Hello, hi, how are you today? Fine. Okay, good. Right. Today we're going to be going over some more physics content. The other day when we did physics for the first time, we looked at energy. Now the next subtopic we're going to look at today is something called forces. So forces makes up quite a big proportion of all physics stutic. Okay, so we have forces. Now that word, forces. I imagine you'll recognize it, but do you think you could explain to me what a force is or what you understand a force to be? Yeah, it does cause something to move yet, so forces are pushes or puols. So they are pushes or puols that tend to change the motion of an object, okay? So if an object is still a force might make it move. If an object is already moving, it might make it speed up, slow down, it might make it change direction, and it could even make it change shape as well. Okay? So forces can change the shape of an object. Okay? We'll say forces can. First of all, they can, number one, make an object move. So if something is not moving and we push it, we can make it move so it can make an object move. Number two, make an object stop. So it might already moving be moving and we make it stunumber three. Maybe it makes an object. Speed up or slow down. Speed up, slash, slow down. It might make an object change direction. And then finally, maybe it makes an object change shape. Okay, so maybe it can make an object change shape. So there are many different forces out there and it really depends on the specific nature of the force, how strong the force ces, which direction the force is acting in, whether there are any opposing force ces that are gonna to determine exactly how that force affects an object. So Isabel, there are two categories of forces that we look at in physics. There are contact forces and there are non contact forces. Okay? So there are contact and non contact forces. Okay? So we have two types of force, contact versus non contact. So a contact force is a force that is exerted when two objects are in direct contact with each other. So one really good example of a contact force is friction. Now do you think you could tell me what friction is? Do you know what friction is? When does friction happen? I don't know. No. So fortunshe happens when two objects robbed together. So for example, if you rub two hands together for a while, what does it feel like after a minute? If you do that for a minute, what does your hands feel like after you've done it like that? I like something hot. Yes, exactly. So friction releases heat. So when two objects rob together, heat energy is dissipated into surroundings. So friction is a force where two objects rub together, okay? Or two surfaces come into contact with each other. So that's friction. So you might not even realize it now, but all around you there's friction, okay? So friction is what's keeping my laptop on the desk, okay? So the friction between the bottom of the laptop and the surface of the desk, that's what keeps the laptop in place. Friction keeps things still on the floor, stops them from sliding around. So imagine right now, you know, in our in our rooms, in our homes, we tend to have carpets and wood and things like that. What would it feel like if the floors in your house were made of ice? How would your life be different if the floors in your house were made of ice? I did not. Not still. Very. Yeah, very smooth. Yeah and would you be able to walk easily? No youslip around, wouldn't you? Because ice is something that doesn't have much friction because of the smoothness of the surface. There is very, very little friction on ice. So when we lose friction, I mean, on planet earth, we have friction everywhere because surfaces always in contact with each other. So we can't really completely take away friction, but we can use things like ice to model what it would be like if there was much less friction present. So as you know, like you said, if you were trying to walk over ice, it's very slippy. If cars or buses try and drive over ice, it's really slippy and it's really dangerous because of the lack of friction. So friction tends to increase when a surface is more uneven. So something that has a lot of friction is like sand, okay? So if you try and walk in sand, it's really hard, right? Because your feet kind of go into it a little bit. If you try and ride a bike on sand, it's really difficult. Grass, gravel, all surfaces have friction. The more smooth they are, the less friction they have. The more rough they are, the more friction they have. Okay, so that's friction. It's a contact force because contact means that it's touching. Okay? The next contact force I'm gonna to put in here is air resistance. Okay? So this is air resistance. So do you recognize that word at all? Air resistance? Correct. Okay, so with air resistance, it's often a little bit difficult to identify this one because when we're just walking through the air, we can't really feel air. But I'm gonna to ask you to do this, Isabella, if you fan towards your face, can you feel air on your face? I can feel when Yeah, exactly. So that there well done that there is air resistance. So you have air around you. I mean we're kind of moving it towards our faces, but when you move through air, there is still something slowing you down. So if you're riding a bike, for example, when you're riding forwards, the air resistance is pushing back against you. So even though it's not very strong, air resistance does try and slow you down a little bit. Have you ever been outside and it's really, really, really