**Concept:** Weight, Normal, Equilibrium

Hey guys. So in this video I want to introduce two new forces the weight force and the normal force and also talk about equilibrium. So let's get started. So objects near the earth. Objects near the earth are really any around any planet are attracted to it to the earth or to whatever planet by a force called weight. We've known this so far in fact we've done problems where things fall and weight can be written as a little w It's a force so it's a vector second part of the vector hat and weight is defined as simply mass times g and g I'l talk about that soon as the acceleration of gravity and this is usually down. In fact we're going to assume that the weight is going to be pulling you down. It could be something different. For example if the earth is here and you're here you're gonna be pulled sort of to the left. Right. But in most cases you're going to be on top of the Earth or whatever object could be on top of the earth. So energy is going to be pulling you toward the center of the earth. That's. Correct. So you have to make a distinction between Gravity, weight and this little G which is this gravity concentrate here nine point eighty feet on the earth. Gravity is a natural phenomenon by which objects attract each other. So it's just how the world works right how the universe works. It's the phenomenon that says that its an angle we give to the phenomenon that says that every two objects will attract each other. Weight is the force that happens as a result of that phenomena. Right. It's the main give into the attraction force. Gravity is the fact that two things attract we call the force of attraction between the two weights which can also be referred to as the force of gravity. And finally little g is the acceleration as a result of that force if you remember F equals ma of force gives you an acceleration. So this is a force and this is an acceleration and this is sort of the physical effects or the phenomena. So G is the acceleration of an object that is in free fall. Free fall if you remember means that the only force acting on the object is the force of gravity. So let's draw free body diagram if the earth is here and this object has no other forces acting on it it's going to have the weight force which I'm just going to write as mg pulling it down. So if I write and this is the only this is the free body diagram right there. If I write the sum of all forces on this object. Is the mass of the object times the acceleration. That object is going to have. And the only force is mg in this case mg is going down and say they're going up as positive so this is negative mg equals ma and the masses cancel and I get that negative. The acceleration is negative g. If you're in the earth that's negative nine point eight meters per second squared. And we knew that. And this is just quickly show how did you get to that using basic F equals ma that the acceleration is negative g. Ok so the word gravity gets used you know very interchangeably to talk about a phenomenon sometimes you refer to gravity as a force and sometimes people refer to gravity as little g. But the biggest thing is to realize that little g isn't really gravity. It's not a force it's an acceleration. OK. So let's keep going an object's mass depends on how much matter makes the object that's the definition of mass. How many little atoms do you have and in most physics problems mass will remain constant. In fact we assume that unless it says otherwise. However g and I'm talking about mg over here mass is going to be constant. But g is going to change g depends on the location. So on the Earth's surface g is 9.8. But if you go to the moon g is one six approximately one sixth of that of the earth or approximately 1.6. OK but if you move an object to the moon it doesn't change its mass but g is different. So it's weights will change because little g changes. OK. So let's do an example here. If a bathroom scale says you wait 70 kilograms What is your real weight. OK. So it's important to realize that bathroom's bathroom scales are really traditional scales and they don't really measure your weight. They measure your mass right. Or at least that's what they show you. They don't show you your weight. They show you your mass. So. Your real weight weight is mg and you're own Earth obviously so it's 70 times 9.8. The answer is six six. So even though they're technically measuring your weight they're calibrated to show your mass. Right. Because nobody talks about you know their mass they talk about weight but they're actually using mass to refer to that. When you say that your weight is 110 pounds that's actually your mass. OK. So this is what your real weight is. You have to multiply that by gravity. Cool. Let's do one more example then I want you to quickly try this practice problem right here. So an object has a mass of five kilograms on the earth. So mass on the earth is five. I want to know what is its mass on the moon. And I want to know what is its weight on the moon. So you should remember that the mass doesn't change if you go to a different planet or a different satellite or whatever. So the mass is going to remain five kilograms. But the way it does change the weight on the moon is just mass times the gravity of the moon which is five times 1.6 which is a 8 Newtons. OK. If you were to do this for the earth by the way the weight on the earth would have been five times nine point eight. Which would have been 49 Newton. So you see there's a big difference. OK. So I want you guys to quickly pause the video and try to solve this one and hopefully you get it. I'm going to keep going but I hope you try. So if an object weighs 300 at the surface of the moon. So weight equals on the moon equals 300 Newtons. By the way every time you see Newton's it has to be a weight, right. If you see kilograms or pounds it's mass. So how much does it weight on the surface of the earth. So what is the weight of the object on the earth. Well weight on the earth is mass times little g on the Earth. If I want the weight on the earth I need to have both of these numbers. I know little g I know gravity the acceleration due to gravity on the earth but I don't know the mass some kind of stuck here. So what I'm gonna do is I'm going to go back here. With this information and try to figure it out. So wait on the moon is mass gravity on the moon and this weight is 300. So I'm able to find Mass because I know gravity is 1.6. So mass of the amount of the object is just 300 divided by 1.6 and this runs to 188 Kilograms. Which I'm able to then plug it in here so the weight of this object on the earth is its mass 188 times the gravity of the earth 9.8. And this gives us if we round this to three significant figures you get 1840 Newtons. This is the final answer for this. Hopefully you got it. And let's keep going. So second point that I want to make on this video is that whenever you push against the surface the surface pushes back. This is because of Newton's third law of action reaction so you push on something that something pushes back on you with the same force the same magnitude but opposite direction. When you do this to a surface the force that the surface pushes back against you with is called Normal. Normal and normal can be represented by big N some books and its of the vectors I could do this. Some books will use a little n so that its not confused with Newton which is a big N or the force of normal like this. I'm going to use big N but again a lot of books and a lot of professors will be using little n I'm just used to using begin. So that's probably what I'm really like most of the time. OK. So normal is a reaction. To a surface push if you push on a surface there is a normal force, normal means perpendicular. Right. Normal is just an engineering term. It means perpendicular. And perpendicular and turn means 90 degrees ok. It means perpendicular to the surface. The symbol for perpendicular is a little penis it looks like this. OK. This is the symbol for perpendicular. And by the way the symbol for parallel. Looks like this. So. You can think of this as a penis and vagina, there you go. So. To figure out the direction of a normal force what I can do is if I have let's say a box here I can just get the penis and put it on the surface in the direction that points in the direction of the normal force. So if you have some harder questions like this. We'll see this later. I can put it here on the surface and I see that the normal force points this way.

