NL2 MOMENTS OF FORCE
This eighth-grade science lesson is about the moment of force and its applications. It is the sixth lesson in a sequence of eight lessons on force. The lesson is 45 minutes in duration. There are 25 students in the class.
| Time | Caption |
|---|---|
| 00:00:07 | Are we all here? Anyone who is sick? |
| 00:00:08 | (inaudible) |
| 00:00:11 | He will be so bummed out. Did anybody bring the class book? |
| 00:00:14 | Wait a second. |
| 00:00:15 | Oh, oh. You're thinking, "I want a leading role right away"? |
| 00:00:18 | [ laughter ] |
| 00:00:20 | (inaudible) |
| 00:00:22 | Okay, uh, you've noticed the camera man is already here... Uh, that's Ruud, he is, uh, filming today. |
| 00:00:30 | (inaudible) |
| 00:00:31 | He told me that it's really not used for television. It is really- it really will be used for a study. So, I don't know if we'll ever hear about it again. I'm guessing we will. |
| 00:00:42 | Thank you. |
| 00:00:43 | You're welcome. |
| 00:00:46 | Just act normal, just as you normally do. I told you that, uh, the last time too... Except you, you have to be a little nicer than usual. A little less talking. |
| 00:00:57 | Uh, well, once again, just act normal, and we'll see how it goes. |
| 00:01:01 | Ronald, if you want to fight again or whatever, even in front of the camera, then //just let me know. |
| 00:01:04 | //[ laughter ] |
| 00:01:08 | Very well, we will begin. Who did not finish the homework? Eight point- uh, six point two. |
| 00:01:13 | (inaudible) |
| 00:01:14 | Everyone else did? |
| 00:01:17 | Yes? Then we'll just check that first. |
| 00:01:19 | Come on, get your things out. |
| 00:01:24 | You guys are more quiet than usual, so, uh, //just be yourself. |
| 00:01:26 | //[ laughter ] |
| 00:01:29 | What? |
| 00:01:30 | (inaudible). |
| 00:01:31 | Be spontaneous. |
| 00:01:32 | Six point two, right? |
| 00:01:34 | No, six point three (homework). |
| 00:01:38 | Yes? |
| 00:01:39 | (inaudible) |
| 00:01:41 | Julia, come on, open your book. |
| 00:01:44 | (inaudible) |
| 00:01:46 | Question one. What do you measure with a dynamometer? //Yes? |
| 00:01:52 | //Forces? |
| 00:01:53 | Forces, of course. B, what is the unit of force? Do you know that, too? |
| 00:01:59 | That is the Newton or something? |
| 00:02:00 | The Newton. Ladies, shh. The Newton. Uh, what is the symbol for that? |
| 00:02:06 | N. |
| 00:02:07 | Capital or lower case? |
| 00:02:08 | Lower. |
| 00:02:09 | Lower case letter 'n'. Is that, is that correct or not? |
| 00:02:10 | No, capital. |
| 00:02:11 | Capital, right? |
| 00:02:12 | Yes. |
| 00:02:13 | Do you also happen to know the symbol for force? |
| 00:02:17 | (inaudible) |
| 00:02:18 | Kilograms? |
| 00:02:19 | Kilo. |
| 00:02:19 | No. |
| 00:02:20 | No. |
| 00:02:21 | Yes? |
| 00:02:22 | F. |
| 00:02:23 | F, right? Do you know where that comes from, the F? |
| 00:02:25 | (inaudible) |
| 00:02:26 | //Force. |
| 00:02:26 | No? //From the English word force. |
| 00:02:27 | Very good. So if you write, "F=5N," you're really saying, "The force is... five Newtons." Very well. |
| 00:02:42 | In a dynamometer there is a spring. You all saw that last time when I opened up the spring. What occurs in the spring when you stretch it? Martijn? |
| 00:02:50 | Um, um, tension. |
| 00:02:55 | Hmm. Yes, a different word? Bobbie? |
| 00:02:58 | Deforms. |
| 00:02:59 | Yes, it deforms, but what happens when you release the spring again? |
| 00:03:03 | Then it jumps back to its original position, it shrinks again. |
| 00:03:05 | Why? |
| 00:03:06 | Because no force is being put on it any longer, (it's less). |
| 00:03:09 | Hmm. Yes? |
| 00:03:10 | Resilience. |
| 00:03:11 | Yes, resilience. Right, that's it. Resilience. |
| 00:03:15 | So the, the reactive force on muscle power, right, because you are stretching the spring and then you feel a resistance and you call that resilience. |
| 00:03:24 | Question two. In the gym you sometimes make use of the resilience of the equipment. Who can name three of such objects? Edward? |
| 00:03:32 | Uh, trampoline. |
| 00:03:33 | Yes. |
| 00:03:34 | A high bar. |
| 00:03:35 | Yes. |
| 00:03:36 | That resiles a bit, too. |
| 00:03:37 | Yes, that's correct, yes. |
| 00:03:38 | And, uh, let's see, the rings? |
| 00:03:41 | Hm, well, if you, can you imagine what it looks like if you are suspended in the rings and they act like springs? |
| 00:03:48 | [ laughter ] |
| 00:03:49 | //(inaudible) |
| 00:03:50 | //They are a little bit resilient. |
| 00:03:51 | Just a little, but that is not really what is intended. The less the better. |
| 00:03:55 | Jumping board? |
| 00:03:56 | Yes, jumping board, very good. Those are the three things I wanted to hear. Three. "You hang weights on a spring. What force causes the spring to stretch?" |
| 00:04:07 | Gravity? |
