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A twist on the hourglass problem



I need a bit of help. (I would've classified the topic, but I'm not
quite sure where it goes.)

Recently, I had a student who was reading "The Flying Circus of Physics"
FOR FUN! (If only we had more of those!) He came across the hourglass
problem, the one which asks if the weight of the hourglass changes when
the sand is falling through it, and he was a bit puzzled.

He knew the mass of the system didn't change (yeah!), but he lacked a
"mechanism" to explain why/how the "free falling sand" was not an
influence. Since I always told him that Physics is supposed to answer
why/how, he tried to simplify the problem (as our textbooks do) to find
the "mechanism".

In his Gedanken experiment, he removed all but one grain of sand from
the hourglass. His question is: While the mass of the system doesn't
change, W=mg and the weight shouldn't change. BUT, why?! He asked
about the momentum transfer upon the one grains impact at the end of the
fall. He knew that the one grain pushing on the air inside of the
hourglass might transmit force to the outside; so, he removed the air
and had his hourglass contain a vacuum and one grain of sand.

By the time he got done, he even had me confused a bit. No matter what
I did, he still couldn't grasp the "mechanism" which made the statement
true that thed weight didn't change -- given his other objections.

Can someone help me? As you can see, he is a bright, above average (to
say the least) student and I'd like to get a suitable answer for him.

Peter Schoch
Sussex County Community College
1 College Hill
Newton, NJ 07860