Errors and Uncertainties in Measurements PDF

Errors and uncertainties Which line is closer to? Well, not always. So what we say is that there is an uncertainty in the measurement. The edge of this block falls between 49 and 50 millimeters. I think it's closer to 50 millimeters. So I'm going to say that the width of this block is 50 millimete...

Errors and uncertainties Which line is closer to? Well, not always. So what we say is that there is an uncertainty in the measurement. The edge of this block falls between 49 and 50 millimeters. I think it's closer to 50 millimeters. So I'm going to say that the width of this block is 50 millimeters. But I have to say that there is an uncertainty of 1 millimeter in my reading. It is also acceptable to say that the uncertainty is half a millimeter. But to be on the safe side, I'm going to say that the uncertainty is 1 millimeter. We write the uncertainty after our measurement. So I can say the width of my block is 50 plus or minus 1 millimeter. We always write an uncertainty like this, even if we think that the number is more likely to be bigger than smaller or vice versa. Uncertainties can also be due to random error. This can be sometimes due to the equipment that you use, but more often than not, it's down to human error. For example, let's say that I want to time how long it takes for this pendulum to complete three oscillations. If I time it with a stop clock, I'm never going to get a perfect reading, but rather I'm going to get a reading that has an error. Error means how far away your measurement or reading is from the true or actual value. It sounds bad, but that's okay. There's always going to be an error. But there are some things that we can do to reduce the effect of this random error. Instead of doing this once, I can do it a number of times. I can do it let's say five times. My five readings are not going to be the same due to random error. But that's okay. Even though there'll always be a random error, a good scientist will always try to reduce random error. One thing that we could do with this is have a slow MO camera, for example, or a light gate sticking with my five times. Though what I can do is calculate a mean average of them in order to reduce the effect of random error. However, there is one time that stands out. Like a sore thumb. We call this an anomaly or an anomalous result. You can see that it obviously doesn't fit. Something went wrong during my timing. I don't know what it was, but I know that that isn't right. It would be silly to include that in my calculation to find the average. So we're going to leave it out or omit it. So to get an average of my other four readings, I add them all up and then divide by the number of readings, that's four. It's worth remembering though, that your mean or average reading needs to be to the same number of significant figures as your individual ones. As per usual, though, we can't just leave it there. We need to be honest about our result and say that there's an uncertainty in our mean to find the uncertainty. In the meantime, all we do is take the range that's the biggest number, take away the smallest number and divide by two. If you're drawing a graph of your results and you find that all of your points are all over the place and they don't sit on the line of best fit very well, that means that you had a lot of random error in your experiment. If they're all sitting quite close or on the line of best fit, then that means that your random error is quite small. While I have the pendulum here, though, it's worth mentioning parallax error when you want to line up something with something else. Let's say that I want to see when the pendulum crosses the midpoint here. That's where the clamp stand is, the retour stand. Then I need to be at the right perspective. If I turn the retort stand sideways, then obviously you're not going to see exactly when it crosses that midpoint. And this also goes for when you are measuring distances with a ruler. If I'm measuring this block with a ruler, I want to make sure that the ruler is as close to the block as possible. If I'm measuring something with the ruler quite far away from the object, then obviously I'm going to get parallax error because I can move my head and it's going to look like the edge of the block lines up with the wrong number. There is another type of error too, though. Let's say you're measuring the block again, but you forget that it's the zero on the ruler that needs to be lined up with the left edge here of the block and you accidentally line up the edge of the ruler with it. That means that every single one of your readings from this point onwards is going to be a few millimeters too small. All your readings are going to have the same error. We call this a systematic error. An example of this could be when your thermometer has a bubble in the liquid inside. That means that the top of the liquid isn't going to be at the right place, therefore you have a systematic error. Or maybe when you're using a measuring cylinder, you forget that you're supposed to be measuring to the bottom. Of the menticus and you measure to the top instead. Another classic is when you're measuring the extension of a spring and you measure the whole length of the spring, when in fact all you want is how much further it has extended. So you need to subtract the original length of the spring, or just line the ruler up with the zero mark at the bottom of the spring ready for when it extends. Systematic errors can often be due to zero error. Just like with our ruler, we didn't line up the zero with the first edge of the block. That means that there is a zero error there. But it can happen for other pieces of equipment as well. Here I have a micrometer. When the jaws of this micrometer are touching, it should read 0 millimeters. But actually what we can see is that it's not on zero when they close. It's actually 100th of a millimeter out. That might not seem like a big deal, but when you're measuring the width of very thin wires, it can make a very big difference. Another example is when you're using a top pan balance and you're measuring something like powder and you want to use a weighing boat to do that. If I turn my balance on and then I put my weighing boat on, well, that has a mass of its own. If I start putting powder in my weighing boat now, then obviously the reading that's on the balance isn't going to be the mass of my powder, but rather the weighing boats and the powder together. What we have to do is make sure that we zero or tare the balance before we put the powder in. So with my weighing boat on, I'm going to tare it and it's now zero whatever I put into the weighing boat now, the reading on the ballast is going to be the mass of just that. When you draw a graph of your results and your line of best fit doesn't look like it goes through 0, 0, also called the origin. Don't try and force it through there. That's bad science. You always want to follow trend of your points. However, if you believe that your results should go through the origin, but they don't, and your line of best fit is shifted up or down, then that probably means that you had a systematic error in your experiment. You might be thinking, what's the point of all this? Why do we care so much about uncertainties and errors? Well, in the real world, they're actually very, very important. If you make a plane, the parts that you make have to be measured to such an accurate size that if there's an error of, say, 0.1%, then your plane won't fly. The electronics in your phone are so finely tuned that if the current from your battery fluctuated even just a little bit, then you've just got a very expensive paperweight on your hands. Life can be pretty uncertain, and so that means that science can be too. But if you're aware of that, then you can carry out experiments that give you results that you can trust just a little bit more. So the point of that is, can we all