So reaction force outputs. Okay, so you've got all these forces and then I should have drawn that arrow in different colour. Let's do that. A different colors. So I see it. And we've also got friction. So which way is friction go? No I can't anymore. Oh sorry, I wanted to do that right? Oh Yeah, click that way. So friction always opposes the motion. Okay? So if the object is being pushed towards the right, then friction is going to go to the left, okay? And then it's just the case of using all of the equations we've got. Maybe I forgot to times it by the core version but really think I did have I just worked this through? If I can check if I did anything wrong? Yes, all right. Oh, I think I thought got wrong. Did you put minus? We know that much. Is that right? Need a we need a plus. Sorry, I'm not going be laser on because so in terms of verhere, you're resolving vertically and vertically were in equilibrium. So all the forces that are going up need to equiable the forces that are going down and this 77 newtons is going downwards. Okay. So the sign I 37 is acting straight down, not strail. But listen, we look like the R is. I'm so confused now that R is always like and the MaaS times g like minus the force, the force is going upwards, then yes. But because because we've got two forces going down. So the 77 is it's not actually straight down, but it's acting a bit down and the mg is actually straight down. So the component that is acting down of the 77 and the mg must add up to the reaction force. Okay, if if this 77 is a pulling force and it's pulling it up, then you take it away because it's acting like down as well. Then he asked why to add them because this is essentially the upwards force. This is your downwards force, like the whole thing. Sorry if it's if it's going down like downwind plus, but why are we why are we bosting it? Like why do we add it? So we add it because both of these are acting downwards to the m times. 9.8 is our mg, which is acting straight down. The 77 is then acting diagonally down. So its vertical component is 77 sign 37. So these bits are both acting down. The R is acting upwards. So because we're in grilibrium, the upwards force must equal the downwards force. But if it goes that waves pulling it up, that means that that we have to minus it. Yes. If if it was, if it was this yellow line and it went that way, then youhave R plus the 77 sign, 37 equals mg, and then youyouto rearrange the get R by itself, youtake it away. Wait, I still don't get why we're taking away, because, okay, if it's pulling love. So so let's imagine your this box, you're this box, if someone is pushing down into you like this, even if they're pushing you forwards as well a bit, if they're pushing you down. You're going to feel a stronger force from the floor pushing you back up, which is what the reaction force ces Yeah whereas if if you had someone pulling you and pulling you off a bit, then you would feel a bit lighter and completely you like you feel less of a force from the floor because the person that's pulling you up is taking some of your weight. Okay Oh then I think that's why I got wrong because I use minus instead that put okay so Oh yes and it all depends on the direction of the force. Yeah if we had another force I'd say there was a force here of I know they've attached the balloons and it's pulling it up then would have R plus whatever that force was plus unknow balloon for balloon force if that was be okay. And then to get our by itself, we then have to take it away. Oh, okay, I got it now. Yeah, okay, I think I'm fine. Now leave question here. I think there is another one. I don't think I don't know why I got this wrong, but it's bit like. Okay, I think I can draw. Efficient. Oh, we're finding the. So are we on the point of slipping? And we moving and we accelerated and we're on the point of motion. Oh, on the point of motion, that's fine. So we're in equilibrium. So the upwards force equals downwards force, the right hand force equals the left hand force, but friction is at its maximum value. Yeah. Oh, you can find everything what we got. So that's our Yeah like that. That's our because that's actually downwards. That's actually not puto take ket away. Mr equals the horizontal component of that, which is friction. Yeah like that. I would lay out in more steps, okay? But Yeah, I think I think I think I like all of that. Answer time. I just didn't know why I did. Maybe it was another direction thing. Maybe Yeah maybe you might have you cause the wrong around. That's that's another common error. Yeah. Okay. I then I think I'm fine with friction. Okay, four and then it's just vectors. Okay. I feel like I find them like a little bit confusing possibly. Oh Yeah, sorry. Before that, can we go through the proving of was that called the proof of cosine rule? Proof of cosine rule? In what