Alright, everyone. Hopefully, you 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-axis. 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 going to do is I'm going to draw a y-axis. That's my y-axis, and this is the x-axis like this. And, basically, I'm going to draw out where each of these things are. So, the first one is a 1-kilogram block or weight at 2 meters positive. So I'm going to say this is the plus y-axis. So I'm just going to draw this out. It doesn't have to be perfect. So this is my 1 kilogram, and my y-value is 2. The next one is a 1.5-kilogram weight at the origin. So, in other words, at the origin here, we have 1.5 kilograms. And finally, we have a 7.5-kilogram weight at negative 1.5 meters. So, in other words, if this is negative 1, this is negative 2, it's going to be somewhere in the middle here, and I'm going to draw a really, really big dot. Alright. So this is going to be 7.5 kilograms. Alright. So, if you could collapse all of these into a single object, where would the center of mass be? Before we even start calculating anything, remember that the center of mass tends to skew 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 be very close to it, right, rather than the other 2. So how do we calculate this? Remember, we just have an equation for x as the center of mass, where you just do m1 x1, m2 x2, as many objects as you have. The only thing that's different is that we're just doing it on the y-axis now. So, we have ycm for our y-axis center of mass. We're going to do m1 y1, m2 y2, and m3 y3. And then, just divide by the total mass. So m1, m2, m3. Alright? So, basically, this m1 here, we're going to have to just assign which one is m1, which one is m2, which one's m3. It really doesn't matter the order in which you do it. So this one could be m1 or it could be m3. It doesn't matter. You'll still get the right answer. I'm just going to call this m1. What does matter is that you keep the positions consistent. So if this is m1, this has to be y1. If this is your m2, this is going to be your y2, which is 0, and then your m3 and then your y3 is going to be negative 1.5. Alright. That has to be consistent. So just plugging this stuff in, we usually have 1 times 2 plus, and then we have 1.5. And if it's at the origin, then the y-value is just 0, and that whole term goes away. And then we have 7.5 times −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 1 + 1.5 + 7.5. Alright. So when you work this out, what you're going to get is you're going to get, let's see, 2 plus and this is going to be −11.25 divided by a grand total of 10. And when you work this out, what you're going to get is a negative 0.93 meters. 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 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 going to be skewed towards the higher mass on the bottom.
Alright, folks. So that's it for this one.