Falling Slinky

If you drop a slinky from a hanging position, something very surprising happens. The bottom remains completely motionless until the top, collapsing downward coil upon coil, crashes into it.

How can this be so? We all know that anything with mass is subject to gravity, and this is certainly true of the lower coils of the slinky. But there’s another force acting on them, the tension due to the stretching of the slinky. When hanging in an equilibrium position, these two forces, gravity and tension, balance exactly, so there is no movement.

When we let go of the top, the tension in the uppermost coils is relaxed and, since there is nothing to balance gravity, they start to fall. But this relaxation has to be transmitted or communicated down the slinky before gravity can pull the bottom downward. This transmission takes time: the time for the “message” to travel the length of the slinky depends on the ratio of the mass to the stiffness.

A slinky has large mass and small stiffness, so this time is relatively large, typically about half a second. But a freely-falling object falls five metres in the first second. Moreover, the top coils of the slinky initially accelerate downward even faster than in free fall, because the downward tension augments gravity. Thus, the slinky reaches a crunch point, where the top crashes into the bottom, before the signal of the release can reach it. You might say that the bottom doesn’t know what hit it!

It is worthwhile playing with a real slinky to study this curious behaviour. If you put the slinky on a table, stretch it, hold one end steady and jerk the other end, you will see the signal propagating along the spring. But the best way to view the falling slinky is in slow motion. There are several videos on You Tube illustrating the falling slinky. A mathematical note giving a more detailed analysis can be found here  (PDF).

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