Advertisement

A Closed Form Solution of the Run-Time of a Sliding Bead along a Freely Hanging Slinky

  • Haiduke Sarafian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)

Abstract

The author has applied Lagrangian formalism to explore the kinematics of a bead sliding along a frictionless, freely hanging vertical Slinky. For instance, we derived a closed analytic equation for the run-time of the bead as a function of the traversed coil number. We have applied Mathematica to animate the 3-dimensional motion of the bead. The derived run-time is incorporated within the animation to clock the bead’s actual motion. With the help of Mathematica we have solved the inverse run-time equation and have expressed the traversed coil number as a function of the run-time. The latter is applied to further the analysis of the problem conducive to analytic time-dependent equations for the bead’s vertical position, its falling speed and its falling acceleration, and its angular velocity about the symmetry axis of the Slinky. It is also justified that a Slinky is a device capable of converting the gravitational potential energy of a sliding bead into pure rotational energy.

Keywords

Angular Velocity Symmetry Axis Closed Form Solution Gravitational Potential Energy Maximum Angular Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Heard, T.C., Newby Jr., N.D.: Behavior of a soft spring. Am. J. Phys. 45, 1102–1106 (1977)CrossRefGoogle Scholar
  2. 2.
    French, A.P.: The Suspended Slinky - A Problem in Static Equilibrium. The Physics Teacher 32, 244–245 (1994)CrossRefGoogle Scholar
  3. 3.
    Wolfram, S.: The Mathematica book, new 4th edn. Cambridge Press, Cambridge (1999)Google Scholar
  4. 4.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products, 2nd edn., p. 276. Academic Press, London (1980)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Haiduke Sarafian
    • 1
  1. 1.The Pennsylvania State UniversityYorkUSA

Personalised recommendations