Conservation of momentum

- [Instructor] Check out this carom shot. We see that the black coin goes, so here is it if you look at it again black coin goes and hits the blue coin. Now imagine we knew the speed at which the black coin is coming and hitting the blue coin. The question is can we predict with what speed the blue coin takes off? Well, we can solve problems like this by using forces and Newton's laws and accelerations and everything, but it might take a lot of steps. In this video we'll see a shortcut. And this shortcut is based on one of the most powerful principles of physics called the conservation of momentum. So we'll explore what this principle says, why it is so powerful, and we'll also use that to explore how rockets work. Okay, so what does conservation of momentum mean? Well, first of all, remember what momentum is? If you take the mass of any object and multiply it by its velocity, then that number is what we call momentum of that object, right? So what does conservation of momentum mean? Well again let's bring back our carom example. Let's say we looked at the situation before collision, before the black coin hits the blue coin, and let's say we calculated the total momentum of both these coins. Meaning you calculate the mass times velocity of this coin, you calculate the mass times velocity of this coin, and let's say you calculate its total value, which we'll call total initial momentum. Initial means before collision over here. And then, let's say you look at the situation after collision, after the coin hits it, and then again calculate the total momentum. We'll call this the total final momentum after collision. Then, this principle says these two will be equal to each other. Think about what this means. You see, after the collision, the black coin has slowed down. It has stopped actually and the blue coin has speeded up. So clearly their individual momentum has changed, right? But the principle says the total value will not change. So even after the collision the total momentum remains the same. And that's why we say the total momentum is conserved. That's the meaning of conservation of momentum. So this might bring so many questions to us like are there any other examples of this, or why does it even work, and does it always work? And, why do we even care about this? So let's try and answer all these questions one by one. So let's start with why do we care about this? So what? What's the point? Well, this principle helps us solve problems on collisions in few steps. So let's take an example. Let's put some numbers to this. I have zoomed in so that we can see this better. So let's say that the mass of the black coin is 10 units. Let's not worry about the units. Let's keep things simple. We'll solve more rigorous problems in other videos. And let's say the blue coin has a mass of 15 units. It was a little heavier than this one. Okay, now if the black coin was coming in with a velocity of say six units, the question is with what velocity would the blue coin take off after collision? How do we solve this? Well we can use conservation of momentum to do that. First let me change the background though because I want to use the same colors and it's not visible on black. Okay now to use conservation of momentum first we need to calculate the total momentum before collision. That will be mass into velocity of the black coin which is gonna be 10 into six plus the mass into velocity of the blue coin which is 15 into zero because the blue coin is not moving at all. It's at rest. That should equal its total momentum after collision. Again that's going to be mass into velocity of the black coin which now is 10 into zero because now the black coin is at rest. That what we saw. After collision it comes to rest. Plus 15 into v which is mass into velocity of the blue coin. And v is what we need to find out. And if you look at this we have setup the equation. Now if you just simplify, we can calculate what v is. So on the left-hand side this goes to zero so we get 60. On the right side this goes to zero we get 15 v, which means we get 60 equals 15 v and if we divide by 15 on both sides we get v equal to four. 60 by 15 is four and that's our answer. So the blue coin after collision takes off with the speed or with the velocity of four units. So within few steps we were able to calculate what is the velocity. Imagine we didn't have this. Then we will have to use force and acceleration and maybe use some of Newton's laws. Ah, that would be so tedious! But with conservation of momentum within few steps we get the answer. That's why we love it so much. Now although this principle is amazing, it has a condition: it doesn't always work. But before we look at what that condition is let's quickly take some more examples and see this principle in action. Take this rifle for an example. Not to encourage violence but it's a good example of this principle. Now before firing the bullet both the bullet and the gun are at rest. So the total initial momentum is zero. Now what happens after firing the bullet? Well once you've fired the bullet (whoosh) the bullet gains a forward momentum. But the conservation principle says if the initial total value was zero even the total final momentum should also be zero. It should remain conserved. It should be same, right? So then how does this conserve momentum? Well, you might know that the gun recoils back. But not just that. To make the total momentum zero the gun gains an exactly equal but negative backward momentum. So that now again if you calculate the total momentum it still remains zero. Momentum gets conserved. Cool, right? And think about this. The more bullets it keeps on firing the more backward momentum it keeps on gaining and the gun can actually speed up. And that's how rockets work. They don't shoot out bullets of course but instead they shoot out hot gases downwards giving them a downward momentum, and you can think the rocket sort of recoils upwards. And since it's continuously shooting these gases down the rocket continuously keeps recoiling up gaining speed conserving momentum. That's how rockets work. So now that we looked at some examples of where it works, the next question we might have is why does it work? Why should momentum be conserved? Well, we'll look at a complete mathematical proof in a separate video but let's try to get some sense for it. The main reason for this is Newton's third law. Again let's bring back our carom board example, and when the black coin goes and hits the blue coin it puts a force, a forward force on that blue coin and as a result the blue coin gains some momentum. However according to Newton's third law the blue coin will put a backward, equal and opposite backward force on the black coin and as a result the black coin loses an exactly same amount of momentum because the forces are exactly equal. And as a result see what's happening. One coin gains some momentum. The other coin loses the same amount. And so as a result can you see the total value remains the same. And that's why after a collision the total momentum has to remain the same. It's just like money. Think of momentum as money. Imagine we have two kids who have a total of 400 rupees and let's say you know one person decides to transfer 50 rupees to another. Now she will gain 50 rupees, he will lose an equal amount 50 rupees, but the total will still remain 400 rupees, isn't it? So just like this during the collision the momentum got transferred from one body to another. That's it. And as a result the total value still remains the same. Thinking of momentum as money really helps me understand this. Finally does this principle always work? Answer is no. It will work as long as there are no external forces acting on our bodies. What do we mean by that? Well again let's come back to our carom example. As long as these coins keep putting a force on each other their momentum will stay the same. It's like how as long as these people keep exchanging money within themselves the total money will remain the same. But what if there's a third person who starts putting a force on these coins? So lets say the carom board starts putting a frictional force on this coin. Now the coin will slow down and the momentum will get transferred to the carom board. Right? And since the carom board is not a part of our equation, we're not considering its momentum in our equation, now the momentum of these two coins will definitely change. This is what we call is an external force. It's a force acting by a body whose momentum we're not considering in our equation. Again if you come back to the money example imagine there is a third kid whose money we are not considering in our equation. And if these people start, you know, exchanging money with this kid now their total money will definitely change. It can change, right? But of course if we consider the money of all the three kids together then that money will still remain conserved, isn't it? In a similar manner if we consider the momentum of all the three things the two coins and the carom board then the momentum will still remain conserved. Right? As long as there isn't a fourth body which starts putting an external force like for example the floor might start putting friction on the carom board. Makes sense, right? So what did we learn in this video? We saw that if there are two bodies or more who start putting forces on each other then you do Newton's third law. They will always put equal and opposite forces and as a result they'll end up transferring momentum from one body to another. And so the total momentum of all the bodies together will remain the same, which is what we call conservation of momentum. This works as long as there are no external forces. Meaning there shouldn't be forces acted upon by bodies whose momentum we do not consider in our equation.