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*From*: John Denker <jsd@av8n.com>*Date*: Tue, 14 Aug 2012 15:38:06 -0700

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).

=========

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 .......

=========

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.

**Follow-Ups**:**Re: [Phys-L] Inference Lab Design***From:*John Denker <jsd@av8n.com>

**References**:**[Phys-L] Inference Lab Design***From:*"Turner, Jacob" <turner@uidaho.edu>

**Re: [Phys-L] Inference Lab Design***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] Inference Lab Design***From:*"Turner, Jacob" <turner@uidaho.edu>

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