# 3-dimensional center of mass problem

1. Nov 25, 2007

### brendan3eb

1. The problem statement, all variables and given/known data
In the ammonia (NH3) molecule, the three hydrogen (H) atoms form an equilateral triangle; the center of the triangle is 9.40x10^(-11) m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is 10.4x10^(-11) m. Locate the center of the molecule relative to the nitrogen atom.

2. Relevant equations
Rcom=(1/M)(sum of MiRi from i=1 to n)

3. The attempt at a solution
I have read through the problem several times, and I started to try and solve the problem by just figuring out the three-dimensional coordinates, but it seems a bit odd for the book to give such a tedious problem. Is there some sort of symmetry or way of re-drawing the problem to eliminate the z-axis that I am not picking up on, or do I really need to use all three axis to figure out the answer?

2. Nov 25, 2007

### BlackWyvern

I think you're allowed to treat the 3 H atoms as one mass focused in the centre of the 3 H atoms. This would have a mass of triple one H atom, and it would be directly under the N atom. I think.