| 00:04:08 | Yes. Gravity. |
| 00:04:15 | "On the scale you read 12N." Uh, Andy, what does that mean, 12N? |
| 00:04:19 | Uh, 12 Newtons. |
| 00:04:20 | Twelve Newtons, right? "How big is the resistance of the spring?" |
| 00:04:27 | If you pull with 12 Newtons on one of those springs... |
| 00:04:30 | Mm-hm. |
| 00:04:31 | Then how much is the resistance of the spring? |
| 00:04:37 | Ronald? |
| 00:04:39 | Uh, 24 centimeters? |
| 00:04:40 | No, you are- you have to listen to the question. You are reading a question ahead. You pull the spring with 12 Newtons. At some point there is equilibrium. |
| 00:04:48 | So, how big should the force be on the other side, the resilience? |
| 00:04:51 | Oh, also 12 Newtons. |
| 00:04:52 | Also 12 Newtons, of course... Did we write that down, that if, uh, if there is equilibrium, then the forces are equal? Remember when Ronald attacked me last time? |
| 00:05:03 | E:00] |
| 00:05:04 | //And that twice he remained standing. And the next- the third time, he fell down. |
| 00:05:08 | [ laughter ] |
| 00:05:09 | How come he kept on standing the first two times? Do you recall? |
| 00:05:11 | Um, yes, you stopped me. |
| 00:05:14 | I stopped you. But can you also, uh, say that in terms of, force? |
| 00:05:19 | Um, opposing force. |
| 00:05:21 | Yes, and how big was my opposing force? You kept standing //and so did I. |
| 00:05:25 | //Equal, uh, to mine. |
| 00:05:27 | Exactly, only, the difference was that your force and my force, they were equal, all right, but why did you keep standing? |
| 00:05:34 | Um- |
| 00:05:35 | What else should hold for those forces? |
| 00:05:38 | Against one another? |
| 00:05:40 | Yes, in opposite directions. Then they nullify each other, yes. How large is the weight of these weights? Kind of a strange question. Sonja? |
| 00:05:50 | I didn't know that one. |
| 00:05:51 | You didn't know that one. Neighbor? |
| 00:05:52 | Um, half of a kilo? |
| 00:05:54 | Um, they're asking for weight, that's not the mass. Kilogram is for mass. And what is weight? |
| 00:05:59 | One point two kilograms. |
| 00:06:01 | Yes, you... you know- you answered the question correctly, only you have the wrong unit. It is not kilogram, but? |
| 00:06:08 | Newton. |
| 00:06:09 | A weight is also in Newton, a weight is a force. |
| 00:06:11 | Twelve Newtons. |
| 00:06:12 | Twelve Newtons, indeed. Exactly. Remember that well, okay? If necessary, make an additional note of this. |
| 00:06:19 | Mass... |
| 00:06:23 | You express... in kilograms, and the weight... in- you express in... |
| 00:06:42 | And when do you answer using one unit, and when do you answer using the other unit? |
| 00:06:47 | When they ask you, "How much do you weigh?" They are really asking, what is your mass? |
| 00:06:52 | Then you say, "I have a mass of 55 kilograms." |
| 00:06:56 | And when they ask you, "What is your weight," and next you say, "55 times 10"--remember, that factor? |
| 00:07:02 | "Five hundred fifty Newtons," then nobody will understand you but you are giving the correct answer. |
| 00:07:09 | So... just leave that be. We go on with the questions. Question four. |
| 00:07:16 | "You are using two different springs. You hang ten equal weights on each spring." |
| 00:07:21 | Uh, Gert, spring A stretches zero point three per weight and spring B zero point five. Which spring is the strongest? |
| 00:07:30 | Spring A. |
| 00:07:31 | Yes, why? |
| 00:07:32 | (inaudible) |
| 00:07:34 | Why is that spring strongest? |
| 00:07:36 | Because it... it holds, uh, they are all equal, uh, all equal, uh, weights. |
| 00:07:45 | Yes? |
| 00:07:46 | And, uh, spring A only stretches out to zero point three centimeters. |
| 00:07:50 | Exactly, it stretches less. It has to deform less in order to produce the same opposing force. Very good. |
| 00:07:58 | Well, you actually gave the answer to question B, too, "Explain why." |
| 00:08:02 | Does anyone still need to write this down? Question B? No? Uh, why are you able to use both springs quite well in a dynamometer, uh, Connie? |
| 00:08:12 | Uh, they, they can both be measured then. |
| 00:08:16 | Yes, but why is a spring... when is a spring suitable for a dynamometer? |
| 00:08:22 | Remember that I had this spring- or that weight beam in my hand, and I kept suspending more weights to it. |
| 00:08:28 | What kept happening to the spring? |
| 00:08:29 | It stretched out. |
| 00:08:30 | Yeah, but how? |
| 00:08:36 | Yes? |
| 00:08:37 | It, uh, it stretched out systematically. |
| 00:08:38 | That's it. Each time I added a weight, it would continuously move further down. Every time it got a half centimeter longer, remember that? |
| 00:08:46 | Well, that's a characteristic that a spring has to have if it is to be used in a dynamometer. It has to stretch consistently the same amount. Well, and how they stretch makes no difference. |
