# Centre of mass confusion!

phospho
http://examsolutions.co.uk/a-level-maths-papers/Edexcel/Mechanics/Mechanics-M2/2010-June/paper.php [Broken]

Question 3)

part a) I got the answer to be 2.5 which is correct

part b) I don't really get how to do this, I understand as a new particle is being added which is the same mass of the total frame that the center of mass will change, but how do I figure out how much it will change by?

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## Answers and Replies

Mentor
part b) I don't really get how to do this, I understand as a new particle is being added which is the same mass of the total frame that the center of mass will change, but how do I figure out how much it will change by?
Just like you found the center of mass of the frame by finding the combined center of mass of its pieces, treat the added mass and the frame as two pieces. If you have two equal masses, where will the combined center of mass be?

Homework Helper
The center of mass of two objects of different masses can be calculated as the weighted average of the two centers of mass, "weighted" by their masses.

phospho
Just like you found the center of mass of the frame by finding the combined center of mass of its pieces, treat the added mass and the frame as two pieces. If you have two equal masses, where will the combined center of mass be?

hm well the total mass is 32 as I figured out from part a), and if I do the same thing as I did in part a):

center of BC is (6,0), center of BA is (3,4), center of AC(9,4)

mass ratio for BC will be M, BA, 10, AC, 10 as M is the total mass which I found to be 32 in part a) then taking moments about B to find y bar:

32*0 + 10*4 + 10 * 4 = 32y
80/32 = y = 2.5 which is the same as part a :s

Mentor
You already found the center of mass of the frame. (No need to start from scratch.) Treat that as mass 1. (What are its coordinates?) Treat the added mass as mass 2. What are its coordinates? Now find the center of mass of those two together.