get your sheet and turn them to the very much to the last. But I don't know, like, it's just. I'm not sure. Made With Glean | Open Event scinece NEwtons second law What we need to do today is we need to go through Newton's second law and we need to go through Newton's third law so that it's going to make more sense for the rockets that we're doing. So the first thing is, Newton's second law is actually a surprisingly easy one, and it relates exactly to what we had with Newton's first law. They're basically the same thing. So, Nash, what was Newton's first thought? That something will keep moving, something that is moving at a constant speed or is that rest doesn't need the rest or a firepower? First walk, please. No, It was really close to the middle walk. Stop walking. Go, Jerry. OK. I think you shut up. Shut up. Don't talk to me like that. I'll be in the middle of the walk. Look, we get it. You were asked yesterday, right? Such an athlete. You're just a strange answer, Josh. You're being very rude because......JV was actually trying to answer the question. Are you serious? Sorry, mate. Sorry. So... No, I think I like when something's moving like it doesn't stop without force playing fireball gravity or air friction elevation. It's when someone has the power to move it's like this. Oh no, it's not going to go down. Everyone's here on the right track. I'm going to walk through here. Alright. Hop up, stand on the left. That's why I said it was really good. So James, what were you going to say? I said it is a force 1-0, an object to stay in motion until acted on by another force. So we've all gone to the roughly the same thing. So what will happen is the definition is this. So an object will continue doing what it's doing unless you apply a force to it. So that means, yeah, and I'm really iterating it. So that means you're moving at a constant speed or it will stay stationary. But you have to be careful because it doesn't mean changing directions as well. Because velocity is direction. Now, if you change direction, you change velocity, so therefore they have to apply force to do that. So change your angle of motion is an appellation of force. It means an acceleration, yes. So that is why we're coming to this part here. The second law here is the same thing, but we're just varying it another way. We're basically saying, what happens is, force, If you have a question, you're going to have to put up your hands. And, lucky, I'll answer it in two seconds. So if there's an overall force, there's an acceleration. That's all this is trying to say. But it turns out if we know the mass and the acceleration of an object we know the force That's what this is trying to say. So force is equal to the mass to my how much the object is changing its speed acceleration Jays Go into it's a square. Yeah, sorry How I play Yes acceleration. James, we won't go into equal terms this way. Sorry, that would be good. How a plane, when it turns, it doesn't add an acceleration, it slides down. When a plane turns, It does actually have an acceleration because it's pulling itself into a circle, right? So if you think, if I was trying to pull something into a circle right now, if you ran past me, can you see I physically grab you and then pull you towards me? So the thing for playing is they do that, but it's using its wings to push itself into the center of the circle There's no change in speed that is a change in direction so there's still an acceleration So there was a good question. Alright. What's the difference between force and net force? So net force is if we add up all the forces on an object, what it adds up to? So the overall force is the net force. Can I be like, fighting the lights up? Yeah, when I say add up, I'm trying to say in like a physics way. So when someone says something the forces of they do mean plus minus because one will be positive. What would be negative in the opposite direction? So basically the overall force of the motion. Overall force is net force. So I know. There's some of those for the results. The overall force of the motion. All right, can I get everyone here to write f equals m a is Newton's second law? We're then going to introduce Newton's third law, which is the trickier one. I want to know that in which it's when... So? I got motion. So net force is a given in the stop deceleration. That's it. Lesson in the net force, even in the mass-concentration. So the net force is in the mass-concentration. Yeah, that's all we need. Thank you, Osh. It was so good for you. Yep. Alright. What? Hydrogen plus hydrogen. So, we are now up to Newton's third law. This one here. What's the title? Newton's law. Mr. Powell. I thought it was the second law. I thought it was a second heart. I thought it was a second heart. I thought it was a second heart. It's true. Who does that mean? It's a mass-planted car. How does hydrogen and true oxygen make you hydrogen? Because that's what it... Oh my god. Two! Two gases. Excuse the question, because it doesn't work. Two gases. We're not going to go into it now and if you want to know I'll tell you but most of them Yeah And that goes on to the question on the topic So we've got this thing called new perspective. Now this is the trickier one, and we have to be very careful about this. I'm gonna get you to write this down quietly, and then I'm gonna have to demonstrate it, and go through some things on this one. This one is tricky. The first law is what the other people were saying. I asked the class what the first law was, and they were keeping it back. There is no formula for the first law. I'll get you to write your class and then I'll get through. That's what he just said. So next we'll take a look at Matt's somethings up at Yorkshire. Hi, Oggie. Sorry I'm late, I was at school. Yeah. Stop, Jad. Okay. Young man. What, so do I need to write that entire paragraph? Yeah, the paragraph actually has... You're gonna have to... The only thing you need to realise is that the obstacle is made to have an offset. Yeah. Yeah. What is that? I'm gonna show you. When were they... Who's Newton? 1700. Newton's second law is your final... So it's half daddy. It's just a calculation. I have a calculator. I'll give you a number. It's half daddy. It's not a calculator. Alright, suit! Can I wait a minute to hear what's up? What does it mean? A body? A. I'll demonstrate it and then I'll put it up and go by. Go on. I'll finish it. Right up there. Wait, I can't put it on there. What about? Are you sure? I'm going to check the tower. I'm sorry. Alright, suit! No, no, no, no, no. What did the charity say? I'm going to have to demonstrate this one. This one is tricky. It's going to be one of those ones where first people are going to get it, yeah, yeah, they get it, but there'll be situations where it will cause some issues unless we really are careful about how we phrase it. Here's the first thing. Newfoundlaw explains all my **** It's also one where it's always true. This is not a situation like bio or anything like this. This is always true no matter what and any motion is actually caused by this. The second major part is can we see that there's actually always two objects in Newton's... Didn't Newton have one? Should I ask you again, you're gonna be finishing it off with much time with this. So there's always two objects. The original is A and B, you have to make it simpler. So if I need to get this object into move, because we now know that if we want to accelerate something we have to put a force into it. Can you see I have to affect the way we put a force into it by kicking out? Remember that? So if I kick this, it moves. Now what this is saying is that when I put a force with my leg into this chair, yeah, that chair is gonna have an acceleration and stuff like that, we all have that, but at the same time, the force of this chair is gonna push back against my leg. So my leg would slow down. So if you think about this in terms of like playing sport, you can