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Numerade Educator

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Problem 34 Hard Difficulty

Calculate the moments $ M_x $ and $ M_y $ and the center of mass of a lamina with the given density and shape.

$ \rho = 4 $

Answer

$M_{x}=12 \quad M_{y}=8$
$(\overline{x}, \overline{y})=\left(\frac{2}{3}, 1\right)$

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Video Transcript

in this problem, whereas to calculate ex moment by moment and central passed off this lemon Elwood trying their shape with a nice job for less first, right, the coordinates off the word sees off this shape. We have two and zero here. We have 03 here, and we have zero is here. Here. Um, we know that X bar is equal to Am I? Why? I say mass times. Why position do I by total list and we know that. Why, Bart, is it going to and my ex? I Some mass times expressions should do I by total ms from this we see that, uh And why, which is the numerator is equal to exports eccentric, divided by total mess. I'm here. We see that ex moment is equal to y bar multiplied by total mess. So let's first find a total mess. Ah, we know that mess is equal to row time sedan city times the volume and were given that this is a lemina. It means that it has a sickness off once with a unit unit thickness sort out a vehicle to go. Ro terms a the area. This is right triangle. So the mess would be equal to that's just given us for an area is, too terms three. Divide by two sort of total mess Here we see as echo, too. Well, all right. Now let's calculate explore And why, Brian Why party? Nord front M y an Imex. So we know that explore for such a shape will be the, uh, charismatic average off the ropes. Sees Senator be escorted. It's mud edit. So zero plus two plus zero Delighted by number of bird species, which is three expert would be to retreat. Why bar White Gordon summed up sort of zero plus zero plus b. Do you want my number for pussies? I got a three by tree and we have one sister vino export. Why Park and total M. We can easily cock let Emma eggs ex moment as why Bryant, which is one times total mess, which is 12. Some of Texas 12 and one moment would then be export, which is Georgie multiplied by total mess. That is 12 and we find that to be eight