Newton's third law | Physics | Khan Academy

Earth puts a force on an apple making it fall down. But the question is, does the apple put a force on the Earth as well? And if it does, is that force bigger, smaller, or the same? That's what we want to find out in this video.

Now, to try and answer this question, let's start with some familiar examples. Consider kicking a ball. When you kick a ball, you put a force on the ball. Does the ball put a force back on your leg? Well, yeah, because your leg does get hurt a little bit, right? I mean, if you want an extreme case, imagine this is an iron ball, and you're kicking it very hard. Now you can imagine that foot really, really hurting.

So yes, when you put a force on the ball, the ball also puts a force back on you. When you kick the ball, the ball kicks you back. Let's take another example. When you're pulling up, you are putting a force. You’re putting a downward force on that bar. Okay, now that force is actually over here, but I'm just putting it over here. Okay, you're pulling down on that bar, so you put a force on that bar down. But then why do you get pulled up? Ooh, that means that bar is also putting a force on you.

So what we are seeing over here is when one object puts a force on the other, the other puts a force back on the first object. So coming back over here, we could now use this, and we could guess that, hey, if the Earth puts a force on the apple, maybe the apple also puts a force back on the Earth as well. But now comes the big question: which force is bigger? Well, for that, again, let's come back to our familiar examples.

What if I kicked the ball harder? Well, now you can imagine your leg getting hurt slightly more than before. In other words, the ball also kicks you harder. Interesting! What happens if you pull on the bar harder? Hey, you get pulled up quickly as well. That means, ooh, the pull-up bar also puts a harder force on you.

Okay, now I'm going to save you the trouble. People have measured these forces, and it turns out that these forces are always of equal magnitude. And that's what we call Newton's Third Law. Newton's Third Law says that when A puts a force on B, B will put an equal and opposite force back on A.

Now we can also write this in the form of an equation. We can say that the force that A puts on B will always be equal and opposite to the force that B puts on A. Think about it. You put a force on that ball; the ball puts an equal but opposite force back on your foot. You pull down on the bar; the bar will pull up on you with an equal and opposite force. And the same thing applies over here. Whatever force the Earth puts on the apple, the apple will put an equal but opposite force back on the Earth. Newton's Third Law.

But wait a second! I have a huge problem with this. We're saying that the Earth and the apple put the same force on each other, but if that is the case, then why is it the apple that accelerates very quickly towards the Earth, but the Earth doesn't accelerate very quickly towards the apple? Ah, now we're talking about acceleration. When it comes to acceleration, we have to think about not just the force but the mass as well.

Remember Newton's Second Law! It says the acceleration is the net force divided by the mass. If objects have a huge mass, they have a lot more inertia, and this makes it much harder for them to accelerate. So now think about this: the Earth has a huge mass, and therefore it's much harder to accelerate. And therefore, when you put that force on the Earth, it'll hardly accelerate. The mass is humongous, so for all practical intents, that acceleration is zero.

But when you put that same force on the apple, that force is exactly equal. But the apple has a much tiny mass, and so because it has a much smaller mass, it's much easier to accelerate the apple. That's why when you put that same force on the apple, you will see a big acceleration on the apple. And since our eyes can see the acceleration, and we usually don't think about the masses, that's why we make a mistake thinking that, hey, if there's a big acceleration, there must be a bigger force acting on it. That's the mistake we tend to make.

But be really careful about that! Newton's Third Law has no exceptions. The two pairs of forces will always be equal regardless of their velocities, regardless of their accelerations. Wait a second! I have another problem with Newton's Third Law. If the forces are always equal and opposite, always, then shouldn't the forces always cancel out? Shouldn't the forces always be balanced? There should never be an acceleration, right? Like, what's going on?

Again, that's an interesting question. But think about it: these two equal and opposite forces are always on different objects. For example, when I kick the ball, the first force is on the ball, and then that equal and opposite force is back on the leg. These are two different objects. Now, for example, I'm thinking about doing the physics for this football. Let's say then I won't care about the leg in my free body diagram. I will only think about the forces acting on the ball.

