 Hi, I'm Zor. Welcome to a new Zor education. I would like to continue talking about the concept of mechanical work and This lecture is about so-called golden rule of mechanics. Well, it's obviously a catchy name it's all about work basically and The previous lecture where I introduced the concept of work and defined it basically for certain cases This is the foundation right now. It's kind of a repetition and One particular very important property of the work, which is called golden rule Will be just illustrated in a few examples Now this lecture is part of the course physics 14 14s presented on unizor.com I suggested to to go to use this Website unizor.com because not only all the lectures are properly comprised into into a course with corresponding menu parts chapters subchapters, whatever you call it And also every lecture has very important and detailed notes Which you can just read as a textbook Plus there are exams For those who would like to be challenged and the site is completely free. There are no advertisements So basically I do suggest you to use the site and the menu you go to physics 14 course then mechanics and in this particular case Go to to the work Chapter and then you will find this lecture Okay, so let's consider Whatever we were talking about in the previous lecture. I was defining the concept of work and I will Do basically a repetition more or less and I will emphasize this so-called golden rule in every case So my first case was When you have a straight line movement of an object and you have the force a constant force Which is basically accelerating this object along its straight line trajectory Now we have derived a very important formula that if you start Acting with this force at certain point where the object is at rest and then you finish it at certain point Where the object has developed the speed? V so act and so your force is acting on this distance s and the force is F and The mass is m then f times s is equal to m v square over 2 Now what I would like to emphasize here that the purpose of acting of This force is to develop certain speed. It's like you're Starting the car. You're pressing the gas pedal. You're accelerating as soon as you reach certain speed You basically just maintain this speed so this Segment of this straight line acceleration is related to the force Which pushes the car forward and it's related to the Final speed Which you have achieved during this acceleration period now? What's important is that this speed v depends on the product f times s the force times Distance and that's what we have called W which is work now What is the golden rule of mechanics in this particular case? Well, the golden rule is that you have to preserve f times s if you would like to achieve certain speed the Which means you can increase the force but by by certain ratio, but then you can actually Achieve your speed by the correspondingly shorter distance or vice versa you can Decrease the speed the force and Increase the distance and the result will be the same So it's the result which is important the final speed v and what's the golden rule if you are well losing let's say in in in Force which means you have to really Exhaught exhort more efforts. All right, you have to use the bigger engine Then you can win in distance which means you can achieve the same goal in a shorter distance or Alternatively, if you would like to win If you would like to lose for instance in distance by winning in force So you can spend a little bit less efforts, but then you will lose in Distance because you will have to Go for a longer Distance to achieve the same The same speed the same final goal why you are actually applying the force. So again lose the force win this is the distance Lose the distance win the force. That's basically the golden rule You always have to preserve this product and that's what basically this golden rule is all about my next Example is very much like this one and again. It was exactly the next example in the previous lecture, right? Was talking about slightly more General character of the movement what if your force acts at the angle and my example was for instance, you have a toy train on the track and the child is basically pulling with with a rope or a thread with a little bit With with it with an angle towards the track then the difference between this and this is Only that instead of f you have to put f times cosine phi This is five because this is projection to this force. This is Another component. So this force is represented as some of these two and this one is basically balanced by Reaction of the track, right? So it's this piece, which is f times cosine of phi Should be substituted in this now phi is a constant obviously Because the child is moving also the same way as the train is moving along the tracks So again, you have f times s being a constant so again, which means you can basically Win in the force by applying it a little bit less, but then you will have to move For a longer distance you will lose in the distance or you can win in the distance have it a shorter But then you will lose the force because you have to apply more force Same golden rule of mechanics Now my next example was and the gain level Illustrate it exactly the same way as in the previous lecture if your purpose is to lift above the ground level by the kite H certain object By pulling it up with the force f now if this is the distance s and The object has a weight p What we came up with is that the f times s is equal to p times h Again, that was my third example in the previous lecture. What does it mean exactly the same as before? you can use a Weaker force Let's say you have a slope like this It's easier to move up This slope then this slope why because f should be equal to p times sine phi that's how I would To to basically smoothly move without acceleration obviously you need To have this force equal to To p times sine of this angle. So if the angle is smaller the force can be Smaller because the angle will be smaller and the sign will be smaller. However My s which is equal to h divided by sine of phi Would be longer So that's why the product Regardless of the angle phi the product f times s will be always P times h the weight times Times the height so again you are decreasing this angle You will win the force because you can apply smaller force But you will lose in distance