Newton's second law & momentum

- [Teacher] While playing cricket, you may have noticed that whenever people catch a ball, they always move their arms down like this. Why do they do that? Why not just catch a ball this way? Well I'm pretty sure you might know the answer to this. It hurts a lot to catch it like this, right? However, for some reason, when you move your arms down, it hurts less. But why? Why does that happen? A similar question could be; when you fall on a hard surface, it hurts. Yup, that hurts a lot, please don't try this at home, it seriously hurts. On the other hand, we know that if you are falling on something soft like a cushion or maybe in my case a bean bag, it doesn't hurt much now. But why? Why does falling on soft surfaces doesn't hurt us but falling on hard surfaces do? Now the answer to these questions might seem obvious but it isn't and there are a couple of ways to answer this. So in this video we are going to use momentum to answer this question. So, what's momentum? Well, momentum, P is defined as the product of mass and velocity. And we can think of it as a number that tells us how hard it is to stop a moving body. For example, if you take a very massive freight train moving very fast with very high velocity, then it has super high momentum because it's extremely difficult to stop that. On the other hand, if you take something very, which has a very tiny mass like a ball of cotton moving with modest speed, then it has very low momentum because it's extremely easy to stop that, it almost stops effortlessly. Anyways, since in this video we want to answer questions like why it hurts more? Or it hurts less in certain situations. We need to talk about the forces that are acting on our bodies or on our hands, right? Which means we need to somehow connect force and momentum. And that's basically what we want to do in this video. So, where do we start? Well we can start from Newtons second law, because it has an equation for force. It says the net force acting on a body equals the mass of that body times its acceleration. And just to give you a brief recap of what this means, the word net force means that if there are more than one forces acting on a body, we have to calculate the effective value. For example, let's say there is a sailboat and imagine there is wind that is pushing that boat forward. Now, we might know that when you're trying to move through water, the water tends to slow you down, and it does that by putting an opposite force, a force in the opposite direction which you're trying to move. So in this example there are two forces acting, right? And so, to calculate the net force, we have to subtract them because they are in the opposite direction. If they were in the same direction, we would add to calculate the net force. Now notice when you subtract them, they don't cancel out exactly, because the force due to the wind is a little larger. And so when you subtract them, a little bit remains and that now is the net force that's going to act on our boat. And what does the equation say? It says as this force that's going to accelerate our boat, it's going to change the speed of our boat. So this means, if that net force is larger, if that force is bigger, that means our acceleration is going to be larger, that means this boat is going to change it's speed very quickly. On the other hand, if that net force is very small, so if this net force is very small, then the acceleration would be very small. That means the boat will change it's velocity but it will change it very slowly, somewhat like this. And if you need more clarity on these equations, we have spoken a lot about them in previous video's. So it will be a great idea to go back and watch them. Anyways, over here we want to bring momentum into the picture, right? And so, what we have to do now is we write this equation in terms of velocity. How do we do that? Well we can write acceleration in terms of velocity. So, let's say that even before the application of the force, even before the net force, the boat was already moving. Let's say it already had an initial velocity, let's call that as U. Now, when that force, that net force acts on it, it's going to accelerate that boat, it's going to increase it's velocity in this case. And as it is...let's say, after some time, it has a new velocity V. Then, the acceleration is gonna be change is velocity divide by time. So this means we can write this now as the net force equals mass times the change in velocity divide by time. What's the change in velocity? Well final velocity's V. Initial velocity is U divided by time T. Okay? And now let's just go ahead and simplify this, see what we get, and solve one of the brackets. Then we'll get M times V, minus M times U, divided by T. And let's look at what we have over here now. We have MV, which is mass times the final velocity of that boat. That represents the final momentum of our boat. And similarly this is the initial momentum of that boat. Oh, this means, I'll write that over here, the net force acting on our boat equals the final momentum of that boat, which I'll call as PF, F for final, minus the initial momentum of that boat, divided by the time, T. Okay, but what is this equation telling us? Well, just like over here, the change in velocity divided by time means how quickly the velocity of an object changes. Over here we have change in momentum divide by time. So the right hand side is telling us how quickly the momentum of an object changes. And the equation is saying that equals the net force. Oh, this means, if we come back to the example of the boat. This means if the momentum of that boat changes very quickly, there is a big force acting on it. On