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# Total Momentum of a System of Objects

Patrick Ford
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Hey guys. So now that we have a basic understanding of momentum in the next couple of videos will search to see what happens when objects are interacting with each other or that you're going to see often is the word collide. And the key idea of momentum is that when you have two or more objects that are interacting with each other, the momentum of the system is going to be conserved. We're gonna talk about this a lot more detail in the next couple videos. For now. I just want to focus on the words system and in this video want to show you how to calculate the total momentum when you have a system of multiple objects. So let's go and check this out. Remember that? The idea behind the system is that it's just a collection of objects. It's just one or two or even three objects. However many you define in your problem. So the idea here is that I have these two objects right? You've got objects A and B. Just to get to the problem here, I've got the massive A. Is four and the mass of B is five. So they both have mass and they also both have speeds, object A moves to the right with 12 m per second. That's 12 object moves to the left with nines, This is nine right here. So the idea here is that both these objects have mass and speed. So what I can do is I can say this one has momentum P. A. This one has momentum P. B. They both have momentum, but in these kinds of problems I don't really care about the individual momentum's of each object. What I care about is the momentum of the entire system as a whole. And the momentum of the system is just gonna be the sum really just the vector sum to be more specific of each object, individual minds up. So the equation for this is that peace system is going to be the sum of all your momentum's. But most of the time almost always your problems are going to come down to just two objects. So it's gonna be P one plus P. Two. These are arrows. So what I can do is I can rewrite this because I know P is equal to M. V. So if P equals M. V then I could rewrite this as M one V. One plus M two V. To remember these are arrows. So this is how you calculate the momentum of a system of objects. Were gonna be writing this a lot in the next couple videos. So let's go ahead and get some practice. Alright, so like we said we want to calculate the total momentum of the system. This is peace system right here and to do this, we're just gonna add together P. A. Plus PB. Remember these are vectors right here. So what I can do is I can rewrite this and say M. A times V A plus MB times VB. So now what I have to do is look at the problem. So I have one velocity that points to the rights and have another velocity that points to the left. Whenever I had these arrows have pointed different directions, I have to pick a direction of positive. That's going to be super important in these problems. So I want to pick the right direction to be positive, which means that this velocity is positive and this velocity is negative. That's really important here. So now what happens is that r. P system is extremely the massive A. Which is four times the speed of A. Which is 12 and it's positive Mass B. Is five. This is gonna be plus five and then VB is gonna be negative nine. Super important that you keep track of the negatives and positives in these kinds of problems. So what you get here is you end up getting 48 plus negative 45 you get a net peace system of three kg meters per second. So that's the answer. So the idea here is that even though you have some objects that are moving to the right into the left As a whole, your system has three kgm per second of momentum to the rights. All right. So that's it for this one. Guys, let me know if you have any questions.

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