| 00:08:53 | Whether that is zero point three centimeter per weight or zero point five centimeter per weight, makes no difference then. As long as the stretch is consistent. |
| 00:09:00 | Make sure you write this in your notebook, because it is very important. |
| 00:09:17 | Are you finished? Yes? |
| 00:09:19 | Then we'll go to question five. That's the last question we will look at, then we go on with the next section. We'll still check that later, for next time, okay? |
| 00:09:28 | It is a little boring to just keep answering questions in front of the camera. |
| 00:09:32 | Uh, you see there is an arrow at Gerard, you see a point P and you see Paul, with an arrow below him. "Gerard and Paul are pulling on a bag in opposite directions. |
| 00:09:44 | In the drawing the forces are represented by arrows. Given is: one centimeter- it says, "is approximately equal to ten Newtons." But what they mean is, "corresponds with." |
| 00:09:53 | So every centimeter of the arrow means a force of ten Newtons. Okay? How great is Gerard's force. How do you find out? |
| 00:10:02 | Yes, well, you have to, uh, measure the line, of the arrow. |
| 00:10:05 | Yes, yes. |
| 00:10:07 | And that's 25 Newtons. |
| 00:10:08 | Um, I think you measured it a little inaccurate. Who has 25 Newtons? Yes? |
| 00:10:15 | So, a distance of two and a half centimeters? Who has, uh, two point six centimeters? |
| 00:10:21 | Yes? Two point seven? That's what I had too. Two point eight? Two point nine? |
| 00:10:27 | Not everybody raised his hand. Who did not raise his hand? What do you have, then? |
| 00:10:31 | Three. |
| 00:10:32 | Three? |
| 00:10:33 | Yes. |
| 00:10:34 | Yes, I measured it from that point. |
| 00:10:35 | Oh, yes, yes, yes, yes, yes. No, you should really measure the length of the arrow. |
| 00:10:40 | Yes. |
| 00:10:42 | So, if you have a force, then we call this, we call it the point of application, right, the tail. Here, like this. |
| 00:10:50 | In the past we always drew these little feathers at the end, right, like a bow and arrow. And the point of the arrow. |
| 00:10:57 | And this length... this determines the length of the arrow and hence also the size of the force represented by the arrow. Yes? You measure that. |
| 00:11:09 | Well, that length was two point seven centimeters. Since you knew that each centimeter--I use this symbol, "is equal to" ten Newtons. |
| 00:11:20 | What does that mean? That two point seven centimeters times the 10 Newtons is 27 Newtons. So the force... |
| 00:11:27 | B:00] |
| 00:11:33 | And this is how you write that. How great is Paul's force? |
| 00:11:38 | (inaudible) |
| 00:11:39 | Andy? |
| 00:11:41 | Forty Newtons. |
| 00:11:42 | Forty Newtons, four centimeters. Good. In which direction will the bag go? You have to use your imagination. Andy, uh, Robert? |
| 00:11:51 | In Paul's direction. |
| 00:11:52 | Why? |
| 00:11:53 | He is pulling harder. |
| 00:11:54 | He is pulling harder, exactly. Paul is pulling harder, so he wins, he wins too, right. He pulls the bag harder. |
| 00:12:02 | With how much force is the bag pulled away? Would that be this 40 Newtons? Just imagine, I'm standing here, you pull this hand and you pull that hand. |
| 00:12:12 | You pull with 27 Newtons, you pull with 40 Newtons. I will move, right? |
| 00:12:17 | That's because she is pulling harder. In which direction will I move? Towards the one that is pulling the hardest. |
| 00:12:22 | But imagine if both of you are gone and a third person comes along and he starts to pull on my arm again. |
| 00:12:26 | And I will move in the same way as I did just now. How hard must that person pull then? |
| 00:12:33 | Three Newtons. |
| 00:12:34 | Watch the values right, 40 Newtons and 27 Newtons. |
| 00:12:37 | Thirteen Newtons. |
| 00:12:38 | Thirteen Newtons. You have to subtract them. If they are equal to each other, they cancel each other out. I remain where I am. |
| 00:12:44 | If one pulls with 40 Newtons this way and 27 Newtons that way, |
| 00:12:48 | Then I will go with a force of 13 Newtons, because 27 Newtons from that side, will, uh, will cancel the 27 Newtons from this side. |
| 00:12:56 | I am left with 13 Newtons. Yes? Yes? Julia? |
| 00:13:03 | No. |
| 00:13:04 | No? Why not? Where does it stop? |
| 00:13:08 | That's, then you have to take 40 Newtons minus 27 Newtons? |
| 00:13:11 | Yes. |
| 00:13:12 | But then, you have to be able to say 27, no, I don't like that. [ laughter ] (inaudible) |
| 00:13:18 | Pay no attention to the camera. |
| 00:13:19 | [ laughter ] |
| 00:13:22 | Laugh as much as you need to. I will explain it once more. |
| 00:13:25 | (inaudible) |
| 00:13:27 | Go ahead, ask your question. It's directed at me again. |
| 00:13:31 | Then you also have to be able to do 27 minus 40, right? |
