some questions that I like, that I like, that I like. I like number two. I like number three. No, I'm going. I like number six. I like number seven. I like number nine. I like number ten. There's your lawnmower type question. Excuse me. Eleven is good. Thirteen is good. Seventeen is good. Nineteen is good. Twenty-four is good. Twenty-five is good. Twenty-six is good. Thirty-four is good. So this is where I mentioned earlier that scholarship questions, questions that used to be scholarship questions, aren't necessarily considered that anymore. Thirty-six, this one here, I actually am pretty sure that I gave you one just like that in the questions that I rattled off that were good. I mean, I can go find it really quick because it wasn't that long to get. Oh, yeah. Isn't that almost identical to number thirty-six? Except in number thirty-six, I've got friction between the car. Okay, one more for us, big one. This is why I said the scholarship questions have started to appear on the tests, on the provincials more recently. And so you'll have some of these. So I would consider thirty-six to be a fairly tough but fairly game question. In other words, there is going to be a question where you have something hanging over a rope and the other mass is either on a downward slope or in this case an upward slope with friction. In fact, this is very similar to the last question on today's quiz, except on today's quiz, the hill went that way, downhill instead of uphill. You have to think a little bit more about your free body diagram, but it's really going to be pretty similar, I think. Thirty-seven, that's more kinematics, although it's nerdly cool. Yeah, see, certainly thirty-eight A, I would have no problem asking you to solve for mu here, especially if it's moving at a constant speed, because if you're moving at a constant speed, what's your acceleration? Zero, what's your net force? It's winter minus loser equals zero, which makes the equation way easier, because usually it means you can plus stuff over and you may be having fun. B, that's a little overkill, but I would certainly consider that scholarship question okay, or even in thirty-nine, although this is a scholarship question, thirty-nine A, that's exactly what I gave you guys on your quiz. And I think B, asking you to find the tension, I would consider thirty-nine completely fair game, even though it says scholarship. Yeah, forty is a graphing one right now, I don't know. So in those questions that I just rattled off, that probably covers about where you won't bring your laptop by if you can, I'm around for a while. Okay, sorry for those of you at home. I figure that covers, I think there's four written questions, and I'm pretty sure you've just seen three of them, or some variation, maybe instead of something moving up the hill, it's moving down a hill, or maybe instead of one mass, maybe there's two masses, or whatever. Okay, so there's your hints. The test, if I recall, the multiple choice is fairly short, I think there's only six or seven multiple choice questions. Then there's a using principles of physics right to explain question, and I've tried to give hints about that one during the unit. There's certain things that I've frequently referred to or emphasized, or if I've gone off on a tangent, probably the odds are pretty good that I was dropping a hint about that one without you realizing it. And then there's four or three written, I can't remember. And I think in the last, specifically today during class, I'm pretty sure I gave you enough hints about guaranteeing what was on the written that you should know at least what two of the questions are, and probably the good idea of what the third one is too. Questions now from the review that you would like me to go over. Did you have a question? Okay, yeah. Number three, have you looked at my online solution key? So I will say next time, check that out first, because you'll have learned it better than me called Turkey explaining it, if you figured it out for yourself. So in number three, I'm asking you to find a mass. Number three is very, very similar to, number seven is very, it says be determined the mass, is very, very similar to, I know there was at least one more. Number 12 is very, very similar to, where else? There's at least one more that I'm finding. Oh, 16. You're being asked to find a mass. It means they're going to tell you the other mass for sure, and they'll tell you one of the things that we usually had to find. Usually we were finding acceleration and tension. If they want you to find a mass, they're going to tell you one mass and they're going to tell you the acceleration or the tension. Now in this case, they gave me the acceleration. I'm going to start out same old, same old, free body diagrams. I'm going to say, what are the M1g tension, M2g normal force tension, any friction in this question? No, if there was, I'd have one more force pointing to the right. Oh, they only gave me one mass. So instead of going winner minus loser down the hole and having mass of both, I'm going to look at one mass. I'm going to write an equation just for this guy here. Who's winning? Just for this guy here. Which way is it accelerating? See the arrow? So who's winning? It can't be Mg, because that's not in the same direction as the acceleration. Who's winning? Yes. Who's losing? It's a trick question. In fact, the equation for this mass here, tension equals M2a. Do I know mass 2? Do I know A? In fact, mass 2 is 4. A is 1.5. Oh, the tension is 6 Newtons. Why does that help? Now I'm going to write a force equation just for this guy. Who's winning? Who's losing? I'm just looking at M1, so it's M1a. Do I know M, what not yet? Do I know G? Do I know tension? Just figure it out. Do I know M, what not yet? Do I know A? You know what? All I don't know is M1. I should be able to solve this. What's G? Instead of writing M1 9.8, can I write 9.8 M1, because we're used to from math having the coefficients in front and then the variable? Minus 6, yes. Equals, what's A? 1.5 M1. This is the same as this equation, 9.8x minus 6 equals 1.5x. How would you solve that? Sure. 9.8 M1 minus 1.5 M1 equals 6. What is 9.8 take away 1.5? 