show someone where you run and hit them. Can you see that you are gonna put a force into them? They are gonna put a force back into you. So both objects, there's two objects here, there's always two objects. One is going to speed up. The other one is also going to speed up in the opposite direction. Oh. Are we happy with that? Is that kind of like, look? Oh, I know my hand up actually. Yeah, okay, let's go. Is that like the bowls where like you bang them and they like push each other up? Yes, and notice he knows once because the masses were the same, they always go the same height roughly. Yeah. Yeah, But if you have situations where the masses are different, so if I ran in hip and shoulder and saw someone that was like a sumo wrestler, the forces are equal. The forces are always equal. But in that situation, you'll notice that I would change speed, accelerate more, like slow down more or bounce back more than the object that had a huge mass. Why? Why? How do they explain to you like mass? Because remember there's Newton's second law which is saying that force is equal to mass times the acceleration and the acceleration is the one you're looking at. You have the same acceleration because of the third law but you... You have the same force but you have different accelerations because you have different masses Yeah, so because of this you both like you're both No, let's be really careful This would always be the both objects would have the same force, no matter what, but they would have different accelerations and different masses. Yeah. Yeah. Are we happy with that? Yeah. Alright, now what most people neglect when they do this is that it has two objects. If I had a baseball and I am hitting a baseball or a cricket ball, what's happening is even when I'm hitting the cricket ball, the forces are equal, but the cricket bat is slowing down. So can we see there's an acceleration there? Yes. Yeah. And in that one there, the critical ball is going to accelerate more. We're gonna give a thumbs up if you get that concept. Right. That is how you get it. Actually, you only just got the... Yeah. He starts out, he's so... Gentle, especially. I said, actually, I wasn't even here. Alright. Oh my god, oh my god. Exactly. That leads to this situation. I have got a table. Everybody's going to throw this table into their book. And then you need to see if you can answer what the two objects are here. Notice how it has to always be two objects and what the forces are. So the first one is you're swimming and if you're doing freestyle or something, you will clearly see where you put your hand in and you push back. You are pushing the water that way and therefore you are getting a force the other way and the forces are equal but the acceleration is different because my mass is a lot different to the water's mass. It pushes you up but your pushing out is a little bit much. Yeah. But what about the front end to the wall? The wall is the moment. All right. The wall does actually do it. What's the issue there? The mass of the wall is technically the mass of the wall plus Earth. So if I run a wall, like if I just run flat out to a wall, what would happen is we could measure that, but you'd be trying to measure the whole earth moving in because while you're pushing all of earth in that space. Do you want to write this down? Yes. And what do you know about the mass of earth? The mass of earth is insanely large compared to the mass of the person. To the acceleration of the wall. What if I was standing on the ground and someone was running to me and I lost my senses and I was back here? Yeah, it's always a situation you probably just get knocked over. So you could take the area out of it, decidify it. If you go through the walls, what happens then? Well actually through the wall, The actual forces are still the same, but because the impact was over a longer time, the force will actually be less on both objects. The forces are still the same. So if you did them to a bouncing castle, right, Can you see it's just over a long time, so the force is actually less. But when you go through the wall you don't have to factor in the earth. Yeah, it will be just how you calculate it. So you have to remember what kind of simplifier there's not just a possible. In that we can technically work it out, you would just have to model everything. Right, you'd have to simulate it. But it would still be used in the same way. Still enjoy this one? Yes, and you need to answer these. I can tell you now these last two are actually really tricky. You might be able to get the Rockets one because we discussed it yesterday, but this one here is probably one of the harder ones if you think about it. I want you to attempt it, do it as a pencil. And I can say that none of these involve air resistance. None of these involve the air because you can skydive, you can jump from out of space where there's very little air, and you are still accelerating, so that means there's a force. So then that's the another force involved, And another object. And the rockets one, rockets can fly in the vacuum, right? So it's not pushing it to the air, and it's not pushing it to the air. Let's try and see how we go. I'm going to jump in there. See this group and then I'll go through. Yeah, So what would the two objects be? It has to always be two objects, I'm just marking right here. Well, it's just like... Yeah, so what would be this... So what would basically have to be happening? What's the heart-tire one? Like what does that mean? What's the heart-tire doing? Oh, dry it. Dry it. Think of cadre. Alright, So if you're jumping, I am pushing against the ground so you can say the force of me. Notice how you're going to always write it like this. So you just say force of person on ground. We all have that? And it always works this way. Force of person on ground, onto ground, and the force of the ground on the person. Are we all happy with that? So in that example where if I try to draw it, you'd have... Can we see we're going to push the ground down and then this person is going to go up and these forces have to be the same. Is there any instance where it doesn't equal each other? No. Yep, the forces are always the same. What is not the same though? So what's the reaction? The reaction. The forces are always the same, but the acceleration is not the same. Okay, so when I throw the 10th organ to the wall, there's like so little acceleration. From the wall? Yeah. Yeah. But probably can be even better. What happens if I break a hole in the wall? Yeah, that's what Lockie was asking. Yeah, it's still the same, but in that example there, there's going to be lots and lots of different pieces. If you're going to work it out it'll be very fun. Okay so if I punch someone here then there'll be less acceleration in my fist than in that way. Only if that example there the masses are roughly the same so they should accelerate the same. What's the reaction force of jump here? Yeah, the reaction force of jumping is, can we see if I physically jump, I am pushing into the ground, we all have that, there's a force into the ground. That actually means that there's a force of ground into me, so I accelerate upwards. What would have to be accelerating downwards? The ground. The ground. What you don't normally notice is that moving, because the mass of the Earth is insane. If you got everyone on Earth to move and jump to the same spot, it would be slightly noticeable. Really? Yeah. If you've got an impact of like a meter on to Earth, that's when you start to notice it. Yeah? But the mass is so large of Earth compared to me, that that's why you don't see or detect any challenge. Most of you though, if I jumped next to you, you can probably feel it. Like you can feel it in the ground. Yeah but how about like, like I'll say for example, when I was putting in like where I'm on the stadium and people are stumbling the ground, you can feel like the whole stadium is shaking. Yeah, that's