| 00:13:36 | And what is that? How much is that? |
| 00:13:42 | Minus, uh, three and, uh. |
| 00:13:47 | Twenty-seven minus 40? |
| 00:13:49 | Minus 13. |
| 00:13:50 | Minus 13. Yes, minus 13. And the minus already indicates that it goes in the opposite direction from the 27. Uh, but that is making things too difficult. |
| 00:13:57 | Just do the biggest minus the smallest, and it goes in the direction of the biggest. Yes? So, write that down in your notebook. |
| 00:14:41 | Just put it on your table. Hey, put it on your table, that makes the writing easier. |
| 00:14:50 | Understood? |
| 00:14:56 | I went ahead and drew them up here. The 40 Newtons, you can consider that two forces. One of 27 and one of 13 Newtons. In the same direction. |
| 00:15:04 | Together 40 Newtons. This 27 goes away against that 27. Leaves me with 13 here. Towards that side. |
| 00:15:12 | All right? All right. |
| 00:15:18 | Now, E we actually did that already. So we actually have this force of 13 Newtons left. And make sure you use that scale, one point three centimeters. |
| 00:15:32 | And P is here. |
| 00:15:36 | Questions about these problems? |
| 00:15:38 | (inaudible) |
| 00:15:39 | Anyone, anyone? |
| 00:15:43 | Very well. The rest we'll check next time. Okay? Let's move on to the new section, six point three. |
| 00:16:16 | The book calls this, uh, conserving force. I myself call it rotating. |
| 00:16:28 | Which one of you is clever? |
| 00:16:30 | Well... |
| 00:16:31 | Gert? Are you clever? |
| 00:16:33 | No. |
| 00:16:34 | E:00] |
| 00:16:35 | Try to open that door in what's for you the most efficient way--so it should take the least amount of effort--try to open that door. |
| 00:16:42 | I'll undo the latch a second... Hmm? |
| 00:16:46 | "He is probably fooling me," he is thinking. Give it a try. |
| 00:16:49 | (inaudible) |
| 00:16:50 | You should use as little force as you can. |
| 00:16:52 | (inaudible) |
| 00:16:53 | Push the door open. |
| 00:16:54 | (inaudible) |
| 00:16:58 | Just walk straight into it. |
| 00:17:00 | [ laughter ] |
| 00:17:02 | That's where you do it? Why don't you come back. |
| 00:17:05 | E:00] |
| 00:17:08 | No, just leave it ajar. Now do it over here. |
| 00:17:11 | I can't do it- |
| 00:17:12 | Just open it, just open it. |
| 00:17:15 | (inaudible) |
| 00:17:17 | Go sit down. Why is this harder? |
| 00:17:19 | Closer to the hinge point. |
| 00:17:20 | What? |
| 00:17:21 | Closer to the hinge point. |
| 00:17:22 | Closer to the hinge point. Does it make sense that if you apply force here, the door opens more easily than if I do it there? |
| 00:17:29 | Yes. |
| 00:17:30 | Yes? |
| 00:17:31 | (inaudible) |
| 00:17:32 | Do you understand now why they call this chapter, "Conserving Force"? |
| 00:17:35 | Yes. |
| 00:17:36 | Yes. |
| 00:17:37 | Because where do I conserve force? Here or there? |
| 00:17:40 | There. |
| 00:17:41 | Because- No, wait a minute. If I press on this side it is true that I have to push less... |
| 00:17:48 | More. |
| 00:17:49 | What? |
| 00:17:49 | More. Longer. |
| 00:17:50 | But longer. No, with less force. This went easier, didn't it, Gert? |
| 00:17:54 | Yes. |
| 00:17:55 | Yes, this went easier, easier than here. But here, to open this door one meter I have to exert throughout one meter. |
| 00:18:02 | And here, to open this door one meter, all I need do is this little bit. |
| 00:18:09 | So where, where do I conserve force, then? Do I conserve force or do I conserve energy? |
| 00:18:15 | Energy. (inaudible). |
| 00:18:17 | //Energy. (inaudible) force. |
| 00:18:18 | Force. |
| 00:18:19 | No, energy. |
| 00:18:20 | Both. [ laughter ] |
| 00:18:24 | Over here I have to use force throughout this little bit. A lot of force, because it is a small bit. And here I have to push very long--a meter--with a little force. |
| 00:18:33 | Which is easier? Which feels easier? |
| 00:18:35 | Well, Gert should know better than anyone. Which goes easier? |
| 00:18:38 | (inaudible) |
| 00:18:41 | That's the easiest. Do you save energy that way, too? |
| 00:18:45 | Um... well, no, not really. |
| 00:18:49 | Yes. |
| 00:18:50 | Not really. No. |
| 00:18:51 | Because over there you carry on longer, and for this one you have to use greater force //by (inaudible). |
| 00:18:54 | //Very good. We call that work. |
| 00:18:57 | This is not an issue now, but if you go on in physics, perhaps next year already, you will call this work. Well, a very logical name, right? Work. |
| 00:19:05 | So, uh, how do we write this down? Gert, you said, "It is farther away from the pivot point," right? I think that's very well put. |
| 00:19:13 | Yes. |
| 00:19:15 | If you apply a force... |
| 00:19:22 | Um. |
| 00:19:29 | Just the other way around, sorry. "If you want to apply a force... |
| 00:19:39 | that's as little as possible.... |