9 take away 1 is 8.8 take away 0.5, 8.3. I get 8.3 M1 equals 6. How would I get the M1 by itself? So for any of these where they say find a missing mass, I guarantee you'll either tell you the tension or the acceleration in the other mass. If they told me the tension, could I found the acceleration? Yeah, and then same procedure here. Or they'll tell you the acceleration, can I find the tension? Yeah, and then same procedure here. All they can do is make it tougher by throwing friction. Big look, it's still buton's a normal force. I don't know, but look, look, look. I know another force. The same size is a normal force. And you know that mass, so you'll know friction. Is that okay? Exactly the opposite. And I think by the way, this fair game, if I tell you how to do a question going forwards, I think it's fair game to expect you to reverse the procedure. So we did questions where I gave you the mass, both masses find the acceleration, we did a bunch of those. I think I can give you one mass and the acceleration. Look through it backwards and find the missing mass. Any others? Yeah, sure can. Did you look at my online solution key? Could you have? Trust me, works pretty well. Number 30. You know what, there's two tensions here. Free body diagram, what are the forces? You're going to have M1G normal force. I'm going to call this Alex tension one. M2G normal force, tension one this way, Alex, and tension two this way. Yes? M3G normal force, mystery force, tension two. I want to find tension two. That's the tension at chord X. Now I could go to find tension, remember we look at one mass usually, right? Winner minus loser. Oh, but do I know mystery force F? Do I know how the hand is pulling? No. Winner minus loser. Oh, do I know tension one? Can I find tension one? I'm here. There's going to be a two-step question. First I'm going to look at the three kilogram mass, and I'm going to say to myself, self, winner equals three times A. There's my MA. Oh, did they tell me A? What? Turns out the tension one is going to be six newtons. Yes? Now let's write the equation for this guy. Winner minus loser equals M2A. Tension two is going to be M2A plus tension one. What did you tell me tension one was, Alex? What's M2? Mass two. Yo, I wrote the tension wrong? Three times six is, oh, I wrote, sorry, tension is six. Three times two, yes? Sorry, guys. I knew it was, I got tension right here. I fixed my mistake without realizing I made a mistake. Mass two is no one? Yes. One, and what's A? It's going to be one times two plus six. I think C if I continue going. That's one way to do it. Okay? Second way, if you really want it to be clever, the second way, Alex, would have been to treat this all as a single solitary mass of four kilograms. Hang on, maybe I can't do that. You would have tension two equals, yeah, treat this as a mass of four kilograms, and you would have tension two, because tension, just pretend these were glued together. Tension two equals four mass times A, and there's your tension two of eight popping out as well. That would be the really quick way of doing it. The first method was the systematic way of doing it. Is that all right? Any others? Yeah? What lesson? What number? Yo. Okay? Love two. Okay? You guys are here after school. Did you get question two? Oh, you did get question two? Did you understand question two? Why am I emphasizing question two? Why am I emphasizing question two to you guys who came here after school in your free time? I don't know, man. But let's do number one, because number one is a very, very similar concept. In number one, we're pushing down, though. So my free body diagram, I have good old MG. I have a force at a 45 degree angle of 500 Newtons. Yes, Nicole? Yes. Sorry? I don't like having stuff coming in, because it just looks yucky to me as a free body diagram. So I try and have my forces leaving my center of mass whenever possible. I wouldn't take marks off, but can I keep going? Is there friction? Read the question. Is there friction? Read the question. Is there friction? How can you tell? Because the word friction and mu k appears in the question. If you read the question. Normal force. I'm going to argue that because we're pushing down and gravity, I think the normal force is about that big. I think it's cancelling out gravity and the vertical component of that guy. And if I asked you to draw a free body diagram, hint, wink, nudge, nudge. If I asked you to draw a free body diagram for a lawnmower question, I would be expecting you to have your normal force roughly to scale. In a lawnmower question, normal force is never the same size as MG. If you drew a normal force the same size as MG, I would take marks off. Got me? Now, that's the free body diagram. If all I asked for was the free body diagram, that's all I want. But they said solve. What do you want me to