In the last example I want to show you is if you have a wall of vertical wall this and you have a box and you push the sparks against the wall. The wall is going to push back. With a force normal. This way. OK. So a very very important point is that there is no equation for normal. There's no equation for normal that you can just plug in you are gonna calculate the normal force by writing F equals ma will do a lot of this and you'll see what I'm talking about. But there's no equation. It depends on the situation. And the last point in this video. So again normal's a reaction to a surface push. It means that you have to have a surface to have normal. OK the last point in this video is that whenever forces on an object cancel each other the object is at a state called equilibrium. So you get equilibrium when forces cancel each other. So. Forces cancel each other means that the sum of all forces equals zero. It also means that the net force which is the same thing as some of our forces equals zero. So look what happens if I write some of our forces equals ma. And all the forces equals zero. This means that the right side equals zero. So that means that the acceleration is zero. OK. So. Equilibrium means forces cancels, the sum of all forces equals zero. And it means that acceleration is zero. OK. Now it does not mean no motion it doesn't mean that you're not moving that your stopped. It means no acceleration. It means that your change in velocity is zero. Let me give you an example if you have a car and cruise control right you press your cruise control but what does it do. It moves at a constant speed. So it is moving its velocity is not zero. But its forces have to cancel. How do I know that that's because its acceleration is zero. It keeps the same velocity acceleration zero. So that means the forces must be canceling. And basically what happens is that if you are in a car their some sort of friction that makes you slow down. So thatÕs why if you stop hitting the gas you just let it go. The car is gonna slow down but to avoid that what you do is you have the engine. Push with a force that's the same as your friction. Right. And if these forces are exactly the same. Then they cancel perfectly and your acceleration zero and your car keeps cruising at the same speed. OK so having talked about these three topics I want to do two examples here real quick. So for each of the situations Draw a free body diagram and calculate all the forces on the object so a one kilogram object sitting on top of a table. So one. There is a table. Now this isnÕt really a free body diagram, free body diagram has to be just a dot with forces on it. The first force I'm always gonna draw is mg. And by the way we ignored mg in all previous problems. I didnÕt even talk about it but every object is going to have an mg pulling straight down. And I can calculate this mg right here if I want to. So mg is mass which is one times gravity 9.8. So its 9.8 Newtons. So this mg is 9.8 Newtons. I donÕt have to say that its negative because its going down because I already have an arrow next to it. So we know that its going up. All right. Any other forces Well this 9.8 here thatÕs pulling on this box is making the box push up against the surface. So the surface pushes back with a force and we call that force normal. Now what's the magnitude of that normal force. There's two ways you can do this. The short way is pretty simple. You realize that this box isn't moving from here. Why. Because it says that it sits on top of a table. It's not just magically flying up or it's not breaking through the table. It just sits there. So it's at rest and it's at equilibrium. It's not accelerating. So the forces have to cancel and for the forces to cancel it means that the magnitude of the normal has to be the same as the magnitude of mg. So if mg is nine point eight normal has to be 9.8. I think this is a tug of war. One forces are the ones pulling down and they cancel each other. So this is sort of the fast way where we will see a 9.8 here and right away realized that this has to be 9.8 as well. The long way would be you would write to some of our forces equals ma. But you know this is an equilibrium. So it's really going to be the sum of all forces equals zero.