the other hand, if the momentum of that boat changes very slowly, it means a small force is acting on it. And if you're wondering, well we just saw this a little earlier, right? Then yes, it's the same thing. Earlier we looked in terms of acceleration. Now, we're looking at that same thing in terms of momentum changes. So, quicker the momentum changes, bigger is the force acting on an object. So let's see if we can use this to answer our initial question. So if you look over here, when you catch the ball this way, look at how quickly the momentum of that ball is changing. I mean if we go back, before making the contact with my hand, the ball has some momentum over here. Now look at how quickly it goes to zero. Boom! Gone! It immediately stops, within one or two frames. Gone. Since the momentum is changing so quickly, a big force is acting on that ball. On the other hand, over here, look at what's happening. The momentum of that ball is changing very slowly. Let's look at it one more time. Again, the ball has some momentum over here, before hitting my hand. Now look, once I catch it, the ball is not at rest. The momentum has not gone to zero yet because my hand is moving. It's moving. Right? And so, it's not gone to zero. It's still taking time. It's still taking time. It's still taking time! Look at how long it takes for that momentum of that ball to go to zero! So that swinging action makes sure that the momentum of that ball changes very slowly. And as a result, the force acting on that ball, will becomes very small. And so this means your hand is pushing on that ball with a small force. So, so why does it hurt more over here? Well Newton's third law. If you are pushing on that ball with a big force, the ball will also push back on your hand with a big force. And that's what makes your hand hurt. Over here, since your pushing the ball with a small force, the ball will also push on your hand with a small force, and doesn't hurt as much. Okay, now can you use the same reasoning to think about why it hurts so much when you fall on a hard surface. And it doesn't hurt that much when you fall on a soft surface. Good. Pause the video and give it a try. Okay, so when you take a fall on a hard surface like this, again your momentum quickly goes to zero. Let's look at that. So, this is just before your hand makes contact with the ground. Now notice how quickly it stops. In the next from it's gone. Stopped. Look at that. Boom! Stopped. Can you see? Momentum change happened super fast. And because of that, the force acting on my hand, on my knuckles over here, is gonna be super high. And that's why is pains a lot. And I'm not acting over here, that really hurts, so please don't try this at home, On the other hand, over here when you're falling on the bean bag, the momentum changes very slowly. Again, let's look at it in slow motion. All right, here it is. I start making contact with the bag, as you can see over here. And now let's see how long it takes to stop. Okay, it's not stopped yet. It's not stopped yet. You see? Because the bag can formed, it allows my hand to travel further, and as a result it takes a long time for the momentum to change. It's not stopped yet. Not yet stopped. Look at that! Look at that! It's still moving! It's still moving! Maybe, maybe some of it over here it stops. And because of that, because the momentum changes very slowly, the force acting on my hand over here is very small. Of course it's another reason which you don't have to worry too much about, but let me just tell you. Another reason why it hurts so much less over here, is because as the bag deforms, more of where my hand comes in contact with it. And as a result, that force actually gets distributed over a larger distance and so it dilutes out. And that's why it hurts, it hardly hurts over here. It doesn't hurt much. On the other hand, over here there's no deformation, and so all that force got concentrated on my knuckle, because that's where the contact was happening. And that's why it hurt like crazy over here. One last beautiful example I want to talk about is if boxers ever get punched in their face, they don't do this. This is not what they do. They aren't trying to stop that punch as quickly as possible. And now this makes sense right? Because if they do, if they keep their neck muscles tight, and they try to stop that punch very quickly, that means the momentum of that hand changes very quickly. And that means a huge force gets delivered. Instead, they do something called "Ride along the punch". Which might look somewhat like this. Okay, now that's a bit of an exaggeration, but you get the idea, right? So the idea is they keep their neck muscles loose and they make sure that the hand doesn't stop immediately. Which means the momentum of the hand changes very slowly, and as a result, the force delivered on that hand will also become a little smaller. Meaning it could hurt much lesser than this, this could be a knockout. And so by looking at all these examples what did we learn? We learned that the quicker the momentum of a body changes, the bigger the force acts on it. And this is technically written as the "Rate of change of momentum", which is the same thing as saying how quickly a momentum changes equals the net force acting on that body. This statement is the same as this equation, just writing it in words. And this is also another version of Newton's second law. And so the second law has two equations: One, this one F equals MA. And the other one which we just learned today. And you can derive one from the other. And sometimes in the exams they ask you to start from this equation and derive F equals MA, in that case you do the derivation backwards.