 Number eight, okay. Number eight says the first thing I would do for number eight is I would, huh, a nice try, 0.25 kilograms. I'm not plugging in 250 grams, right, is moving to the left at 25 meters per second. The person catches it and stops it in 0.32 seconds. Find the horizontal force, magnitude, and direction exerted by the person's hand. Here's my free-body diagram. What are the forces acting on the ball? Get the obvious ones. Gravity down. Is the ball falling downwards in this person's hand right now? So there's an equal force up. I'm not gonna label those. I'm not gonna label those because I don't want diagram to get too cluttered. What other forces? Well, looking at this, the ball was moving to the left and it's been stopped. You know what? I think I exerted a force to the right. Horizontally, that's the only force acting on this ball. Something is bringing it to a stop. So when I go winner minus loser, there's only one winner. There's no loser. My equation is gonna look like this. And I usually call, if a hand applies a force, I usually call it F applied. That's my notation. You can call it whatever you want to. Yes, you could even call the force Simran if you really want it. You can. Anyways, winner, no loser, and that equals MA. There's my force equation. Now, do I know the mass? Do I know the acceleration? Not yet. Did they give me V initial? Do I know V final without them having to tell me it? Why? What is V final? Zero. Do I know T? I think I can use that VF minus VI over T to find A and when I get that answer, plug it in there. The tricky part was recognizing, well, if it's coming to a stop, something must be stopping it. That's the only horizontal force. Is that okay? Any others? Yeah. Sure can. I'm gonna do five A. I'll hint you towards five B. I'll laugh at you about five C. Okay. Five A, a five kilogram rock is moving upwards on the earth. I guess someone has thrown it into the air. It's on its way up. What are the four, oh, free body diagram. What are the forces acting on this rock? Get the obvious ones. And G. And then it's talking about air resistance. Which way in A is the rock moving? So which way is air resistance? Down. Who's winning? And that's gonna be positive then. Okay. So my equation's gonna look like this. Winner. Now F air, look at its direction. Is it a winner or is it a loser? Ah, equals M A. Do I know M? Check. Do I know G? Check. Do I know F air? Ah, oh, how would I get the A by itself? That's gonna be your equation for part A. Now for part B, which way is the rock moving? So which way is air resistance? It's gonna be winner minus loser for part B. And what about part C? What does it say? Look at the answer for part C. What does it say after the dot, dot, dot? So no air resistance. It would just be MG, but G would be 1.6 of the moon, not 9.8 on the earth. Does that make sense? Nice little question. By the way, it is true. When you drop something on the moon, there's a famous video. I can't find a very, very good copy. I'm trying to, the astronauts on the moon when they were on their moon, moon, moon, fake. No, it was not. They took a hammer and a feather and they dropped them in a vacuum and they do hit the ground at the same time. On earth, the feather would drift because of air resistance. But in real life, if there's no air resistance, objects fall at the same time. Or if the air resistance is the same, objects fall at the same time. Questions, Spencer? You're looking more confused than usual. You're sure? Okay, never mind. I'll take that as your normal look. Questions, any more? 10 C? Absolutely. By the way, for what it's worth, do you know which questions my block F's asked? Number eight, number five and 10 C. In other words, you guys are asking the questions that I'm kind of expecting you to ask. When I'm pausing and when I say any more and I look around, I'm going, they either didn't do the homework or they're too embarrassed to ask. Do not be embarrassed to ask. I know by the way that there are about 10 kids that couldn't get 10 C. You are the one that had the guts to ask. Thank you. Thank you. What does C want me to find? Which one? Oh, so I'm going to do my V final equals question mark. I'm going to defect. Now, now we're back in the last unit, okay? What does this tell me, Simran? Vi is zero. What's this number here? We travel for eight. What did you find in part B? I'm going to start to clue in on a multi-step question. If they ask me to find something, often I'll be using the previous question's answer to find the next one. I would have said, I'll bet you since I found the acceleration, which was 2.22, I'll bet you I'm going to use that. Okay? Did you get the 2 okay? Right? Which one am I going to use? Which equation am I going to use? The squared one. Yep. Okay. And all it took was a little defect. Nice question. Combine some last unit and this unit. Yay. Okay. Simran, what if this mass had been slowing down instead of speeding up? The only addition I would have had to do if it's slowing down, make the acceleration negative because it's slowing down. I just gave you a hint somewhere in