what, so that would be the whole stadium moving. Mum, when you're there you can feel the shot of stadiums. Yeah. Yeah. No. Alright so we're up to the car to make sure this is car driving. Maybe not as long as we can. Do it. So the force of the car on the ground and the force of the ground on the car. So in this one here it's actually simpler than you think. So if you scaled it up and you had a car driving on a big ball, can we see that the car is going to go this way and then push the ball in the opposite direction. So you don't see like that's all it is. It's just it's on a larger scale. But can we see any time it has motion, any time it has acceleration, There has to be two objects. So foot jumping, with little reaction force, before pushing on the person. The ground push up. Yeah, that's why we're a person on the ground. Ground push up. Alright, rockets and skydiving are the hard ones. So, rockets, what do we think? Has anyone got an idea? Has anyone done this one? Put your hand up and move. Can you like, ground, wouldn't it be? It's the same, or the atmosphere? Alright, so, this is a common one person, people will say, ground and atmosphere, you can have a rocket flying in the middle of space and it is accelerating. It's getting faster. So can we see it coming into the ground and atmosphere? It looks like a thrust expulsion of gases. Yes, yes. So when we played with the rockets yesterday, did we notice that the water got pushed out and it went downwards? And therefore the rocket went up. So for a rocket, it actually is probably helpful if you draw it, and this is going to be the one that's useful because we're actually physically going to do this with proper rockets not too long away. So if we've got a rocket like this, can we see that it's easier if I draw it like this, where this is your rocket and this is going to force of gas on the rocket and this is going to force of the rocket on the gas. Are we happy with that? Like it's pushing out. So we see the mass of this is getting less and less and less because it's effectively pushing against yourself. It's doing no different to if you were in space and you threw something. If I throw something in space, he will see this speeds up. That means I speed up in the other direction. Yeah. Has anyone stood on a boat, pushed someone off the back of the boat and the boat moves forward? That's the same thing, that's new to Third Law. So if I push someone off the boat, I'll go the other way. Oh, you know what, I'm standing on my **** drop, I'm just moving, and you're on the drop off the side. Close your feet and push them in that way. Then move them down. No, sit down. Which that way. Yeah! Oh, if you see someone. There's someone. Yeah, she's just being like so mean how about you guys go to Glyce James okay gentlemen How are you going to lose? Usher, where were you last night? In the house. Where were you taking your down syndrome person? Josh. Josh, you were the best in Stela last night. Who was Stela? Who's getting out of hand, sir? I... I... The three of you are all three boys. It's me and Josh, we're a couple. It's just not working out. Alright. Couple's gonna be gay. Sorry. No, just the three throw you at the end of us. Sorry. Alright, so, yeah, yeah, yes, so if you think about it, if you've actually met the situation, if you jump off a jump or a boat or if you've ever seen someone try and jump off a skateboard you'll see the skateboard goes off in the other direction really quickly because of the different masses. So can we see the rockets it's against the gas? This third one, this fourth one, is the hardest one. Oh, it came from moving into a floor back. Yes, it comes out there. Yep, what's the difference? What's the most popular thing? So like pushing off the skateboard, we're going to ask for as you can go. Right, so the forces are identical when as the incident is happening. Their accelerations are not because the skateboard is considerably lighter. Then you've got another force which is a friction. So if there's space, it will just keep going. It will just keep going, yeah? Yeah. But I know, but if we leave gravity pushing, I can see out, and then skateboarders keep going until friction's gone. Yeah, which is another, can we see that that's another situation? What was your question? Is the skydiving in European parachute? The parachute part would need to do with air and air assistance and stuff like this. Can you see if you... Does anyone see the one where they did years ago the red ball guy jumped out and it was like really fire up and then accelerated down. Because there's an acceleration, can you see there's a force there? It has to be another force. The plane goes up and the person goes down. Oh, so My gravity pushes against the earth and the earth gravity pushes me. Good but I would say pull prop. Pulls, yeah. I have a question. Right, actually that was really good. Most people don't get that straight away but effectively what it is, is if you have earth and you have a skydiver with weird legs, a skydiver, can we see that the force downwards by gravity is actually going to be the same as the force up by this person's gravity. So it turns out gravity is to do with mass. So this person would be actually pulling the person Earth up. But we wouldn't see really any movement because acceleration is so tiny. Wait, where is it that Earth comes up to? A little bit. The forces would be the same, no different to all those other situations, and the acceleration is just going to be tiny like insane as small if we actually we wouldn't be able to measure it. However, if you... The Earth pulling up to the other side. By the same amount of force because any two objects of mass actually get pulled together. So that's why the moon is pulling the earth. Earth is pulling the moon. That's why you get the tide. The same about the sun. The sun is pulling the earth and the earth is making the sun wobble. All right, so both of these forces are equal and opposite, but the acceleration is not. Remember a wobble? Yeah, so. Remember a wobble? Er, how it sounds. How it sounds. It goes around and it pulls the sun. Don't know how you push someone. I'll just write. The forces are equal. You can actually do it later. The equation is massive there times the mass of the sum. The forces are always equal each other between the two masses. And it's basically the same law. However, which one would get the biggest acceleration? It would be the one with the small mass. But the earth and the sun are the same mass. And they're like, leaving their part. There's a pencil right here. Is it pushing against me? Is it pushing against the table? It's pushing against the table it's like oh yes because of its mass yes yeah you wouldn't be able to notice it it wouldn't overcome the pressure all magnets all objects have mass therefore they have a gravitational pull yeah any object is massive which is a difficult one. Yep. All right. Okay, what was your question? Mm-hmm. But like, shouldn't they not have, you know, like we were just talking about if the skateboard goes further because it's way lighter. Like shouldn't this just be moving away from me because of the force it's like that's going out because it's way lighter than I am. But yeah like shouldn't it? Yeah yes you are right and you should notice the acceleration is being huge but gravitational force is insanely small compared to other forces like friction and magnetism. But like in the earth, the earth has quite a big gravitational force so how does the Sun like stay where it is? Because the sun is insanely massive compared to the Earth. So shouldn't we be flying into the sun? The sun is nearly as time to massive, more massive. Are we slowly going towards it? Every now and then. We're going in orbit, So we're going to pull towards it. Well, we're going to circular. We're going to stop. Every time we change direction, that's going to work. So we get closer and closer to the sun. No, we are in an orbit