Intro to forces (part 2) | Physics | Khan Academy

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 is gravity acting downwards, giving it its own weight. And then the floor is pushing up on it, giving it a normal force. So many forces acting in so many directions.

If we take a more outdoor example, let's say a rocket. Again, a rocket has its own weight acting downwards, this thrust force acting upwards, and air is resisting and putting a force downwards. So many forces! How do we calculate the total force? How do we find the effect of all these forces together? That's what we want to try and figure out in this video. We're going to 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: "Hey, why can't we just add all the forces?" Well, the problem in that is that force is a vector quantity, which means that it has both a magnitude and a direction. 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.

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 wat"? 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. It is the standard unit of a force.

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 want to have a feeling for that. If you want to feel how big a Newton is, you should pause the video right now and grab an apple. I 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 is about a Newton. You're experiencing a Newton right now! Isn't that amazing?

Now, if you want to experience 10 Newtons, you can imagine it's going to be about 10 apples' worth of force. So 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. In fact, in reality, the forces would be even larger, so maybe you can imagine these are baby rockets 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 to take your rocket, redraw that rocket, but redraw it as a boring box. 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, and now draw all the different forces acting on it in such a way that all the forces start from the center. Here's what I mean. So, here's a thrust force. A thrust force goes up, so I draw it from the center. You see that? I find that much easier to work with, and that's going to be 50,000 Newtons.

So it's going to be 50,000; you know a thousand 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 downwards, so I'm gonna again draw from the center. So it's going to be my weight. That's going to be 10,000, so that thousand is again kilo—10 kilo Newtons.

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, and so this is five thousand, so I'm just gonna call it five kilo Newtons. Tada! 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 surroundings. We're not drawing any surroundings over here. We don't care about the forces acting on the surroundings; we're only drawing the forces on that particular body that we are interested in, freed from its surroundings. 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? Well, when the forces are in the same direction, you just add them up. And when the forces are in opposite directions, you subtract. That's what you do. We can do this in our heads, but this is the first one, so let's just show all the steps.

Let me redraw this. Now I'm going to add these two forces because they're in the same direction. 10 plus 5 is 15. So I get a total of 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 are proportional to the magnitude.

This means that 50 kilo Newton should be way bigger than the 10 kilo—at least five times bigger than this 10 kilo Newton arrow mark that you have drawn. But we don't have space for that, and I'm not going to worry too much about that. So, of course, if you want to be accurate, that's what you should do.

Anyways, finally, we now have two forces acting in the opposite direction. They try to cancel each other out. Forces in the opposite direction don't add up; they subtract. But of course, this is bigger, so this one wins. So what do we get? We get 50 minus 15—that's 35—and this one wins because this is larger.

So the 35 kilo Newton is in this direction, upwards. And so, you see, when the forces are in the same direction, we add, and when they're in the opposite direction, we subtract. 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.

Finally, 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.

Or you can also write this as Sigma F. Sigma stands for summation 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. There 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 valid free body diagram for this. It'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.

But 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 to consider the horizontal forces and the vertical forces separately—that's it! They will be independent of each other; we'll just deal with them independently.

So, if I just look at the vertical forces, 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—so you can also write F_y is 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 Newtons, you have friction over here, so we subtract there in the opposite direction, but this wins.

So you get the net force in the horizontal, which we usually like to call as x, or I can also write this as Sigma F_x. How much is that? Well, that's 100 minus 75; you're subtracting them because they're in the opposite direction—that's 25 Newtons.

And what direction is that? That's leftwards. 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? By the way, whenever the total force acts, whenever forces cancel each other out giving you zero, we usually say the forces are balanced.

Because these two forces are balancing each other, and so we'll say in this case the forces are balanced in the vertical direction. In the horizontal, you can see there are unbalanced forces. The same was the case over here; are there balanced forces? No, they are unbalanced forces over here.

And what I find fascinating is that it doesn't matter what kind of forces we are dealing with. Look, 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?