The effect of the tied top turns on the fall of a slinky

Abstract The dynamics of a falling slinky is revisited with the usual discrete model, where the slinky is treated as a chain of small masses connected by small springs. The motion of the falling slinky is described analytically by assuming that the masses accelerate due to the spring force and gravity. They inelastically collide with one another from the top down, forming the falling section, while uncollided masses are still at rest. In this study, the initially tied top turns of the hanging slinky are taken into theoretical account. This sole feature robustly solved several existing problems in a past model (Calkin 1993 Am . J . Phys . 61 261), which were discussed in a different study (Cross and Wheatland 2012 Am . J . Phys . 80 1051). The involved physics principles and the mathematical approach in this study is highly suitable for physics freshmen. The model derives the velocity, position, and acceleration of the slinky’s top as explicit functions of time, which showed good agreement with measurements.