Right. And because the acceleration is zero. But on the left here I'm going to list my forces. I have two forces. And they equal zero. Now let's list my forces. Normal is positive because it's going up. So I'm going to use the conventional going up as possible keep doing and mg is going down. So it's negative. And then look what happens. Normal equals m g. Which is the same thing I told you earlier without and we did that without having to do all of this just by realizing that the forces had to cancel for this thing not have any acceleration. So this is a long way I get nine point eight which is only the magnitude but I know that the direction is up. OK. So in this situation here I have a two kilogram object that is hung by a light rope. So you're sort of the ceiling. And here's a two kilogram object. And let's just assume the floor somewhere over here it's hung. So it's not touching the floor. I want you to pause the video and do the same thing I did draw a little free body diagram connect all the forces acting in this block and on this object and. Find the forces, calculate the forces. So pause video I'm going to keep going. Hopefully you try it in down here first force I'm gonna draw is mg. And mg is just mass times gravity so it's two times 9.8 So it's nineteen point six Newtons. OK. And then any force is going up. Yes otherwise subject would be accelerating downwards. Hung So that means there has to be a force pulling it up and that force here is a tension. There is no normal. Because it's not pushing against the surface the block doesn't even touch a surface. And tension has to be nineteen point six Newtons because these forces have to be the same so that they cancel each other. If you wanted to do this the long way sum of all forces equals ma. There are two forces but the acceleration is zero. So the side here I can just make is zero. Why because this is at equilibrium. It's not accelerating. The forces are tension up and mg down. So tension equals mg. It's the identical set up that I had last time except now instead of having normal when I have a tension. So this is nineteen point six. And I hope you got that. And that's it for this one.