There might be this force because of the kick; there might be other forces acting on it. And I'll take the net force of that and divide it by the mass to calculate the acceleration. Notice the force that comes on the foot is no longer in my equations, okay? Because I don't care about that. So since these two forces are always acting on two different objects, they will not cancel out.

Okay, another question that we could be having is that in a lot of places, you will see Newton's Third Law written as action and reaction. Every action has an equal and opposite reaction. I don't really like that wording, mainly because words like action and reaction make us feel like we're talking about some kind of an action that you're doing, right? But when it comes to Newton’s Law, we're not talking about any action. We're talking about forces! It's only applicable to forces and nothing else.

So because there's a chance of misconception, I usually don't like to talk about that. But there's another big problem with using the words action and reaction. See, reaction usually happens after action. So again, this might make us feel like you know, you first hit the ball, so this is the action force, for example. Then the ball hits you back as a reaction force; you might think like that. But it turns out that's not true! These two forces always happen at the same time.

When you're kicking the ball, at the same time, the ball kicks you back. It's not that one force happens before the other. It happens at the same time! The forces last for the same time as well. Similarly, when you are pulling down on the bar, at exactly the same time, the bar is pulling back up on you. Since these forces act at the same time and they last for the same time, that's why again the words action and reaction can be highly misleading. So I'm just going to get rid of that.

Okay, the last question that we could be having is where would Newton's Third Law be applicable when it comes to, say, problem solving? For example, it's mostly applicable when the force on one object is given to you, but you're asked to do the calculations in the physics—or maybe, say, asked to calculate the acceleration of the other object. For example, let's say we're given that, hey, a fish is swimming in water and it's pushing the water back with a force of 10 Newtons.

So this 10 Newtons of force is on the water. But now what if we are asked to calculate the acceleration of the fish? How do we calculate that? Because we don't know the force acting on the fish. Well, this is where we can use Newton's Third Law. Well, if the fish pushes the water back with 10 Newtons of the force, then the water will push the fish forward with exactly an equal but opposite force—so 10 Newtons of force as well!

So now that I have that force, and if there are other forces acting on the fish as well that's given to me, then I can calculate the net force acting on the total force acting on the fish, and then I can calculate the acceleration of it. Another example, another familiar example could be when you fill up a balloon with air and you let go of it. What happens? The balloon flies off. Why does that happen?

It's a classic application of Newton's Third Law. You can see the balloon is pushing down on the air with some force. Now, according to the Third Law, the air pushes back on the balloon with exactly the same force in the opposite direction. And it's that force that makes the balloon go up.

And yes, if you're wondering, rockets also work on a very similar principle. Now, of course, rockets are way more complicated than a balloon filled with air, but at the end of the day if you're thinking about the forces over there, the rocket puts a lot of force on the hot gases that come out, and the gases will put a lot of force—a equal and opposite force on the rocket itself—making the rocket accelerate upwards. But of course, there's a lot more going on when it comes to rockets.

Okay, let's take one last example before wrapping things up. We have Batman standing on the ground, and we know that gravity is pulling down on him. But the ground puts an upward force on him, the normal force. Are these two the equal and opposite forces that Newton's Third Law talks about? Why don't you pause the video and think about it.

Well, the answer is no, because remember the way I like to think about it. For me, the biggest clue is that the equal and opposite forces are always acting on two different objects. Think about this: always on two different objects. But here, this gravitational force is acting on Batman, and the ground is pushing up on Batman. So this normal force is also acting on Batman. So these cannot be equal and opposite forces that Newton talks about.

In fact, these need not be equal. There are cases in which the normal force can be bigger or smaller than the force of gravity. So to wrap this up, what are the equal and opposite forces of these two forces over here? Well, if you think about gravity, I think about it. Earth pulls down on Batman; therefore, Batman will pull up on Earth. That is the equal and opposite force of this one.

What is the equal and opposite force of this one? Let's see. The ground pushes up on Batman. That's how you do it! You just state the sentence and then reverse it. So the ground pushes up on Batman; therefore, Batman will push back down on the ground with an equal and opposite force. So the equal and opposite force of this one will come on the ground.