Types of forces and free body diagrams | AP Physics 1 | Khan Academy

In this video, we're going to discuss different types of forces, but we're going to do it in the context of free body diagrams. So let's say that I have a table here, and I have a block that is sitting stationary on that table. What are all of the forces that are going to act on this block?

Well, to do that, to think about that, I can draw a free body diagram where I'm only going to draw the block. Remember, when free body diagrams, you only care about the forces acting on one of the objects in your system. So if we're looking at only the block, what's going on?

We're going to assume that the block is on Earth; we're assuming that it's stationary. Well, if it's on Earth, the block has some weight. You have the force of gravity acting on the block, and so let me draw that in my free body diagram. So you're going to have a downward force, and its magnitude is going to be ( f_g ). We could also call that ( w ).

Even though this block has contact with a table, which maybe has contact with the Earth, weight or the force of gravity is a long-range force. Even if this block was in orbit, even if it wasn't in orbit, it would still have gravitational interactions with the Earth. The Earth would still be pulling on it.

But going back to this free body diagram, if this were the only force acting on the block, the block would accelerate downwards. But we're assuming it's stationary, so there must be another force that is netting out against the force of gravity. And what would that be? Well, that would be the force of the table pushing on the block. This force of pushing in a direction that is perpendicular to the surface of an object is known as the normal force, and its magnitude you could denote as ( F_n ).

Let's do another example, but this time instead of having the block on a table, let's say it is hanging from a string, which is attached to the ceiling. But once again, everything is stationary. Draw a free body diagram for that. Well, once again, I am only concerned with the block. It's still on Earth, we're assuming, so you're going to have the force of gravity acting downwards on the block.

But what's keeping it from accelerating downwards? Well, you might say, "Well, you've got the string that's holding it up." That is pulling on it, and that pulling force is known as tension. So what you would have here is an upward force that nets out against the force of gravity, and sometimes its magnitude is denoted by ( T ) or it might be ( f_t ).

Now, let's make things a little bit interesting. Let's try to kind of combine these things, and we'll actually introduce a new force. So let's say that we—this is the ground right over here—I have a block on the ground, and I have a situation where I am pulling on this block using a rope with a force of magnitude. Let's just call this the force of tension. I am pulling on that block, but the block is not moving.

What would be the free body diagram for this block? Well, I'll do the same thing again. I'm going to draw the block. Now, in the vertical direction, you have the same thing that you saw in that first scenario. You’re going to have the force of gravity or the weight of the block pulling downward on the block, and that's going to be counteracted by the normal force of the ground on the block. The ground is holding up the block, is one way to think about it; it's keeping it from accelerating downwards.

So the normal force is acting upwards. But what about the horizontal direction? I already said that I'm pulling to the right with a force of magnitude ( f_t ). So let me do that on my free body diagram. So this would be ( f_t ). But I said it's stationary, so there must be something that is counteracting that, that is netting against that going in that direction. What force would that be?

Well, that would be the force of friction. We've all experienced trying to pull on something, trying to drag something across the ground, and it doesn't move. And that's because there's friction between the object and the ground. Friction fundamentally could be because the surfaces of the two objects are rough, and you kind of have to grind them past each other. Or sometimes it can even be due to molecular interactions where they're kind of sticky, where the objects are attracted to each other, and you've got to pull past that.

And so in this situation, you have the force of friction counteracting this pulling force, the force of tension. The force of friction is really interesting because it always goes against the direction of sliding; it always goes against motion.

Now, with all of these examples out of the way, let's try to do a more complex scenario. Let's say that I have a shelf, and it has a weight of 10 newtons sitting on that shelf. I have an object that has a weight of 5 newtons, and let's say I have two wires, and everything is symmetric. This weight is right in the middle, and these wires are both at the ends of the shelf. This is wire one, and this is wire two, and they are attached to the ceiling.

For the sake of simplicity, we're going to assume that the wires have no weight. In actuality, they would, but for the sake of this argument, let's assume that they are weightless. What would be a free body diagram for this 5 newton block that sits on the shelf? Well, that one's actually pretty straightforward, and it's analogous to this first scenario that we saw.

You have your block; you have the force of gravity pulling down with a force of magnitude 5 newtons, and that's going to be counteracted by a normal force of the same magnitude but going upwards. So let me make sure I have enough space. So that's going to be counteracted with the normal force, which is going to be equal to 5 newtons upwards.

And to be clear, this 5 newtons—this is equal to the weight, the magnitude of the weight of the object. So that was pretty straightforward—the free body diagram for just the block. It's really important to see that because notice in the free body diagram all you see is the block.

But now let's draw the free body diagram for the shelf. So if I have the shelf right over here, pause this video and try to do that. Well, we know its weight; it's 10 newtons, so we can do that first. So it has a weight of 10 newtons. So the force, the magnitude of the force of gravity downwards, is 10 newtons.

Is that the only downward force? Well, no. You have this object that's sitting on it, and gravity is pulling down on that object with a force of 5 newtons, and that causes that object to push on our shelf. So that pushing force is actually a normal force; it's due to the gravity on that 5 newton object.

But the end result is a 5 newton object is pushing down on our shelf. So what you have is another force that is pushing down. It is going to be a 5 newton force, and really we should view that as a normal force. It's a contact force; it's a pushing force of the 5 newton object on the 10 newton shelf.

So this is going to have a magnitude of 5 newtons. Assuming that it's completely stationary, there must be some counteracting forces here. Where is that going to come from? Well, that's going to come from the pulling forces of these wires. So you're going to have the tension from rope 1. We could call that ( T_1 ), and you're going to have the tension from wire or rope two ( T_2 ).

And because this thing is stationary, ( T_1 + T_2 ) should be equal to 10 newtons plus 5 newtons. So I'll leave you there. We've done a nice survey of various forces you might see in a first-year physics class, and we've been able to think about them in the context of free body diagrams.