windy and the wind pushes you over a little bit. Yeah, that would be an example of quite a strong air resistance. That's the wind pushing against you. Now, we don't often get that, but air resistance is more significant when we are riding through it. So maybe if you're running or cycling, or if somedy's falling through the air. So for example, if somebody was to jump out of a plane whilst they're doing a parachute, theyfeel a lot of air resistance, because as they fall down, the air is pushing back against them. Okay? So that's air resistance. The word resistance means to try and slow you down. So if you resist something, you're trying to go against it. Okay? So air resistance means air going against you. So if you're moving through air, you have air resistance working against you. Now Interestingly, we have water resistance. So I'm going to ask you something whenever you've been swimming, whether it's in the pool, in a pool or in the sea, is it easy to walk through water? Easy no it's not easy as it's quite difficult. You end up being pushed back. That's water resistance. Now the reason water resistance feels stronger than air resistance is because water is more dense. So a liquid is gonna to push back on you more than a gas does. Okay? So when you're swimming or when you're trying to walk through water, you feel that resistance, you feel the water pushing back on you and that's water resistance. Now we can use water resistance for other liquids as well. It doesn't just have to be water, but we tend to use that term water resistance for liquids overall. Okay? So air resistance is through the air, and water resistance is through liquids. And air resistance feels less than water resistance because water is more dense. So all of these so far are contact forces, meaning that we have to be in contact, like for air resistance to act on me, the air has to be touching me. For water resistance to act on me, water has to be touching me. Friction friction has to be you know you have to be touching another surface. So that's why all of these are contact forces so far. I'm gonna to give you a couple of non contact forces now the next one is gravity. Okay, so tell me what you know if anything about gravity. I think. What does gravity? Do. I don't know. Okay. So gravity is a force that keeps us pulled down. Now all objects have gravity. So you have gravity and I have gravity as well, because we're objects. We have mabut, our gravity is so, so, so, so, so small. It doesn't affect anything around us. So if I bring, let me just get this. If I put a pen, if I put a pen near me, it doesn't stick to me, right? It doesn't suddenly move towards me because my gravity is so small, it won't affect objects around me. But if I drop this pen, what's going to happen to it? All Yeah so it's the earth's gravity that's doing that. Whereas if I put the pen near me, it still dropped down. It's not going to suddenly stick to me because my gravity is not big enough. I do have gravity because I'm an object of MaaS, but my gravity is not big enough. So it is earth's gravity. So the planet that we live on, planet earth, is so big it's a huge object that it has a very, very strong force of gravity. And that's what keeps us held down, right? That's what keeps me anesat down right now. That's what keeps our houses, our vehicles, our buildings. That's what keeps everything down on the ground. Gravity. Now, the reason gravity is a non contact force is because when I hold this pen up, as soon as I drop it, it drops. But it's not really touching anything. It's not touching the center of the earth and yet gravity still acts on it. So the center of the earth is where gravity comes from. And I will, I am gonna na add a picture in for you in a little while once we've talked about all of them. But gravity comes from the center of the earth now literally I mean the middle of the earth. So we can't get there, okay? So we can't get to the earth center because it's too far away. So we humans, we live on the outer layers of the earth, okay? All of the buildings that we have, and we all live on the top of the earth. Now gravity is pulling us in like this. It's not enough to make us go into the middle of the earth, but it's enough to keep us down, which is why no matter where you are in the world, you always stay down on the floor, okay? Because it's interesting, because when I first teach this to students, we know that the earth is round Yeah we know that the earth is a circular well, it's spherical. It's a rock. So if gravity pulls us down, how is it that people at the bottom don't fall off? How is it that people at the southern hemisphere don't fall off? Well, because we're all being pulled into the middle. So it doesn't matter where you go, you are all being pulled into the middle like this. And obviously, when you are in different countries, you don't feel like you're upside down, because we're all just being pulled down to the center of the earth. So gravity originates from the earth's center. It's this invisible force that is always pulling us all down, no matter where we are on planet earth. That's why if you jump up, you will always fall back down. You arenjust float doesn't matter where you are. If you jump up in the air, you'll always fall back down because gravity is pulling you back down. So that's the first one. Okay, gravity. The next one is magnetic force. Now we talked a little bit about this one, didn't we, the other day, because we were talking about magnetic energy, so magnetic force. So we mentioned, I'm just going