The Center of Mass of Sulfur Dioxide Sulfur dioxide (SO2) consists of two oxygen

Question

The Center of Mass of Sulfur Dioxide Sulfur dioxide (SO2) consists of two oxygen atoms (each of mass 16 u, where u is defined in Problem 40) and a single sulfur atom (of mass 32 u). The center-to-center distance between the sulfur atom and either of the oxygen atoms is 0.143 nm, and the angle formed by the three atoms is 120 Degree as shown in the figure(Figure_1). Find the x and y coordinates of the center of mass of this molecule. Express your answers using two significant figures separated by a comma. Xcm, Ycm = m My Answers Give Up

Explanation / Answer

since the distribution of mass is symmetrical about y-axis , the x co-ordinate of the centre of mass molecule will be zero , means the centre of mass will be on y-axis itself.

now Y coordinate of sulphur atom = 0.

since the angle formed by three atoms is symmetrical about y-axis.

the angle between y-axis and line joining COM of any of the oxygen atom with origin = 120/2 = 60.

so the projection of this line will be length of the line*cos(angle)

thus , Y coordinate of oxygen atoms = 0.143*cos(60) = 0.0715 m .

and so Y-coordinate of molecule = (16*0.0715 + 32*0 + 16*0.0715)/(16+32+16) = 0.03575 m

so the coordinates ae (0 , 0.03575)

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