Modeling a falling slinky
(2012)Abstract
A slinky is an example of a tension spring: in an unstretched state a slinky
is collapsed, with turns touching, and a finite tension is required to separate
the turns from this state. If a slinky is suspended from its top and stretched
under gravity and then released, the bottom of the slinky does not begin to
fall until the top section of the slinky, which collapses turn by turn from the
top, collides with the bottom. The total collapse time t_c (typically ~0.3 s
for real slinkies) corresponds to the time required for a wave front to
propagate down the slinky to communicate the release of the top end. We present
a modification to an existing model for a falling tension spring (Calkin 1993)
and apply it to data from filmed drops of two real slinkies. The modification
of the model is the inclusion of a finite time for collapse of the turns of the
slinky behind the collapse front propagating down the slinky during the fall.
The new finite-collapse time model achieves a good qualitative fit to the
observed positions of the top of the real slinkies during the measured drops.
The spring constant k for each slinky is taken to be a free parameter in the
model. The best-fit model values for k for each slinky are approximately
consistent with values obtained from measured periods of oscillation of the
slinkies.
Description
Modeling a falling slinky