to take my iPad up its case here for a second and I'm going to show you something. So one sec. So my apple pen is magnetic, so there is a magnet here and the pencil also has a magnet in it. So when I put that there, it sticks, okay? So it stays there because of the magnet, but I can feel the magnetic attraction there, okay? So I can feel the force even when the pen is not touching the iPad. Look, it pulls it in there. See? So I can feel that force there and the pen is not touching the top. So there is an invisible force there working between the magnet in the pen and the magnet on the iPad without them actually touching each other. Okay? So that is why we call it an invisible, that's sorry, a non contact force. So magnetism is a non contact force because we don't have to be touching to feel that force. And you mentioned this when we were talking about magnets the other day, that if a north and a south pole face each other, so if we have the north pole here, so this is the north pole of that one, and then we have the south pole of this one. So we have this irs. There would be a force between them, okay? But we can't see that and they're not touching right now. So this is why we refer to it as a non contact force, a magnetic force. Okay? And then finally, we have electrostatic force. Now, electrostatic force, this was another one that we mentioned the other day. It was an invisible force between positive and negative objects or particles. So this one is going to be positive, okay? So this one's going to be positive and this one is going to be negative. And again, there is an invisible force between these two objects, positive and negative, that isn't doesn't require them to be touching, okay? So that force is there. So here, the north pole and the south pole, they are not touching each other, but there is a force between them here, the positive and the negative particle. They are not touching each other, but there is a force between them. Okay, so that is our forces. There are a couple more that I haven't mentioned for contact, which I'm just going to talk about now. So a contact force. Another one is tension. Tension. Now tension is where we pull an object to its maximum. So tension is found in a rope, for example. So if you tie a rope to something and you hold it up, there is tension in that now actually I'm gonna to I'm gonna to give you an example of this I'm just gonna to use my charger wire here hopefully I don't damage it I'm just going to tie my staper to my charger wire okay so let's see if this works so here is it right now it's going have to do this way so that it don't fall okay so before I let this go there isn't much tension in this okay so you can see right now it's quite looops Yeah no tension whereas if I let go and I'm just hanging the stapler from my wire there is tension in this wire it feels tense it feels like it's being not stretched because it's not elastic but it's it's got a force at the bottom of it that is pulling it tight so this would be no tension because I'm holding onto the staler right now and the wire is loose Yeah and this would be tension because the wire is holding the stapler up and you can see that the wire has now gone straight it's now not got a curve in it because there's tension and whereas I let go we can curve that wire again because there is no tension but that's what tension is. It is a fault that is present when an object is pulled through ropes for example ropes, strings or cables which is the example I gave there. So that is your contact forces, friction, air resistance, water resistance, and attention. We may meet another one a bit further down, but these are our sort of core forces. And then non contact forces are gravity, magnetic force and electrostatic force. Okay, so that is your forces. Your forces. Now let's have a look at how forces act on objects. So how forces act and resultant force, we're going to call this. So how forces act and resultant force. Now, Isabella, do you know what forces is measured in? So you know how we measured distance in meters and time in seconds? Do you know what we measure force in? I don't know, okay, force is measured in newtons. Now the reason for that is because a very famous scientist called Isaac Newton, have you ever heard of him? Isaac Newton? Oh, yes. Yes, Yeah are you thinking about the apple on the tree? No, no. The he has long like a beyeah. So forces measured in newtons named after Isaac Newton who he basically he did a lot of work with forces. He discovered gravity because I will show you what happened. Okay, so this is how Isaac Newton discovered gravity, which is one of our forces. Let me go on to here. So Isaac Newton, I'll show you a picture of. What happened? This is the famous story anyway. Okay? The story is that one day Isaac Newton was sat in front of an apple tree or underneath an apple tree. And the story is that an apple fell off the tree and onto his head. So here was that under the apple tree, the apple fell off the tree and onto his head. So he started thinking, why did the apple fall down? Why didn't it fall upwards or sideways? Why specifically does it fall down? So that's when he started doing some investigations, and he came up with the concept of gravity, this idea that there is an invisible, non contact force coming from the center of the earth, because he figured out that no matter where you were, objects always fell downwards. They never went sideways or upwards. So that's why he started realizing that there must be this force, this this pull that makes objects always