Some more suggestions for measuring some things that are not /directly/
measurable:
*) Accurately determine the external volume of an unopened soft-drink
can. This is something you might want to know in the following situation:
Suppose you have 1000 cans, all the same size. You want to know which
of them will float in water. It turns out that the process control
is really sloppy at the filling plant, so there is a wide variation
in the amount of liquid inside. You can easily determine the mass
of each can. If you knew the volume, you could predict which ones
would float.
The direct technique of measuring its dimensions with a caliper or
whatever is not practical, if you want any serious accuracy, because
of the somewhat-irregular shape
The 2000-year-old technique of measuring how much water it displaces
turns out to be rather inconvenient and inaccurate.
.... So, the assignment is to come up with something better. I can
think of at least three techniques that are dramatically more accurate
and convenient (compared to direct calipering and/or simple displacement).
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As a lesson that does not involve inference so much as scientific
prediction, consider this: Get two quartz-regulated clocks (or
watches), accurate to the nearest second (or better). Set clock A
it as a signal to pay attention to the clocks. Predict that clock
A will read 11:01:00 when clock B reads 11:00:00. Observe again
tomorrow. Note that one second accuracy is one part in 86400, which
is rather more precise than anything they did in high school physics
lab.
This is more important than the students could possibly imagine,
for reasons that will become apparent shortly .......
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Almost anything having to do with astronomy needs to be measured
indirectly.
*) Suppose you lived 1000 years ago, before GPS, and even before
telescopes. Explain how to measure the diameter of the earth.
*) Suppose you lived 250 years ago. You have
++ telescopes
++ remarkably accurate clocks
++ accurate maps of the earth, with distances, latitudes and
(thanks to the aforementioned clocks) longitudes
-- no GPS
-- no radar
-- no spacecraft
Explain how to measure the distance from the earth to the moon.
Answer: You can either use an insanely accurate telescope
... or use an occultation with a very modest telescope and
a good clock.
*) Same as above, but now we want the distance from the earth
to the /sun/ ... which is a rather bigger challenge, for a
couple of reasons.
Hint: There was a transit of Venus a few months ago. I
wonder how many students have any clue about this. Note:
this is in some sense just like an occultation ... except
that it happens in the daytime.
Huge hint: Did I mention clocks? For hundreds of years,
physicists have been able to measure time much more accurately
than almost anything else.
If you want to make this a real experiment, as opposed to a
Gedankenexperiment, you should be able to set up some sort
of model system that they can measure using stopwatches.
There's no advanced physics in this; it's basically just
simple geometry. However, it is still verrry difficult
for students, because it involves inference i.e. reasoning,
and in particular because it involves /multiple steps/ of
reasoning. Keep in mind that college freshman have lived
for 12 years on a steady diet of questions that can be
answered in a single step or not at all ... questions that
can be answered by rote regurgitation in 45 seconds or not
at all.