which still means you're being pulled in. You're asking a good question, right? So after 100... This is outside the course. Anytime you go in a circle, you can have a pull inwards that is just enough that you end up back at the same spot you ended up at. So after 100, really, we wouldn't like a lot of stuff. No, the only way would that happen is if our speed slows down due to impacts. Is that possible? Yeah. What if I hit by a meteor, like what do we do? It slows down. No, I mean like what do we do? We do. We're about to meteor on this one. What if something ends up exploding? Alright, so Obviously a big one. Now, I need you to go into the style, and we can go through these ones. You'll see that there's a new second law and a new third law won't open. We only have about 10 minutes left so can we please go through that. I want to see the laptop open Josh. Well we go ahead. You'll see that there's a new second one and a new third one. Wow, steel. Made With Glean | Open Event Acceleration and velocity Transcript Velocity over the acceleration will be how long it's taken to accelerate. Yep, velocity, change. Velocity, acceleration time change. Acceleration equals change of velocity over time. Yeah. Which is. It's here and it's on the sheet that I gave you as well. So this method here is just so that you don't have to rearrange it to find something. So, if I give you an example, if we are looking for an acceleration. So if we go to an example. Yeah. Sorry, we're not. Look, I understand it's Friday, and I understand that'd be gross. It's been a bit more all over the place, but can we actually just focus? Otherwise what's going to happen is. So what we can do is, I can show you an example. So, if we have something like this and we're asked for the acceleration, can we see that if you cover the acceleration, it's going to be the change in velocity over time. So you thought you first do this. The way you work with these questions is there's actually clear steps. So what you would do is this, you would basically go, okay, from rest to 45 meters/second now, that means that we know the change in velocity is 45 meters/second nice. Can I get a thumbs up with that part? Yeah, we're trying to find a. They're trying to find a. I actually, it's going to sound really dumb at the start, but can I get you to write down a question mark? When we have more formulas and they're more complicated, it is actually useful to write down the symbol that we're looking for, because we don't know what a equals. That's velocity. It is. Jebbia, next time just put up your hand. But what we're trying to say is we don't know the number for the acceleration, and that's what we're looking for. So it exists, this one here. Okay. So in this one here, can we see that we are looking for, and then we want to write down the formula. Now, if you look for acceleration, that means you have to cover the acceleration part here, and you'll see that it's acceleration equals change in velocity over time. So, in this one here. All right, James, Aurora, can we actually get a pen out and copy this down? Okay, now we've rearranged it, so we don't have to worry about that. What's the triangle again? Change this one. Yeah. Change of velocity. Acceleration is just changed. And then, then you put it into the calculator. Don't overthink it, don't try and simplify it just put it into the calculator. Archer, you've got your computer in front of you open, so you should be able to calculate what's 45 divided by 3.7. What is up? Is it. It's 12.1. 612.2. I've done it slightly differently, but I prefer this way. 12.16. Wait, what's milliseconds squared, Jamie? So the next part is this. Acceleration is one of those ones that students mix up a lot, and it is actually a slightly more complicated topic to get because you're so used to people just talking about speed. And intuitively, acceleration is the only thing you feel. So if you're on a train, a high speed train, you don't feel that you're going at 400 kilometres per hour. You're in an aircraft, you don't feel you're going at 900. Only time you feel something is when your velocity changes. Now, this unit here is trying to say that. It is actually trying to say. It is actually trying to say that youre a meters per second is changing every second. Does that make sense to you? So my velocity has changed, my meters per second has changed every second? Yeah, it is. And you'll find that when we do Newton's laws very shortly, acceleration is a major part of it. Yeah. So do we have to divide it again or, like. No, this is how we write it. Meters per second squared. But it's technically trying to say meters per second per second. You only build acceleration for 3.7 seconds. Oh, in this example here. Yes, yes. Because he only accelerated for 3.7. So if you are in that example. So if this is a drag car, that basically means that this person would feel 12.2 meters/second acceleration for three and a half, 3.5. I want to be able to write a Mario Kart so badly. And. Which would be about right every second. Yeah, that's exactly what it's saying. All right, the three of you there, Jamie. All right, you probably missed that conversation, which was relevant. All right, so the person here is only accelerating for 3.7 seconds. So that means they're only actually going to feel it for that amount of time. Shouldn't you use a different, like, measurement, then? Because, like, that's like, that feels like it's on a completely different, like, plane. Like. No, that's just what acceleration is. Yeah, but, like, I mean, yeah, yeah. Like, I understand it. It just seems, like, odd. Yeah. All right. See, what's gonna happen is everyone's here, gonna attempt this question here. Everyone's gonna attempt this question here. Notice here it's asking what the **** final velocity is. So, first of all, you need to work out. No, because he's gonna keep going, he keeps skiing. So in this one here, they're speeding up, so their acceleration is increasing. So I want everyone to have an attempt at this. I don't want to see anyone having an excuse or a laptop open. There needs to be a pen in hand doing this. Stella, is hedgest right down this? Right down the steps. And let's get started. It's a different one. What is this? He accelerates at 3 miles an hour. Does that mean he's 7 meters/second oh, 7 meters/second does that mean his overall going seven, or is he slowing down to accelerate? No, he's increasing. Otherwise, besides the ball. Hello. Yeah. 15 plus one. Hello? Yeah. What made it 10 seconds? I think so is what. I'm done. Okay, but that would be how much the speed has changed. Read the question. I actually think you can get me the answer. Yeah. Okay, so let's start with this. How's it going to do this one? We need, effectively, we need to find the change in velocity we have with that. So if we cover the change of velocity here, we see it's acceleration time to time. I don't know how to do this. All right. You're so close. Did you add on 4 meters/second oh, no, I don't want to. All right. To me, is she pretty? All right, so, once again, I know it's annoying, but the reason is everyone else is actually trying to do the question. These guys are done with honey. They're talking about their life outside of school and Aurora and Lance. Thank you. My shoulders hurt. All right. Okay. So why are you still talking Ar when I did the car? You're not helping the situation. He's talking **** about Huddy. Please. All right, can I just. I need my eyes to the front. And we are going to put up and, well, we are getting Nash. I'm going to go to the point where I'm going to put a dash on the board, and after that, you're going to be here after class. But one dash for five minutes. Now, Asher, before you say anything, this is going to involve you as well. And I'm going. Made With Glean | Open Event Kinematics Transcript Have a direction. So the obvious ones that we just said is distance. What's the title of it? So the title, the title is