11. Momentum & Impulse

Intro to Center of Mass

# Center of Mass on Y Axis

Patrick Ford

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Alright, everyone hopefully got a chance to solve this one. We have these three weights and we're given the coordinates of where they are on the Y access and we want to find the center of mass of these three weights. Remember the center of mass is just if you could collapse all of these into a single object, where would that be located? So what I'm gonna do is I'm going to draw a Y axis, that's my Y axis and this is the X. Like this. And basically I'm gonna draw out where each of these things are. So the first one is a one kg block er waits at two m positive. So I'm gonna say this is the plus Y axis. So I'm just gonna draw this out. It doesn't have to be perfect. So this is going to be um my one kg And my wife value is two. The next one is a 1.5 kg at the origin. So in other words at the origin here, we have 1.5 kg and finally we have a 7.5 kg at negative 1.5 m. In other words, if this is negative one, this is negative two, it's gonna be somewhere in the middle here and I'm gonna draw a really, really, really big dot. Alright, so this is gonna be 7.5 kg. Alright, so if you could collapse all of these into a single object, where would the center of mass B before we even start calculating anything. Remember the center of mass tends to sort of skewed towards the higher mass. So in other words, this one here which has a higher mass than anything else, is probably going to have the center of mass to be very close to it. Right, rather than the other two. So how do we calculate this? Remember we just have an equation with this for X. The center of mass. Where you just do em one X one, M two, X two. As many objects as you have. The only thing that's different is that we're just doing in the Y axis now. So we have Y. X. For our Y axis, center of mass. We're going to do M. One, Y. One, M. two, Y 2 & M. three, Y 3 And then divide by the total mass. So m. one M. Two, M. three. All right. So basically this M. One here, we're gonna have to just assign which one is M. One which is M. Two. Which one's M. Three? It really doesn't matter the order in which you do it. So, this one could be M. One or it could be M. Three? It doesn't matter. You still get the right answer. I'm just gonna call this M. One. What does matter is that you keep the positions consistent? So, if this is M. One, this has to be Y one. If this is your M. Two, this is going to be your Y. Two which is zero And then your M. three And then your Y three is going to be negative 1.5. All right. So that has to be consistent. So just plugging this stuff in, we usually have one times two plus and then we have 1.5 and if it's the origin then the Y. Apple Y. Value is just zero and that whole term goes away and then we have 7.5 times negative 1.5. The negative does matter in this case because that's the position. Right? So now we divide by the total mass which is one plus 1.5 plus 7.5. All right. So when you work this out, what you're gonna get is you're gonna get let's see two plus. And this is gonna be negative 11.25 divided by a grand total of 10. And when you work this out, what you're gonna get is a negative 0.93 m. That is your final answer. So, that's where the center of mass is located. And if you were to draw this out, this would be somewhere around here, somewhere like right under right above the negative one mark. This is where your center of mass is. And that makes some sense. Again, the center of mass should be sort of in the middle of all of them, but it's gonna be skewed towards the higher mass on the bottom. Alright folks, so that's it for this one

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