| 00:19:47 | it is smart to push... |
| 00:19:53 | as far as possible... |
| 00:20:07 | from the pivot point." We just saw that there. |
| 00:20:20 | The further you are away from the pivot point, the easier. |
| 00:20:28 | Okay. |
| 00:20:34 | We can continue. |
| 00:20:40 | In this way you conserve force. That is nice. |
| 00:20:44 | All right, um, I made a little setup here. It can turn, just like the door which turns, too, right? |
| 00:20:52 | So if you apply a force from the pivot point, it is logical that it will turn. |
| 00:20:56 | Well, this turning we call a moment, but we will get to that later. I have a weight here--I have a lot of weights-- |
| 00:21:03 | and I suspend one... here. There, like that. |
| 00:21:13 | Is it possible to use a same kind of weight, and get an equilibrium so that this thing-? |
| 00:21:17 | Yes, (inaudible). |
| 00:21:18 | Yes? |
| 00:21:19 | If- if you hang it right. |
| 00:21:20 | Then you have to hang it precisely right. |
| 00:21:23 | Then go ahead and hang it. |
| 00:21:40 | Very good. What did you do now? |
| 00:21:43 | Using equilibrium. I have, uh- there area four in between here, and over there, too, so then here (that gives me) an equal position. |
| 00:21:50 | Okay, please sit down, thank you. Is it logical that this has to go on the other side? |
| 00:21:57 | Yes. |
| 00:21:58 | Of course. If I have only this one, it will turn that way. If I hang it there all by itself, it will turn this way. So this one causes it to turn in this direction, Ronald. |
| 00:22:06 | This one causes a turn in the other direction. And they cancel each other out. |
| 00:22:09 | The moment, you say, is equal. Only in opposite directions. |
| 00:22:15 | I'll add another one. With this one. Now I have still another one. Now it is really getting tricky. |
| 00:22:24 | I'll place this one, this one- let's see- |
| 00:22:32 | I'll hang it, uh, here. |
| 00:22:39 | Where should I hang this weight now to get equilibrium? Who thinks he knows how to do that? It is not a matter of trying. |
| 00:22:46 | I'll just tell you what is hanging on this side. I have one, two, three, four, five, at a distance of six of those, uh, of those nails, there are two weights. |
| 00:22:56 | And on that side there is at one, two, three, four, a force of one weight. So where should I hang the fourth... Katja, any idea? |
| 00:23:08 | Um.... |
| 00:23:10 | Give it a try. |
| 00:23:19 | Hold it. |
| 00:23:21 | Here. |
| 00:23:22 | See if it works. |
| 00:23:28 | Well, that doesn't work. |
| 00:23:29 | Doesn't either. |
| 00:23:31 | Yes, like //this. |
| 00:23:32 | //Hoopla, that's it. Could you count them? On the right side. |
| 00:23:38 | Um... (inaudible) |
| 00:23:42 | The distance- the number of nails from the pivot point. |
| 00:23:46 | Of this one? |
| 00:23:47 | Yes. |
| 00:23:49 | Seven. |
| 00:23:50 | And of the first weight? |
| 00:23:52 | Three. |
| 00:23:53 | Three. Seven and three. I don't think you are counting quite right, but go ahead and sit down. Thank you. |
| 00:23:58 | One, two, three, four- you were one short each time. You forgot the first one. |
| 00:24:03 | This is at a distance of four and this one is at a distance of one, two, three, four, five, six, seven, eight. Let's write down what we saw. |
| 00:24:12 | (inaudible) |
| 00:24:21 | On the left side we first had, in the first case, uh, one on a distance of four. |
| 00:24:29 | And it was made to balance, also one on four, on the right side, wasn't it? |
| 00:24:37 | And by "on four" I mean the fourth nail. That should be clear to everyone I. And if it wasn't, then you know it now. |
| 00:24:44 | Second situation. We had two on six. I already hung one on four. |
| 00:24:57 | And where did Katja hang the second one? |
| 00:25:00 | On the eight. |
| 00:25:01 | On the eight. One on eight. |
| 00:25:07 | The really smart ones can already see a certain //connection? |
| 00:25:09 | //Yes. |
| 00:25:11 | Tell me. |
| 00:25:12 | Well, look, if you have, uh, this two to six- |
| 00:25:15 | Yes. |
| 00:25:17 | So you just do "two times six is twelve." |
| 00:25:19 | Let me write that down. "Two times six is twelve." |
| 00:25:23 | And you have four with the other one, plus eight is also twelve. And then it is balanced. |
| 00:25:27 | May I write that as "One times four plus one times eight"? |
| 00:25:31 | No. |
| 00:25:32 | Why not? |
| 00:25:33 | Then you are saying that one times four is equal to, uh- |
| 00:25:35 | No, one times four plus one times eight. |
| 00:25:37 | Oh, yeah, that's okay. |
| 00:25:38 | That is okay, right? |
| 00:25:39 | But you don't need to. |
| 00:25:41 | No, I don't need to but I'll do it anyway. Okay. The second situation... |
| 00:25:49 | Oh, oh, now we're really making it difficult. We've got a third one. |
| 00:25:54 | B:00] |