**Concept:** Equilibrium in Vertical Axis

Hey guys and I want to show you a few more problems of equilibrium in the y axis in the vertical. Let's get started. So remember real quick an object at equilibrium is at equilibrium when its forces cancel. Another thing to remember is that in that situation your acceleration is zero. So forces cancel an acceleration zero. Remember also that weight is a force that acts on all objects that are near the earth or any other plane an asteroid the moon whatever. And we're always going to draw weight first. The reason for this is because weight always exists. weight's just mg. And most of the time it's going to be going down. Now the reason I put a little asterisk here is because even if you're far from the earth you'd still be pulled on with some gravity. But we'll talk about that a little later. Than another thing to remember is normal normal act an object when the object pushes against the surface. So the surface pushes against the object. Right. So we are just normal last normal, normal is just N, We're going to run on the last because sometimes you won't have normal force. Right. So let's do two quick examples here for the following situations draw a free body diagram and calculate all the forces acting on the object. So you push down on a three kilogram mass on a table with a force of 10. So I got a three kilogram object over here chilling on the table and you're going to push down on it with a force of 10. Now remember I don't like drawing forces and pushes them one of them and pulls someone I actually move this over here. F equals 10. The first force I'm supposed to draw is mg graph, the force of gravity weight. So it's going to be mg over here and it's mass and gravity so it's three times nine point eight. And that gives us three times nine point eight gives us twenty nine point four Newtons. OK. And the other forces. Is there a normal force here. Yes why because you're pushing against the surface. So the surface has to push back. Also if you didn't have normal force this would mean that the object would be accelerating down. If you only have forces going down F equals ma tells you that force equals mass and acceleration. So the forces are down. The acceleration will have to be down. But I know that in this case this object sitting on the table. So the acceleration is zero. It is at equilibrium the forces have to cancel. So then if there's two forces going down there has to be one force going out to cancel that. And that's normal. If I'm pushing down with a total of ten plus twenty nine thirty nine point four. So normal has to react with thirty nine point four. OK. In this case normal equals mg plus F. For thirty nine point four Newtons because Normal has to cancel both of those forces. So that's the quick way of doing that so you can just kind of look and say the force going up as to equal the force is going down. So that I have equilibrium the long way would be to write it to some of our forces equals ma And I realize the acceleration is zero so the right side of this equation is zero. There are three forces here so they can do three little parentheses. And that adds up to zero. The forces are normal which is going up. So I can make a positive F which is going down and mg which is going down and I can show you that normal equals positive F plus mg So you can do it this way. Right. Basically by writing that the sum of all forces equals zero and working it out like that. Or. Or you can do it this way you can say all the forces the sum of all forces going up equal the sum of all forces going down. Ok which is basically what I did when I said this has to be 34 because that's the to so these two guys. Now when you do this you ignore the sign so it's really just the magnitude of these forces and the magnitude of all the forces Going up has to cancel all the forces going down. All right. So I want you to try this out. Pause the video and try this. I'm going to draw this for you real quick before you do it. So I have a two kilogram object right here on the string. It's being I'm sorry it's actually being pulled up. It's on a table that's being pulled up. With a force of five or you can call this tention if you would like. Doesn't matter. OK. So I want you to draw a free body diagram with all the forces and I'm going to keep going. But you should pause the video and try this yourself. So the free body diagram would look. I would have mg down mg is two times nine point eight. So this is nineteen point six. And the question here that's the first force I draw the question here is are there any other forces any other additional forces. Is there normal here. Well if I'm pushing if I'm being if I'm pushing against the surface with 19 but being pulled up with a five this five is not enough to lift me off of them off of the table. In fact there is that means that because it's not enough I'm still going to be pushing a little bit against that table. So there's still going to be a little bit of a normal force. OK. The only difference is the setup here is a little bit different. And all the forces going up equal all the force is going down. So I can write N plus T equals mg. I know N I know T and mg so I can find N. N is mg nineteen point six minus T minus five. So normal is nineteen point six Newtons. OK. That's the final answer. And I found all the forces. Now one thing that I didn't do actually is I didn't bother free body diagram exactly how is supposed to be for either one of these problems. Remember free body diagram isn't supposed to be a box it's supposed to be a dot. So technically I got to put a dot and a big dot because I have a bunch of arrows coming out of it. And this is in and this is T. And this is mg. Now if you wanna make this is even more correct you should draw the normal a little bit bigger than the tension. To indicate that it's a stronger force and the mg should be bigger than both of them. That's if your professor is really picky about these. So. That is the free body diagram for this object that looks very much like what I drew here. The only difference is that it's a dot instead of a box. OK. So let's keep going I hope you got that one right. Remember that when we're working with multiple objects we want to begin with the simplest. Object the object has the least amount of things going on around it with the least amount of forces acting on it. So it's usually going to be an object that is at the end of the problem or at the ends of the problem or at the edge. So in this case here it will be the three. And in this case here it will be the four you want to start with those guys first. So very similar. I want to find I want to draw a free body diagram for each and calculate all the forces so let's start with the three free body diagram of the three would look like this. Let's do it right this time with a little thought.