technically called kinematics. The car's going at 30 km/hour yeah. So this time get a pen out, otherwise you're not gonna. And if you're doing physics next year, this is, this is it. So you need to, could you pass? All right, so this is a scalar, which means it doesn't have a direction, speed, that is 60 km an hour. Can I borrow this for a bit? Is a scalar, time is a scalar, mass is a scalar, temperature is a scalar as well. That is. Thanks. Does that count as, does that count as energy? No, but temperature and energy are very, very closely related. I mean there is a relationship between the two. All right, so if you actually look over here, it turns out pretty much all these are scalars. The monsieur kilogram. Yeah. Wait, is a scalar. Alright, so the next part is going to introduce a vector. Can you get a pen out? Get your module out. We need to get this down and this one is the important one that we're going to deal with most. So I'm going to try, and I've got some devices here that we can sort of apply these out. It turns out we kind of care about direction more than you think. If you're in a car and you're doing 60 km an hour and there's another car doing 60 kilometres an hour, there's lots of different situations that could be, if you had a collision, that could be the two cars going along at the same speed and they bump into each other, or they could be going head on or side on. Can we see that the direction is going to really matter in this situation? Can I get a thumbs up if that sort of makes sense? Not really. Not really. So if I'm talking about, if I'm talking about a speed, what does it mean when it says like magnitude and direction? Like could you just give me an example of what like the vector of something is? Yeah, I'm going to demo it in a second. So for the first one, for displacement, the direction will be where else the object is. All right, so now we're all going to work in meters. Just close it up. So we're going to start with the scaler and distance and compare it to the vector displacement. Nash, volunteer someone, always someone. You're fine. Whoa. All right, there we go. You get to stand up. Alright, so I'm going to try and draw it on the board and we're going to show the difference between a scalar and a vector. All you need to do is you just need to walk to the back of the room and then walk to behind Izzy. Yeah, and then I'll draw it down here. So, so how far do you think Jambia has walked? 10 meters. 10 meters? What, five and five, you say 15? Five and five, no, three and seven. It's more than three. Seven, four and six. All right, just stop, stop back there because it's gonna. Alright, so let's say eight, 8 meters. So what is the distance you've walked? 24. So can we see the distance? In this example would be 24 meters. We all have that. Yeah, but his displacement from the start would be what? 8 meters? 8 meters is only half the information. So 8 meters straight east. Oh, that's good. So 8 meters, can you just say to the left? Right. All of those were good ways of doing it. It depends on how we define it. In this example it's probably going to be easier by saying ease. How do you know that? Taste, because that, like not, I'm just guessing, how do you know that? Was that actually normal? Yeah. Oh no, but how do you know that? How do I know that? Because I've been teaching this classroom for a while, so I know that it's not exactly north, it's a little bit hot, but it's close enough. All right, so yeah, it does. So let's, so let's look at these two things. The scalar is 24. So in this example here, the scalar was the distance he's travelled is 24 meters. Notice here it doesn't have any direction associated with it, it's just a number. This one here is his displacement, so you have to have a number and a direction. So in this example here, his displacement was 8 meters east. Can I get, you have to write the, the unit plus the direction. Yeah. So I was going to get you to stop here and then how do you think you'd do it? And then what? Then you have to sort of say like southeast or. So scalar is just 8 meters and vector is 8 meters each. So in this example here, no, the scalar would be 24 meters. Oh, and the displacement is just like point, the difference between point a and point b. Yeah. So the displacement is always measured from like the origin from the start point, let's say. I shouldn't see any laptops open. It's quite rude, but four minutes into the class. Yeah. All right, so can we see that? We've defined one thing, we've defined distance is just how far the object travels. And we've got displacement, which is how far away it is from the up. Yep. Thumbs up with that. All right, the next one is speed and velocity. It's the same thing. Speed is how fast something's traveling. Like 60 km an hour. If you're talking about the velocity, we're actually going to define the velocity in a little bit. But the velocity is effectively like the speed with the direction. So if you travel into Melbourne, it would be like, what's the velocity? 60 kilometres down northeast. So it's just the same, but it says what direction you're going. Yeah. Velocity and vectors have to have a direction. And I'll show you why it's important soon. Yeah. So 60 km northeast. But why does the northeast matter? Because if you had a situation where, unless it's to do with, like, wind. But isn't that like, an outside effect, like an outside factor? It's to do with, like, up and down really matters. So if the rocket is going. Let's go. Rocket example up versus down. And we're going to talk about acceleration and stuff like that. Yes. Any coordinates matter. Like, you could do true angles if you've done bearings. Bearings are perfectly fine. You know, like true bearings and stuff like that. That's fine. Later on, you'll find that we use angles. So volunteer somewhere. So we're now going to talk about some graph stuff, but I want to. Why is it not working? All right, so. So what we're going to do now is we're going to start talking about going, um, describing displacement, which is the one we really care about. And we're going to do a graph of displacement versus time. So can we all have get a ruler out or something like that, and draw a displacement on this axis and time on this axis. So you're going to get a ruler. So it's displacement time, and we're going to get Lachlan to follow there. So this is displacement. I'm going to give you symbol f for displacement. Oh, **** that was round. Okay. Oh, wait until we got this done. Yeah. So where it says position that you're talking about displacement, right? Yeah. For some strange reason, the software just writes position, but I can't. I want you to write display. Yeah, like that. Perfect. All right, so can we see this? S means displacement. I won't. It's just. Why does that mean. Just accept it, unfortunately. And we'll write in meters, and this is in seconds. All right, so in this example here, can we see the object is just let's say, 2 meters away. Can we see that for the first? Look at this. For the first half second, the object is 2 meters away. Then what's happening from here to here? He's moving in that direction. Yeah, sorry. He's going, like, northeast. Oh, okay. So no good. This will be. Let's say that this direction is in the north if it's positive. Yeah, technically, it will be south if I do it. Exactly right, because lachlan's going to have this out. So can we see? I understand what you're thinking was, but this is really just up and down. So what this is trying to say is, over time, lachlan's going in the south direction, but then he comes back down. That's just that one. Yeah, I can make it. I can flip it around. So is this like a. Like, is it, in theory, like a bird's eye view map? No, this is not a bird's eye view map. Okay, so, Asher, you're on the next part. Yeah. So can we see that? What we're trying to show here is this is how long it takes him to move 2 meters a second. So it takes a second to move 2 meters. So