because the distance will be longer and wise words if you want to apply a stronger force a Bigger force whatever your You basically lose in efforts because you have to exhort more efforts But you will win in distance because this one is shorter than this one. So again Win in this losing that Win in that losing this Same thing golden rule Now my last example is Now by the way, what was the purpose of this particular? Example, which I was just talking about with a incline. Well, the purpose was to lift the object to the height h So and that is the purpose and it requires certain amount of work. That's it. It doesn't matter how more Steep-slope slope will require stronger force on a shorter distance. It's a less steep slope it will require less of the force but longer the distance But if the product which is important and the product is the work so the purpose is height and the amount of work is W and they are related Force and distance can vary as long as their product is the same Now and the same kind of a concept, which I did not really talk about in the previous lecture But I think it's kind of important if you have a lever where you would like to basically lift this particular Weight now The the regular thing is this should be shorter, right? This is LP Now this is the force Well, I shouldn't really put the force this way. I should put it perpendicularly Okay, apply force F. Now. This is LF So this arm is LF and this arm is LP and what we can Say basically that You always have to Apply the force Which is balanced by by the weight And that's the minimum actually force which you should really apply Now if you are pushing vertically down And this is vertically down and this is some kind of an angle phi Then obviously the force which is perpendicular to this To this arm Which is basically the force which rotates it, right? It's equal to what? So this is phi So What else is phi Between this and this this is phi, right? And this is phi So the force F Uh perpendicular, let's call it FP and this is just F The force perpendicular would be would be equal to F times What cosine phi Same thing here You have P. You have P and you have P perpendicular Which is equal to P times cosine phi Now what's important is That if you compare these two forces FP and PP, which is perpendicular forces to the arm You always have to have the balance between the moments of these forces Because this is how Uh Equilibrium in Rotational motion actually can be reached which means FP times L Force times this this times this should be equal to PP times LP, right? now Since FP and PP are nothing but F times cosine Phi and this is P times cosine phi And L we have this equation Where cosine phi is Going out and we have the most important Equation in this particular case now What does it mean? Well, that's basically Means exactly the same as before We probably should Use the concept of work, but concept of work is related to force and the distance it's it's applied to right? So if we are moving with certain During the certain distance to lift up this thing and let's say again the distance is is is is phi then the S uh, phi S Fee is equal to Times L F times angle Right, so if we are moving from this position to the horizontal position To lift up our weight. We have to move it by angle phi and the lengths of the Arc which we are actually moving On this side would be equal to S F, which is radius times phi And on the right side Um, we will have Times S P which is equal to P times LP times the same angle phi Which means that if alpha F times L F is equal to P times S P then F times S F Which is by phi greater would be equal to P times S S P, which is also by the same phi Equal so we have an equation F times S F is equal to P times Uh, S P Now this is the purpose We have to lift by certain distance along the arc and this is The work Basically, right? Well more precisely the work is F P But what's my point is in this particular case That F P is probably by a factor Different from F and P P is by factor Different from from the P. So the equation is still the same And since equation is still the same, we have exactly the same principle here Because this is the constant. This is the purpose we would like to achieve And this is the work which we have to spend to achieve this We have to perform not spend perform to achieve this goal And again you can reduce the force But you can have a longer arm Then it will give you longer Distance this force is acting upon right And you will achieve exactly the same result So you can win in the force, but you will lose in the distance or again you can Win in the distance have a shorter Lever But then you have to apply greater force to achieve the same result because it's the product which is important The work which is important again the golden rule Win in one losing another winning this losing that So basically my point was for this all these Examples which I have Considered basically again more or less the same as before To show that a concept of work is extremely important in mechanics and it's related To the goal to the result to the purpose if you would like to achieve certain purpose Then you have to perform some work Nothing comes for free That's what it is actually And again how you spend how you perform this work is In most cases kind of irrelevant Now in this case, for instance, we are not talking about you move down and then up and then down and then up again To achieve the same goal. No that would be waste, right? We're talking about more kind of a normal situation So you would like to lift it up push it down. That's it. I mean some simple case In these simple cases where there are no Waste or something like this You have to you have to perform certain work and that work actually is It's a quantity. So based on whatever you would like to achieve you can Calculate this part and that means it's equal to this part, which means it's required to perform That much work basically Now again, how is your business? Longer arm Weaker force shorter arms stronger force Whatever as long as the work is performed And that's why it's very important characteristic in mechanics the work now, obviously We will gradually introduce the concept of energy and work is basically kind of a Very much related to the concept of energy But that will be in the next lectures Okay, that's it for today. Thank you very much and good luck