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The masses m; are located at the points P Find the moments Mx and My and the center of mass of the system ` M1 = 2, m2 = 1, m3 P1(2, -5), P2(-3, 3), P3(3 , 5)...

Question

The masses m; are located at the points P Find the moments Mx and My and the center of mass of the system ` M1 = 2, m2 = 1, m3 P1(2, -5), P2(-3, 3), P3(3 , 5)

The masses m; are located at the points P Find the moments Mx and My and the center of mass of the system ` M1 = 2, m2 = 1, m3 P1(2, -5), P2(-3, 3), P3(3 , 5)



Answers

The masses $ m_i $ are located at the points $ P_i $. Find the moments $ M_x $ and $ M_y $ and the center of mass of the system.

$ m_1 = 5 $ , $ m_2 = 4 $ , $ m_3 = 3 $ , $ m_4 = 6 $ ;
$ P_1 (-4, 2) $ , $ P_2 (0, 5) $ , $ P_3 (3, 2) $ , $ P_4 (1, -2) $

To find, um X. We have to do the summation off the masses with their respective Why coordinates and to find and why we need to do summation of the masses with respect to the X coordinates. So for MX, we get for into minus three plus two into one plus four into five. And for em why we get for two plus two into minus three, close for him to three. So our MX is 10 and R N Y is 14. And now, in order to find the X and the Y coordinates first we need decimation of the masses, which will equal 10. And then from the given formula, our X coordinate will be. And why Over the total mass, which is 14/10 1.4 and the Y coordinate, we'll be. And next over the tour s, which is 10/10. What you need want one

In this problem, we're given three messes. Andy coordinates. Those messes are located. Where has to find the moments in exile y directions as a lesson to Central press office system. We know that why movement is summation off mess times distance about origins of it'll be four times two plus two terms native three plus three, uh, or less Director masters four times three and that is 14. Ex moment will be an eye. Why I saw mass times. Why position? So that it will be four times negative. Three plus two times one plus four times five and that is equal to 10. We know that X bar so central meson extraction is in my ex I divided by summation off mess that is the Y moment, which is 14 divided by summation of Mass four plus two plus four that is 14 over 10 and that is equal to 7.5 or 1.4. And why bar is equal to M X, divided by summation of total mess and a mess. In the first part, we found one. It's 10 summation off mess here. We found it as 10. So what Bars? Look at it. One. So the center of mass is looking at you that negative or positive one over four and one

Yeah problem. We wish to find the center of mass of the given system of mass is where we have four muscles and one is equal to eight according negative 44. M two is 605. Eb three is 364 at f four is five, negative three negative five. This question is challenging our understanding of center of mass, an application of integration in the realm of physics. To solve. We must remember the center of mass of a plane. Is the coordinates X by Y. Bar. Where expires this expert is the some of the products of the masses and coordinates for X divided by total mass and wine bar identically is the some of the products of the masses and Y coordinates divided by total mass. So just all we find the three quantities. The expo numerator is some M I X equals negative 32 plus 18 minutes, 15% to 29. Similarly why bar is 49 and the total mass is simply 22. From this we plug into our center of north korean formula in order to solve so. Senator Mass is going to be negative 29 22 X 49/22 and Y. This is not simplify further. So this is our center of mass

Problem. We wish to find the system center of mass for the four masses. The system where I'm one, it's for negative 12. M two is three at coordinate 23. M three is three at coordinates 45 and M four is five coordinate 36. This question is challenging understanding of center of mass and application of integration in the realm of physics to solve. Remember at the center of mass on a plane is X bar wine bar where exposure is the some of the products of the masses and X coordinates divided by total mass and wine bar is identically the some of the massive products of the masses and Y coordinates divided by total mass. To solve the center of mass, we therefore have to derive the four quantities given thus we have expert numerator, some M I X equals negative four plus 6 to 12 to 16, 29. Using the four masses and X coordinates. Similarly, we find Wiebe are equal to 62 and at the denominator or total mass is simply 15. From this. We plug in these quantities into our formula to obtain center of mass 29/15 for X 60 or 15 for why we cannot further simplify so this is the final center of mass


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