the future. This one's not slowing down, but in the future, should you ever see a mass that's slowing down and you've just finished finding the acceleration, you may want to remember that that mass, this acceleration, when you go to kinematics, unit one is negative because there we did put negatives and positives in last unit. This unit, we're letting the tug-of-war decide what's positive and negatives and off the word. Anymore? Those are the ones that my last class asked. Sure can. You know how I'm going to do number 12? You know what the first thing I'm going to do here? Take a guess. What's the first thing I'm going to do here? The ends of the letter F, ends of the letter D, has a B right in the middle of it and no other letters. FBD stands for help them out. There you go, Alex. There's my rocket. What are the forces acting on this rocket? Get the obvious ones. Absolutely. Is the rocket falling down to the earth? Then there must be more forces. What else? I think thrust. Why did I draw, I'll call it FT for thrust. Why did I draw the thrust arrow so much bigger than gravity? Which way does this question suggest that the rocket is accelerating? So who must be the winner upwards? Can you take it from here now? Winner minus loser equals MA. Winner minus loser equals MA. What are they asking me to find in this one? So get this by itself. How? How would I move this over? Yep. And then do I know the mass? Check. Do I know A? Oh, they told me A right here. Do I know the mass? Check. Do I know G? Check. Is that okay? What we're really saying is the rocket has to cancel out gravity and then anything extra goes into thrusting the acceleration upwards. Lesson 3. By the way, if you're done lesson 2, if you'd be so kind as to hand it in back there, that would be wonderful. If you're not done. Lesson 3. Folks, be quiet. Please, but be quiet. Because the idea here is I can give you enough time to get this done and maybe no homework on the long weekend or minimal amount of homework on the long weekend. Friction. Friction. And again, today should be 99% review, I think, but we're gonna fine-tune it and fussy eyes things just a little bit. If fussy eyes is a word. Friction is due to the interlocking of molecular hills and valleys between a surface and an object on the surface. Although a surface like your table, like your desk, might appear smooth. If you zoom in on a molecular level, it has a bunch of hills and valleys. And when you're pulling a surface across another surface, they're rubbing together like sandpaper and gravel. Friction resists sliding. And as such, it can either resist motion, like when you try and pull something across the floor. It can also create motion. We said that when you walk, it's friction that pushes you forwards. That's why it's so tough to walk on ice. Or when you drive, it's friction that pushes your car forwards. That's why it's so tough to drive on ice. Which force stops your car? I'll give you a hint. Is it tough to stop on ice? So which force stops your car? Friction. Okay? Friction is in the opposite direction of the motion between the two surfaces. So if we're sliding to the right in example A here, friction would be to the left. How big would this arrow be? I would have a problem now if you drew the arrow like this way bigger than this force. I'd have a, because friction is not bigger than anything. Friction is only as big as it needs to be. In fact, since it's moving to the right, I think it's fair to assume that friction is smaller. What about for car speeding up? Well, here we have the wheels pushing backwards against the pavement. Which way does friction push them? Forward. In fact, remember Newton's third law? I said forces come in pairs for every action. There is an equal and opposite reaction. Friction is a Newton's third law reactive force. It doesn't exist until you try and do something in the opposite direction. Right now there is no friction between your tables and the floor, but as soon as you start to tug on it, friction rears its ugly head and said, no, no. So car pushing that way would give you friction pushing it forwards or tires pushing forwards would give you friction pushing backwards. The amount of friction depends on two things. The first thing it depends on is the type of surfaces that are in contact. How smooth the surfaces are. And we give this quality, the smoothness, a name. We call it the coefficient of friction. And the symbol is this Greek letter. What sound does a cat make when it's on the ice? Nothing because there's no mu. Lots of dumb physics jokes along those lines. Okay? So the Greek letter mu. The coefficient of friction, people often get it mixed up with force. It's not measured in Newton's. What are the units for the coefficient of friction? There aren't any. It's just a number that describes how sticky something is. Close to zero. Slippery ice has a coefficient of 0.01. Bigger, stickier. Can you have a coefficient of friction more than one? Yeah. Blue. It holds its own weight plus more weight. Blue would have a coefficient of friction more than one. The really, if you watch