go down to the earth ever. It doesn't matter where you are or what object jects it is. So that's the story about Isaac Newton. He did a lot of work with forces so he had the the unit named after him. So we measure force in Newton's. Okay, so force ces always measured in newtonons. Now I'm gonna to show you a skydiver. Okay, so I'll write in about Isaac Newton after so let's talk through the journey of a skydiver. Let's talk through the journey. So the skydiver is going to jump out of a plane, okay? And the the point is they are going to fall down to the ground at first and then, well that's what they're going to do. So we'll talk about this. So the person first of all is going to be falling down, okay? So they're going to go like this. This is them falling downwards. Now there are going to be two main forces acting on this person. Okay, so two main forces, which force do you think is pulling them down? Let me go back up to our forces. Which force will be pulling the skydiver downwards? What's making him fall? Gravity. Well done. Excellent gravity. Now we are going to learn a different word for gravity in a moment. But for now, gravity is fine. So gravity is pulling the skydiver down. Excellent. So what do you think is working against him? What force will be working against him as he falls down? What is this nearly? But he's not falling through water. You're very close. Air, yes, air resistant, excellent. So air resistance is going against him. Okay. So what we usually find, Isabella, is that forces work in pairs like this. So you might have two forces working on you. Usually they are in opposite directions. So what we've got to understand this, how if we have forces working at us, on us in both directions, how is it that we move? Because why don't they balance each other out? Well, it's all about the size, okay? So the gravity of this man is going to be the size of the force is going to be 850 newtons, okay? So that's the downward force. The air resistance I'm going to put as 770 newtons. So which one is more? Which one is stronger? Gravity, gravity, well done. So in this case, the size of the downward force is larger than the upward force. Okay. So the size of the downward force, ours is larger. Than the upward force. Okay? Now we have to figure out by how much. Okay? So you now know that there are two forces acting on this object, but we want to just show the overall force, okay? So Isabella, what we do is we take the biggest force and we minus the smaller force from it. Okay? So to work out, this is what we call resultant force. So the resultant force is the total overall force acting on an object. So this is when you've considered all of the forces. So the resultant force is a total overall force acting. On an object. Okay. And the way that we calculate it is this, the resultant force. Is the bigger force. Minus the smaller force. Okay. So for us, our resultant force, you correctly said that gravity is the bigger force. So we do 850 minus the smaller force, which is 770. What's the answer to that? What's left over? What is our resultant force? 100. So you can you can a callator, you can use a calculator if you want to. You'll always be allowed one, 850-770. 80. So our resulting force is 80 newtons. So that's just one force now. And we because we've considered so now there is just when we talk about the resultant force, we just draw one force and it's acting downwards because remember, we said that the resultant force, well, the stronger force was downwards. So now we correct it and we say 80 newtons downwards. So that's the resultant force acting on this object. So the resultant force is shown as a single number. There's only one. Is shown as a single number. Acting in the direction of the stronger force okay, so acting in the direction of the stronger force. So as you said the stronger force for us was gravity that is acting downwards so our resultant force is gonna to act downwards right? Let's do a few examples of this okay, so I'm gonna to talk you through another example and then I want you to have a go at a few that I do okay, so for each example, the question is going to be what is the resultant force and which direction is it acting? Okay, so let me just talk you through this one more time. So the resultant force is going to be 17, which is the bigger force. So resultant equals 17-15, which is the smaller force. So we have a resultant force of two newtons. And because the bigger force is acting in this direction, my resultant force is also going to act in this direction. Okay? So I get rid of the force acting in the other direction and I just put a two newtons there, okay? So this one shows the value of the resultant force and the direction that it's acting in, okay? So what I'm gonna to do is I'm gonna to make the screen smaller, I'm gonna to leave everything that we've done there and I'm gonna to give you a few examples and give you the pen and I want you to fill in the resultant forces of each one. By the way, I'm just drawing boxes because in physics, that tends to be what we do. So rather than drawing all different shapes, we do just tend to draw boxes to show. That this is an object, it just helps. Okay. So what I want you to do is have a go. I'll give you the pen of filling in all of the resultant forces of those diagrams. Which direction is it acting in? Remember as well. Next one. There's just one more down here. Okay, well done. So of 570, okay, well done. Excellent work. Great work. So I know that you've got the idea of resultant force there. Okay, excellent. So