Problem

For the following exercises, calculate the center…

Problem 258 Medium Difficulty

For the following exercises, calculate the center of mass for the collection of masses given.
$m_{1}=1$ at $(1,0)$ and $m_{2}=4$ at $(0,1)$

Answer

$\left(\frac{1}{5}, \frac{4}{5}\right)$

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus

Chapter 2

Applications of Integration

Section 6

Moments and Centers of Mass

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Video Transcript

So we're given the following information. M one is equal to one, and it's located at the 10.1 comma zero and then to sickle to four. And it's located that went zero comma one. So if we just pro an axis according it access in place these two points, we have em one at one comma Syria, which is one right here a name to locate at zero comma one, which is this one right here. And with this information, we want to find the center for mass of the system. So you want to find its X and y coordinate. So we know that the X coordinate of the center of mass is gonna be the summation off I from one twin off m want Adams. A pie comes except by divided by the total must capital M and it's white Coordinate. It's gonna be the summation from Icicle to want to win off M one service from M I to why I we brought it again by the total mass of the system Capital M. So let's first find the the total mass of the system. So in this case, we have m I Sorry, m one plus m took two. In this case, it's gonna be fine. So the total mass of the system for this problem is gonna be five. Now, since we have any sequel to two will just be multiplying M one temps x one plus m took du temps except two. And this is gonna be the same for Why? So am someone. It's gonna be one times except one is one plus four times our except to zero our m one for why it's gonna be one and our white coordinates for this particular massacre of zero. Now we'll have our master, which is four times or white coordinate for M two, which is one divided by five. This coordinate right here simplifies to one over five, and this one right here simplifies to for over five. So in this case, our center of mass is located at one divided by five coma for divided by five. And this is a solution to this question.

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