First for someone who drives an mg, mg this is the mg of the three. In the mass of it is three kilograms. That's why I call that the three. So this is twenty nine point four Newtons, first force I draw mg next force. The only other force I have used normal. So I do have normal because this thing is sitting there it's not going up or down it sits there. So these two forces have to cancel I hope you agree that normal has to be twenty nine point four. These two have to be the same so that they cancel. OK let's. And that's my two forces the free body diagram is. This piece right here. OK. Now let me do the four. To the four over here. The four. Has mg it's been pulled down by its own weight by mg 4 which is thirty nine point two Newtons. I get that right. Yep and what else yes the three is on top of the four. So the energy of the three actually pushes down against the four as well. So if you're four the mg of the three is pushing down against you but I'm going to draw that as a pull down here. All right. Let me raise this mess. So I gonna draw this over here. It's a little weaker. Some of the make a little bit smaller. This is mg of the three kilograms. I'm gonna put the value over here to the side. We know this is twenty nine point four. Any other forces where there has to be a force balancing this out because we know that this entire system is equilibrium it's not accelerating up or down. So there has to be a normal force also because I'm pushing against the surface. So the surface pushes back. All right and again I can say all the forces going up cancel with all the forces going down. So normal is mg three plus mg four it's just these two guys added together which is sixty eight point two Newtons oK. So that's it for this one. I want you guys to try out part (b). So pause the video follow the steps and I want you to draw free body diagram for each one of these. And I want you to find these two tensions here. I'm gonna call this one tension one. I'm gonna call this tension two because we're going to do this question this block first and then that block and and then find all the forces and mg is tension, normal if you have any etc. And by the way the floor somewhere down here so she pauses video. Give this a shot. You know how it works I'm going to keep going in but I hope you try, So here is the most out of four. By the way I can do. I can kind of put a four kg here. To signify that that's the 4 right there. I could do the same here three and four. So here are four kilogram first for some of the Draw on it's the mg. This is the mg of the four which is four times nine point eight which is thirty nine point two Newtons. Any other forces. Well if you look at the four it's sitting there right it's not accelerating up or down. So there has to be a force pulling its up. That force is not normal. There is no normal in this problem because it's not touching the floor that forces my tension one. And I know that these two have to cancel so this thing is at equilibrium so this is thirty nine point two as well. These two forces have to cancel. All right so I'm done with this first one. Let's go to the three kilograms. So here are three kilograms. I'm going to draw bigger dots because it there's bigger more forces on it. The first force of all draw is the mg of itself which is three times nine point eight which is twenty nine point four Newtons what else. If you are the three you're also being pulled down by T-1. And you're being pulled up by T2. Now T-1 I already calculated, T-1 what is this. So I just put it here. Thirty nine point two. And if this thing's in equilibrium that means that the forces up cancels the forces down. So T-2 must be the addition of these two forces. Sixty eight point two Newtons. OK. So that's it. That's why you have to work out the force first. And so yeah the four first I can find this T-1which I would then plug it in here. That's why you start from simplest from the edge and then you work your way up in this case. If all you wanted to know is this T-2 here by the way. Look at this T-2 what is it doing it's holding the whole thing. Right. So if all I wanted to find was T-2. I could have said that I'm just hanging three plus four. Seven right. And then I would have an mg of seven times nine point eight which is sixty eight point two. And then I will have a T-2 of Sixty eight point two because these have to be the same. And that answer. Would have been the same. So you can always combine objects. But here I was just working for looking for both T's and other forces. So that's everything that you should have had there. I'm going to do one more example and then we're done. You have a uniform 10 kilograms two meter long chain, so chains kind of like a rope or string holding something. But now it has a mass so it's going to act as an object and it's attached to the ceiling and supports a 20 kilogram object. So let me just draw a few pieces of the chain here. Six little change things. So I'm going to put a 20 kilogram object and the floor's down here somewhere. Cool.

