The Slinky Drop Experiment Analysed

[Orodruin]

Figure 1: A slinky, the subject of the slinky drop experiment. Attribution: Roger McLassus. CC BY-SA
The slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye. For a better view, using a modern smartphone to capture a video of the experiment also helps to capture the falling slinky. Apart from the commonly quoted result, Insight will discuss the evolution of the slinky shape during the drop using only high-school physics: mechanical equilibrium and the conservation of momentum.

What is The Slinky Drop Experiment?
The slinky drop experiment is exactly what it sounds like:

Support a slinky at one of its ends. Let the rest of it hang freely under...

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[pines-demon]

Oh you beat me to it! It seems that you finally used my suggestion of using the displacement field! I have a similar solution that I might share later.

 

[Orodruin]

Oh you beat me to it! It seems that you finally used my suggestion of using the displacement field! I have a similar solution that I might share later.

No, the displacement field is still the dependent variable. The slinky fraction $s$ is the independent material variable. This is the way I did it from the beginning.

The only addition is a non-zero rest length of the slinky. Otherwise the analysis is the same as my post #5 of that thread, just a bit more polished.

 

[pines-demon]

The only addition is a non-zero rest length of the slinky.

I was talking about that.

Otherwise the analysis is the same as my post #5 of that thread, just a bit more polished.

Thanks for the clarification. Anyway, great article!