sense? And we just kind of have to prove the if to prove the cursion. What do they give you? Oh, okay, that way. Yeah. And then they gave you the first line of proof. This is x el, is it? That's Yeah that's. And then. And then just say like we need to complete the proof and explain why. What does this say? I'm sorry, let's see you soon, okay? Because a rksahe combined the two Yeah so y squared is that minus that squared? Yeah and y squared is that minus that squared. And put you put them equal to each other, you have. All right. And now then all we need to do so we need we know where the formula of cursoverall rule is going to be a cha. Yeah. So we need essentially if fact we're nearly there already if you look at it. Okay. So in our triangle lamp, so we've got cos a. It's an adjacent side over our hypotenthesis. So it' S B plus x there c. And then. Now, what do you do? C squared, is this? Is this all given? Is this all right? Is this definitely correct? I have to explain why as well. All we for a for a squared equals b squared plus c squared minus two bc cos okay, let just go rid of x. All right, so rearrange that for x. And then zoit into this. Oh, okay. And then I'll be honest, I don't think I've seen this question ever really, but Yeah, I've never seen it. Do you do nxl? Don't you? Yeah Yeah I thought you do the following that. I don't think I've ever seen this. A nice question that let's let's just should we just check if it works? So we get x equals what we get. We get C A minus minus b. Yeah and then we Plinto that. So we've got c squared minus b squared minus two B C because a minus b because a squared, c squared minus b squared minus plus two b squared. There we go. Yeah. Plus two b squared minus two bc, cos a equals a squared b squyeah, there you got, I like that. I'm not to save that. I use that in the future. But if you're going to explain why, just explain what we've done. Yeah because maybe I get when you write it out, I get how it works. But then if there's like another one that that told me to prove the sign rule, then might understand they're working, but that I just can't think of it Yeah for why it works. I mean. It's I don't I don't understand why they're going to put it into words because it is just is just manipulation of already accessible maths. Like all it is is this is it's just Pythagoras Yeah along with socket titrigonometry and then it's just rearranging it for however you want it to be. Well, I don't. I don't really, I don't see what they want you to write for an explanation of why it works other than inot this because like the actual formula itself is, Yeah, it's useful, but it is just ultimately it's just an arbitrary formula. Like we didn't have to settle on this formula. We could have gone, you know what? I really like a different formula, a different form like is just, well, why does it work? It works because we can do Pythagoras on the big dry angle triangle. We can do Pythagoras on the small dry angle triangle. We can then use these two equations to eliminate the y unknown because that's that's what we did hit first. Then we can go, okay, on the big triangle. I know that cause a must be this thing here. And then again, we can use these two to get rid of x so that we only have unknowns in this one irregular triangle. And then it's every. Another question, but like this one asks for, I just want to know how to do it graphically. If I just run my. Casecond. This full screen here, what we got diagram shows parts of the curve. Y equals six side ine squared x and y equals four plus Cox. Where x is in degrees, solve the inequality. Six sine squared x is greater than four plus Cox for zero, 360 solution based, talon graphical and numerimethods are not acceptable. Okay, so we're going to show algebratically. Okay, so which graph is which? What's the I can't read the numbers on. The axis is it zero six? Okay, so that means the smaller one is the four plus cosacks. Okay, so we want to know when is the sgraph? Okay, that's fine. We can do that. I don't want to comment out unless so let's have a quick sketch also supposed to do graphically purely if you've got a graphical calculator you could just use that. Oh really? How wait I'll be Honi could tell you I would duit, okay. They're really complicated I find Yeah it's in there somewhere and no we no use if I draw that right Yeah, Yeah. And it goes between Oh, I think that was eight, wasn't it? And zero. That was six, sorry, six, the top. And then that went between x axdoes it in the middle. Yeah Oh, it's going to be apparently I hate the rubber on this system. I can do that. I can do that. No, it's okay. It's okay. We can just leave it. Some Nondas are. So the graph is there essentially to give you a clue of what sort of ansyou're looking for. So we wanted to know what were the equations. You want to write the equations, though. In