And I want to know the tension at the top bottom and middle of the lake. So it starts with what is the tension here, what is the tension here and what is the tension here these tensions will be different because they're holding different amounts of mass of weight. Right. So let's start with the bottom right here. What is the tension at the bottom. Well look at what it's holding. At that point you're holding a 20 and that's it you're right here. So T bottom all that it's holding is a 20 kilogram. So the mg that it's holding is 20 times 9.8 and that's 196. So Tb has to be 196. If you go to the top of the chain you're holding the whole thing. So if you're at the top of the chain. You are holding the chain itself which has a mass of 10 kilograms and you're holding the object which has a mass of 20. So if you're here. Tension top you are holding both of these guys. So you're going up against a 196 Newtons that's the mg for this guy. And you're going up against the mg for that change because you're holding that as well. So that's 10 times nine point ninety eight. He holds more weight so there's more tension there. And this number is two ninety four. Now if you're in the middle of the chain Tmiddle. You are holding you are in the middle of the chain. This is my single chain here. And if you're in the middle of the chain What are you holding you're holding Tmiddle you are holding the 20 kilogram box. So you're going up against an mg of 196. You're holding a 20 here But also holding half of the chain. So you're also pulling only five kilograms of mass. So there's the mass of the chain right here. mg of the chain which is five times nine point eight which is forty nine. So if I combine these two the tension in the middle is going to be 49 plus one and 96 and that's two forty five Newtons. These things are all forces so they're all Newtons. So again the difference between when you have a rope or chain or whatever that actually has mass it's going to have different tensions in a vertical situation is going to have different tensions at different places because it has to hold its own weight as well. So that's it for this one. Hope it makes sense. Let's go to the next one.

When an object moves very fast in air, the air resistance is proportional to the square of the speed and it is called the drag force: f = Dv^{2}, where D is constant. Assume that a person with mass m jumps from an airplane flying at an altitude h and is subject to the weight and drag only. What is her terminal speed?

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A chain anchored to the ceiling is made up of links, each of which has a mass of 27 g. If the maximum tension the anchor can withstand is 1000 N, and the chain was 100 links long, what is the maximum weight the chain can support without breaking the anchor?

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A chain is made up of links, each of which has a mass of 15 g. If the chain is 100 links long, and supports a mass of 15 kg at the bottom, what is the tension in the middle of the chain?

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A chain is made up of links, each of which has a mass of 15 g. If the chain is 100 links long, and supports a mass of 15 kg at the bottom, what is the tension at the top of the chain?

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A chain is made up of links, each of which has a mass of 15 g. If the chain is 100 links long, and supports a mass of 15 kg at the bottom, what is the tension at the bottom of the chain?

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A 5kg box rests on a flat surface. If a force of 10 N is applied to the top of the box, what is the normal force on the box?

A) 39 N

B) 49 N

C) 59 N

D) 69 N

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