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Here's one which is bugging me today. Maybe some of you can enlighten me.
It deals with a very simple and easy-to observe phenomena.
Stand on a lecture desk, holding one end of a Slinky (TM) spring. Wait
till the spring quits bouncing. Predict what will happen when you release
the spring. In particular, what will be the motion of the lower end.
a) The lower end rises as the upper end falls, the center of mass
falling, and when the spring fully closes the whole thing falls with
acceleration g.
b) The lower end remains at the same level, while the upper end falls.
When the spring fully closes it falls with acceleration g.
c) All parts of the spring fall, the spring closing as it falls. The upper
end falls faster than the lower end until the spring closes.
Now for the analysis. Why does the spring behave this way and not some
other way? Simple, yet correct, analysis, please. Would the same result be
seen with two balls on the end of a spring made of stretched rubber bands?
Would the rubber band demo behave the same if the two balls were of
different mass? What if just one ball is at the lower end of a string of
rubber bands? In this case the result is quite different than it was for
the Slinky. Even with the slinky, does the spring constant matter? Would
we get the same result with a limp spring as with a stiff one? Must the
particular spring constant, length, and mass of the slinky be exactly
right for the observed result?