 Hi, I'm Zor. Welcome to a new Zor education. I would like to move a little bit further, talking about forces from relatively simple cases, which we were considering before, like for instance there is one force which is moving an object in the direction of the straight line the force itself is also directed to the same direction. So these are kind of simple cases. Well, rotation was slightly more difficult, but it's still simpler than I would like to address right now. So this next category of complexity involves multiple forces. So we are talking about cases when an object is a subject of action of many different forces from many different directions in a three-dimensional world. Now, before talking about how these forces act and what's the result of this, I would like to spend a few minutes basically talking about what kind of forces we are dealing with. And I have actually a list of forces which are, well, it's not complete exhausted listing, etc., but these are major forces we will be dealing with in studying physics. Now, the type of force which we have already discussed many times, it's the force when one particular object acts upon another. And it's really like touching it. For instance, I'm pushing the cart or car engine is moving the wheels, something like this. This is applied force. So the force which is really has a close relationship, close in geometric sense, relationship between the source of the force and the subject of the force. Okay, so these are applied forces and we talked about this many times. And obviously, there are many different kinds of this, but more or less they're all related to a close contact between the source of the force and the object which we are moving. Now, next I would like to talk about is the force of friction. We're all familiar with the force of friction. If you are moving an object on a surface, obviously surface has certain resistance, if you wish. Now, the source of this resistance is, well, the surface is not straight and the object is not really straight. Although we were talking about objects as point objects, which have zero geometric size. We still should understand that this is just an abstraction. And in reality, obviously, these uneven surface and uneven object which is moving, they are touching each other and basically these unevennesses prevent the object to basically slide without any kind of resistance from the surface where it's sliding. Well, in certain cases we have an approximation like whenever we are sliding on the ice, there is a very, very little resistance and the person on a skating rink can actually go very, very far without basically moving. He gains the speed and then moves just completely on inertia. Resistance is very small, but still resistance does exist, even in this case, and eventually he will stop, right? So, the friction is caused by this type of unevenness between the surface and the object. Now, what's very important is to measure this particular force, how it can be measured. Well, we will definitely talk about this separately, but in general, I would like you to understand that the more pressure the object has towards the surface, which in horizontal, for instance, case, means just the weight, the more resistance, because these unevennesses are more deeply going into each other. So, basically, we can say that the friction is more or less proportional to how much weight in the horizontal case our object exhausts on the surface. Now, in the non-horizontal cases, there are different actual calculations and we will talk about this later on, but just in general, I wanted to have an impression what is the friction and what's the source of friction is these unevennesses between the surface and the object. Now, to the same category as the friction, we should actually put something which is called air resistance whenever the plane is flying in the air. The molecules of air actually are, well, scratching, if you wish, the surface of the plane and prevent it to go forward. Well, obviously, the plane has a very strong engine and the air does not present such a big, actually, resistance. So, under many circumstances, we can just completely forget about the plane resistance. But if you are talking about higher speeds, then the plane actually does experience this type of a friction. And the perfect example of this is when the spaceship coming down from the orbit into the Earth, well, you know that it gets hot, very, very hot because the air resists and this friction between the air molecules and the body of the spaceship is so great because of the speed is so great that it actually heats up the surface significantly. And the same thing, actually, when submarine, for instance, is under sea, same thing, water resists. And in this case, water is much more dense than the air, so resistance is definitely significant. So whenever my submarine is going with a relatively high speed, it really has to exhaust a lot of energy to overcome the resistance of the water. Next, next is tension. Well, tension is also just yet another kind of force. And the perfect example is if this is a rope and this is the person who basically holds this rope and moves the object forward. Now, the person does not touch the object, it's the rope. So the person pulls the rope how this force which the person exhausts on the rope goes to the object. Well, this is basically what tension is all about. The rope has, well, you can just imagine they have little links and each link pulls another link, that other link moves the next one, etc. And that's how the whole force is transferred to the object. And meanwhile, rope is getting tighter and that's what's the tension. So basically you can say that what actually pulls the object is the tension of the rope. And the source of the tension of the rope is the person who pulls it. So that's basically the tension is always the