# Vector based problems

1. Oct 3, 2007

### smileandbehappy

1. The problem statement, all variables and given/known data

A christmas decoration consitse of a 15 gram ball at (1,1,1), a 5 gram ball at (2,-1,0) and a 10 gram ball joined with thin wires. Where should the decoration be placed if the decoration is to balance at the origin?

2. Relevant equations

3. The attempt at a solution

Err... well not that much. I have worked out that the 3rd ball is going to have to blance with the other two but thats about it. Can you please NOT do this for me but rather nudge me towarsds what i should be doing.
Many thanks

2. Oct 3, 2007

### Sourabh N

For balancing, centre of mass should lie at origin. Do you know how to calculate the position of centre of mass of 3-body system?

3. Oct 3, 2007

No i dont.

4. Oct 3, 2007

### Sourabh N

For an n-body system, COM = (M1*r1 + M2*r2 + ... + Mn*rn)/(M1 + M2 + ... + Mn).

5. Oct 3, 2007

### Sourabh N

for (1,1,1) : r = $$\hat{i}$$ +$$\hat{j}$$ +$$\hat{k}$$

6. Oct 3, 2007

### smileandbehappy

i get the answer to be (2.5, -1,-1.5) is this correct?

7. Oct 3, 2007

### Sourabh N

Nope. It should be (-2.5,-1,-1.5).