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Re: Newton's Second Law Lab

I will try to replace the "dynamical" accelerometer
by the motion detector which is 100% "kinematical".
The modify setup should show similar output. The
workshop starts in 5 minutes.

At 8:13 PM -0400 7/4/00, Bob Sciamanda, asked about Newton's
Second Law Lab:

is the accelerometer directly measuring a kinematical quantity,
or a
dynamical quantity?

At 09:10 PM 7/4/00 -0400, Chuck Britton replied:

dynamical, it is a piezoelectric strain gauge with a small
cantilevered mass.

Is this a serious pedagogical problem?

I'd say this piezoelectric device is suitable for use as an
accelerometer
for practically every purpose _except_ this one! It's only an
accelerometer if you assume the validity of Newton's second law,
which
makes the demo in question a pointless exercise in circular logic.

But we can do much better.

1) I wholeheartedly endorse the suggestion of measuring the force,
rather
than trying to create an ideal force using pulleys and other
contraptions. That's because it is far easier to measure an
arbitrary
force than to create a force that is independent of the position,
velocity,
and acceleration of the cart being studied (the "CBS").

2) But it is a step in the wrong direction to put an accelerometer
on
board. It is simpler to measure the position as a function of time.
This
directly makes the intended point about force and motion.
Differentiate
the position to compare with force, or (better) integrate the force
to
compare with position.

An ultrasonic rangefinder aimed at the cart should do nicely. Even
cheap
ones have resolution on the order of a millimeter. See also next
note.

3) Note that it is not necessary to have the force transducer on
board the
CBS either. It can just as well be on another object, connected by
a
thread to the CBS. In the readily-achievable limit that the mass of
the
thread is small compared to the mass of the CBS, this works just
fine. It
also circumvents a telemetry problem.
| |
| cart |--------SG--hand
| |

4) While you're at it, demonstrate the effect of two or more
measured
forces, acting via two or more threads. For example, a very nice
version
of this is

| |---------SG--|
| cart | |______hand
| |---------SG--|

^
^
(free-floaing
lever or bridle)

where the string going from the bridle to the hand is _not_
symmetrically
disposed with respect to the strings going from bridle to cart.
This
allows the force in one string to be quite different from the force
in the
other string.

This makes an important point about forces, namely that there is a
physical
logic to forces. A force is not just an "m" times an "a". There is
a
force in each string, and you don't need to know anything about what
produced the force to know that it is a force, and that the two
forces have
an additive effect on the CBS.

You can go nuts with this if you want. For instance, an interesting
embellishment is

| |---------SG--|______hand
| cart | |______other hand
| |---------SG--|

This allows the two SGs to record arbitrarily complex signals
individually,
but their sum will be strongly correlated with the acceleration of
the cart.