fact, just write the inequality thatwork. Stuff. Okay. So we want to know what is there's this one in blue greater than the one is red. So the orange, the graph is useful because it shows us we're after two separate regions. We're after a region there and a region there. If you had a graphical calculator what youdo is, you would so I could do it on desmos. To be fair, if you know the website desmos Yeah, Yeah. So you could just plot both graphs and you're just reading off those values. Oh, you're just reading off the regions. Yeah, exactly. To do it algebraically, you solve the quality. So have you seen these before? Have you done this intricky? I think so. Yeah, we moved on it. Yeah. So this will eventually become a quadratic in the trig function. And you use the fact that sine squared equals one minus cosquared. Yeah. And then you solve it in terms of why are we selling in terms of cause. So when you've got an equation that evolves two different trig functhree to, but essentially when there's lots of different trig functions, there's a couple of ways you want to solve them. The first way is, if possible, convert everything into the same trig function. So you've only got one trig function. And then normally you get like a quadratical. You get a linear equation or maybe a cubic in that function. The other way to do it is if you can rearrange it, so you get multiple different trick functions being multiply together, you can then solve as well. But in this case, we're able to change everything to its in terms of causes. So we can go, well, that's sine squared. Well, that's one minus cosquared. Okay. And now all of a sudden we've got an equation that is just in Cox and it's it's essentially, it's a quadratic, so hidden quadratic. So if you wanted to, you can go, Oh well, cosqured x equals y. You don't have to do that. Some students are happy just to do it in terms of Cox, if not that, that's fine. You go, Oh, well, this is six minus six y squared. It's greater than four plus y. And then you solve this quadratic and y till eventually you get down to y or something, and then you get, Oh, Cox equals that. And then from there you then convert it into hopefully four different solutions. And we have to use inequalities as well. Okay, so for this one, what we get, we got six y squared plus y minus two is less than zero. And then we're looking to factorize that. There we go. We got three y, two y two, one plus minus. I think that works. And then from there we go, okay, so y equals minus two thirfind, it's fine half. So then you have Oh well, Cox equals minus two thirds or a half. And then from there you'll get two different answers within the zero to 360 range. So so what do you get? I don't actually know, but I don't know exactly advice. Shockingly, I think it's Yeah and then so normally with a quadratic, but this the the nasty part is defining the regions. That's where the graph then comes into play because you'll get four different answers as critical points for where they're equal to each other. And you go, well, I know it must be between the lower two and between the upper two because the graph shows us that Oh, okay, okay. So a bit bit of a weird one. Oh Yeah Yeah and there's another one. That's this what times like a circle. Just even what we got Reis on a Ferris wheel. Oh, I love the Ferris wheel. Ones watched by our friends directly blow the wheel as shown in the diagram. This tai Yeah Tash looks up and sees brucapsel directly overhead in position mt slione. Hundred seconds later, Bruce's capsule is directly overhead again. Position. Whatever letter that is the Ferris wheel turns anclockwise as shown by the arrow, given that the Ferris wheel has radius 15m, but it's going at a constant speed and the Tash is a horizontal distance of 9m from the lowest point of the wheel. Okay, no misses from okay. Yeah, no. Okay, Yeah, no misses from there. Yeah. Work out how long the first will it takes to make one full revolution. What a lovely question. Oh, no. Gosh. All right. What we got so we've got wheel. We've got, let's do a different color our for sh tashes this dot. Then we've got, what's it? M1 and M2. Take one and M2 there 150s part and we know that distance. So that distance is 9m, and then we told the radius was 15 for the radius. Yeah, I missed and we ₩1 full revolution here. It also says that ashlosuband semaurie's capsule directly overhead in position M1 exactly 150s later, hundred 50. Okay, okay. So that's all they are fairly given. I'm just really lost. I feel like, okay, so we know that distance is nine. No, this is 15. From there, we could actually work at an angle. Yeah and then Oh Yeah, that thing else we do. So you work at the angle. What does the angle end up in? Let's call the angle x. So x equals. What we got using so no, not using cars. Plus the minus one of nine over 15. So x equals, what does that give us? That's 53.13. 