The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and

Question

The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and a sulfur atom. A sulfur atom is twice as massive as an oxygen atom. Using this information and the data provided in the drawing, find the coordinates of the center of mass of the sulfur dioxide molecule. Express your answers in nanometers (1 nm = 109 m).
x = nm
y = nm

The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and a sulfur atom. A sulfur atom is twice as massive as an oxygen atom. Using this information and the data provided in the drawing, find the coordinates of the center of mass of the sulfur dioxide molecule. Express your answers in nanometers (1 nm = 10?9 m). x = nm y = nm

Explanation / Answer

Let mass of Oxygen atom is m2 = m2= m    Let mass of sulfur atom is m1 = 2m ---------------------------------------------------- Consider the origin at the sulfur atom . So the coardinates of the sulfur atom are (x1 , y1) = (0 , 0) The position of the Oxygen in positive x-y plane is (x2, y2) = (0.143nm sin60o,0.143nm cos60o ) (x2, y2) = (0.124nm, 0.0715 nm ) (x2, y2) = (0.124nm, 0.0715 nm ) The position of the Oxygen in negative x-y plane is (x3, y3) = (-0.143nm sin60o,0.143nm cos60o ) (x3, y3) = (-0.143nm sin60o,0.143nm cos60o ) (x3, y3) = (-0.124nm, 0.0715 nm ) (x3, y3) = (-0.124nm, 0.0715 nm ) (x3, y3) = (-0.124nm, 0.0715 nm ) ---------------------------------------------------------------------------- X-coordinate of the center of mass is Xcm = (m1x1 + m2x2+ m3x3 ) / (m1 + m2 + m2  ) Xcm = (0 + m (0.124nm) - m (0.124nm) ) / (2m + m + m ) Xcm = (0 + m (0.124nm) - m (0.124nm) ) / (2m + m + m ) Xcm = 0. nm Xcm = 0. nm Xcm = 0. nm Y-coordinate of the center of mass is Ycm = (m1x1 + m2x2+ m3x3 ) / (m1 + m2 + m2  ) Ycm = (0 + m (0.0715 nm) + m (0.0715 nm) ) / (2m + m + m ) Ycm = 0.036 nm Y-coordinate of the center of mass is Ycm = (m1x1 + m2x2+ m3x3 ) / (m1 + m2 + m2  ) Ycm = (0 + m (0.0715 nm) + m (0.0715 nm) ) / (2m + m + m ) Ycm = (0 + m (0.0715 nm) + m (0.0715 nm) ) / (2m + m + m ) Ycm = 0.036 nm Ycm = 0.036 nm Ycm = 0.036 nm Then the position of center of mass is (Xcm , Ycm ) = ( 0 , 0.036 nm)

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