Re: Why does a stretched slinky first spring together, then fall?

Becca:

You realize that I had to go to Wal-Mart at the height of the post-
Thanksgiving shopping rush just to BUY A SLINKY??

But you're right -- Despite what common sense would seem to indicate, the 
bottom part of a Slinky does not fall until the whole toy has completely 
closed up!

I performed a few experiments using a tennis ball as a control.  I urge 
you to replicate them, both for the fun of it, for curiosity, and because 
that is what scientists do.  First I held the Slinky up, with the tennis 
ball at the level of the bottom,  and released them at the same instant.  
(NOTE:  This is not too accurate.  The correct way to do this would be to 
hold them up with electromagnets, switching off the current at the same 
time.  Trouble is, I had to get a plastic Slinky nor did I have big 
magnets on hand)

At any rate, when the ball was at the bottom end of the Slinky, it hit the 
floor first.  So the end of the Slinky does not accelerate at the same 
rate as gravity.  Then I held the ball at the midpoint of the Slinky.  I 
theorized that the center of mass of the Slinky would fall at 
gravitational acceleration. Results were inconclusive -- the thing moved 
too fast.  Then I held the ball at the same height as the top of the 
Slinky.  Here, the Slinky outran the ball by a large margin.

I borrowed a digital camera, took several runs with the help of my friend 
Bill Z, and viewed the results frame by frame.  In the first 
frame,about .2 seconds after Bill let go,  the tennis ball is trailing the 
Slinky by about 40 or 50 cm. The part below the folded up section has not 
moved.  In the second frame,taken about .14 second later, the Slinky is 
mostly collapsed, and the tennis ball is even farther behind.  In the 
third frame, another .14 seconds later, the Slinky is completely folded 
up, at the elevation that the bottom was at when it was released.  The 
tennis ball is at Bill's chest level. 

As to why:  Looking at the falling Slinky again, you can see that the top 
begins falling down faster than the tennis ball, i.e. faster than gravity 
alone would accelerate it.    That's because it's also being pulled down 
by the spring constant, which is a force measured in so-many grams per 
centimeter of spring extension.  Because of Newton's Third law -- every 
action has an equal and opposite reaction -- the force of the spring 
pulling down the mass of collapsed Slinky results in an equal force 
pulling up -- a force equal to the spring force, which is equal to the 
weight of the spring underneath, since that's what extended the Slinky in 
the first place.  

Another thing that affects this phenomenon is wave speed in the Slinky.  
Hold up the Slinky, wait for it to stop vibrating, then lightly pluck it 
near the top.  A wave will whiz down the slinky and back up.  This wave is 
traveling at a speed set by the configuration of the spring and the 
material the Slinky is made of.  The stiffer the spring, the faster the 
wave travels.  The speed of this wave traveling through the Slinky governs 
how quickly the information that the spring has been released will reach 
the other end.  It's like the speed of sound -- you won't hear something 
until the sound waves reach you.  When the Slinky is dropped, the top 
falls faster than the speed of the wave.  The top of the Slinky reaches 
the bottom before the information that the top has been released (i.e., 
the wave) can get there.  Inertia plays a role here, too.

I congratulate you on an excellent observation.  Every engineer I 
mentioned this to didn't believe it, until I dropped the Slinky for them.  
One other thing I'd like to try would be to put two slinkys together, end-
to-end, hold them out a second story window and see if the effect still 
occurs when there's more than 3/15th of a second.