Intro to forces (part 2)

0:00- [Instructor] Everything around us is being pushed and pulled in so many directions. For example, you may be pulling on a couch with your applied force, but friction will oppose that. Then there's gravity acting downwards, giving it its own weight, and then the floor is pushing up on it, giving it a normal force.

0:14So many forces acting in so many directions. If you take a more outdoor example, let's say a rocket. Again, a rocket has its own weight acting downwards, this thrust force acting upwards, air is resisting and pulling a force downwards. So many forces. How do we calculate the total force?

0:31How do we find the effect of all these forces together? That's what we wanna try and figure out in this video, and we're gonna do that by drawing something called the free body diagrams. But before we do that, the first question that could come to our minds is that, hey, why can't we just add all the forces?

0:50Well, the problem in that is that force is a vector quantity, which means that it has both a magnitude and a direction. And whenever you're dealing with vectors, you can't just add them up. You have to take care of the directions, and that's what we'll see, how to do that.

1:04And the next question that could pop up in our minds is, what's the unit of a force, right? Like, how do you put a number to it? Like, force is 100 what? What's the unit of a force? Well, the standard unit of a force happens to be something called a newton. Yes, it's named after Sir Isaac Newton, and we use capital N to represent that.

1:24That's the standard unit of a force, and whenever you learn a new unit, the first question you should have is, how big is that unit? So how big is a newton? We may have a feeling for that. And if you wanna feel how big a newton is, you should pause the video right now and grab an apple.

1:44I mean, seriously. Do that. If you have an apple around, just grab it, hold that apple in your hand, and the force that the apple is putting on your hand right now, that is about a newton. You're experiencing a newton right now. Isn't that amazing? And so now if you wanna experience 10 newtons, you can imagine it's gonna be about 10 apples worth of force.

2:07So now that we've defined what the unit of a force is, let's put some numbers over here and see how to calculate the effective force. Let's start with our rocket. So here are some numbers. Yes, these are big numbers because rockets have huge forces acting on them.

2:23In fact, in reality, the forces would be even larger. So maybe you can imagine these are baby rocket or something. But anyways, these are the numbers. These are the forces. How do we figure out the total force acting on the rocket? What do we do? Well, the first step is take your rocket, redraw that rocket, but redraw it as a boring box.

2:46And the reason we do that is because we want to not worry too much about the pretty picture and nitty gritty details. We want to just focus on the forces. So the first step is to draw a box, and you can draw whatever shape you want over here. So that's my rocket. Okay?

3:02And now, draw all the different forces acting on it. And you draw it in such a way that all the forces start from the center. Here's what I mean. So here's a thrust force. So thrust force goes up, so I draw it from the center. You see that? I find that much easier to work with.

3:18And that's going to be 50,000 newtons. And so it's gonna be 50,000. 1,000 can be written as kilo, just a short form. So I will just write it as 50 kilo newtons. And you have weight that's acting downward. So I'm gonna, again, draw from the center. So it's gonna be my weight. That's gonna be 10,000.

3:38So that thousand is, again, kilo. 10 kilo newtons. And there's also air resistance. Now, even though air resistance is acting from the top, you can draw the forces wherever you want. You can move the forces around. So I'm gonna, again, draw it from the center.

3:55And so this is 5,000, so I'm just gonna call it 5 kilo newtons. Ta-da! That's a free body diagram. Congratulations. Our very first free body diagram. It's called a free body diagram because we are freeing the rocket from its surrounding. We are not drawing any surrounding over here.

4:15We don't care about the forces acting on the surrounding. We are only drawing the forces on that particular body that we are interested in, freed from its surrounding, and that's why it's called a free body diagram. Okay, now that we've drawn this, how do I calculate the total force?

4:30Well, when the forces are in the same direction, you just add them up, and when the forces are in the opposite direction, you subtract. That's what you do. We can do this in our heads, but since it's the first one, let's just show all the steps. So let me redraw this now.

