Pendulum project update
Bert Freudenberg
bert
Mon May 5 08:53:40 PDT 2003
Am Donnerstag, 24.04.03 um 15:50 Uhr schrieb Phil Firsenbaum:
> 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?
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.
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.
HTH
-- Bert
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