professional drag racing, the dragster tires, because friction is the force that pushes your car forwards, those tires have a coefficient of friction of about four, as it turns out, not 0.4, about four. Specifically when they do that smoke show, they're heating up the tires. They're actually melting the rubber to make them really, really, really sticky. It's not for the crowd to make the crowd happy. They want the tires to be melted, and that gives them higher coefficient of friction, more friction, faster acceleration. So friction, the first thing it depends on is the smoothness between the two surfaces. And we give that a name. We call it the coefficient of friction. By the way, what's the coefficient of friction of rubber tires on concrete or pavement? Pretty good. What about when it rains? Do you know what this drops to when it rains? About 0.2. So I'm going to get a little serious to you young stupid drivers, which all of you still are. You know what? When it's raining, slow down. It has nothing to do with your skill level, Andrew. You cannot stop as fast, no matter how good a driver you are. It's the physics taking over. Every time I'm on the low heat and someone goes by me on the low heat at 120, if it's a dry day, I just think, well, they're in a rush and kind of dumb, but they're not risking my life. If they're doing 120 on a wet day, I guarantee on a road that's designed for 80 kilometers an hour, they cannot stop safely the way they think they can. They're hoping nobody in front of them has to hit the brakes. That's dumb. That's dumb. So public service announcement over. Slow down when it rains and then there's no back to the real world here. The second thing it depends on Eric is the force pushing the surfaces together. The heavier an object, the harder it is to push or pull it. And so Courtney, a lot of people might say, oh, it depends on gravity. But I'm going to say, actually, it's a little more subtle than that. If I walk over to this table, if I pull it straight horizontally, I just overcame the force of friction. I can reduce how hard I have to pull by lifting up as I pull. It barely has to pull it off. Is the mass of the table change? So did gravity on the table change? Or I can make it really tough to push this table. If I'm dumb enough to push down, I can increase friction so much that I can't overcome it. Is the mass of the table change? No. Mg change. No. So saying that friction depends on mg and you never heard us say this last year. We never said friction was equal to mu mg. It is sometimes, but that's not the rule. Instead, we said friction depends on the normal force. Right now on all of your lab tables, the normal force equals mg. The normal force is having to push up to cancel out gravity. They're equal. But if you lift up on your lab table, you're canceling out some of gravity, but normal force does not have to be as big. That's why when I lifted up since the normal force got smaller, friction got smaller and I was able to pull it easier. Or if you push down on your lab table, not only is the normal force having to cancel out gravity, it's having to cancel out your push. It's going to get bigger. Friction is going to get bigger. Consider the block below, which is being pulled by student number one across a rough surface at constant speed. You know what? I'm going to underline the phrase constant speed. That's really, really important, almost always in physics. So I've learned it whenever I see that one underline it. So let's make this a nice concrete example. Yeah, you're busted. So let's put this into a specific context. The big benches in the gym, the ones at the back of the gym, you're pushing one of those along the floor at a constant speed. So you're sliding it. And then one of your friends says, I'm going to come along and jump onto the bench. Okay, does the mass of the bench increase? No. We have an outside force acting on the bench. What's going to happen? Pardon me? What's going to happen? Normal force gets bigger than what? Friction gets bigger than what? I even I can be more specific than it's harder to push. Look at what I underlined. If I'm at a constant speed, what can you tell me about the force that you're pulling with right now, and the force of friction right now? They're equal. So if you increase friction, it's not going to get harder to push, it's going to do what actually, it's going to stop completely. It's going to stop. Has to, because it says I'm remaining a constant applied force if you read the question very, very carefully. So in situation one, I've got it moving, but I'm just keeping it at a constant speed. That means I'm pulling exactly as big as friction. If you increase friction, how do you increase friction? Well, it says, what happens to the weight? So let's make a little list here. There's the weight. There's the normal force. There's friction. What happens if you jump on the bench? What happens to the actual mass of the bench itself? Nothing. What does change then? Jessica, what force did increase? That's my abbreviation for increases. Do you know what my abbreviation is for