4:46I'm gonna add these two forces because they're in the same direction. 10 plus five is 15, so I get a total 15 kilo newtons acting downwards now, and I have that 50 kilo newtons acting upwards. And by the way, if you want to be really super precise about drawing the free body diagrams, you need to make sure that your force vector arrow marks be proportional to the magnitude, which means that 50 kilo newtons should be way bigger than the 10 kilo, at least five times bigger than this 10 kilo newton arrow mark that you have drawn.

5:19But we don't have space for that. I'm not gonna worry too much about that. So, but of course, if you want to be accurate, that's what you should do. But anyways, finally, we now have two forces acting in the opposite direction that try to cancel each other out.

5:32Forces in the opposite direction, they don't add up. They subtract, but of course, since this is bigger, this one wins. So what do we get? We get 50 minus 15. That's 35, and this one wins because this is larger, and so the 35 kilo newton is in this direction upwards.

5:54And so you see, when the forces are in the same direction, we add, and when they're in the opposite direction, we subtract, and you keep doing that and you get your net force. And there we have it. The total force acting on my rocket is 35,000 newtons upwards.

6:12Finally, another last notation is if you want to write it in a sentence, or mathematically if you want to write it, we write this as the net force. That's the word we use. Net means total force, okay? And of course, we should always put an arrow mark on top of it because that's a vector.

6:28Or you can also write this as sigma F. Sigma stands for submission because we're summing up all the forces. Anyways, that is 35 kilo newtons. And since we're dealing with a vector, it means it should always have a direction, so we should show the direction some way.

6:45There are multiple ways to show the direction. The easiest way is to just draw an arrow mark. And so there we have it. That's our net force acting on the rocket. All right, let's move on to our couch. Let's put some numbers over there as well. And I want you to try and draw a free body diagram for this.

7:05It's a little bit more complicated than the rocket. Yes, I see that, but why don't you take a shot at it? Don't worry about getting it wrong. Try it, and then let's do it together. All right, here we go. That's our free body diagram. Pretty much the same as what we have over here, except that our couch has now become this beautiful square.

7:26But the problem is that we have forces in both the vertical and the horizontal. We didn't have that problem over here, so what do we do? Well, the solution is you consider the horizontal forces and the vertical forces separately. That's it. They'll be independent of each other.

7:42We'll just deal with them independently. So if I just look at the vertical forces. Look, we just have to have two equal and opposite forces, we just subtract them, and when you subtract, you get zero because they're equal in size as well. So immediately, I can say the net force in the vertical, and for vertical we usually use Y.

8:03So you can also write FY. That's zero. And this is a vector. So this is telling me there is no net force acting in the vertical. They're canceling out. What about the horizontal? Well, in the horizontal, the applied force wins, right? You have 100 newton. You have friction over here, so we subtract.

8:22They're in the opposite direction, but this wins. And so you get the net force in the horizontal, which we usually like to call as X. I can also write this as sigma fx. How much is that? Well, that's 100 minus 75. You're subtracting them because they're in the opposite direction.

8:41That's 25 newtons, and what direction is that? That's leftwards. And so what's the total effect? What's the total force acting on the chair? Well, there's zero in the vertical, but there's 25 newtons acting leftwards on this particular chair. Amazing, isn't it?

9:00And by the way, whenever the total force acts, whenever forces cancel each other out giving you zero, we usually say the forces are balanced. That makes sense because these two forces are balancing each other. And so we'll say, in this case, the forces are balanced in the vertical direction.

9:19And in the horizontal, you can see there are unbalanced forces. The same was the case over here. Are there balanced forces? No, there are unbalanced forces over here. And what I find fascinating is that it doesn't matter what kind of forces we are dealing with.

9:33Look, whether we're dealing with air resistance, tension, friction, it doesn't matter. As long as you're dealing with the force, we know it's newtons and you can just add and subtract newtons this way. Isn't that beautiful?