effectively, what that means is the person would have had to have walked in this direction and ended up 2 meters after 2 seconds. What? 1 second? Sorry. What does that mean? 1 second? Is it 0.51? Yeah, 1 second. And then what happens from here to here is the object moving from here. Can we see down here? What's Lachlan doing? He's going backwards. All right, so effectively, it's going in the positive direction or negative direction. So can you see this way? He's decreasing his getting closer to the origin. So can we all look here? I'm actually going to get Lockwood to act this out, and then I'll change the grass around. If you look, you need to start at 2 meters. So if I. So you're a little bit off. Yeah. Well, now it's not. Stand in front. Okay, so can you stand in front of this? Hold on. And just stand there. So this is basically just saying he's standing half a meter away. You moved the bed. Yeah, I was a noise because it bounces and. So up the back. Can we. Can you just slowly keep your chest in front of it, because it's bouncing off the chest, and then just slowly walk backwards and see what happens. I just recall. Wait, what is that like? Unfortunately. So. All right, and then do you want to come back? Because it can't go too far, and obviously it's having issues with. All right, so you go back slowly again. Asha, stop messing around, please. All right, so can we see in that one there? He stood still for a while, and he moved back slowly. Yeah. Can I get you now to walk backwards and then forwards and backwards, just so we can see what it looks like? Do some sprints now. Come back forward. Oh, so in this one here, can we see that he stood still? He moved back, and then he moved forward. Yeah. Headphones for both of you. Yeah, we will do those because it's an acceleration. We don't want to run those that. But first of all, can I get you to see if you can follow this graph down? That's gonna be hard. You gotta make quick. Oh, yeah. You're gonna have to do some sprints. Okay, you ready? Sure. No, no, sorry. When I talk, it changes as well because it sounds. No, it's listening for an explicit frequency. The issue, actually is I'm not trying to move across there. It does reflect off. Once it gets further out, it does reflect off tables and people. All right, so that's right. That's back. Now forward. When the line is, like, flat, it's staying still. Right. I really hope I don't embarrass myself. All right, so you know what? I might do 4 meters. That's, like, down. I'll start it a bit closer. About one and a half meters. Ashley, can you just move across? Because obviously it reflects off. You move around. Yeah. All right, where's 4 meters? I need a four meter mark. It'll be about the table. I might. How about this? I might. The table get safer. All right, how's that? That's still pretty quick. Okay, so let's go. Are you ready? Yeah, I'm ready. All right, come back. Mom's. I got it. That's pretty good. All right. There is an issue at the start. What was the start? You should have waited. You have to wait and you'll probably be close. Yeah, I'll get it. What? No, I wasn't ready. All right, go back. I'm here. I'm here. The other problem is you have to face it or have your back to it, because it needs to reflect off your kick back. You can't move. You can't move for like, 2 seconds. You can't move. Yeah. Three, two. Don't move. Go down. I mean, that's as close as you're gonna get. A. So can we have a quick look at what's happening here? This is the important part. How do you measure, like, if it's going left or right? Like, if you had it come towards here instead. So this one is only just back and forward. What would you call this bit where it's moving over motion? The Leonard velocity. Velocity. And it's actually the definition of velocity. So can I get. All right, sorry, can I get. The definition of velocity is a change in displacement over time, which is, I'm going to write on the board. So can we see James's velocity here was changing over time. Placement was changing over time. What do you mean? His velocity? Sorry, his velocity was that way. Correct. But his velocity. Not like the speed in a direction. Yeah. So his velocity was this way. We'll say south. Yeah. And it was roughly about 2 meters/second but can we see that? The definition is how much his displacement changed per second. So I'm going to rub this off and I'll put velocity on. Does this mean that when he's stationary, could be traveling west and east in this example? Yeah, just about set up. But how would this, how would you, on this graph? You couldn't. It would have to be a 3d graph. Yeah. Like, it would have to be literally a 3d graph. Okay, so velocity, this is going to be the one where. Notice how I keep putting arrows on the top of these? This is to tell you it's a vector. It means it has to have a direction. What is vector? Which is. Because it has a magnitude and a direction. Yes. Which means it has a number and a direction. Yep. So velocity. And it means the way we define it is the change. So that means the displacement. It's a change in displacement over how long it took the time. So can we see from the graph? Let's clear the graph. So we just. So can we see from here his velocity, his displacement was changing over time. Does that make sense? Like he was moving away over time. This is one where you kind of want to concentrate. Once you get it, it's. Okay. All right. Now it's going to be very rare that I'm going to write it like this. Can we see that? This is saying meters per second. How much is meters per second? Is changing. Scientists, mathematicians, super lazy. They're not going to write like this. They're going to write it as delta, which basically means change. If you ever see the triangle, it means change. And s is displacement over time. So this here is saying how much he moved over the time it took. Wait, what is the equality? Velocity. Yeah. So this is the velocity and we measured it in meters per second. This is displacement. Change in displacement. And that's in meters. And this is time in seconds. Why do I ask? It, does it always have to be seconds? It does, yeah. It always has to be made. Just a second. We'll show why when we get to acceleration. Like if we. If we're talking about, say something that's not on earth, like an actual station, that'll be too hard to quantify. So you. You probably would still write it in meters per second? Like spend it writing kilometers per second. Yeah, it's to do with. When we do acceleration. Acceleration. We measure in meters per second and that's what matters. All right, so let's look at James's one here. Can we see that he went from 2 meters to 3 meters? From 2 meters to 3 meters in half a centimeter. Does that make sense? James? Yeah. Can you see? You went from 2 meters to 3 meters? Yeah. I was saying how quick it was in half a second. Yeah. So the change is. So how do I. So, yeah, so his change is 1 meter. So it's two. It's 1.5, which is two. Right. So it would be 2 meters/second because it is a velocity would have to say the direction as well. 2 meters/second what way is that? South. In east. Is it east? West? In west? Wait, why is it in south? Because it's only backwards in ports. But south is on that side. I caught it. But this graph is saying south is that way. He's still going south. How? Sorry, how. But shouldn't he be going west? All right, so can we see that he went 2 meters/second south in this one? Let's have a look over here and have a look at the other one here. This one will be interesting to see how it goes. So how far did. What was James's change in displacement? One. One. Like one, two. Like 2 meters is the first point. Like the. No, I want to do this point here. So can we see negative 1 meter? Why is it negative 1 meter? And this is going to matter. So can we see from here to here? Let's say from a to b, his velocity will be negative 1 meter over 0.5 seconds. Again. So he's going to have negative 2 meters/second and that's