find Nicole? Which way is this thing accelerating? I think to the right. Who's winning? Who's losing? There's our starting equation. Oh, I don't know after x. Oh, wait a minute, wait a minute. I think fx is going to end up being 500 cos 45 minus friction is what times what? I don't know the normal force. But you know what? This time when I say look, look, look, look, look, I don't know another force the same size as a normal force. I know two forces that add up to the same size as the normal force. The normal force is going to end up being gravity and that vertical component right there. And this is a complicated enough one that I think I'll actually instead of just substituting, I'll calculate the normal force, do the math, carry a few extra sig figs and put that number there. Oh, I better not forget the mu. Normal force is going to be m 25 g 9.8 plus f y I think ends up being 500 sin 45. I think the normal force is going to end up being 25 times 9.8 plus 500 times the sin of 45. Normal force ends up being 598.553390. I'll go 598.55. That's five sig figs. That should give me some breathing room. In fact, I'll keep this on my calculator. But I'll write 598.55 So this is going to be times 598.55. And Nicole, if it's okay with you, can I divide by m on this line here to get the acceleration by itself too? There's your answer. Now one thing I don't like about this question, Nicole, the fact that it's 45 degrees turns out the sin of 45 and the cosine of 45 are the same, which means you could get this one and this one mixed up and still get the right answer. I'll never give you a 45 degree angle because it's too easy to fluke into the right answer. 45 degrees, the sin and cos will be the same because it's an isosceles triangle which means your opposite and your adjacent are the same length. That's why I also like never too better because it's 40 degrees which makes it more interesting. Is that okay? Is that okay? Okay. Number three, this one's a little overkill. If you get this, you've handled something that I think is harder than I would ask on the test. Certainly harder than I would ask on the written. As a nasty multiple choice. What is the nasty multiple choice on this one? Yes, is it here? There is one kind of tricky multiple choice but I did a huge song and dance about the demos so I'm very very hopeful that you folks will get it. You should clue in often if I do a demo and only one on its own, the odds are I'm thinking about the test. If I do a bunch I'm trying to teach a lesson so the first force lessons we did the push-ups and all that stuff. I mean that was great but otherwise usually I'm dropping a hint. I'm gonna hit pause. That's the same as dividing by 10. I rest my case. I'm right, you're wrong. Okay, any more questions please? Did I say at the beginning that she is fun to? Okay. Rob, I don't care we're both here. Rob, lesson five, number three, the Atwood machine. Nombre trois. Oh yeah. Apparently I did this one already in that class. Let me see if I didn't do it in my block Fs. Otherwise I'll erase everything but I have a feeling I did in both classes. I think I think I think I think let's see. No, okay. All right. Rob, I'm gonna go mass one, mass two, mass three and our standard left to right notation so that we don't have any confusion. What are the forces acting on mass one? Get the obvious ones. What else? How many ropes are there? No, how many ropes are there? I have to go tension one. So this is gonna be M2G tension one. Oh and tension two pulling down. M3G normal force tension two. Who's winning? Well, there's no way it's going to the right. There's nothing that could pull this guy up. Forces don't work. It doesn't work that way. It's gotta be if anyone's winning M1. So it's gonna be M1G, yes? And then I have minus loser. Oh but I have plus winner. Then I have minus loser. Minus loser. Oh but I have plus winner equals and have I walked down the entire rope and run into all three masses. M1 plus M2 plus M3. Is that all right? Mr. Dewick, why didn't you use the normal force? Where do I use the normal force when there's friction? Because friction is what times what? You know what? Since it's frictionless, which is a silly silly, yeah, mu times the normal force you're gonna say. Since it's frictionless, I don't really, you know what? I labeled it but it doesn't show up in my equation anywhere. Hey Rob, I'm relaxed. Oh, I said tension one and I wrote tension twos and tension threes like a meathead rob. Is that why you were confused? Can I do that and that, please? I did say tension one and tension one, didn't I? Bizarre. Anyways, I can still relax. Tension vanishes. Looks like it's gonna be M1G minus M2G and divide that by all three masses. That's my acceleration. Right here. That's the only place it appears. Here's what, let me go to the next equation and I'll show you how it slows things down. So you have M1G minus M2G all divided by M1 plus M2 plus M3. If this gets bigger, this number gets bigger, which means my overall acceleration will get smaller. It will slow things down but it slows things down by being in the denominator. Yep. Is that it? Yep. No problem. Sadly Joel, no matter how hard you do that, you'll never lift off. No. Sadly, the force that you're generating is parallel to the earth. You're not generating any lift force. No, you didn't. No, it's not how helicopter works. Helicopter, the blade has, the blade has to be angled. The blade has to be angled and right now your blade is completely perpendicular to your rotation. Sorry Joel. You can dream but the physics won't let you go further. John, lesson five scholarship question. No, because it's a scholarship question but it's nearly cool. Did you get the answer? 