A closed form solution of the run-time of a sliding bead along a freely hanging slinky

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2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)319-326
Number of pages8
JournalLecture Notes in Computer Science
Volume3039
StatePublished - 2004

Fingerprint

Angular velocity
Potential energy
Animation
Closed-form Solution
Clocks
Kinematics
Mathematica
Coil
Gravitational potential energy
Vertical
Motion
Symmetry
Closed
Energy

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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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.",
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AB - 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.

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