| 00:25:56 | I'll move them around a bit. |
| 00:26:02 | I am hanging- can you see it? One, two, three, four, five; one on five, one on seven, and one on nine. |
| 00:26:25 | Now I have two weights with which I want to achieve a balance. |
| 00:26:32 | Can I do this only one way, or can I do this in more ways? |
| 00:26:36 | More ways. |
| 00:26:38 | A lot of ways. Think of one. How can I get a balance with two weights, so that the bar becomes nice and horizontal again? |
| 00:26:47 | (inaudible) |
| 00:26:48 | What? |
| 00:26:49 | How many nails (inaudible)? |
| 00:26:52 | Good question. One, two, three, four, five, six, seven, eight, nine, ten. Ten nails. |
| 00:26:59 | So write down for yourself a number of possibilities of which you think, well, if I hang two weights in this way I'll have a balance. |
| 00:27:07 | Do you (inaudible)? |
| 00:27:08 | No, two. |
| 00:27:09 | Not possible. |
| 00:27:10 | Not possible, (inaudible). Can't do that. No. (inaudible). |
| 00:27:17 | Can the camera stop for a moment? |
| 00:27:18 | E:00] |
| 00:27:20 | My mistake. Then we'll place one at, three, five, and seven. [ laughter ] Well noticed. |
| 00:27:28 | Fifteen. |
| 00:27:32 | (inaudible) |
| 00:27:33 | You guys are doing it better than me. |
| 00:27:35 | (inaudible) |
| 00:27:41 | It's making me nervous. |
| 00:27:42 | You are getting nervous. |
| 00:27:43 | Yes. [ laughter ] |
| 00:27:45 | (inaudible) |
| 00:27:58 | Julia, don't. Well, think of three possibilities, come on. |
| 00:28:04 | (three) |
| 00:28:07 | Is that possible, three? |
| 00:28:08 | (inaudible) Yes, sure. |
| 00:28:09 | Good. |
| 00:28:09 | Yeah, sure. |
| 00:28:10 | (inaudible) |
| 00:28:12 | Uh. |
| 00:28:24 | Now you better write neatly, kiddo, because he is taping it. |
| 00:28:26 | (inaudible) |
| 00:28:27 | Oh, oh. |
| 00:28:28 | (inaudible) |
| 00:28:30 | Oh, oh. |
| 00:28:31 | (inaudible) |
| 00:28:40 | Well, who, who, who? Julia. |
| 00:28:42 | Uh, ten plus five, nine plus six, eight plus seven is seven on eight. |
| 00:28:48 | I'll write the, "one on four," I'll just write that as "four," okay? Or not? Um... yes, let me just do that. "Five and ten," you said. |
| 00:29:00 | Nine and six. |
| 00:29:01 | Nine and six and? |
| 00:29:02 | Eight and seven. |
| 00:29:03 | Eight and seven. |
| 00:29:04 | Is seven on eight. |
| 00:29:06 | Can I also find, uh, a position where I suspend both of these weights to create a balance? |
| 00:29:12 | No. |
| 00:29:13 | Why not? |
| 00:29:14 | Fifteen is uneven. |
| 00:29:15 | Yes, very good. Fifteen is uneven. And if I- shh- if I have to calculate that, it will ultimately become a given distance which can never be 15. Yes? |
| 00:29:25 | I don't get it. |
| 00:29:26 | You don't get it? What don't you understand? |
| 00:29:30 | Uh. |
| 00:29:32 | You understand this? |
| 00:29:34 | Yes, that I do. |
| 00:29:35 | Do you understand that if I place two on six, that I place one to four and one to eight? |
| 00:29:41 | Oh, yeah, sure, yes. |
| 00:29:42 | Oh, the light went on. |
| 00:29:45 | Yes. |
| 00:29:46 | It is about making a balance in terms of weights relative to distances. |
| 00:29:50 | :00] |
| 00:29:55 | One on four and one on eight together makes twelve as well. |
| 00:29:57 | Oh. |
| 00:29:59 | Only, now we will use different, uh, uh, numbers of weights. |
| 00:30:04 | Not the same amount of three on that side and three on this side. No, we take three on this side, two on the other side. |
| 00:30:10 | How did you get the five point ten, then? |
| 00:30:14 | (inaudible) |
| 00:30:15 | You are allowed to laugh when something goes wrong. |
| 00:30:16 | E:00] |
| 00:30:20 | (inaudible) |
| 00:30:22 | Three, five and seven. I had two. Well, one answer was five and ten, from Julia. |
| 00:30:29 | One on ten. Let's hope it keeps hanging. And the others, one, two, three, four... five. |
| 00:30:36 | Tah-dah! |
| 00:30:37 | //[ laughter ] |
| 00:30:38 | //As they do in Groningen. Tah-dah! Yes? Yes, thank you. |
| 00:30:44 | Because, one on three, one on five together is eight. Right? And one on seven. Together fifteen. |
| 00:30:53 | This is one on five, together five. And one on ten. Together also fifteen. Now let's try to think of a formula for this. |
| 00:31:02 | This is physics, so we go back to formulas again. |
| 00:31:12 | What we kept doing was the number of weights-- |
| 00:31:15 | And we did that with numbers, but you can imagine now, I hope, that you can also express it the weight itself, right? |
| 00:31:22 | For example, uh--I have to say this right--a mass of 50 grams. For example. What we did every time was multiply the downwards force with the distance. |
| 00:31:33 | Have a look. Two times six. That's the number of weights, two weights times the distance six is 12. One times four plus one times eight. |
