Re: TIDES, pedagogy.

[John Clement <clement@HAL-PC.ORG>]

I think that an explanation based on simple force ideas is reasonably
appropriate, and can be constructed as follows.
1.  Ask students if the force on 2 objects of equal mass is the same when
they are positioned at slightly different distances from the moon.  Once
they agree that the closer one has more force on it, you have the means to
explain tides.
2.      Now ask how to assess the force on the earth.  Do you consider the center
or the edge of the earth.  Once they agree that the center is appropriate
place to consider, you have established some of the force ideas that they
need.  At this point you need to consider how much hand waving you think is
needed.  If the students are advanced you need to ask them to consider how
the acceleration due to the moon varies with the distance from the moon.
Lower level students may not understand acceleration, so just appealing to
forces may be necessary.
3.      Then they need to consider the acceleration of the water on the surface
near the moon compared to the Earth as a whole.  They should be able to say
that the water is accelerated more due to the moon.  This establishes the
presence of the tide on the moon side.
4.      Then they need to consider the acceleration of the water on the surface
away from the moon compared to the Earth as a whole.  It is less due to the
moon, which establishes the tides on the far side.
5.      Of course these sorts of arguments just establish and make reasonable
symmetrical tides, but they do not actually calculate the size.  This
particular problem is extremely difficult even for college students.  Since
most HS students use concrete rather than formal reasoning, going beyond
these sort of simple arguments is difficult, and the lower reasoners will
have difficulties with these arguments.  On the other hand the formal
thinkers should have no difficulty.  In some cases you can give this as a
lecture presentation to formal thinkers, and some of them will get it.  You
certainly can appeal to the difference in potential energy, but that
argument will probably be too far removed from student's ability to
understand.

BTW sometimes this problem is sprung on unsuspecting PhD students during
candidacy exams.  Of course grad students should be able to talk about
gradients etc.

> I have no doubt that an "ideal planet" would have the textbook-
> like tides as explained on the website of JohnD:
>
> http://www.monmouth.com/~jsd/physics/tides.htm
>
> The so-called "ideal planet" would have no spin and would be
> entirely covered by deep ocean. Suppose that the depth is the
> same everywhere, that the viscosity is negligible and that there
> is no friction at the bottom of the ocean. In this idealization
> bulges would follow the earth-moon axis.
>
> The problem is how to explain the phenomenon in introductory
> courses. Arguments based on vector calculus can not be used
> in such courses; one is limited to basic kinematics, to the
> F=m*a law and to free body diagrams. Oh yes, they also know
> that water will position itself to minimize potential energy. So
> why is the energy minimized when two bulges have equal size?
>
> Can this question be answered without using advanced calculus?
> I do not think so. Most textbooks say that two bulges of equal
> size are "expected by the theory" but they do not attempt to
> justify this outcome of "more advanced" calculations. In other
> words we describe what would happen but we do not explain
> it. Those who disagree are challenged to produce a pedagogically
> sound explanation for an introductory physics course (or to
> calculate the minimal and maximal depths when the depth
> without moon being present is given, for example 10 km.)
>
> In my opinion, there is nothing wrong with descriptions without
> explanations, as long as we are honest about this. Most of my
> students are not equipped with conceptual tools needed to explain
> tides. And many teachers, including myself, do not remember
> what they learned (long time ago) in advanced courses. The old
> saying "you loose it if you do not use it" is applicable here.
> Ludwik Kowalski