Answer to Question #100727 in Classical Mechanics for PETER

Question

A water molecule consists of an oxygen atom with two hydrogen atoms bound to it. The angle between the two bonds is 106°. If the bonds are 0.1nm long where is the centre of mass of the molecule?

Answer 1

$$x=0.1\cos53=0.06\ nm,y=0.1\sin53=0.08\ nm$$

$$\bold{r_1=0.06i+0.08j,r_2=0.06i-0.08j,r_3=0}$$

$$\bold{r}=\frac{m_1\bold{r_1}+m_2\bold{r_2}+m_3\bold{r_3}}{m_1+m_2+m_3}$$

$$\bold{r}=\frac{(1.008)(\bold{0.06i+0.08j+0.06i-0.08j})}{2(1.008)+15.999}$$

$$\bold{r}=(6.71\cdot 10^{-3}\bold{i})\ nm$$