Pendulum project update

Andreas Raab andreas.raab at squeakland.org
Fri Apr 25 02:30:55 PDT 2003


Hi Darius,

> Scary!

No, not really. One of the interesting issues about the model I was using is
that it is in fact relatively close to the "real" one (as Alan noticed the
sine is close to being linear for small degrees) and that it requires either
some deeper understanding of the underlying math or some practical
experiments to find out that the model is in fact wrong. A very important
part of science is just that - validating our assumptions and see if they
are correct. Without this, you can make up any kind of system as long as
it's consistent - but the ultimate question in science is: Does it stand up
to the test of reality? For my model, for example it would be interesting to
make up a movie of a real pendulum and see if its motion matches what our
model predicts. If it doesn't, then something is wrong with our model and we
need to come up with a different one. Many (all?) of the major breakthroughs
in science go this way - build a model, see if "reality works as the model
predicts" and if not, find out why.

Probably nothing you want to do with fifth graders but if we talk about
science then we must ultimately validate our models.

> Using your project and unmodified script, I rotated the 
> pendulum so that the bob started above horizontal and then
> started the timer.
> 
> The pendulum accelerated! (Great for a perpetual motion 
> machine. You need to patent it.)

Oh, good idea! I'm sure I'll get it considering the patents I've seen over
the last couple of years ;-)

> Does the pendulum accelerate at the same speed and travel 
> distance as a free falling object starting at the same height?
> Or does, assuming a frictionless pivot, the limited length of
> the shaft slow its rate acceleration?

No on both accounts. What I did was essentially taking the simplest function
that matches the observations one could easily get (e.g., if gravity and
pendulum point in the same direction then gravity does not affect the
acceleration and acceleration increases up to 90 degrees).  What's wrong is
the relation between angle and acceleration (but it is pretty close for some
ranges of angles which make it look "sort of okay").

Cheers,
  - Andreas





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