decreases? A Z. No, that's not what, yeah, down arrow. Down arrow. Okay, so you can use that in your notes. You can use it with me on a test. Oh, there is no provincial this year. So I guess you can use it. On a provincial, I would always write increases or decreases, right? Oh, so what happens to friction if normal force increases? Friction increases. Therefore, stops since originally my abbreviation for originally is origin friction, equaled the applied friction got bigger, the applied is not big enough. Now, friction actually isn't going to get bigger than the applied. It's only going to get big enough, a tiny bit bigger than the plot. Stop it and then quit. Because if it actually got bigger, you have an unbalanced force going to the left. If it actually got bigger, you would be able to tug on a table, let go, and it would slingshot that if you have an unbalanced force. Friction is only as big as it needs to be and it adjusts as fast as the universe moves. Friction right now is as big as I'm pulling. I'm pulling harder. Friction right now is as big as I'm pulling. I stop. Friction now is what? Zero. You know how I know? There's no reason. That we're moving that way. Right? Yes or same? So as an equation, we said this, friction is equal to mu times the normal force. And this is going to lead us to one of our biggest challenges because almost never will we know the normal force. There is no equine to solve for the normal force in physics well, you'll almost always have to figure it out indirectly. Those of you who had to be for physics 11, you're going to hear me say, I don't know the normal force, but look, look, look, look, I know another force the same size as a normal force. I repeated that phrase all the time last year on purpose. I'm trying to get it to become a trigger for you this year so that when you ask yourself what's the normal force, you'll say, look, look, look, there's something else the same size. Those of you that are having now for physics 12 didn't have you last year, prepare for it. Turn the page. And next time we'll turn the page without all of us having to talk a whole bunch. That would be even cooler. Yes, and look into the back row there. Okay. Example three. Alexis, a student gives an old shopping cart a big push on a rough surface on a flat rough surface. Which of the following is the best force diagram for the cart after the student has released it. So I'm going to assume all of you have pushed a shopping cart at least once in your life. Justin says, I haven't. Well, we need to go shopping with mommy once in a while and offer to push the cart for her or go shopping with daddy once in a while and offer to push the cart for him. Or in a couple of years, you'll be pushing the cart yourself anyhow. Okay. So Justin, suppose you're on the parking lot and you get the cart going nice and fast, and then you let go. Which of the following is the best free body diagram once again, we're going to vote once again, how high you hold your hand is how sure you are of the answer. I'm positive. Maybe do it's going to make fun of me if I don't vote. So I better vote something. Okay. Which of those is the best free diet, free body diagram for when I let go of the cart? Who says eight? 123456789101112. So I saw 10 and then three peer pressure votes that looked around everybody else and then suddenly put their hand up. I don't know. Okay. Who says B? What about a proud confident vote? You saw that? Wasn't like, okay. Who says C? Who says D? Who can add those two together for me? Are there 14 people in this class? Who says a looking for people who didn't vote a last time? Okay. Thank you. Tell me why a is correct, Shannon. A little louder by the way. Okay. Now it's a tough you're having a tough time finding the words. But because I am going to ask you on your test, some kind of right to explain this is part of the practice. I'm going to get I'm going to say, let's go back to first principles. What are the forces acting on the cart at the obvious ones? Gravity is it sinking into the ground? Okay. Uh is it flying into the air? That's why the vertical ones are balanced. So I make a little note to myself. Vertical forces are balanced. What's this force here? Friction. Which way is the cart accelerating? Uh I this is what I asked. Which way is the cart not traveling? Which way is the cart accelerating? Is the cart speeding up or slowing down? When you let go of the cart, will it speed up or slow down? So which way is it accelerating? Forwards or backwards if it's slowing down? So where had I better have an unbalanced force? Forwards or backwards? Which of those diagrams has an unbalanced force backwards? That's how I would expect. I would say this. Okay. So definitely A is correct. How would I answer this? Uh cart slows down. Arrow pointing there. Which means that acceleration is to the left. So far so good in the finisher. Only A has unbalanced force to left. That's how you could answer it with words. Another way you could answer this, make up reasonable numbers and just crunch the numbers. Make the cart ten kilograms maybe. I don't