8.17. Now I'll be honest, I would have no problem if on, let's say a final exam for the year, this was one multiple choice and it was like the nasty. So if I had 40 multiple choice and one was like this, then I'd live with it. I wouldn't be comfortable with this. Definitely not on the written. And since I've had very few multiple choice on this particular test, John, not even on this test. If I had 10 multiple choice questions, maybe as one, specifically since I talked about it in class, okay, that's my answer to you. But right now I don't think you'll see it in the future. It is nearly cool though. There was a question I sensed over here. No? Any others? Okay, any more? I told you a bunch of questions that would be on the test. Have you looked at my online answer key? Here's what I'm going to say in all honesty. Well, no, it isn't that. It's if you haven't bothered trying, all you're going to learn is that I can explain things good, which doesn't help you at all. In fact, over the last few years, Nicole, I've tried to be a lousier teacher. I think for a while I was explaining things so well that everyone would leave thinking, oh, I understand it. No, you understand me explaining it. And that's not the same as learning it, which is why I've started to put more and more stuff online and say, have you tried it yourself? It's not that I want to be a jerk. You have me. I love explaining. I really do. I love teaching, but I have to rein it in a little bit and say, no, you need to wrestle with this to learn it. So questions that you've tried, yes. Lesson seven, example three or question three? Example three. Okay. This was on your quiz. Okay. Let me just erase a bunch of stuff here. Here it is, because I do like this question. It's, are you okay on the free body diagram? Okay. Okay. The real issue that we had here was figuring out which way this was going to slide, because whichever way it slides, friction is going to point in the opposite direction. Now, if this was 10 and this was eight, the heavier mass, since it's being pulled down by gravity will always win if it's hanging in midair. The issue here is this is a lighter mass. This is not. It depends. It really depends on your angle. If this was a triangle that looked like this with a five kilogram here and an eight kilogram here, I'd be pretty sure the eight would win because it's nearly vertical. If this was a triangle that looked like this, a ramp that had barely any angle with a five kilogram here and an eight kilogram here, I'd be pretty sure the five kilogram would win and the eight would be getting tugged up. You can see it depends on the steepness. Does that make sense? Okay. So how can I tell ahead of time? Now, I told you guys, if you're not sure, just guess. And if you get a negative acceleration, you guessed wrong, quickly redo the question, which is pretty easy to do because you have your free body diagram. You're only changing a few pluses to minuses and a few things. But for what it's worth, the guys that are in the tug of war with each other, Itzel, are the two gravities, but the two gravities parallel to the ramp. Give your calculator. Can you go M1G? What do you get? That's pulling down with 49 newtons. Can you go M2G parallel, which is opposite? You know what? It's M2G sign. Can you go eight times 9.8 times the sign of 30? That's pulling backwards with 39.2 newtons. Who's stronger? This guy, which means he's going, which means he's going, which means friction is pointing. And then it's going to be winner minus loser. If you weren't sure, I think with one block, I deliberately guessed wrong. I had friction pointing this way. When we got the negative acceleration, all you had to do was erase your friction, point it that way, and then double check your signs, make your winners positive, make your losers negative without even bothering to rewrite the equation, because all you had to do was realize, oh, this was the winner. Put a plus sign in front of him. This was a loser. Put a minus. Oh, the tensions are still going to cancel. You could kind of ignore the tensions, but this was now a loser. Put a minus sign in front of it, and make sure you had friction pointing in the loser direction and then the way you go. Turns out, because friction was in this question always a loser, even if you had, when we had it pointing the wrong way, we still had a negative in front of it. When you had it pointing the right way, because you flipped this direction, you still had a negative in front of it. Does that make sense? Is that right? I tried it new this year. I think last year I actually told the kids to calculate both of these ahead of time and didn't just figure it out, and that's probably what I would do on a test to save time. Which two forces are really pulling at each other? Ignore friction, because I know it's going to go in the opposite direction that I'm moving. What's causing me to move gravity? Because friction is only as big as it needs to be. Any others? I thought someone else asked something from the big review. Did you try it? Did you try it? Would you like me to? I can get you started on it. You know what I'll probably do is give you a hint and then shut up. I mean, I'll shut up. No, I wasn't saying shut up to you, although, oh, 22. What's the equation that has acceleration and net force in it? Okay, I