Impulse | Physics | Khan Academy

You know what? I always wondered as a kid, when I took my car and dashed it into a wall, it would just like immediately go and bounce back and nothing would happen to it. But real cars are very different. Real cars are so fragile that, you know, even at modest speed if you were to go and RAM into this no parking board, then it would very easily get dented, damaged, and whatnot.

Well, I used to wonder why real vehicles are not made with much stronger materials that ensure that none of this happens. Well, guess what? Turns out this is a deliberate choice. We deliberately make sure that vehicles easily crumple; they get easily damaged. Why, you ask? Because that actually makes things safer for the people sitting inside.

But how? How does that make things safer for people sitting inside? One way to answer that question is by introducing a new quantity called impulse, and that's what we're going to do in this video. So let's begin.

So where do we start? Well, we'll start with Newton's Second Law, the cornerstone of our physics, right? So Newton's Second Law can be written as—we've seen this in the previous video—we can write it as net force acting on a body equals the rate of change. Sorry, let's use a different color. Okay, rate of change of momentum.

This means that if there's a lot of change in momentum per second, then there must be a big net force acting on it, and if there's a very tiny change in momentum per second, there must be a very small force acting on it. Now, let's rearrange this. Um, let's multiply by the time, delta T, on both sides. So if we do that, we will now get the net force multiplied by the time over which that force is acting equals the change in momentum.

And we're going to box this. You know why? Because this quantity on the left side is what we call impulse. Now the first question that could come to our mind is: why do we do this? Like, why are we just rearranging that same equation and now calling this a new quantity, calling it impulse? Why do we do that?

Well, the short answer is because it helps us gain a new perspective of that same equation. Some perspectives are useful in some scenarios; other perspectives could be useful in some other scenarios. And we will see how this impulse idea is so useful in some specific scenarios over here.

But anyways, let's try to learn more about impulse. We can immediately see from this equation that impulse will always equal the change in momentum, right? Impulse equals change in momentum. That's the perspective we're looking for, actually, and we'll take some examples in a while. But before we do that, can we talk about its units?

Whenever we learn a new quantity, we should try and identify its units. Can you identify its units? All right. Since impulse is the product of force and time, well the unit of force would be Newtons and the unit of time would be seconds. So we could say it is Newton seconds.

I could also, for example, substitute for Newton. Remember, Newton, which is force, is MA. Force is mg, which means Newton should be—um, M, which is kilogram, and A, which is m/s squared. So let me just write that down: m/s squared.

So this should be your Newtons multiplied by seconds; seconds cancel out and we can also say it is kg·m/s. And that's nice because that is the unit of momentum. Remember, momentum is MV, M * V, and look, the unit of momentum is kilogram·m/s. And that's nice because we just saw impulse equals change in momentum, so the unit of impulse should be the same as the unit of momentum.

And that's what we see: the unit of impulse is the same as the unit of momentum. Makes sense, right? Now to see the power of this new perspective, let's take a scenario. Imagine we have two toy cars fitted with rocket engines. The first one is fitted with a giant rocket engine and the second one is fitted with a very tiny rocket engine.

Let's say the first one produces an enormous thrust of 25,000 Newtons, but that rocket will only last for 0.1 seconds. That thrust will only last for 0.1 seconds. Okay? The second one has a much more humble thrust, let's say only a mere 50 Newtons, but this rocket will last—this thrust will last for about a minute.

So now you can imagine this scenario, and the question is: if these two cars are identical, they have the same mass and everything, and they were initially at rest, then after their thrust ends, which car will have more speed? This one at the end of 0.1 seconds or this one at the end of 1 minute?

How would you answer that question? Well, if I didn't have the idea of impulse, then I would think about, okay, I know the force from that; I can try and calculate the acceleration, and then after calculating the acceleration, I'll try to figure out what the final velocity is. Yuck! I'll have to do all of those calculations. But you know what now I can do? Now I can say, hey look, all I need to know is figure out which one has more final momentum.

In other words, I need to figure out which has more change in momentum. The one that has gained more momentum would definitely have more velocity. And what decides that? What decides that is impulse. See, the change in momentum only depends on the impulse. So all I care about—I don't care about the individual force and how long the force acts; I care about the product because it's the product that decides the change in momentum.

So in my head, I'm now thinking, hey, whichever has the bigger product will end up having a bigger change in momentum and therefore we'll end up having a bigger final velocity. So which one has the more bigger product? Which one has a higher impulse? Well, let's see.

For the first one, the impulse—and the symbol that we use for impulse is J. Don't ask me at this point why you use J for impulse, but I think that's what we use. But what is impulse over here? It's Force multiplied by the time over which that Force acts. So force is 25,000 Newtons multiplied by 0.1. Will that become one decimal? Will shift. It'll be 2,500 Newton-seconds. That's the impulse here.