know. Now let's start using the equation. Example five says this. For each of the blocks below, write a vertical force equation. Find the force of friction. Write a horizontal force equation. Find the acceleration. Since there's two blocks, I'm going to go right down the middle of my page. What's the very first thing I'm going to do here? Seagulls found something apparently outside. Meanwhile, back to here. What's the very, it's a force question. What's the very first thing I'm probably going to do here? Uh-huh. There's the box. There's the mass. What are the forces acting on the mass? Get the obvious ones. Tyson, is this box sinking into the ground somehow? Then there better be a force pushing. Is it lifting off into the air? Then there better be equal vertical forces. This would be the normal force. We have an applied force to the right and we have friction. Slowing it down. Cassidy, why did I draw friction so much shorter than the applied? I'm pretty sure the applied's winning. If not, the thing ain't going anywhere. A says write a vertical force equation. Okay. Who's winning? Vertically. That's a trick question. It's a tie. Put your pencils down. You could go like this, Courtney. Maybe that's the winner. Maybe that's the loser. But the acceleration is zero. So the net force is zero and then you would plus this over to this side and you would end up with that. But if you just clue in, everything up equals everything down and go straight to that. Good. That sometimes I won't even write this. I'll just keep this in my head although they asked me to write it here specifically. B says find the force of friction. Friction is what times what? Mu times the normal force. I don't know the normal force. Oh, but look, look, look, look. I know another force the same size as the normal force. What? Gravity. So I'm going to write in my notes friction equals Mu Mg. Now that's not going to be the case. Most of the time starting this year now, we're going to have other vertical forces and it's not going to be Mg. That was last year. And those of you that had me last year, anytime somebody said, Oh, friction is Mu Mg. I barked at them. I said, No, it's not. It isn't. It wasn't physics 11 because we kept the questions fairly simple. Actually, you know what I should have written? Sorry. If you don't erase this, that's fine. But I meant to write Mu Fn and then go Mu Mg to show that it's Mu times the normal force, which equals Mg in this case. If you didn't write that, that's fine. Do I wish into friction? It's in the diagram there somewhere. He's in what is it? Sorry, I can't hear. 0.12. Do I know the mass? Yep. 10. Do I know G? 9.8. 9.8 times 10 is 98 times 0.12. 9.8 plus 19.6 is going to be 10 point. What do you get? Did I miss something? Oh, screen's frozen. Okay, that's interesting. Pause the video for a second. Sorry, let's keep going. What do you get? What's friction? How big is friction? How big is friction? I'm getting 11.76. Now, that's to four sig figs. I'll use that later on, but for my answer I'll write 11.8 Newtons to two or three sig figs. C asks for a horizontal force equation, so now let's look horizontally here. Who's winning in my free body diagram? Who's losing? It's going to be winner minus loser equals my net force ma. Eric, what's de-asking me to, there's my equation. Eric, what's de-asking me to find? How to get the acceleration by itself here. Even easier than that, way too much work. I'd divide by m and be done with it myself. That's what I would do. D is going to be, so the acceleration is going to be f applied minus friction all divided by the mass. Was the applied force 20? I'm going from memory. Was it 20? 20 minus 11.76 all divided by 10. Actually, I can do this in my head. 20 take away 11 is 9, take away 0.7 is 8.3, take away 8.24 divided by 10. 0.824? It's dividing by 10. I can do that in my head. 0.824 meters per second squared. Still accelerating, Kirsten. Not very fast, but we're still winning. This second one, this second one. Well, free body diagram. What are the forces acting on this guy? Get the obvious ones. Gravity down. What else? Now, you might be tempted, this is wrong, don't write this down. You might be tempted to draw the normal force like that, the same size as gravity, except my vertical forces here have to be in balance. And as I'm looking at this, there is another vertical force. See it right there, Kirsten? There's a 15 down. I think the normal force is going to have to be about that big to cancel out gravity and the 15. And then we have the applied force and friction. A says, write a vertical force equation. What does the normal force equal this time? I'll give you a hint. Not mg. What does it equal? mg plus 15. The normal force got bigger. You know what that means? What's going to happen to the friction force? It's also going to get bigger, because friction is mu times the normal force, which in this case is going to be 0.12 times mg plus 15. It's going to be bigger than 11.76. How big? Don't all rush for your calculators at once for me. 0.12 times bracket. 