# A really close answer-why? (conter of mass)

1. Nov 13, 2009

### stanton

1. The problem statement, all variables and given/known data

A water molecule consists of an oxygen atom with two hydrogen atoms bound to it as shown in Figure P8.8. The bonds are 0.100 nm in length and the angle between the two bonds is 106°. Use the coordinate axis shown and determine the location of the center of gravity of the molecule. Take the mass of an oxygen atom to be 16 times the mass of hydrogen.

2. Relevant equations

y com = $$\Sigma mixi$$ / $$\Sigma mi$$
Same with x

3. The attempt at a solution

Let mass of H atom =m, Mass of O atom = 16m

Coordinates of upper H = (0.100cos 53, 0.100 sin 53) (in nm) = (0.06,0.08)
Coordinates of lower H = (0.06,-0.08)
Coorinates of O=(0,0)

x-coordinate of COM = sum of (mass of each particle* its x coordinate ) for each particle , divided by total mass = (1/M)Σmixi

Here total mass M = m+m+16m = 18m
∴xCOM = (m*0.06+m*0.06+0)/18m = 0.12/18 = 0.0067 nm

Similarly , yCOM = ((m*0.08) + m*(-0.08) +0)/18 m = 0 nm

∴ COM of molecule = (0.0067 nm, 0)
-------------------------------------------------------

But the answer is 0.00669, not 0.0067. And according to me calculator, it is 0.006666667.
Where did 0.0069 came from?

2. Nov 13, 2009

### Delphi51

If you want 2 digit accuracy in the answer, you should record
.1*cos(53) as 0.0602

3. Nov 13, 2009

### stanton

Ah.. I see. ^_^ That tiny bit of omission makes answer different. I was curious because the homework required me to express very accurately. Thanks!