On Fri, 25 Apr 2003 03:05, Kim Rose wrote:

I think it is wonderful to see how the Etoy system can motivate and promote learning in *us*! The adults! Look how Phil has been motivated to read and explore more by seeking out expert advice. Look how our community (thanks to Bert and others) are responding and adding to Phil's "knowledge base" -- geesh, maybe we've got a tool to amplify adult learning! (I know it has worked for me!)

Perhaps more a better slogan might be something along the lines of:- "A superbly effective tool to enhance learning for people of all ages". Without a shadow of doubt that has been the case for me. It has also given me the motivation to learn something of the underlying computer language.

Certainly this "Pendulum" thread has been one of the more informative and interesting threads I have had the priviledge to read since I have been on e-mail lists.

Now for the real purpose of the message. I seem to somewhat vaguely remember from the misty, distant past of some 45 years when I did my bit of School Physics that our teacher, one Dr. Watson, explained the motion of the pendulum using the fact that while energy can be converted from one form to another, it can never be destroyed. In the case of the pendulum the forms of energy are the Potential Energy imparted to the bob by lifting it up to the extremity of its swing. This is completely converted into Kinetic Energy at the bottom of the swing, and then totally converted back again to Potential Energy at the moment when the bob is stationary at the other end of the swing.

Therefore, if my failing memory serves me correctly, at all times:-

mh - mv^2 = k

Solutions of the Pythagorean geometry, for which the missing square-root arithmetic function in the e-toy tile would be _really_, _*really*_ useful, are left as an exercise for the reader. :-)

Is there perchance a "Within-the-scripting-window" method of doing interations so that the Newtonian approximation method can be used in a way which is understandable to a school pupil?

It'll be interesting to see what I come up with as an implementation of the simulation.

Thanks for the great exploration, and support of learning no matter who the learner.... best to all, -- Kim

...

So, I've done a little reading (Physics Made Simple, etc,) and most recently consulted with a physics professor who happens to be in the family. As a result, I'm fairly (if not completely) convinced that creating a realistic pendulum is well beyond what 5th graders could do. I'm not even sure if I'll ever be able to complete the project myself. I have learned a lot about pendulums, gravity, etc. I realize now that my pendulum does not reflect reality because it moves at a steady rate through it's swing when, in fact, a pendulum accelerates in its downward motion and decelerates in its upward motion. In order to simulate reality I need to be able to change the rate of acceleration of the heading of my pendulum. I now have a formula that would accomplish this, however, it includes a square root function. Is that possible in the etoy environment?

Hi Folks --

A good side point about pendulums is that the motion is harmonic only for small excursions, since harmonic motion is roughly the spring law which is proportional to x, and pendulums are proportional to sine x. Sine x and x are close to the same values only for small angles.

All these subtle details are reasons why we don't do pendulums with 5th graders. Compare this to gravity near the surface of the earth where the accelleration is constant to about 1 part in a million (note that it isn't really constant because it is inversely proportional to the square of the distance and this is changing a little bit -- about 4 meters in the ball drop example).

Cheers,

Alan

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At 7:09 PM +0200 4/24/03, Andreas Raab wrote:

Hi Bert,

...

I guess you are a little bit blinded by all the math. It's really simple - the acceleration of the pendulum depends on its position. If it is vertical, you have zero acceleration (because the force of gravity is straight down and does not cause the pendulum to swing). If it is horizontal, you have the maximum acceleration, again because the force points straight down, but now this is exactly the direction to make the pendulum rotate.

Exactly right.

...

This trivially maps to an etoy (just increase the speed by the acceleration value), the only obstacle is to get the acceleration depending on the current angle. This is what the "weighing angles" discussion was all about. Either you do this (best for 5th graders I guess), or you "measure" it, like in the pendulum project I sent last week. It works fine without any trigonometry or square roots: You basically just take the _horizontal_ extent of a line that represents your pendulum. If the line is vertical, its horizontal extent is zero. If the line is horizontal, its horizontal extent is maximal. You still need a sign for the force, which you can get by checking the extent relative to the line's reference point.

That's a little too abstract for my taste. One really needs to explain why the relation between gravity and pendulum is not strictly linear because otherwise you can do a very reasonable first order approximation of a pendulum by simply subtracting its direction from gravity's direction. Note that this fulfills all your constraints: It's zero if the pendulum points into the same direction as gravity and it increases up to 90 degrees.

I've attached a project with this (wrong!) model to illustrate the fact. And my challenge is: Explain why this can't be correct (heh, heh ;-)

Cheers,

• Andreas

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