 It says this, I'll put the name on here, Mr. Dook. Energy is the ability to do work. That's how it is defined, one mark. What's the minimum amount of work that it would take for a 55 kilogram student to climb a six meter high flight of stairs? And the reason I said minimum is there is friction forces in the direction of the ramp of the stairs. We're gonna ignore those. Minimum, you're having to increase your potential energy. Minimum, you're having to resist gravity in that direction. You're gaining potential energy and that work is coming from your muscles. That energy is coming from your muscles, which is coming from the food that you ate. Minimum, it's gonna be 55 times 9.8 times six. And 55 times 9.8 times six is going to be, yep, times 9.8 times six. You need 3,230 joules of energy. 3.23 times 10 to the third joules. Is that right? Yeah, okay. Now, was this asking for a change in or anything like that? Nope. And I could use this definition of work. Now, by the way, what I really did, I guess technically was this. I really said work equals the change in potential plus the change in kinetic. And then I said, Brianne, they're not talking about a final and initial speeds. I'm gonna assume you start at rest and end at rest. So I'm gonna assume your change in kinetic is zero. What's change in anything, Brianna? And I'm gonna assume initial potential is zero and that's where the MGH comes from. But you can also derive it from force times distance. Which force, gravity? Which distance? Vertical distance, okay? You're on the ground. Your initial height is zero. I'm talking number two here. I'm still talking question two, okay? Okay, question two, we're good? Now, question three is different. Question three says total energy. When I say total, I think that means find everything and add it up. That usually what it's meant, total something up. So for question three, I think total energy is gonna be, I'll call it energy T for energy total. It's gonna be all of the potential plus all of the kinetic. How much potential? Well, that's MGH. How much kinetic? That's a half MV squared. And now it's plug and chug. It has this much energy at that particular time. It has mass two G, 9.8. Brett, what's the height? Five plus half M two V squared. Also five meters per second squared. The total energy is two times 9.8 times five plus 0.5 times two times five squared. I can do this in my head. This is gonna be 25 and 98. 25 and 98 is gonna be 124, I betcha. Wow, what, no, I'm way, oh, I did 25 squared, Mr. Dewey, come on, don't tell me my math was that off. 123, oh, I was off by one. And Cara, the law of conservation of energy says the ball has that much energy anywhere in its flight. At the top, it has 123 joules of potential, no kinetic. At the bottom, it has 123 joules of kinetic, no potential. In the between, it has in between. Using the following graph of force versus position, find the total work done in moving an object from zero to five meters. The total work done, well, work equals force times distance. They haven't really given me a force and a distance. Oh, wait a minute, here is where I'm gonna use Joel, the area underneath a force versus distance graph. It's going to be that area. Now that shape is a trapezoid. Who knows the area of a trapezoid equation? So the reason you don't know it is, Matt, it's kind of redundant. Really, what almost everyone does is they go, oh, okay, I'm gonna call the triangle area one and the rectangle area two. The work in area one is gonna be base times height divided by two, which is gonna be base three times height divided by two, which is gonna be 300 joules. The work in area two is going to be, oh, that's just gonna be length times width because it's a rectangle. Length is two, the width is 200, 400 joules. Total amount of work, seven, B, 700 joules. Yes, by the way, if you were pushing on an object, if this was saying, oh, and you were pushing on an object, you actually know how much kinetic energy the object gained. You know how much kinetic energy the object gained? 700. And if you knew how much kinetic energy it gained and you knew its mass, you could actually find out how fast it was traveling, B squared, so for B. Oh, apparently I thought of that question number five. That makes sense, that's going, the great question to ask. If the graph in question four represents the work done on a four kilogram mass, find the speed if it was initially at rest. So work is also change in kinetic plus change in potential. Nicole, does this question mention a change in height at all? What was my initial kinetic? Well, it says initially at rest, so what's my initial kinetic? And what's change in anything? I think you thought it right and said it wrong, but that's okay. You know what? The work is actually gonna end up being the final kinetic energy. It's gonna end up being a half MV final squared and it was, I believe, 700 joules of work. I think the final velocity is gonna be two times 700 divided by the mass square rooted. Yes? Okay. Two times 700 divided by the mass square rooted. You know what? It's gonna be 18.7 meters per second. I like that question, that combination of four and five. Yo, no, you know why? Force times distance only works when your force is never changing. What's happening to the force for this section? It's