And of course, impulse is a vector quantity, which means its direction is important. And since the force is to the right, the thrust is to the right over here, that means impulse will also be to the right direction. This means its momentum will change towards the right; it'll gain momentum towards the right side, and that makes sense.

And what's the impulse here? Well, the impulse over here is going to be the same thing: force multiplied by time. Well, the time now, if I use seconds, I should use seconds over here. So 60 seconds. So 50 * 60, 5 * 6 are 30; that's 3,000 Newton-seconds.

Look at that! This has a bigger impulse. So now I can immediately say, aha! Therefore, this will have a larger change in momentum, therefore this car will be faster at the end of its thrust compared to this car. Isn't that amazing? I could literally do this in my head without having to do a lot of calculations. I could answer that question.

So remember, what decides the change in momentum? It's not the force alone; not the time alone; it's the product. So whenever you want to think about how much the momentum changes, all you got to say is, I just want to care about that product; how much is the product? How much is the impulse?

All right, another example: another question. You drop a couple of eggs from the same height: one on a very hard rock and the other one on a very soft pillow. We know the one that lands on a rock will crack, but the one that will land on the soft pillow will probably not. Why? Well, we might think that it's because it's softer. You know, if you have softer things, it cushions, and it doesn't— you know, the forces over here would be smaller compared to over here.

But why think about why? We can now answer that question using the idea of impulse. Think about it: because they were dropped from the same height, just before hitting—just before these eggs hit the, you know, the rock or the pillow, they had the same velocity because they were dropped from the same height. So they had the same velocity, right? Which means they had the same momentum. The initial momentum just before hitting was exactly the same.

What happens after hitting? Will their momentum again become the same? Because their momentum will be zero; they'll come to a stop, of course. But their momentum becomes zero, which means the initial momentums are the same; the final momentums are the same. So their change in momentum is the same.

In other words, if the change in momentum is the same, the impulse delivered to both these eggs are exactly the same. Ooh, interesting! So the impulse here is exactly the same as the impulse here, and I say, I'm talking about impulse at the point of impact, okay? The impulse is exactly the same.

But there's a difference between the impulse here and the impulse here. The difference is, when you land on a pillow, because the pillow is soft, it gives a little bit; it can deform. Because it can deform, the egg can actually get embedded a little bit over there. It can travel a little bit more over there, which means it takes more time for the egg to stop.

In other words, because it is softer, the time over which that momentum changed was large. It took more time for that egg to stop compared to over here. The rock is not soft at all; it's very hard, which means it doesn't give. It doesn't allow it to embed itself; it doesn't deform, and so the egg almost stops instantly.

In other words, the time over which that impulse acted—the force acted—was very tiny. Now think about this: we know the impulse has to be the same. This means the product of the force and the time must be the same, which means if the time is bigger, the force will be smaller. If the time is smaller, the force will be bigger.

So notice over here, because the time is big, the net force acting over here would be very tiny. But since the time over here is much smaller, the net force acting over here is much bigger. And there you go! Now we understand exactly why hard things put a bigger force.

Because the momentum changes very quickly, and then you have an impulse with a very small time, we get a much bigger force. Isn't that amazing? So long story short, if you want things to crack, we make sure you have very hard collisions. This means that you make the time of contact very small, make the momentum change very quickly, you'll end up having big forces.

On the other hand, if you don't want to break things, you want to have softer collisions, which means you want that time of impact to be much bigger, and therefore the force ends up becoming much smaller. Beautiful, right?

Now we can come back to our original question. Let's say our car was made up of very strong, almost indestructible material. Then what happens when it goes and just rams into it? Well, it's going to stop almost instantly, just like the toy cars that we have over here.

Or maybe it'll bounce back, but in all that case, what happens is the time over which that collision lasted would be very tiny—just like over here. So we're dealing with a hard collision over here, meaning we're dealing with much larger forces of collision.

Now, that's not bad for the car because the car is made of indestructible material, but that's bad for us because we will also stop almost instantly, and therefore the forces acting on us will also be much larger. That's bad for us.

On the other hand, what if the car has some crumple zones? Well then, what happens is that crumple zone will allow that car to travel slightly further before coming to a stop. In other words, it allows that car to take more time before coming to a stop, kind of like what happened over here.

Because of that, the time of collision is increased, and as a result, the forces acting over here would be much smaller. Now, because the car is fragile, the car gets damaged, but that's fine. An even smaller force will be acting on us compared to over here, and therefore this is much safer.

And you can now see how airbags will further increase the time over which our bodies come to a stop, further increasing this number, further reducing the net force acting on our bodies. Beautiful idea, isn't it?