| 00:31:44 | Um, how do we write that down? |
| 00:31:49 | The product of these two multiplied with each other we call the moment. So if you take the distance... |
| 00:32:00 | from a mass... |
| 00:32:06 | to the pivot point... |
| 00:32:13 | and multiply it... |
| 00:32:43 | If you multiply the distance from a mass to the pivot point with the mass... |
| 00:32:49 | You calculate the moment. And the symbol for this is capital M. |
| 00:32:58 | That can cause a little confusion with the lower case 'm' of mass. |
| 00:33:04 | (inaudible) |
| 00:33:06 | I've said it wrong. With the force. Excuse me. |
| 00:33:16 | That takes care of that little M-problem. |
| 00:33:22 | An example. |
| 00:33:54 | I have some kind of, uh, seesaw or something. |
| 00:34:01 | And the distance of the force to the pivot point. So this is a force that goes down. |
| 00:34:07 | This is the force downward and this is the distance. |
| 00:34:11 | Let me take this out right now. Here we go. |
| 00:34:17 | Now you can calculate the moment, or the tendency to turn, by multiplying the force with the distance. |
| 00:34:28 | So that's ten times two. |
| 00:34:34 | But then, what is the result? The number is not very difficult. But like with everything, you have to think of a unit for this. Yes? |
| 00:34:46 | Twenty M? |
| 00:34:48 | Twenty M? Um... because it has an M there? |
| 00:34:51 | Yes. |
| 00:34:52 | Yes, but that's the symbol of the unit: moment. And just like you call the mass lower case 'm', right, you express that in kilograms, that's a different unit. |
| 00:35:02 | You can deduce that from the unit of force. What was that again? |
| 00:35:07 | Force. |
| 00:35:09 | Yes, okay, that gave us the letter F. But how did you express force? |
| 00:35:12 | Newtons. |
| 00:35:13 | Newtons. And distance we expressed in? |
| 00:35:15 | Meters. |
| 00:35:16 | Meters. So Newton meter. So that's 20... Just put them down after each other: Nm. |
| 00:35:28 | (Newton meter). |
| 00:35:37 | Who knows what time it is? |
| 00:35:40 | Almost quarter to eleven. |
| 00:35:42 | Quarter to eleven? |
| 00:35:43 | No. |
| 00:35:44 | Forty-one. |
| 00:35:46 | Forty-one, so another nine minutes. Okay, uh... |
| 00:35:55 | Just an example to let you calculate the moment by yourselves and then you can go on with the questions of six point three. |
| 00:36:01 | What did "Nm" mean again? |
| 00:36:03 | Newton meter. |
| 00:36:05 | Newton meter. |
| 00:36:10 | Example. |
| 00:36:21 | B:00] |
| 00:36:42 | There we go, little Peter is sitting on the seesaw. |
| 00:36:49 | Peter has a mass of 50 kilograms, so what is his weight? Let's hear it. |
| 00:36:55 | Five hundred. |
| 00:36:56 | Five hundred Newtons. |
| 00:37:02 | And now I'll ask two questions. The distance here... is two meters. |
| 00:37:11 | Little Annemiek... sits on the seesaw together with Peter. |
| 00:37:20 | But Annemiek is not a featherweight, she weighs 100 kilograms. |
| 00:37:24 | [ laughter ] |
| 00:37:29 | There. |
| 00:37:33 | (inaudible) |
| 00:37:34 | First question: Given is... Annemiek's mass. |
| 00:37:45 | First, what is the weight of Annemiek. So the weight, not the mass. |
| 00:38:05 | And B, who can predict? What question am I about to ask? |
| 00:38:09 | Yes? |
| 00:38:10 | (How far is Annemiek away from the pivot point, or something). |
| 00:38:12 | Brilliant. How far is Annemiek from... the pivot point... to attain a balance. That's important. |
| 00:38:33 | But you already know Annemiek's weight, don't you? |
| 00:38:35 | No. That's the mass. |
| 00:38:37 | Oh. |
| 00:38:38 | Weight is the force with which the earth pulls at the mass. |
| 00:38:42 | And that's in Newtons? |
| 00:38:43 | That's in Newtons, yes. |
| 00:38:50 | Now, on your own. You may consult with your neighbor, as long as you do it quietly. |
| 00:39:03 | You have it already? Very good, very good, very good. Do you also have a formula? If you have it already, over here is someone who got it already. |
| 00:39:10 | Try to also explain it in formulas. So by calculating the moment and completing it. You've got it. But now in formulas. |
| 00:39:26 | You've got it already? Very good, kiddo. |
| 00:39:30 | (A) simple question. |
| 00:39:31 | Simple? |
| 00:39:32 | (inaudible) |
| 00:39:33 | Well... |
| 00:39:34 | (inaudible) |
| 00:39:35 | What? |
| 00:39:36 | (inaudible) Annemiek. |
| 00:39:37 | How heavy is Annemiek? |
| 00:39:39 | How heavy? |
| 00:39:40 | Compared to Peter? |
| 00:39:41 | Two times as heavy. |
| 00:39:42 | Two times heavier. |
| 00:39:43 | A thousand. |
| 00:39:44 | A thousand Newtons, very good. If Peter is sitting at two meters and she is two times as heavy, where should she sit then? |
| 00:39:49 | Four meters? |
| 00:39:50 | Can you imagine it? Imagine, you're on the seesaw, okay? Annemiek comes along and she sits on the seesaw. |
