3-dimensional center of mass problem

[brendan3eb]

Homework Statement

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.

Homework Equations

Rcom=(1/M)(sum of MiRi from i=1 to n)

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?

 

[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.

 

[ogb p]

As a scientist, it is important to approach problems with an open mind and consider all possible solutions. In this case, it may be helpful to consider the symmetry of the molecule and how it relates to the center of mass. The equilateral triangle formed by the three hydrogen atoms suggests that the molecule may have a plane of symmetry, which could simplify the problem. Additionally, the fact that the nitrogen atom is at the apex of a pyramid may also provide clues about the location of the center of mass. It is important to carefully consider all given information and use the appropriate equations to accurately calculate the center of mass.