Question

The distance between the oxygen molecule and each of the hydrogen atoms in a water
(H2
O) molecule is 0.96 Å and the angle between the twooxygen-hydrogen bonds is
105°. Treating the atoms as particles, find the centre of mass of the system.

Answer 1

Answer on Question #41549, Physics, Mechanics | Kinematics | Dynamics

The distance between the oxygen molecule and each of the hydrogen atoms in a water (H2O) molecule is $0.96\mathring{\mathrm{A}}$ and the angle between the two oxygen-hydrogen bonds is $105{}^{\circ}$ . Treating the atoms as particles, find the center of mass of the system.

Solution

The first step is to choose a coordinate system, such as the one in the diagram, and locate each particle. The chosen origin is the location of the oxygen molecule.

The coordinates of the center of mass are given by

$$x _ {c m} = \frac {\sum m _ {i} x _ {i}}{M _ {\mathrm {T o t a l}}} = \frac {0 . 7 1 1 5 3 4}{1 8} = 0. 0 3 9 5 \mathrm {A},$$ $$y _ {c m} = \frac {\sum m _ {i} y _ {i}}{M _ {\mathrm {T o t a l}}} = \frac {0 . 9 2 7 2 8 9}{1 8} = 0. 0 5 1 5 \mathrm {A}.$$

Answers will vary based on the choice of coordinate system.

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