transfer mechanism of the force from one place to another. Next is elasticity. Ok, elasticity, perfect example is a spring. So the spring can be stretched and when you are stretching the spring from its neutral position, it actually exhausts certain force on the object which is down there which pulls it up. On the same object there is, let's say, weight which goes down. So if object is in a balance in the state of rest, it means that the weight is balanced by the elasticity which is the property of the spring. Now similarly, obviously we can have a rubber or something which is elastic. So elasticity is such a quality, such a characteristic of a material that if it's deformed, then it has a tendency to go back. And if you prevent it to go back, then it actually exhausts the force which is trying to put it back. And the source of this, again, is molecular. That's how this particular material is built inside. If it's a spring, then the material, let's say steel which is usually used for the spring, is such a material which can be deformed. Well, up to an extent, of course, not to break it, but it can be deformed slightly. And then the molecules are kind of stretching or whatever you can call it. And then it attempts actually to go back, unless you stretch it really so strongly that you break it. But that's a different story. They're talking about normal stretching mechanism which doesn't break it. And obviously the quantitative characteristic of the spring is how much effort it actually can make to pull this thing back into the original state of neutral position. Well, it's usually related to how much you stretch it. So the amount of stretch is probably proportional and we will basically talk about this. There is a Hooke's law about this. So the stretching, the more you stretch this spring, the more force it exhausts on the object which is attached to it. Okay? So elasticity force. Next. Next is gravity. Well, we all know what gravity actually is. All masses are attracted to each other. And it's always attraction. Now, we are usually talking about gravity in reference to Earth. So everything has certain weight which is basically a measure of how strongly Earth pulls down the object on it. But don't forget that this particular object pulls with exactly the same force the Earth's. Different story is that the Earth is big and the object is usually small. So the Earth maybe doesn't feel very much how this particular object pulls it. Besides, there are many, many objects on the planet and each one of them pulls in its own direction and all of them might actually be nullifying each other. The Earth pulls everything towards its center. And the surface of the Earth, since it's solid, it prevents us from basically falling down. Because there is another force, the reaction of the surface where we are standing on, like on the floor or on the ground. The reaction is going opposite to the force of gravity. Now, again, gravity is between any two masses. And the perfect example, by the way of this, is the discovery of the planet Pluto. I think it was Pluto discovered this way, or Neptune. I don't remember. One of the planets actually, it was discovered by knowing that another planet is not having exactly the same trajectory around the Sun as it's supposed to by itself, which means there is another body which pulls it somewhere else. And that body was basically discovered by calculations. And then the astronomers pointed the telescope into that place where the calculations predicted should be another planet, which distorts the orbit of, I think, the orbit of Neptune. And that's how the Pluto was discovered. So the gravity. Next, electricity. Well, electricity is in some respect like magnetism, sorry, like gravity, which means it just two electric charges are attracted to each other. But there is a condition. They are attracted only if they are charged with opposite charge. One, as we call it, is positive. Another, as we call it, negative. Let's not delve into what is the reason for positive or negative. Anyway, there are two kinds of charges. Now, in case of gravitation, all masses are the same. They are all attracted to each other. Now, we are not talking about antimatter. That's a different story. But whatever we are actually dealing with is always a normal mass, and all normal masses are attracting to each other. Dealing with electricity, we have two different kinds of electric charge, which we call positive and negative. So positive and negative are attracting to each other. And this is exactly like in the gravitational case. In case of gravity, attraction is proportional to each mass. In case of electricity, attraction is proportional to the electric charge. Now, if, however, you have similar charges, like positive to positive or negative to negative, well, instead of attracting, they are repelling to each other. And the force of repelling is also exactly the same quantitatively as if they were of different charge of the same magnitude and attracting to each other. So that's my electricity. And finally, I would like to talk about another thing called magnetism. Now, magnetism is just yet another physical quality. And in case of, again, it's similar and it's different. It's similar to electricity in such a way that things which are magnetized can be attracting to each other or can be repelling. However, in case of electricity, we can have one object which is charged positively and another which is charged negatively or positively and then we can attract or repell each other. In case of magnetism, any one object has always two things inside it, two poles. One pole is called conditional, it's called north and another is called south. So these are two poles within the same object always. You cannot have one object which is only north and another is only south. No, each object has north and south. And if they are attached