resultant force, the value of resultant force is Abella is that even though in any scenario where an object is moving, there are generally multiple forces acting on it, the resultant force really enables us to figure out what the outcome of those forces is going to be. So if a force is stronger in the downwards direction, it means that the gravitational force has more significance and probably the object is going to accelerate downwards. If a force has more significance in the forward direction than the object moves forward. Okay, so really great work there. So resultant force is that overall force acting upon an object. Okay. Now I did mention just before that gravity is usually replaced with the word weight. Okay. So the term gravity when we talk about forces, so the term gravity. Is usually. Replaced with weight. Okay, so the term gravity is usually replaced with weight so I'm gonna to give you a couple of new terms here, okay? Because you might probably know a couple of these, but we often use them incorrectly just because that's how we use them in society, not because you're doing anything wrong. But it's like when we say the weight of something, what we actually mean is the MaaS, okay? So maybe I say I weigh 60 kilos, okay? So whereas actually that's my MaaS, that's not my weight. That's my MaaS because weight is a force. So force is measured in newtons. So we're going to talk about MaaS. First of all, MaaS is a measurement of amount of substance, okay? So max is a measurement of amount of substance. Weight is a force that is calculated using MaaS. And gravitational field strength, which is going to be my last point, don't worry, using mouse and gravitational field strength. Okay. And then gravitational field strength. This is the strength of gravity on planet earth, okay? So the strength of gravity on planet earth. Now, MaaS is measured in kilograms or grams, okay? So kilograms or grams. So if you ever weigh something out, like if you're cooking or something like that, you're actually measuring the MaaS of something. Weight is measured in newtons, okay? Because weight is a force, and that's where we always get confused. And then gravitational field strength is a number that is given to us in newtons per kilogram. Okay? So on planet earth, where we live and where we are probably going na stay for our whole lives on planet earth, the gravitational field strength. So the gravitational field strength. Is 9.8 newtons per kilogram. Okay? That number never changes. So this number will never change. It is a constant. So as long as we are on the planet earth, this number will never change, okay? So this number will never change. So it will always be 9.8. So here is a formula, okay, to work out the weight of an object. And we have to remember this formula for physics to work out the weight of an object, we have to do the MaaS multiplied by. The gravitational field strap. Okay, so we're always doing it times 9.8. Whatever your object is, we multiply it by 9.8. So gravitational field strength, so weight is measured in newtons. Remember, MaaS is measured in kilograms. And gravitational field strength is always 9.8 newtons per kilogram. So let me talk to you through an example. If a man has a MaaS of 85 kilograms, if a man has a MaaS of 85 kilograms, what is his weight? Okay, so what is his weight? Let's work it out. So his weight, he's going to be the MaaS which is 85, multiplied by his gravitational field strength, which on earth is always 9.8. So I'm going to do let me just use my calculator here. 85 times 9.8, that is going to give me a number, 833 and that is a downward force. So it's in newtons. So this man that I'm talking about, he has a MaaS of 85 kilograms. So his downward force, the force of gravity acting on him is 833 newtons. Okay, so the downward force acting on him is 833 newtons, right? I'm going to give you another example. I'm gonna leave this up here again so we can see the formula and the example we've gone. And the question is going to be. You're going to need a calculator for this one. And I get my car. Okay, there are a few questions for you. Okay. And I'm going to scroll up so that you can see the information there. I'm also going to work it out. Well done. Yeah, that's what I got. Well done. Well done. Perfect. Excellent. Okay, well done. Okay, so now just briefly we're going talk about so like I said, not many of us can not many of us will ever leave planet earth. Okay, so we'll always have the same weight. Isabel, have you ever seen videos of the moon landing when humans went to the moon? Or do you know what do they walk like on the moon? So there was it was a long time ago now, a long, long time ago, but humans went to the moon and they have to wear spacesuits because they, there is no air out there. But do you know what they walk like on the moon or what it might feel like to be walking on the moon, walking in the air? Yeah seems to be like that. Well done. Absolutely. So they're walking in the air. The reason for that is the moon is much smaller than planet earth. Okay, so here's planet earth. Just gonna draw like a few. This is not representative of the actual shape of countries by the way, but there is planet earth. Okay, then we have let me Yeah then we have planet mercury which is smaller than. Okay. And it's like a. Hot pped planet okay so that's mercury. And then we have the moon. Okay? So the moon you probably see at night time is much smaller than the earth. So on the earth, the gravitational field strength is 9.8 newtons per kilogram. On the moon it is 1.6 newtons per kilogram. What would you guess? And I just want a suggestion, Isabella, just to guess there is a number of correct answers here. So if on the earth it's 9.8 and on the moon it's 1.6, what could it be on mercury? Just a guess, no calculation involved. It's just you choosing a number that would make sense. 