changing. You found the average force. You went 200 divided by five? How'd you divide, 700 divided by, okay, okay, now, here's what I'll say. You didn't actually go force times distance. You went average force times distance by finding out the total amount of energy and then working backwards. Yes, I think that is a valid approach. I'm gonna say mines way faster, okay? But the risk is, like a lot of kids will say, oh, the force is 200 times five, oh, 1,000. That's how much energy, no, that you cannot do. So if you corrected for that, then yes. Good question. All right, number six, huh? Well, they want power, so I wrote down, I know that power is work over time. That must mean that there's a time in this question and there is, I think the amount of time we're talking about is 60 seconds. That must mean there's a work, work is what times what. Well, first thing I'm gonna go, I'm gonna think work is force times distance. Now it's an escalator, which means you're doing work against gravity. I think it's gonna be MGH. I think work is gonna be, how much mass? Well, one passenger is 60, but how many passengers are we moving in a minute? I think the total mass is 60 times 20. G, good old 9.8. Why did they give me this particular diagram to confuse me? They're hoping some kids will use the 10 and I'm willing to bet one of these answers is what you get if you use 10 as your distance because, well, it's moving in that direction, yeah, but the force is not in that direction. It's not the direction that you're moving. It's which direction is the force that you're resisting, vertical, so you look at your vertical displacement? In fact, I think it's gonna be 60 times 20 times 9.8 times five. Conveniently, I think I can do this Mitchell without a calculator because those 60s will cancel. And I know that 25 times, 20 times five is 100. This is 100 times 9.8. I'm pretty sure the answer is at 980. What? Ooh, no calculator, Mr. Deuxie. The minimum motor that that escalator can have is a 1,000 watt motor if it's planning on having that kind of an output. If it wants to be able to move 20 passengers a minute, that's one passenger every three seconds. I'm guessing they would actually have a bigger motor than that because escalators I think can move more than 20 passengers in a minute. How many of you have been on SkyTrain before? In Vancouver? Okay, so I think it's the waterfront station. There's one very, very, very long escalator. It's like a two and a half storage. So that one there, much bigger height, that's got to have a pretty hefty, because that would give you a bigger number here, a bigger number here, that's got to have a pretty hefty electric motor. Because it is one continuous one. They don't usually, they'll stop, build a ramp, and then have you walk on to the next one. That's to save money and use a smaller motor. But this one for some reason they couldn't or they didn't. And that's also why you rarely see hugely, hugely long escalators. You need a huge motor to run them. Much easier to break it into two or three. Make sense? I would love to find out how many watts, how many watts the electric motors on the roller coasters, the chain motors. I'd love to find out how many watts those are, because I'm pretty sure those are electric motors, not gas. They've got to be pretty hefty as well. Number seven, how much work is required to stop a 1200 kilogram car moving at 10 kilometers per hour? Well, see here, Jacob, I would think work equals force times distance. And you can probably calculate the acceleration, go MA in force times distance. I think it's going to be easier to say it's that. Plus the change in potential, but let's assume the car isn't changing height, which is going to be ke minus ke initial. I think the amount of work is going to be zero minus a half mv final squared. I got a bit of a problem with this 10. V final is actually going to be 10 divided by 3.6. That's going to be meters per second. And I was going to go to my calculator and I said, hey, wait a minute, why don't I just put that in over here and save myself the type in Kayla. I think it's going to be 0.5 times the mass, 1200 times 10 over 3.6 squared. I get 4,629, actually 4,630 joules of work. Is that okay? Which force is doing the work? Which force is doing the work? Matt, friction, okay? Now this is where Jake's question about force times distance is kind of nice. On an icy day, is friction bigger or smaller? Smaller, so the distance has to get bigger. That's why it takes you longer to stop on an icy day and you have to give yourself more stopping. Ah, makes sense, but there's the physics explanation. I kind of figured that out by draw, I think, yeah, but that's why, okay? Tarzan says, use the following information for eight and nine. Tarzan swings from his vine. I guess he starts right here from a height of 2.5 meters at the end of his swing. He is only 2.5, four meters above the ground. How much work has been done by friction? Is there a change in height? Yeah, is there a change in speed? Probably. Is it a nice straight path or is it a curvy path? This is where I'm gonna use conservation of energy because when they say how much work has been done by friction, what we call that all the time is heat. And I'm gonna go like this. Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final plus heat. Are any of these zero? How fast is he traveling right here? How high is he right here? Zero? Nope. How fast is he traveling right here? How high is he right here? Zero? Okay. Oh, but it looks like I think heat is just gonna be your initial potential energy minus your final potential energy. It's gonna be MGH initial minus MGH final. Do the M's cancel this time? No, there's no M in heat. This is going to be mass 75 times 9.8 times 2.5 minus 75 times 9.8 times 2.4. You get 73.5 joules. Heat equals 73.5 joules, which I believe is answer A. Nine, now if there was no friction, what would Tarzan's velocity be at the bottom of the swing? Is there a change in height? Yeah, and a change in speed. I'm gonna use conservation of energy. Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final. No heat. And again, I think initial kinetic is zero. And I think at the bottom of the swing, the final potential is zero because you're on the ground. I think I can go MGH initial equals 1.5 MV final squared. Now this time as it turns out, the masses do cancel because we're ignoring friction. Yay. In fact, I think V final is gonna be two GH initial square rooted. I think it's gonna be two times 9.8 times 2.5. Oh, square root of 49. Is it exactly seven? Seven. A roller coaster car of mass 1,000 kilograms traveling with an initial velocity of four meters per second is 18 meters above the ground. It drops to the ground and then climbs a 10 meter high hill. A, how fast is it traveling at the bottom of the hill? Okay. Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final. Thankfully, I'm pretty sure that's zero. I don't think initial kinetic is though. It's got a velocity here in my diagram. Don't, needs a bit more work. A half MVI squared plus MGHI equals a half MV final squared. Masses cancel, which is nice. And this is also Conor where I tended to go times by two, times by two, times by two to get rid of that one half and that one half. It gave me a prettier equation. I get this. V final squared equals V initial squared plus two GH initial. And you may see VF squared equals VI squared plus 2AD. That's where the equation actually comes from. V final is gonna be the square root of four squared plus two times 9.8 times 18. Four squared plus two times 9.8 times 18 equals square root. You get 19.2. Yeah, keep on wanting. In terms of marking, I would probably go something like this. One mark if I saw that, one mark if I saw that and then one mark for the answer. How fast is it traveling at the top of the second hill? I'm gonna start out exactly the same. Kinetic energy initial plus potential energy initial equals kinetic energy final plus potential energy final. Sadly, none of these is zero. Okay, so it's a little bit of plug and chug. A half MVI squared plus MGH initial equals a half MV final squared plus MGH final. Once again, the mass cancels. Once again, I'm gonna times by two times by two times by two times by two so that they cancel here and they cancel here. I'm gonna get this. V initial squared plus two GH initial equals V final squared plus two GH final. Say how would I get the VF squared by itself? Subtract this first, yes. I canceled out my M's because I could and I multiplied by two to get rid of fractions. You don't have to, I just do because it makes the numbers cleaner. So if I hear you correctly, we're gonna get this. VF squared equals VI squared plus two GHI minus two GH final. Or, okay, VF is gonna be the square root of four squared plus two times 9.8 times 18 minus two times 9.8 times, what's the second hill, 10 high? Is that what I did? Conveniently, I have half of that already typed on my calculator. See, one less mark? Minus two times 9.8 times 10 square root. Do you get 13.1? Because it is. In terms of work, I'd give you one mark if I saw that, give you one mark if I saw that, one mark for that, one mark for the answer. Yo, you canceled potential and initial, you still got that answer? Good enough. So what did you cancel? Tell me. That. And, so you canceled that, which would have canceled that, which would mean your equation would have been this. I'm just multiplying it by zero to cancel it. See how clever? No way you could have got that, you would have got a calculator error. Okay, Shawn, if you use this at the bottom, then you could cancel out, but okay. You need to tell me that, because doing it the other way, no way. Now, that's a perfectly valid way, the only risk is you're gambling, this better be right. Otherwise you could be using a wrong answer to find the wrong answer. For me, I almost never do that on a test, Rick, quiz, even if it's more work, I'll use the information that they gave me almost whenever possible, unless I'm absolutely positive I've done it right. Yeah, that's valid. Sorry, I was like, don't think you can, I'm getting a negative when I do it in my head. Yeah, negative square root. What was this quiz out of? Out of 16? Give yourself a score out of, does that work, 16? Let's see. Seven marks plus nine. Sure, that works. Give yourself a lovely score out of 16, please. Brandon, put an omit on yours, please. I would normally collect these, but you probably want these to study from, yes? So person on the end of each row, write your name on a piece of paper, put the score there, and pass a piece of paper along.