would do this first of all. What's on the y-axis in each graph? Get the a by itself. How? No, you're overthinking it. Get the a by itself. How? So it looks like the equation is actually force divided by mass. Okay, what would that look like? Well, what they're graphing is acceleration. Keep looking up for a while versus force. Take a deep breath and then pay attention. Ready? If it was a squared, what graph would that be? Math 11. Oh, no, no, no, no, no shrugging. If it was a square, a quadratic, what graph was that? Okay, if it was a square, it'd be a parabola. Was it a squared? If it f was on the bottom, it would be a reciprocal graph. Now, we did math 12. Reciprocals had asymptotes and things. That's a reciprocal graph. It's not that. It's a linear graph. All right? What can you tell me about this slope versus this slope? One of them is positive and one of them is negative. Which one is a positive slope? Is there a negative here at all? Can the mass be negative to give you a negative or is mass a scalar? It's got to be that graph. Now, here's what it's really saying. Ready? Look up. As your force gets bigger, you'll accelerate more. Oh, yeah. Of course, if you push something harder, it'll accelerate faster. So definitely not as your force gets bigger, the acceleration gets less. I would cross that guy out. Definitely not as your force gets bigger, your acceleration gets less. In fact, eventually, you'll hit an acceleration of zero with a really big force. No. And I know it's not a quadratic because there's no exponents. It's got to be that. Oh, if there's no force, what's your acceleration? Should this graph go through zero-zero? Yes. Does it go through zero-zero? So there's all sorts of little built-in checks that I can do to think about. By the way, you know the unit we just started on working energy? You know what lesson four is? Interpreting graphs. I haven't given you, I gave you one graph question on the kinematics one because that was actually physics 11, but I'm going to show you how you can interpret or figure out pretty much any graph by being medium clever. Any others? So I've given you hints about the written. What about the multiple choice? Well, when I was blazing through the I like these questions, I like these questions, I like these questions. There was at least two there that were multiple choice that I said I like these for a reason four. Put the phone away. You're not that important. You can be out of contact. You can expect some basic conceptual stuff or maybe some algebraic ones. So instead of me giving you numbers, I may say, hey, what if you double the force? What happens to the acceleration? Or what if you triple the force? What happens to the acceleration? If you're not sure, make up reasonable numbers. We actually did some like that in the homework, probably lesson one, I think. Or no, I think we did some in the, excuse me, in the notes, didn't we, Mr. Dewey? Let me look. Let me look. Let me look. No, I think it was in the homework. Or was this in two? Oh, yeah, like something like number three here. And I said to you for number three, well, if you're not sure, just make up reasonable numbers and crunch the numbers and ask what happened to the numbers. You're using principles of physics right to explain there is going to be one on there. I've tried very hard even today to drop a hint during this tutorial about what one of them might be, but you're clever. Yeah, potentially, but if you write the Blackeddy theorem or in my, for the other class, it was the Weenus theorem, either of those, I won't accept that as an answer, you have to explain what it means. But what both of those were was if you're not sure, think about level, think about vertical, ask yourself how did you get from level to vertical, what would happen in between to get there. That's what I often use for ramps as well, figure out what's going on with a normal force or a force of friction or something like that. This one, though, in particular, you haven't specifically seen before. I've dropped lots of hints about it. You've seen the first part of it before, and you've seen the second part of it before. I just haven't combined them into a single solitary question. Any other questions at all? Really, if you work through the review, you won't find any real surprises. There's one, they're using principles of physics right to explain, I kind of combined a couple from the review and added one to the question. But everything else will be, I've seen that before, seen that before, seen that before. On the other hand, hey, what if something's not moving, what's the acceleration? Zero, so what's your net force? Zero, which makes things easier, actually, because your winner minus loser probably becomes a winner minus loser equals zero, means you probably plus some stuff over. I think there's one question where I did that. I can't give you too many more hints, but give me a specific question. For me, I didn't do one for this unit. I generally find kids do pretty good on this. If you've done the homework and you understand how to do a good pre-body diagram and how to handle lamps on inclines, you're fine. In fact, honestly, most of the mistakes of this unit I find are mistakes. Emily, you're good. Duran, you're good. Normally, I would offer to print the tutorial. I didn't really write much. I went through questions with you, but there were questions from the homework side. I didn't create a separate tutorial page, so I'm not printing this up. I will put this online. Right-click,