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 (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 nm = 10^-9 m).

Explanation:

Step1: Determine the formula for the center - of - mass coordinates

The formula for the \(x\) - coordinate of the center of mass \(x_{cm}=\frac{m_1x_1 + m_2x_2+m_3x_3}{m_1 + m_2+m_3}\) and for the \(y\) - coordinate \(y_{cm}=\frac{m_1y_1 + m_2y_2+m_3y_3}{m_1 + m_2+m_3}\). Let the mass of an oxygen atom be \(m\), then the mass of a sulfur atom is \(M = 2m\).

Step2: Find the coordinates of each atom

For the left - hand oxygen atom: \(x_1=-0.143\cos60^{\circ}\text{ nm}\), \(y_1 = 0.143\sin60^{\circ}\text{ nm}\)
For the right - hand oxygen atom: \(x_2=0.143\cos60^{\circ}\text{ nm}\), \(y_2 = 0.143\sin60^{\circ}\text{ nm}\)
For the sulfur atom: \(x_3 = 0\text{ nm}\), \(y_3=0\text{ nm}\)

Step3: Calculate the \(x\) - coordinate of the center of mass

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Step4: Calculate the \(y\) - coordinate of the center of mass

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Answer:

(a) The \(x\) coordinate of the center of mass is \(0\text{ nm}\)
(b) The \(y\) coordinate of the center of mass is \(0.062\text{ nm}\)