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Re: Setting up problems



"I think, Bob, what people were responding to is the part about
'have them look at the related equations'".



OK here's related equations:

The generalized solution for numerical modeling of two dimensional
orbits is:

Q(i) = AX(i)(x^2 + y^2)^B where to model the earth:

A is GM [Cavendish constant; reduced mass] and
B is -3/2 for inverse square central force

A = 39.5 AU^3 / yr^2 [astronomical units] and B = -1.5

and initial condix: x(0) = 1 AU; x dot = 0; y(0) = 0; y dot = 2Pi AU
/ yr;

t(0) = 0; and delta t = 1/52 yr

I've done this for a constant force [B = -0.5] to model a puck in a cone
(constant angle). However, I don't have the wherewithal to make a
conical air table and have instead video taped a steel ball in two
different angled cones. The friction loss is, I observe, not
significant in several orbits, and the precession is, again by eye,
constant. Now I've convinced myself that in one dimension the I of the
ball just lowers the acceleration by a constant 5 / 7 [the other related
eq.]. What about in a cone?

I was about to compare the numerically generated orbits with the videos,
but first I'd appreciate a prediction.

bc, not a theoretical Physicist

p.s. videoing done for a Prof's lecture on Hooke; the numerical and
Galileo rolling from Eisberg.




Jack Uretsky wrote:

I think, Bob, what people were responding to is the part about
"have them look at the related equations". I certainly reacted to that.
"The related equations" are not separate entities that are to be
somehow related to a set of facts. Forget that the equations exist!
Treat mathematics as a language to be used to state relationships. Then
"solving" a problem means turning a crank to associate numbers with the
entities involved in the relationships. This way, the student is
ecouraged to create the "formula", not to "find" it.

On Wed, 8 Oct 2003, Robert Patton wrote:



I guess I simplified my approach to much. I, too, require sketches and
free body diagrams, if appropriate, to have the students "visualize" the
situation. This is done along with the listing of the info in the


cut