Question

current attempt in progress
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 coordinates of each atom

Let the mass of an oxygen atom be \(m\), then the mass of a sulfur atom is \(2m\).
For the left - hand oxygen atom (\(O_1\)): \(x_1=- 0.143\cos60^{\circ}\text{ nm}\), \(y_1 = 0.143\sin60^{\circ}\text{ nm}\)
For the right - hand oxygen atom (\(O_2\)): \(x_2=0.143\cos60^{\circ}\text{ nm}\), \(y_2 = 0.143\sin60^{\circ}\text{ nm}\)
For the sulfur atom (\(S\)): \(x_3 = 0\text{ nm}\), \(y_3 = 0\text{ nm}\)

Step2: Calculate the \(x\) - coordinate of the center of mass

The formula for the \(x\) - coordinate of the center of mass is \(x_{cm}=\frac{m_1x_1 + m_2x_2+m_3x_3}{m_1 + m_2+m_3}\)
Substitute \(m_1 = m\), \(m_2 = m\), \(m_3 = 2m\), \(x_1=- 0.143\cos60^{\circ}\), \(x_2=0.143\cos60^{\circ}\), \(x_3 = 0\)

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

The formula for the \(y\) - coordinate of the center of mass is \(y_{cm}=\frac{m_1y_1 + m_2y_2+m_3y_3}{m_1 + m_2+m_3}\)
Substitute \(m_1 = m\), \(m_2 = m\), \(m_3 = 2m\), \(y_1 = 0.143\sin60^{\circ}\), \(y_2 = 0.143\sin60^{\circ}\), \(y_3 = 0\)

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Answer:

(a) \(x_{cm}=0\text{ nm}\)
(b) \(y_{cm}=0.062\text{ nm}\)