Physics (10th Edition)

a) $x_{cm}=0$ b) $y_{cm}=+0.036nm$
We take the mass of the oxygen atom to be $m$ and that of the sulfur atom to be $2m$ a) On the x-coordinate, 2 oxygen atoms have positions $x_{O1}=-0.143\sin60$ and $x_{O2}=+0.143\sin60$ and the sulfur atom has position $x_S=0$. So the x-coordinate of the center of mass is $$x_{cm}=\frac{(mx_{O1}+mx_{O2})+2mx_S}{m+m+2m}=\frac{0+0}{4m}=0$$ b) On the y-coordinate, 2 oxygen atoms have positions $y_{O1}=+0.143\cos60$ and $y_{O2}=+0.143\cos60$, and the sulfur atom has position $y_S=0$. So the y-coordinate of the center of mass is $$y_{cm}=\frac{(my_{O1}+my_{O2})+2my_S}{m+m+2m}=\frac{2m(0.143\cos60)+0}{4m}$$ $$y_{cm}=\frac{1}{2}(0.143\cos60)=+0.036nm$$