53. Oh Yeah, nice. It's that triangle. It's the famous three, four, five pythic triangle. Okay is that that's quiz isn't actually matter so then we can get okay so two lots of x is double that. That's 106, not point 13 mamar, there we go, point 26 and then it's ratio. Okay, so it takes 106 degrees. Is 150s. I want 360 degrees. So you work out what time that is. It's going to be, what's that? Something like 550 ish, 500 ish. So around there it's just ratio that. So you take 150, divide it by 106.26. Timit by 360. 508.187. Sorry, 187, 508.137, 187 easily. Yeah. Okay. So the hard part about that is getting this triangle, I think because so so the way I got it is we were told she was 9m from the lowest point, which would be directly below the center. And then M1 and M2 are directly above her. So the distance from her to the lowest point is the same as the center to in line with where they are. And then when you got the triangle, it's then just ratio. This is assuming though that we're traveling at a constant speed, which I think it said in the question. Yeah Yeah if not that sometimes theyhave it as what assumption have you made about the velocity of the about the speed of the Ferris wheel? And then yousay, Oh Yeah, this constant, okay, that's nice. A lot of that. I tiwhat topic did that. Come on, thunder. There is a bit of trade brethey're. A strange release. This, it's one of those non topic questions. Three good identities trigidentiever. We used. Trig identities Yeah I there isn't that many identities there you be able to check if it is the other down was after I don't I don't have the answer I'm doubt if that is it that's I don't know it must be it but how do we know how do we know that is the same triangle like as in both of these? Yeah because the center to M2 and sento M1 are both the radius Oh, okay, okay. So that's why they're the same angle. Be God. Hello, we got compuslide. It's okay. It's charged now we'll Yeah, Yeah I'm if it's under trigger identities, I'm doubting myself because we haven't used the trigger identity. Maybe it's another way of between king maybe. Let's what also there? Have we used the 150s? Yeah, we used the 150 air the ratio, but. I'm not sure. I think it should be fine, I bet. Do we know do we need to use that or why is it there? So again, sorry for the Green triangle. Do we need to use our all? No, the watriangle, the Green one. I don't know that that that the Green d triangle just there as a support for the Ferris wheel. That's part of the Ferris wheel diagram. Okay. That's just like it's stunned because they don't give us any numbers for that. Yeah, I'm I'm almost sasit's that it looks a bit weird, but there's not there's not anything else we could do really. So. Okay, happy with that. And let me just see if I have any more questions. That's like. Oh, those one Brillion college trigraph. Now on which of the axes is a sketch of the graph? Oh, that is horrible. Y equals two to the minus x sine squared, x squared. Okay. I can't read the numbers. What numbers have we got? I think the easiest way to do this would be to check some coordinates. So for example, if you look at the top right, one top right, there's something in the negatives. That's the only one that goes into the negatives. So I would I would plug in whatever that x value is and see what happens. And I would assume it's not that one because it's the only one that show is negative. Well. Yeah I think what's the difference between okay, then they start zero. Okay. I was I was trying to decide what was the difference between the first and the last one and see again, I'd plug in x equals zero and just see what happens. So if x is zero, what you get, you get zero, don't you? Because you get one times sine of zero. Yeah. So it's going to be either A, B or c based off of that and then plug in whatever that one with the negative. I'm assuming there's no negatives in this because two is the minus x is never negative and then sine squared will never be negative. So I assume it's not c, which then leaves either a or c. What's difference between a and c? It's just the amount of oscillations, isn't it? Yeah. So what numbers have they got? Are there numbers along? I can't read the scale. Is it one, two, three, four, five? Yeah. And then on the other one, it is the same thing, 0.2, zero point I can't read it as well. What's the x axis effyou? See is the same one, two, three, four, five, six, okay, the same it with less? Yeah, that's peaks. Okay. So how do we work out how many peaks we're going to get? What's going to be the best way to do this? I reckon the best way to do this is can you see so on a between 23, you get y equals in no, you just you just put equal to zero. You you find its roots. If find misyes. So there is about I'll I'll write it down. So what the equation is y equals two to the minus