How can i solve this ..!?

Question

To see the Question click on the link ..

http://solar.njit.edu/~cdenker/physics111h_quiz09.pdf

My comments : is do i have to use theta ..?
Do i have to use m1 , m2 , and m3
what are the components of the oxygen
How the equation looks like

Answer 1

First how do we find a center of mass and then let's get to it

X= (sum of moments about y ) / (total mass)
Y= (sum of moments about x ) / (total mass)

Let oxygen atom be in at the origin of xy coordinate system.
m1 and m3 are Hydrogen atoms
m3 is Oxygen atom

Now let's do it

Total mass = 8 + 1 + 1 =10

sum of moments about y = x1m1 + x2 m2 + x3m3
sum of moments about y=.100 x cos (53) x1 + 100 x cos (53) x1 + 0 x (8) = 0.120 nm

sum of moments about x = y1m1 - y2 m2 + y3m3

= 100 x sin (53) x1 - 100 x cos (53) x1 + 0 x (8)=0
sum of moments about x =0

Finally

X= sum of moments about y / (total mass)=
X= .120/10= .012nm

Centroid (X,Y) =( .012, 0)

Answer 2

steps:
- centre of mass is on dotted line due to reasons of symmetry
- project H atoms on dotted line
- distance O atom and projected H atoms is cos(53') * 0.1 nm (say delta)
- centre of mass lies at the dotted line, between O atom and the two projected H atoms
- the distance (x) between O atom and centre of mass is:

x * 16 = 2.02 * (delta - x)
x * 16 = 2.02 * delta - 2.02 * x
x * 18.02 = 2.02 * delta "thanks, Andrew"
x = 2.02 * delta / 18.02
x = 0.06746206 nm



(Edward mistakes: the mass of an Oxygen atom is "16", not "8")

Answer 3

Minor math error corrected on third line.

x * 16 = 2.02 * (delta - x)
x * 16 = 2.02 * delta - 2.02 * x
x * 18.02 = 2.02 * delta
x = 2.02 * delta / 18.02
x = 0.0067 nm