Question

The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and a suifur atom. A sulfur atom is twice as massive as an oxygen atom. Using this information and the data provided in the drawing, find (a) the x coordinate and (b) the y coordinate of the center of mass of the sulfur dioxide molecule. Express your answers in nanometers 1.00 x 10 m). (1 nm Oygen Orygen 60.0 60.0 0.143 n O.143 nm Sulfur (a) xs -Select Select Select GO Tutorial (b) yomy

Answer 1

Free body diagram is as shown below:

rsin 0rsin т т r r rcos rcos

The formulae for centerr of mass is X_cm

$r_{cm} = \frac{\sum m x_{cm}}{\sum m}$ eq-1

Now,

From the above diagram the moments along x axis are

$\sum x = m(r cos \theta) - m(r cos \theta)$

which gives us

$\sum x = 0$

by plugging this in eq-1 we get

$\boxed{r_{cm} = 0}$

Now,

Again

$\sum y = m(r sin \theta) + m ( r sin \theta)$

$\sum y = 2mr sin \theta$

by plugging this in eq-1 we get

$r_{cm} = \frac{2mr sin \theta}{M+m+m}$

or

$r_{cm} = \frac{2mr sin \theta}{M+2m}$

Here M is the mass of sulphur atom while m is the mass of oxygen atom

by plugging all the values we get

$r_{cm} = \frac{2(16 gm)(0.143 \times 10^{-9}m)sin(60)}{32gm + 2(16gm)}$

which gives us

$r_{cm} = 0.036 \times 10^{-9}m$

or

$\boxed{r_{cm} = 0.036 n m}$

hence,

the x and y coordinates of the centerr of mass are

$\boxed{(x,y) = (0nm , 0.036nm)}$