in such a way that north and south, they are attracting, but north and north or south and south are repelling to each other. And again, it's relatively the same way it's proportional to the magnitude. The force is proportional to the magnitude of the magnetic of magnetism which this particular object has. So this is a very short introduction into different kinds of forces which we will study separately, each one separately. So now when we know that the research in multitude of forces, let's talk about how the object behaves if multiple forces are applied to it. And in this particular case, I would like to say that it doesn't really matter what's the kind of the forces which are applied to this particular object. Whether it's applied force or is it a friction or whatever, forces are forces. And each force is a vector which means it has a direction and a magnitude. And if these are the vectors and they're all applied to the same object, which again, let me remind you, we are considering a point object which has zero size, which means all of these forces are applied against the same point where a certain mass basically is located. So the principle of superposition which we are talking about today, superposition, this is a very important principle. It states that all these forces combined together which are acting at the same time on the same point object can be replaced by one force which is a vector sum of all the vectors of all these forces. So we are adding them as vectors. And this particular one force which is a vector sum of all the forces which are acting on the object produce exactly the same effect on the object. So object will move in exactly the same fashion if only that one resulting force is applied as all of these forces separately are acting on the object. This is called the principle of superposition. Well, now a couple of examples. If you have a rocket, for instance, which is vertically starting from the ground, you have two forces. One is its own weight, and another is the force which basically the engine develops which pushes the rocket up. So these are two forces. One of them is up, another is down. And if I will do this, which in this particular case since the forces are acting along the same vertical line, this one is down, this one is up, then my result will also be this vertical line and the magnitude will be the difference of the magnitude between f1 and f2, right? So that's a simple case. So this particular vector sum is almost like an algebraic sum. One is a positive, another is negative. And obviously we hope that the magnitude of f1 is greater than the magnitude of f2, otherwise the rocket would not fly. Okay, next. Simple example of car which actually moving uphill. This is a car. What kind of forces are acting on this particular car? Okay, well, first of all, obviously there is a force of its own engine which pulls it uphill. On another hand, there is a weight which goes down, right? Are there any other forces? Well, let's just think about it. If there are no other forces, the car would just go, what's the algebraic, what's the vector sum of this? The car would go down, which doesn't really happen, which means there is another force actually, right? So what is another force? The reaction of the road which it goes along. And the reaction is always perpendicular to the surface of the road, which means there is another vector which is vector of reaction. This is the force and this is the weight. Now some of these three better be in this direction and that's exactly where we are going. And the chase. I mean, the calculations will show whenever we will do this problem in real, we will see that the calculations are actually showing that the resulting force will be obviously along the road uphill. Now why? Well, because this reaction force and this weight are very much related to this angle. So if you will do the calculations, everything will be fine. Car will not go under the ground. It will go along the road uphill. And the third example which I wanted to present is, let's say you have a pendulum. So it goes left and right. Now what kind of forces act on this guy? Now let's assume that it's a vertical plane where this pendulum is moving. So obviously there is a weight here, but it doesn't move down, right? It moves along the arc. Why? Well, obviously there is another force. This is a tension force. Tension force doesn't let it go down. It acts on the same object and it pulls it this way and the vector sum of these would be a tangential line to this arc, obviously. And that's what moves it. And it's always tangential because in this particular position it will be this. So whatever we have, whatever the position we have, the object will move around this point on a circle within this arc left and right. So we always have to consider all the different forces which are acting. And if you miss something, you will have the wrong result, obviously. So in this particular case, don't forget there is a tension here and there is a weight. You cannot do any kind of calculations if you don't take into consideration the tension of the thread, right? Same thing with the previous problem, the car. If you don't take into consideration the reaction of the road, you will not have the correct equation of motion and your car will go under. All right. So basically that's it. What I suggest to you as usually is to read notes for this particular lecture on Unisor.com. And the site Unisor.com is, well, first of all, it's a free site. There is a whole course of advanced mathematics, math for teens. This is the physics for teens. So there is a prerequisite which is a math for teens. And also there is even something called, there is a civics course, US law for teens if you're interested. And again, the site is free, no advertisement. So please use it. Well, that's it. Thank you very much and good luck.