the velocity it is possible. All it means is a negative just means that the direction is the opposite direction. But wouldn't that just be the right direction if you are the other way? But then it becomes positive too. I mean, two minutes a second. Yeah. Not, yeah, but it's negative. Two minutes a second set. Correct. So a negative and a positive just switches the directions. Right. So you can just write it as positive or with the opposite. Yeah, so I could write it as positive. Nor. Or I could write it as negative. So what you're going to find is from now on we're just going to say positive and negative. So up and down we can say up is positive, down is negative. Can we see that? We can say that way is positive, that way is negative. No. Yeah. Do we have any questions? This is, this is jumping through it really quickly. That actually makes sense. I need you to draw down the graphs and then have a think about it. I'm going to show you some, some stuff on this and I expect some of you to take a little bit longer to get this at the start because we've only done like two or three wraps. And then I need a volunteer and I'm going to try and get some more people to do different graphs on here. Just so we've got an intuitive understanding. So the change in deployment, that word. Yeah. Is the, is the velocity over time. But like, what do you mean over time? Well, if I went from here to the other side. Yeah, yeah, yeah, that's what I meant. I know that. Yeah. But I did that in a year, then it'd be a really low velocity. Yeah, but if I did it in half a second, then it's a high velocity. So is like to a high velocity, 2 meters/second is. Oh, actually I forgot about it was per second so much. So it is times it roughly. So it's about just under 8 km an hour. Does it have like its own measurement or is it always in like. Yeah, or kilometers per hour or something. All right, can I please get everyone to draw this graph down and label what, the parts on it and what it means? Okay, so what's happened here? What's happened here? And then I'll get people to try and draw some more complicated ones while I come around and check what you're doing. Get this stuff down. Include in the graphs. The graphs matter. Yep. Cool. Hey, just get a coloured pen and write what the person's doing. See if the person's not moving. Did you see that they're standing still? Yep. Then they're running to the back of the room. They're standing still here and they're running towards. Back towards the start. Yep. Write down what's happening here so when we come back to it. Underrated. Show Loki. Oh, I'm taking. No, you always do motion dimensions. It is actually quite easy. And then they had to stand still here and then run back towards. Oh, my God. I do. What? Okay, I'm not a genius, but we couldn't get that from day one. Guess what. That I'm not very smart, but I wouldn't have guessed it. It's on a notebook. It's not Felix specifically because if it was about Felix. But I feel bad that I was mean to him for that reason. He hasn't done anything to me, honestly. Come back to bite me. We're going on a. We're going on a trip to Townsville. Is he even going to that? Yeah, he is. Okay. So, acceleration. We're going to define acceleration as the change in velocity over time. So that's how we define it. It's a change in velocity over time. If we look at a graph like this, we do time displacement, and I try and get some to act this out. Can we see how it's occurred here? Did you notice here? Did you notice when every time someone tried to do this, it was actually curved? It was never a perfect straight line? The reason is because their velocity was actually changing over time like they're accelerating. So in this example here, the person is getting faster and faster and faster and faster. So if I got someone to act this out, they would have to run flat out into the table at the back. They'd have to accelerate into the table at the back. So if you want to be, like, accurate, are you supposed to say, like, if, like, to give an accurate measurement, would you be going like, the car goes like, accelerates at a speed of. We haven't introduced that. And then with. With like, a displacement of 8 meters and a velocity. And, like, are you supposed to use all of these? Yes. Or do they all, like, come together like. So, look, you're asking a good question. You'll see all of the. We're gonna do notice here, we're only doing position time graphs here. Like, what information do you need to, like, you do need all three. And that's just like displacement, acceleration and. Yeah. And so what happens is all three will describe the situation. But do you notice the one here? If you're standing still, your position is like 2 meters, your velocity is zero, and your change in your speed is also zero. Yeah. So you need the three to describe the situation. Yep. All right. Can I get you to just to pretty much. We're finishing up. Can I get you to write down the acceleration is equal to. Remember this, it means change, change in velocity over time. Once we do that, I'll get someone to try and do an actual acceleration on the graph. How do you spell acceleration? Thank you. But does it have a two c's or two L's? I put it with two c's. Why are you. Right, you're too small. Dyslexic queen, how would you spell deceleration? Or d, is that d acceleration? Right. You can say deceleration, which is just d. Yeah. Thank you. However, what you'll find is we're not going to try and use that word. We'll just use acceleration because it's the same thing, isn't it? Negative acceleration? It is negative. Depending on the five is then moving a constant beat. But every time. And if you're in that squad, you can just ask to move. I'm supposed to have rowing from five to six, but I'm gonna go talk to Sal after French. How come? I'm a band girl. Yes, exactly. But I went to. I, like, I really wanted to do guitar ensemble, but I went, and there was only middle school, like, Charlie Velvet. And it was really bad. It was really bad. All right, can you. And guitar is kind of subjective. Like, I don't really love classical. Do this one. Because I want to see. Especially because they were trying to, like, teach me the piece in tab. And I was like, yeah, can you. Sorry. And this is how we're going to finish off. So. Wait, is this measuring accelerate. Notice it starts off, it's not moving. And it's slowly getting faster and faster and faster. You started the meter, so the meter in front of that. I'm so sorry. I think I'm just going to click slowly. Oh, **** I told her that ditch, you can figure out. Okay, go. That's a lot. Embarrassing. All right, so you. If you look closely, this is roughly a constant speed. So you have to actually accelerate. You have to get faster and faster. You ready? Faster, faster, faster, faster. All right. Yeah. See, can I have eyes to the front here, just so I don't have to repeat this. Can we see? It is curving here. What you need to realize is that anytime you see a curve on a distance time graph or displacement time graph, you see that the person has to be getting faster and faster and faster and faster. That's all I need you to get at the moment. Yep, that was that. Because when we do the rockets, we're going to basically work out the height with these graphs. All right, thank you. It. **** me. That's a great. Made With Glean | Open Event Slides and Notes 2 - Vectors and Scalars Position Slide 3 - Distance & Displacement Slide 4 - Speed vs Velocity Slide 5 - Average velocity gives you an overall summary... Slide 6 - 1 2 3 4 5 Slide 7 - Distance vs. Displacement Example Slide 8 - Describing Motion Speed Slide 9 - Speed - Transposed formulae Slide 10 - 1 2 3 4 5 Slide 11 - 1 2 3 4 5 Slide 12 - 1 2 3 4 5 Slide 13 - Additional Questions Slide 14 - Describing Motion Velocity Slide 17 - 1 2 3 4 5 Slide 15 - Velocity - Transposed formulae Slide 16 - 1 2 3 4 5 Slide 17 - 1 2 3 4 5 Slide 18 - Additional Questions look over Made With Glean | Open Event