x sine squared of x squared. Is that right? So I would put it equal to zero. And then go, okay, so if this equals zero. Then we get either. Turns the minus x equals zero, which is you're going to have fun with that one or. Sine squared of x squared equals zero. And then you look at is it n degrees? Nice was my ions. I have no one of the axis a skegraph. Which of these axis sketch of that graph? I mean, you could go out. The way I was going to say is you look between 23 on a, there's a robut. On b, it's a lot higher. So you could mess around with the calculator that way. Let's have a look what we got to the power minus x. Ssquared of x squared. And where we want to plug in what we plug it in, x equals somewhere between 23. No, no somewhere between can't right that number 23. So in a between 23 we get. Two maxima and one minima on c. Between 23, we just have a maxima. So between. 23, there's no. I would try some numbers essentially. So let's try or should we try 2.5? Yeah, winner. Okay, I'm doing it with a slider. Let's do that. So if it is. 2.5, we've got 0.00019. So that would imply that x is 2.5. We've got a root. Which means it must be. A okay, he could have how would we go about like that isn't not the most mathematical way. So you could go back to what we've got here and solving this sine squared x equals zero. And then for that. I think we were in radians. So then we're going, what bodies of x do that? And it's square as well. Actually that won't matter thus far. So we've got sine of x squared equals zero. But he looked at radians yet. No, we just do trig identity and we're going to move on to vectors. Okay, I think this is in radians. What is radiance? So radiance is a another unit of angles. So you've got degrees and degrees work by. There are 360 degrees in a full term. And then to one degrees, one, 360 tieth of a full term. The way a radian works, erasion is the angle. So imagine you've got a sector. If the arc length is the same as the radius, the angle is a radian. That again, so if we've got a sector of a circle and this is R, the radius is R and the arc length is also R, then this angle is one radio. Okay, okay, so instead of having 360 degrees in a full time, you've got two pi radians. Okay. I think we'll have to that later. Yeah, I think this is that's a mean question giving you now because I think this only works in radians because the size of x. So one radian is let's like 60 degrees. Basically. So if we were to solve this wewant. All we go test my radians now. So we get x squared equals zero one's our x 101 80. So that's pi over the two. I have two. No, it's no, it's pi. We want the square root of pi. That is horble square root of pi. And then we want 360, which be the square of two pi. So if you Yeah so you could do it this way. And then if you in your calculator, if you type in the square ropi, you will get so that's partly 1.77. If you go back to that diagram, that's the first non zero route. And then the square root of two pi is the one that we were looking at, the one that's about 2.5, I think Yeah 2.506 is the square root two pi. So that would be the more sophisticated way to do it to adberkly. But if you're not doing radians, that's quite mean. Okay. But eliminated the way we eliminate b and d like that, they're the same. Okay, there's no negative. So it can't be. I think it was b that went negative and then D, I don't think D D didn't start zero, did it? Was that along with d? No, we didn't start. Yeah. So so that's that's why we eliminated d because it didn't start zero, zero. Okay. Okay. Yeah, thank you. Was that in the last one for them? Yeah. And I was thinking maybe we could just do some maybe perhaps questions on really like mechanic stuff, like really hard mechanic stuff, but some of the nasty mechanics from from friction, we can do friction or or is it newtonons laws, second laws, police. Okay. I'm trying to think, have we used the textbook questions for the polyet? If we done it, I can't see it in here, so I will upload it, so my drive, I'll play it. Yes, which chapter is it? Year one, chapter ten. Go on, that build I'll do on the mix exercise about all that. Start supported there. And then it should appear that wise, is it not here in there? There we go, slowly converting. So I've got you down for an hour a week. And now, is that right? That's next week. Well, Yeah. What's your half term looking like? I've got three weeks and then I'm off to know about you weeks. Yes, we've got this week, two more weeks and then we're all off a week. Oh Yeah, same this week and then two more weeks and then we offer a, well, how much I'm going do because Chinese New year, that's maybe like once, twice. I just want to check with the same the same week off really because I know I know you like to do more in the holidays, but if I'm at school, it's not really a possibility Yeah or like we