| 00:39:54 | Yes. |
| 00:39:55 | Easy. |
| 00:39:56 | She is two times as heavy as you. |
| 00:39:57 | Oh, yes. |
| 00:39:58 | One meter. |
| 00:39:59 | One meter. |
| 00:40:00 | Very well, Bob. |
| 00:40:01 | One. |
| 00:40:02 | Yes, you had that. |
| 00:40:03 | It's one, yes. |
| 00:40:04 | It's logical. |
| 00:40:06 | (We're done). |
| 00:40:07 | Who has got no idea? |
| 00:40:09 | (inaudible) |
| 00:40:11 | If you have no idea try to imagine it. |
| 00:40:13 | (inaudible) |
| 00:40:15 | You're on the seesaw. |
| 00:40:16 | Oh. |
| 00:40:17 | You weigh 50 kilograms. |
| 00:40:18 | Yes. |
| 00:40:19 | Yes? A weight of 500 Newtons. Here is the pivot point, two meters away from you. |
| 00:40:22 | One kilo is one- that is ten Newtons? |
| 00:40:24 | One kilogram is ten Newtons, very good. Annemiek goes to sit on the other side. |
| 00:40:27 | Yes. |
| 00:40:28 | Annemiek is 100 kilos... |
| 00:40:30 | A thousand Newton. |
| 00:40:31 | Are we just walking through the class like this? |
| 00:40:33 | (inaudible) |
| 00:40:34 | What? |
| 00:40:34 | (inaudible) a leaking pen. |
| 00:40:35 | Are you trying to get a leading role again? |
| 00:40:36 | No, a leaking pen. |
| 00:40:37 | [ laughter ] |
| 00:40:39 | He would love to have a //leading role. |
| 00:40:40 | So where would Annemiek sit? If Annemiek is 100 kilograms and you are 50 kilograms? |
| 00:40:44 | Five hundred Newtons. |
| 00:40:46 | She sits in the middle. |
| 00:40:47 | Wait a second, you are saying, "500 Newtons," and you are saying... |
| 00:40:50 | She sits in the middle. |
| 00:40:51 | "She sits in the middle." What do you mean by 500 Newtons? |
| 00:40:54 | They cancel each other out, don't they? |
| 00:40:57 | They do- they should cancel each other out. Only one is heavier than the other. How do you cancel that out? Don't pay any attention to him. How can you cancel that out? |
| 00:41:07 | If both of you sit down on a seesaw. |
| 00:41:08 | Yes. |
| 00:41:09 | Yes? I don't know how heavy-, how heavy are you? |
| 00:41:11 | Me? Sixty-five. |
| 00:41:12 | You are 65 kilograms. //And you? |
| 00:41:13 | //Me too. |
| 00:41:14 | You too. Well, that doesn't help me. I am, uh, 150 kilograms. |
| 00:41:17 | Oh. |
| 00:41:18 | You go on that side, I go on this side. You sit at two meters. Where should I sit so that we can still have fun seesawing? |
| 00:41:28 | You are sitting at two meters? Where should I sit? |
| 00:41:33 | Suppose I sit down at the same distance from the pivot point as you. |
| 00:41:35 | Yes. |
| 00:41:36 | What will happen then? |
| 00:41:37 | I'll go up. |
| 00:41:38 | Then you go up. So what should I do to get a better balance? |
| 00:41:43 | Go backwards- no, go forward. |
| 00:41:44 | To the front, how far? I am two times heavier than you. |
| 00:41:48 | One meter? |
| 00:41:49 | Yes, I have to cut the distance in half. |
| 00:41:53 | Okay, most of you got it already? |
| 00:41:55 | Yes. |
| 00:41:57 | Now let us tackle this very scientifically. First question A, the weight. Well, if you have to, uh, calculate the weight- |
| 00:42:06 | Guys, quiet a bit. Shh, in the back. |
| 00:42:10 | If you have to calculate the weight, you calculate the force with which the earth pulls at a person. Yes? You know the mass. Hundred kilograms, we'll write that down. |
| 00:42:21 | Then the weight is mass times ten. |
| 00:42:27 | That is 1,000 Newtons. This weight is a force, so we say... |
| 00:42:35 | Oops! F is 1,000 Newtons. Now first calculate the moment for Peter. We'll call that Peter's moment. |
| 00:42:50 | (inaudible) |
| 00:42:51 | Wait a minute... How do I calculate Peter's moment? Think about the formula on the left there. There, M is F times D. |
| 00:43:00 | Five hundred times two. |
| 00:43:01 | Five hundred times two. |
| 00:43:10 | Is 1,000 Newton meter. To get a balance, Annemiek has to have the same moment. But because she is twice as heavy, the distances has to be halved. |
| 00:43:19 | B:00] |
| 00:43:21 | So Annemiek's moment... is also... 1,000 Newton meters, to maintain the balance. |
| 00:43:39 | Therefore 1,000 is, uh- the mass was 1,000 kilograms--so we have to determine the weight of that too--is 1,000 times the distance D. Well, then this D has to be one. |
| 00:43:58 | So--I'll just continue writing here--so, one meter. |
| 00:44:04 | B:00] |
| 00:44:06 | Well, I have been talking longer than I wanted to. But- what time is it? |
| 00:44:11 | It's time. |
| 00:44:12 | It's time. Quickly get your day planner. Homework: six point three, one through four. |
| 00:44:18 | (inaudible) |
| 00:44:20 | Homework for Friday... |
| 00:44:24 | (inaudible) |
| 00:44:49 | Of what? |
| 00:44:51 | Did everyone write down the homework? |
| 00:44:52 | (inaudible). |
| 00:44:53 | Of what then? |
| 00:44:54 | Then you may leave. |
| 00:44:57 | (inaudible). |