School of Physics and Astronomy, University of Minnesota
Physics 1102, Introductory Physics II, Homework 4, individual problem solution
Here I reproduce a sketch of the model of a water molecule interacting with
a sodium ion which was briefly discussed in class. The distance between each
hydrogen and the oxygen is denoted a. The distance between the Na and the
oxygen is denoted r. The angle between the lines from the O to the H’s is 90o . (In
real water it is 108o .) Values of a and the charges on the H’s, O and Na are given
in the sketch.
a. Draw arrows on a reproduction of the sketch showing the direction and relative
magnitude of
the force on the Na due to the O
the force on the Na due to each H
the total force on the Na due to the water molecule.
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Do you expect the Na to be attracted or repelled from the water molecule?
Attracted
b. Write formulas in terms of r, a, the charges and K for the magnitude of each
of the forces.
c. Use the result of b. and an analysis of the geometry to write a formula for
the net force in the x direction on the Na ion due to the water molucule.
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d. For extra credit, make a graph giving the force in the x direction as a function
of the distance r, using Excel or some other numerical method.
An Excel spreadsheet is posted if you want to study how this was generated. It
also contains a graph and calculation for the next part.
Next, suppose that the Na ion is in the position shown in the next picture. Draw
arrows as before, indicating the forces. Do you expect attaction or repulsion in this
case?
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