11.7, 4.7, you know, well done. You're almost perfect. It's actually 3.7. Okay, well done. So you chose a number that was between 9.8 and 1.6. Okay? So well done. So what you can see is the bigger a planet is, or the bigger an object is, the more gravity it has, the stronger its gravity is. So with the earth, on planet earth, we said that the man who had a MaaS of 80 to say 85, Yeah so 85 kilograms on earth is equal to a force of 833 newtons. Now let's work out what 85 kilograms would be in terms of weight on the other structures. So on mercury and then on the moon. So remember to work this out, we're gonna to do weight is equal to the MaaS, which is going to be 85 multiplied by the gravitational field strength which is the number we've given. Okay, so for mercury, what should we do to make to work out this man's weight? How much would he weigh on mercury? And you can use your calculator again of course. Times 3.7 85 times 3.7. 315.5 what? 14 or 14 314 40 or 14 like four zero or 14 14. Like that. Yeah 314.5 yes. Okay. Okay. So then what would his weight be on on the moon? 136. Well done. 136 newtons. So tell me then based on the numbers that we've worked out, my question to you is why does the man. Feel lighter on the moon even though he has the same. So why does the man feel lighter on the moon even though. He has the same MaaS. Because on the. She's more lighter. Why though, what have we said is lower? Because. It has 1.6 neutron. Yeah so what is less? What's acting on him? Less when he's on the moon, there is less something acting on him. Wait, Yeah, well done. So there is less weight, which is the force. Yeah. So there is less force acting on him. Less weight acting on him. Absolutely. So there is less weight or force acting on him. So even though he's not smaller, he's not lost any MaaS. He's still the same MaaS. He feels lighter and like you said, when he's on the moon he can like sort of jump up and it looks like he's flying now. He will still go back down to the surface of the moon because there is still some gravity. Okay, let me ask you one more question. Here is what the sun would look like, okay, in comparison to the earth, okay? So the sun would be like this and the earth would be like this. Okay? So I'm not drawn this scale perfectly, but this would be the earth. This be the sun, okay? So that that's how much bigger the sun is than the earth. Actually way bigger than that, but I don't want to make my earth too small. So there's your sun. What would you say that gravity is like on the sun? If you were able to go there, which obviously we can't, what would gravity be like on the sun? I don't know. Do you think it would be bigger or smaller than on the earth? You think gravity on the sun? Look at the size of the sun. Oh, know, bigger, bigger way bigger. Yeah, absolutely. So remember, on earth it's 9.8 newtons per kilogram. On the sun it is 274 newtons per kilogram. Now you don't have to remember this. Okay, Isabella, the only one you have to remember is earth. I'm just giving you these numbers so that we can compare the context. But on the sun it would be 274. So remember that man who had a weight of 833 newtons on the earth? Okay, so hehave a pretty normal life on the sun. Let me just calculate it. On the sun, his weight would be 274. His weight would be 23290 newtons on the sun. Now, obviously we can't travel to the sun, it's too far away and it's too hot, but that is the how much different it is because the sun is so much bigger. So what I want you to realize is that the bigger an object is, the stronger the gravity is. Okay? So planets that are bigger than earth, like Saturn, like Jupiter, they have more gravity than earth. Planets that are smaller than earth, like mercury or like the moon, which isn't a planet, but it's smaller than earth. They have less gravity than the earth. Okay? So the bigger an object is, the more MaaS an object has, the more gravitational field strength that that object has, and that's why we would experience different weights. However, as I said, you only ever have to remember the one on earth because most of us will only ever be on planet earth. Most of us are never gonna na go to the moon or any other planet. So we would only need to figure out earthgravitational or field strength. Okay? So on the earth, our gravitational field strength is 9.8. So that is the force that is acting on us at all times. All right, okay, a lot to go through there, Isabella. We've gone through a lot. We've talked about resultant forces, contact and non contact forces, what forces can do. We've talked about gravity and we've talked about weight. Okay, so do you have any questions? Is there anything that that hasn't made sense today? No, you've done really well. Well done. All of the calculations you've done correctly and you've picked it up well. So you're doing really well so far. I will send you I've realized that we haven't sent the note from yesterday. I've been a bit ill, I'm afraid. So I'll get back on top of that this afternoon. I will send you the note from yesterday and the note from today. I don't think we have a lesson tomorrow, but I think the next one is on Thursday. Okay, so I'll see you then. Yeah. Okay. Bye bye, Isabella. See you soon. Bye.