10 times 9.8 plus 15 close bracket. Yeah, 26.76? Anyone else? I don't think that's right, or is it? That's funny, because my last class had a couple of kids get 26.76 as well, so they must have done the same typo error. It's in the 13, does it not? 13.56? I'm guessing brackets or something wonky. Oh, and if they wanted the final answer for friction, 13.6. Newtons. Yep. C wants the horizontal force equation. Who's winning? Who's winning? Who's winning? Friction is never winning. Who's winning? The applied force. Winner minus loser equals ma. Eric, how would I get the a by itself? I think we would. You back with me now? Good recovery. It's going to be 20 minus 13.56 divided by 10. I can do this in my head too. 20 take away 13 to 7, take away 0.5, 6.5, take away 0.4, 6.44 divided by 0.644. Yes, 0.644. 0.644 what, Hesham? meters per second squared. That's the reason why I said it was worth memorizing the unit. That's not what you're thinking. So there's an example where the normal force was not mg. The normal force will not be mg if someone else is lifting or pushing or if you're on an angle, because then you're not level with a parallel to gravity. Turn the page. There can be friction on an object even when it's at rest since the hills and the valleys will lock up when we apply even a small force to an object. The force of friction on an object at rest is called static friction because static means not moving or changing. Example six, if we pull on a desk with a force of two newtons and the desk does not move, which of the following is true? A static friction is greater than two newtons. B static friction is two newtons. C static friction is less than two newtons. D there is no static friction. And once again we're going to vote. So what we're saying is supposing I pull on this desk right here with two newtons it doesn't move. What can you say about the static friction between the desk and the floor? A, B, C, or D. Who says A? Two, three, four. Come on folks. Justin voted this way. You sure don't even want to jump on the bandwagon? Although then again Tyson voted it. I understand. Okay. No, you know what? It's like equilibrium. Right? Friction and non-free. Okay. They cancel each other out. B, lots, C, D. Why is A wrong? Sorry Justin. Carissa, if it was greater than two I'd have an unbalanced force and I'd be able to go tug and then let go and it would slingshot that way. Friction is only as big as it needs to be. If I pull with two and it doesn't move, friction is two newtons. If I pull with 10 newtons and it doesn't move, friction is 10 newtons. If I pull with 12 newtons and it starts to move, what all that tells me is that friction is less than 12 newtons because it couldn't get that big. Okay. So the correct answer. Why? Desk does not move. So the net force has to be zero. That means you can't have an unbalanced force. That's Newton's first law. In reverse, but we said look if we had an unbalanced force it would be moving since it's not moving. I know I got to have balanced forces. So static friction actually varies. It varies from zero when you're not pulling on it at all up to a maximum value and as soon as you pass that maximum value, Rob, it'll start to move. So I'm going to take this and I'm going to slowly tug and I'm slowly increasing my force and I can feel it almost going. It's almost ready to go right now. Maybe not, then pull there. I just passed static friction. A little longer than I planned because I got more extra stuff on top of finding a bigger normal force down, increasing the normal force. There's a second type of friction called kinetic friction. You never notice if you're sliding something really heavy getting it moving is tough but once you've got it moving keeping it going way easier that's the two types of friction. There's static. It's tough to get fingers moving because it's really settled into those microscopic valleys but once you get it moving just like when you're on a gravel road if you're going fairly quick you don't go into down into every single pothill it's actually smoother to go quick. It's smoother to pull it fast and so it doesn't sink as much and it's easier. Having said that, to analyze both of those properties properly is beyond the scope of this course. We're going to pretend there's only one type of friction. We're just going to call it friction. We're going to pretend there's only one type of cohesion friction. We're going to call it mu although technically there's two static and kinetic. So you can do that. What's your homework? First of all I notice a few of you have some NHIs. I'm going to be sending out an update this weekend probably tonight. Some of you that haven't handed anything in may get an email recommending that your parents curtail your social activity. I'll get you grounded until you're caught up. I don't want to treat you like a kid. Get your homework done, okay? One, two, three, four, five, six. Skip seven. Oh, you want me to do seven? Is that the yes that I heard was? I thought that was yes. I want to do seven, Mr. Dewick. You sure? Eight is good. Ten is good. So one through ten, skip seven and nine. Before I turn you lose.