can do more in East Thirty half later time. Yeah, because then I'm going to be revising for my some exam. Great ereaster should be pretty much the same. Do you know when you Easter holiday years off the top of your head? And I've got five weeks after I know I know that much. Don't five weeks. I don't know the date of Easter. And I've got the one week off at feand. Then five weeks. That's one, two great for faster than Monday the thirtieth of March. I break up and that's nice to line up. Why? Why is time so quick? Like now so quick? It's not good. Oh gosh. Okay, so done then. We gonna miss that. Okay, so chapter ten is the chapter where please come up in this bit here, which I think is ten f. Ten f is just pulleys. But then the mixed exercise will then have a mixture, obviously everything further on the rather than poly questions which are next here. So there's three Polly questions at the end. Should we look at one of them justraight into Yeah which one do want which one you fancy? Oh sorry, I just asked document. Only 14, and then we'll will do 15 next. Yeah, that works. So 14 hours. Block ckawood a of my 0.5 klograrein a rough horizontal table attached to one end of a light in a sensible string. String pasover a small smooth pulley. First there's are the table. Other end hangs freely. Ball MaaS 0.8. Just instance motion of a from the rough table. Conom matude f system is released from rest string torort. After release, b descends 0.4m in 0.5s, both particles or the acceleration of b okay, what we're doing first, then. Oh, my gosh, seems like so long. Why? First we can find the. The force of a being of being. I mean, you want to do like a diagram? Yeah, draw a diagram. Let get a lot of some Dargon. Can't we? That's 0.8g and this reaction. Is there a reaction? I mean, I mean not reaction. I mean like tension. I mean tension. Yeah, Yeah, there's tension. I think that's totally two forces. That's it for b Yeah okay then Oh my gosh, I memory you. Acceleration of b. After release. Oh, use these two. Yeah so we're use that that info. So this one is actually nothing to do with forces this pie. This is just using our constant acceleration stuff. Guess just suequation. This play. We that know. Distance we do know. Do ashyeah we do this? Sorry. Yeah sorry, I misread ddit we know it down point four. Yeah. So what do we know? We know do we know the initial velocity zero, zero yet? Why don't? Because it's from rest. Do we know the final velocity? Sorry, I'm zero. Maybe no, I know. Remember, distance or displacement should be s that's fine. So s point four. U use super zero we don't know there, do we know way? No, no, it's what they're asking for and then do no t. No. So there you go. What equation links Suu of a and t? We don't know what he is was v, we know we have, we have three. If you know three of them, you're good. You just need. I'm looking for questions. Rooms s equals. So s equals ut plus a half at squared. You don't need to know them. They're in the formula. Look x equto U plus a half 80 square. Yeah and then Yeah, you just plcking what you know. So we know ask we know you, we know t. Probably don't know A A which you want to find. Oh Oh Yeah. Have you got a minus? Is that what that is? Yeah no mintimes Oh sorry sorry. Okay I equal see t plus a half 80 square. Yeah, we go and you go from there. So what does that give us? An eighth 3.2, I think. For two f for a sorry. I'm still doing it. 0.8. 3.2Oh sorry I did add square. I still think that's right. Me sorry. So a half squared is a quarter times by a half is an eighth. So I'm at 0.4 equals a over eight and I'm doing eight times 0.4 to get a is 3.2. But then don't you like square first before you add them together? Yes, you square you square the point five like it a quarter point 25. Okay, and times not by half I think again, jourwhat's going on you got calculator Yeah you type in a half times zero five. Yeah you get an eighth. Yeah Yeah and then that equals zero. So an eighth of a equals 0.4. So your times by the eighth. Targeted by the eight Yeah a divided by eight equals 0.4 more so times by size by eight there. Yeah Yeah happy. Yeah. Okay, okay. Yeah, Yeah. I think I think probably me. I think I need to do more vision on stories. Yeah there's a lot on pulies. Pulies comes up again year two as well when you've done all of the friction stuff. So like this question, they could have had a curefficient of friction instead of A F, make it a bit. You'll also get some questions later on way on a slope instead of a horizontal table, which will make it more fun as well. Well, don't they covered lots there lots lots of questions answered for you. So I hope it was useful and do a of police and applied provisions as well. Yeah we did that. Yeah we'll do small police and then we applied in general. Okay, thank you so much. Welcome to the bit. Thank you. Bye, bye, bye.