Vectors question requires answering please help?

I need help with the following vector question i have worked part a) out and that answer is correct, but i am struggling to find b) out, any help would be of great help.


The position vectors r1,r2,r3,r4 of four masses m1,m2,m3,m4 are given by:-


r1=(10,16,17), r2 =(16,16,18), r3 =(4,13,14), r4 =(3,9,12)


Masses are m1=5, m2=6, m3=8, m4=10.


Centre of mass R =m1r1+m2r2+m3r3+m4r4 divided by m1+m2+m3+m4.


a.) Find position vector of centre of mass, i have worked this out myself and it is correct= (7.1724,12.7586,14.65517).


b) Mass m4 is to be moved to new position, the 3 other masses remain in their original positions. m4 is to be moved so that centre of mass moves to (11,12,12) find the new position of m4. Answer of vector to be in form (a,b,c) where a,b,c are the components

Vectors question requires answering please help?
Easy!





Write the new centre of mass as





R = (m1r1+m2r2+m3r3+m4(r4+x)) / (m1+m2+m3+m4)





where x is a vector, and r4 is the original location





Now, since you know m1, r1, m2, r2, m3, r3, m4, r4 and R, you just need to resolve the components, find vector x using simple algebra, and the new position of m4 is r4+x.





I'm pretty sure that will give you the right answer, but since I haven't run it through to the end, I don't know for certain, but when I started writing this, you had no other answers, so it's better than nothing. Frankly, I don't have time to do this, and I should be doing other things.





Hope it helps, anyway.





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Edit:


Looking at it now, it's even simpler than that. Surely you don't need to put r4+x, just put the new position is x, and solve m4x instead of m4(r4+x).





Anyway, I'm busy...





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Edit:


I hate these questions. I know I can do them, so it's too irresstable not to!





a = 17


b = 9.7


c = 7.2





Sums done in a bit of a rush, and in my head, so no guarantee of accuracy. That's what I make it, anyway.





Now, I've rekindled the memories of being a student, and I'm glowing in the memory of good times past. I must move on now. I've got more important things to do...

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